Measurement of charm and bottom production from semileptonic hadron decays in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:math> collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>200</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:mrow></mml:math>

Measurements of the differential production of electrons from open-heavy-flavor hadrons with charm- and bottom-quark content in $p+p$ collisions at $\sqrt{s}=200\text{ }\text{ }\mathrm{GeV}$ are presented. The measurements proceed through displaced-vertex analyses of electron tracks from the semileptonic decay of charm and bottom hadrons using the PHENIX silicon-vertex detector. The relative contribution of electrons from bottom decays to inclusive heavy-flavor-electron production is found to be consistent with fixed-order-plus-next-to-leading-log perturbative-QCD calculations within experimental and theoretical uncertainties. These new measurements in $p+p$ collisions provide a precision baseline for comparable forthcoming measurements in $\mathrm{A}+\mathrm{A}$ collisions.