Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
Internal Precision: 320
\[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]
↓
\[\Re(\left(\frac{\left(\left(e^{\left(\left(-xre\right) + \left(-xim\right) i\right)}\right) + \left(e^{\left(xre + xim i\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]

Error

Bits error versus xre

Bits error versus xim

Derivation

  1. Initial program 0.0

    \[\Re(\left(\frac{\left(\left(e^{\left(xre + xim i\right)}\right) + \left(e^{\left(-\left(xre + xim i\right)\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]

  2. Initial simplification0.0

    \[\leadsto \Re(\left(\frac{\left(\left(e^{\left(\left(-xre\right) + \left(-xim\right) i\right)}\right) + \left(e^{\left(xre + xim i\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]

  3. Final simplification0.0

    \[\leadsto \Re(\left(\frac{\left(\left(e^{\left(\left(-xre\right) + \left(-xim\right) i\right)}\right) + \left(e^{\left(xre + xim i\right)}\right)\right)}{\left(2 + 0 i\right)}\right))\]

Runtime

Time bar (total: 12.8s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.0100%
herbie shell --seed 2018286 +o rules:numerics
(FPCore (xre xim)
  :name "exp with complex power real part (p55)"
  (re (/.c (+.c (exp.c (complex xre xim)) (exp.c (neg.c (complex xre xim)))) (complex 2 0))))