Average Error: 0.0 → 0.0
Time: 18.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r1752523 = 0.5;
        double r1752524 = re;
        double r1752525 = cos(r1752524);
        double r1752526 = r1752523 * r1752525;
        double r1752527 = im;
        double r1752528 = -r1752527;
        double r1752529 = exp(r1752528);
        double r1752530 = exp(r1752527);
        double r1752531 = r1752529 + r1752530;
        double r1752532 = r1752526 * r1752531;
        return r1752532;
}
↓
double f(double re, double im) {
        double r1752533 = im;
        double r1752534 = exp(r1752533);
        double r1752535 = -r1752533;
        double r1752536 = exp(r1752535);
        double r1752537 = r1752534 + r1752536;
        double r1752538 = 0.5;
        double r1752539 = re;
        double r1752540 = cos(r1752539);
        double r1752541 = r1752538 * r1752540;
        double r1752542 = r1752537 * r1752541;
        return r1752542;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))