Average Error: 0.0 → 0.0
Time: 16.8s
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 r2030570 = 0.5;
        double r2030571 = re;
        double r2030572 = cos(r2030571);
        double r2030573 = r2030570 * r2030572;
        double r2030574 = im;
        double r2030575 = -r2030574;
        double r2030576 = exp(r2030575);
        double r2030577 = exp(r2030574);
        double r2030578 = r2030576 + r2030577;
        double r2030579 = r2030573 * r2030578;
        return r2030579;
}
↓
double f(double re, double im) {
        double r2030580 = im;
        double r2030581 = exp(r2030580);
        double r2030582 = -r2030580;
        double r2030583 = exp(r2030582);
        double r2030584 = r2030581 + r2030583;
        double r2030585 = 0.5;
        double r2030586 = re;
        double r2030587 = cos(r2030586);
        double r2030588 = r2030585 * r2030587;
        double r2030589 = r2030584 * r2030588;
        return r2030589;
}

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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))