Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r32539 = 0.5;
        double r32540 = re;
        double r32541 = cos(r32540);
        double r32542 = r32539 * r32541;
        double r32543 = im;
        double r32544 = -r32543;
        double r32545 = exp(r32544);
        double r32546 = exp(r32543);
        double r32547 = r32545 + r32546;
        double r32548 = r32542 * r32547;
        return r32548;
}
↓
double f(double re, double im) {
        double r32549 = 0.5;
        double r32550 = re;
        double r32551 = cos(r32550);
        double r32552 = r32549 * r32551;
        double r32553 = im;
        double r32554 = -r32553;
        double r32555 = exp(r32554);
        double r32556 = exp(r32553);
        double r32557 = r32555 + r32556;
        double r32558 = r32552 * r32557;
        return r32558;
}

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

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

Reproduce

herbie shell --seed 2019208 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))