Average Error: 0.0 → 0.0
Time: 18.2s
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 r34532 = 0.5;
        double r34533 = re;
        double r34534 = cos(r34533);
        double r34535 = r34532 * r34534;
        double r34536 = im;
        double r34537 = -r34536;
        double r34538 = exp(r34537);
        double r34539 = exp(r34536);
        double r34540 = r34538 + r34539;
        double r34541 = r34535 * r34540;
        return r34541;
}
↓
double f(double re, double im) {
        double r34542 = 0.5;
        double r34543 = re;
        double r34544 = cos(r34543);
        double r34545 = r34542 * r34544;
        double r34546 = im;
        double r34547 = -r34546;
        double r34548 = exp(r34547);
        double r34549 = exp(r34546);
        double r34550 = r34548 + r34549;
        double r34551 = r34545 * r34550;
        return r34551;
}

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 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))