Average Error: 0.0 → 0.0
Time: 13.4s
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 r45483 = 0.5;
        double r45484 = re;
        double r45485 = cos(r45484);
        double r45486 = r45483 * r45485;
        double r45487 = im;
        double r45488 = -r45487;
        double r45489 = exp(r45488);
        double r45490 = exp(r45487);
        double r45491 = r45489 + r45490;
        double r45492 = r45486 * r45491;
        return r45492;
}
↓
double f(double re, double im) {
        double r45493 = 0.5;
        double r45494 = re;
        double r45495 = cos(r45494);
        double r45496 = r45493 * r45495;
        double r45497 = im;
        double r45498 = -r45497;
        double r45499 = exp(r45498);
        double r45500 = exp(r45497);
        double r45501 = r45499 + r45500;
        double r45502 = r45496 * r45501;
        return r45502;
}

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 2019235 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))