Average Error: 0.0 → 0.0
Time: 35.3s
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 r3856370 = 0.5;
        double r3856371 = re;
        double r3856372 = cos(r3856371);
        double r3856373 = r3856370 * r3856372;
        double r3856374 = im;
        double r3856375 = -r3856374;
        double r3856376 = exp(r3856375);
        double r3856377 = exp(r3856374);
        double r3856378 = r3856376 + r3856377;
        double r3856379 = r3856373 * r3856378;
        return r3856379;
}
↓
double f(double re, double im) {
        double r3856380 = im;
        double r3856381 = exp(r3856380);
        double r3856382 = -r3856380;
        double r3856383 = exp(r3856382);
        double r3856384 = r3856381 + r3856383;
        double r3856385 = 0.5;
        double r3856386 = re;
        double r3856387 = cos(r3856386);
        double r3856388 = r3856385 * r3856387;
        double r3856389 = r3856384 * r3856388;
        return r3856389;
}

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 2019200 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))