Average Error: 0.0 → 0.0
Time: 18.2s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
double f(double re, double im) {
        double r1798447 = 0.5;
        double r1798448 = re;
        double r1798449 = cos(r1798448);
        double r1798450 = r1798447 * r1798449;
        double r1798451 = im;
        double r1798452 = -r1798451;
        double r1798453 = exp(r1798452);
        double r1798454 = exp(r1798451);
        double r1798455 = r1798453 + r1798454;
        double r1798456 = r1798450 * r1798455;
        return r1798456;
}
↓
double f(double re, double im) {
        double r1798457 = im;
        double r1798458 = exp(r1798457);
        double r1798459 = -r1798457;
        double r1798460 = exp(r1798459);
        double r1798461 = r1798458 + r1798460;
        double r1798462 = 0.5;
        double r1798463 = re;
        double r1798464 = cos(r1798463);
        double r1798465 = r1798462 * r1798464;
        double r1798466 = r1798461 * r1798465;
        return r1798466;
}


\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)

Error

Bits error versus re

Bits error versus im

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 2019102 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))