Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{\cos re \cdot 0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r1095615 = 0.5;
        double r1095616 = re;
        double r1095617 = cos(r1095616);
        double r1095618 = r1095615 * r1095617;
        double r1095619 = im;
        double r1095620 = -r1095619;
        double r1095621 = exp(r1095620);
        double r1095622 = exp(r1095619);
        double r1095623 = r1095621 + r1095622;
        double r1095624 = r1095618 * r1095623;
        return r1095624;
}
↓
double f(double re, double im) {
        double r1095625 = re;
        double r1095626 = cos(r1095625);
        double r1095627 = 0.5;
        double r1095628 = r1095626 * r1095627;
        double r1095629 = im;
        double r1095630 = exp(r1095629);
        double r1095631 = r1095628 / r1095630;
        double r1095632 = r1095628 * r1095630;
        double r1095633 = r1095631 + r1095632;
        return r1095633;
}

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. Simplified0.0

    \[\leadsto \color{blue}{(\left(e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) + \left(\frac{0.5 \cdot \cos re}{e^{im}}\right))_*}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))