Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r48626 = 0.5;
        double r48627 = re;
        double r48628 = cos(r48627);
        double r48629 = r48626 * r48628;
        double r48630 = im;
        double r48631 = -r48630;
        double r48632 = exp(r48631);
        double r48633 = exp(r48630);
        double r48634 = r48632 + r48633;
        double r48635 = r48629 * r48634;
        return r48635;
}
↓
double f(double re, double im) {
        double r48636 = re;
        double r48637 = cos(r48636);
        double r48638 = im;
        double r48639 = exp(r48638);
        double r48640 = 0.5;
        double r48641 = r48639 * r48640;
        double r48642 = r48640 / r48639;
        double r48643 = r48641 + r48642;
        double r48644 = r48637 * r48643;
        return r48644;
}

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019291 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))