Average Error: 0.0 → 0.0
Time: 22.5s
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 r5133385 = 0.5;
        double r5133386 = re;
        double r5133387 = cos(r5133386);
        double r5133388 = r5133385 * r5133387;
        double r5133389 = im;
        double r5133390 = -r5133389;
        double r5133391 = exp(r5133390);
        double r5133392 = exp(r5133389);
        double r5133393 = r5133391 + r5133392;
        double r5133394 = r5133388 * r5133393;
        return r5133394;
}
↓
double f(double re, double im) {
        double r5133395 = re;
        double r5133396 = cos(r5133395);
        double r5133397 = 0.5;
        double r5133398 = r5133396 * r5133397;
        double r5133399 = im;
        double r5133400 = exp(r5133399);
        double r5133401 = r5133398 / r5133400;
        double r5133402 = r5133398 * r5133400;
        double r5133403 = r5133401 + r5133402;
        return r5133403;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(e^{im}\right), \left(0.5 \cdot \cos re\right), \left(\frac{0.5 \cdot \cos re}{e^{im}}\right)\right)}\]
  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 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))