Average Error: 0.0 → 0.0
Time: 14.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r1023384 = 0.5;
        double r1023385 = re;
        double r1023386 = cos(r1023385);
        double r1023387 = r1023384 * r1023386;
        double r1023388 = im;
        double r1023389 = -r1023388;
        double r1023390 = exp(r1023389);
        double r1023391 = exp(r1023388);
        double r1023392 = r1023390 + r1023391;
        double r1023393 = r1023387 * r1023392;
        return r1023393;
}
↓
double f(double re, double im) {
        double r1023394 = re;
        double r1023395 = cos(r1023394);
        double r1023396 = 0.5;
        double r1023397 = im;
        double r1023398 = exp(r1023397);
        double r1023399 = r1023396 / r1023398;
        double r1023400 = r1023396 * r1023398;
        double r1023401 = r1023399 + r1023400;
        double r1023402 = r1023395 * r1023401;
        return r1023402;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))