Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \frac{0.5}{e^{im}} + \left(\cos re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r28526 = 0.5;
        double r28527 = re;
        double r28528 = cos(r28527);
        double r28529 = r28526 * r28528;
        double r28530 = im;
        double r28531 = -r28530;
        double r28532 = exp(r28531);
        double r28533 = exp(r28530);
        double r28534 = r28532 + r28533;
        double r28535 = r28529 * r28534;
        return r28535;
}
↓
double f(double re, double im) {
        double r28536 = re;
        double r28537 = cos(r28536);
        double r28538 = 0.5;
        double r28539 = im;
        double r28540 = exp(r28539);
        double r28541 = r28538 / r28540;
        double r28542 = r28537 * r28541;
        double r28543 = r28537 * r28538;
        double r28544 = r28543 * r28540;
        double r28545 = r28542 + r28544;
        return r28545;
}

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

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))