Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\frac{0.5 \cdot \cos re}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}
double f(double re, double im) {
        double r51537 = 0.5;
        double r51538 = re;
        double r51539 = cos(r51538);
        double r51540 = r51537 * r51539;
        double r51541 = im;
        double r51542 = -r51541;
        double r51543 = exp(r51542);
        double r51544 = exp(r51541);
        double r51545 = r51543 + r51544;
        double r51546 = r51540 * r51545;
        return r51546;
}
↓
double f(double re, double im) {
        double r51547 = 0.5;
        double r51548 = re;
        double r51549 = cos(r51548);
        double r51550 = r51547 * r51549;
        double r51551 = im;
        double r51552 = exp(r51551);
        double r51553 = r51550 / r51552;
        double r51554 = r51550 * r51552;
        double r51555 = r51553 + r51554;
        return r51555;
}

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-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))