Average Error: 0.0 → 0.0
Time: 4.3s
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 r57636 = 0.5;
        double r57637 = re;
        double r57638 = cos(r57637);
        double r57639 = r57636 * r57638;
        double r57640 = im;
        double r57641 = -r57640;
        double r57642 = exp(r57641);
        double r57643 = exp(r57640);
        double r57644 = r57642 + r57643;
        double r57645 = r57639 * r57644;
        return r57645;
}
↓
double f(double re, double im) {
        double r57646 = 0.5;
        double r57647 = re;
        double r57648 = cos(r57647);
        double r57649 = r57646 * r57648;
        double r57650 = im;
        double r57651 = exp(r57650);
        double r57652 = r57649 / r57651;
        double r57653 = r57649 * r57651;
        double r57654 = r57652 + r57653;
        return r57654;
}

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 2020020 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))