Average Error: 0.0 → 0.1
Time: 5.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}
double f(double re, double im) {
        double r23721 = 0.5;
        double r23722 = re;
        double r23723 = sin(r23722);
        double r23724 = r23721 * r23723;
        double r23725 = 0.0;
        double r23726 = im;
        double r23727 = r23725 - r23726;
        double r23728 = exp(r23727);
        double r23729 = exp(r23726);
        double r23730 = r23728 + r23729;
        double r23731 = r23724 * r23730;
        return r23731;
}
↓
double f(double re, double im) {
        double r23732 = 0.5;
        double r23733 = re;
        double r23734 = sin(r23733);
        double r23735 = r23732 * r23734;
        double r23736 = 0.0;
        double r23737 = im;
        double r23738 = r23736 - r23737;
        double r23739 = exp(r23738);
        double r23740 = exp(r23737);
        double r23741 = r23739 + r23740;
        double r23742 = 3.0;
        double r23743 = pow(r23741, r23742);
        double r23744 = cbrt(r23743);
        double r23745 = r23735 * r23744;
        return r23745;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\sqrt[3]{\left(\left(e^{0.0 - im} + e^{im}\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\right) \cdot \left(e^{0.0 - im} + e^{im}\right)}}\]

  4. Simplified0.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}}\]

  5. Final simplification0.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \sqrt[3]{{\left(e^{0.0 - im} + e^{im}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))