Average Error: 0.0 → 0.0
Time: 21.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r12631 = 0.5;
        double r12632 = re;
        double r12633 = sin(r12632);
        double r12634 = r12631 * r12633;
        double r12635 = 0.0;
        double r12636 = im;
        double r12637 = r12635 - r12636;
        double r12638 = exp(r12637);
        double r12639 = exp(r12636);
        double r12640 = r12638 + r12639;
        double r12641 = r12634 * r12640;
        return r12641;
}
↓
double f(double re, double im) {
        double r12642 = 0.5;
        double r12643 = re;
        double r12644 = sin(r12643);
        double r12645 = r12642 * r12644;
        double r12646 = 0.0;
        double r12647 = im;
        double r12648 = r12646 - r12647;
        double r12649 = exp(r12648);
        double r12650 = r12645 * r12649;
        double r12651 = exp(r12647);
        double r12652 = r12645 * r12651;
        double r12653 = r12650 + r12652;
        return r12653;
}

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 distribute-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +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))))