Average Error: 0.0 → 0.0
Time: 21.2s
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 r12638 = 0.5;
        double r12639 = re;
        double r12640 = sin(r12639);
        double r12641 = r12638 * r12640;
        double r12642 = 0.0;
        double r12643 = im;
        double r12644 = r12642 - r12643;
        double r12645 = exp(r12644);
        double r12646 = exp(r12643);
        double r12647 = r12645 + r12646;
        double r12648 = r12641 * r12647;
        return r12648;
}
↓
double f(double re, double im) {
        double r12649 = 0.5;
        double r12650 = re;
        double r12651 = sin(r12650);
        double r12652 = r12649 * r12651;
        double r12653 = 0.0;
        double r12654 = im;
        double r12655 = r12653 - r12654;
        double r12656 = exp(r12655);
        double r12657 = r12652 * r12656;
        double r12658 = exp(r12654);
        double r12659 = r12652 * r12658;
        double r12660 = r12657 + r12659;
        return r12660;
}

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))))