Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{im} + e^{0.0 - im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{im} + e^{0.0 - im}\right)
double f(double re, double im) {
        double r18605 = 0.5;
        double r18606 = re;
        double r18607 = sin(r18606);
        double r18608 = r18605 * r18607;
        double r18609 = 0.0;
        double r18610 = im;
        double r18611 = r18609 - r18610;
        double r18612 = exp(r18611);
        double r18613 = exp(r18610);
        double r18614 = r18612 + r18613;
        double r18615 = r18608 * r18614;
        return r18615;
}
↓
double f(double re, double im) {
        double r18616 = 0.5;
        double r18617 = re;
        double r18618 = sin(r18617);
        double r18619 = r18616 * r18618;
        double r18620 = im;
        double r18621 = exp(r18620);
        double r18622 = 0.0;
        double r18623 = r18622 - r18620;
        double r18624 = exp(r18623);
        double r18625 = r18621 + r18624;
        double r18626 = r18619 * r18625;
        return r18626;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019291 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))