Average Error: 0.0 → 0.0
Time: 38.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right) + \left(0.5 \cdot \sin re\right) \cdot e^{-im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\sqrt{e^{im}} \cdot \left(\sqrt{e^{im}} \cdot \left(0.5 \cdot \sin re\right)\right) + \left(0.5 \cdot \sin re\right) \cdot e^{-im}
double f(double re, double im) {
        double r1029640 = 0.5;
        double r1029641 = re;
        double r1029642 = sin(r1029641);
        double r1029643 = r1029640 * r1029642;
        double r1029644 = 0.0;
        double r1029645 = im;
        double r1029646 = r1029644 - r1029645;
        double r1029647 = exp(r1029646);
        double r1029648 = exp(r1029645);
        double r1029649 = r1029647 + r1029648;
        double r1029650 = r1029643 * r1029649;
        return r1029650;
}
↓
double f(double re, double im) {
        double r1029651 = im;
        double r1029652 = exp(r1029651);
        double r1029653 = sqrt(r1029652);
        double r1029654 = 0.5;
        double r1029655 = re;
        double r1029656 = sin(r1029655);
        double r1029657 = r1029654 * r1029656;
        double r1029658 = r1029653 * r1029657;
        double r1029659 = r1029653 * r1029658;
        double r1029660 = -r1029651;
        double r1029661 = exp(r1029660);
        double r1029662 = r1029657 * r1029661;
        double r1029663 = r1029659 + r1029662;
        return r1029663;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0 - im} + \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\left(\sqrt{e^{im}} \cdot \sqrt{e^{im}}\right)}\]

  6. Applied associate-*r*0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0 - im} + \color{blue}{\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{im}}\right) \cdot \sqrt{e^{im}}}\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))