Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)
double f(double re, double im) {
        double r15713 = 0.5;
        double r15714 = re;
        double r15715 = sin(r15714);
        double r15716 = r15713 * r15715;
        double r15717 = 0.0;
        double r15718 = im;
        double r15719 = r15717 - r15718;
        double r15720 = exp(r15719);
        double r15721 = exp(r15718);
        double r15722 = r15720 + r15721;
        double r15723 = r15716 * r15722;
        return r15723;
}
↓
double f(double re, double im) {
        double r15724 = 0.5;
        double r15725 = re;
        double r15726 = sin(r15725);
        double r15727 = 0.0;
        double r15728 = im;
        double r15729 = r15727 - r15728;
        double r15730 = exp(r15729);
        double r15731 = exp(r15728);
        double r15732 = r15730 + r15731;
        double r15733 = r15726 * r15732;
        double r15734 = r15724 * r15733;
        return r15734;
}

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 associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020018 +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))))