Average Error: 0.0 → 0.0
Time: 18.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\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^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r18699 = 0.5;
        double r18700 = re;
        double r18701 = sin(r18700);
        double r18702 = r18699 * r18701;
        double r18703 = 0.0;
        double r18704 = im;
        double r18705 = r18703 - r18704;
        double r18706 = exp(r18705);
        double r18707 = exp(r18704);
        double r18708 = r18706 + r18707;
        double r18709 = r18702 * r18708;
        return r18709;
}
↓
double f(double re, double im) {
        double r18710 = 0.5;
        double r18711 = re;
        double r18712 = sin(r18711);
        double r18713 = r18710 * r18712;
        double r18714 = 0.0;
        double r18715 = im;
        double r18716 = r18714 - r18715;
        double r18717 = exp(r18716);
        double r18718 = exp(r18715);
        double r18719 = r18717 + r18718;
        double r18720 = r18713 * r18719;
        return r18720;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied distribute-rgt-out0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))