Average Error: 0.0 → 0.0
Time: 13.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r12782 = 0.5;
        double r12783 = re;
        double r12784 = sin(r12783);
        double r12785 = r12782 * r12784;
        double r12786 = 0.0;
        double r12787 = im;
        double r12788 = r12786 - r12787;
        double r12789 = exp(r12788);
        double r12790 = exp(r12787);
        double r12791 = r12789 + r12790;
        double r12792 = r12785 * r12791;
        return r12792;
}
↓
double f(double re, double im) {
        double r12793 = 0.0;
        double r12794 = im;
        double r12795 = r12793 - r12794;
        double r12796 = exp(r12795);
        double r12797 = 0.5;
        double r12798 = re;
        double r12799 = sin(r12798);
        double r12800 = r12797 * r12799;
        double r12801 = r12796 * r12800;
        double r12802 = exp(r12794);
        double r12803 = r12802 * r12800;
        double r12804 = r12801 + r12803;
        return r12804;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 +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))))