Average Error: 0.0 → 0.0
Time: 19.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(\sin re \cdot 0.5\right) + e^{0.0 - im} \cdot \left(\sin re \cdot 0.5\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{im} \cdot \left(\sin re \cdot 0.5\right) + e^{0.0 - im} \cdot \left(\sin re \cdot 0.5\right)
double f(double re, double im) {
        double r886770 = 0.5;
        double r886771 = re;
        double r886772 = sin(r886771);
        double r886773 = r886770 * r886772;
        double r886774 = 0.0;
        double r886775 = im;
        double r886776 = r886774 - r886775;
        double r886777 = exp(r886776);
        double r886778 = exp(r886775);
        double r886779 = r886777 + r886778;
        double r886780 = r886773 * r886779;
        return r886780;
}
↓
double f(double re, double im) {
        double r886781 = im;
        double r886782 = exp(r886781);
        double r886783 = re;
        double r886784 = sin(r886783);
        double r886785 = 0.5;
        double r886786 = r886784 * r886785;
        double r886787 = r886782 * r886786;
        double r886788 = 0.0;
        double r886789 = r886788 - r886781;
        double r886790 = exp(r886789);
        double r886791 = r886790 * r886786;
        double r886792 = r886787 + r886791;
        return r886792;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))