Average Error: 0.0 → 0.0
Time: 19.5s
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 r611641 = 0.5;
        double r611642 = re;
        double r611643 = sin(r611642);
        double r611644 = r611641 * r611643;
        double r611645 = 0.0;
        double r611646 = im;
        double r611647 = r611645 - r611646;
        double r611648 = exp(r611647);
        double r611649 = exp(r611646);
        double r611650 = r611648 + r611649;
        double r611651 = r611644 * r611650;
        return r611651;
}
↓
double f(double re, double im) {
        double r611652 = im;
        double r611653 = exp(r611652);
        double r611654 = re;
        double r611655 = sin(r611654);
        double r611656 = 0.5;
        double r611657 = r611655 * r611656;
        double r611658 = r611653 * r611657;
        double r611659 = 0.0;
        double r611660 = r611659 - r611652;
        double r611661 = exp(r611660);
        double r611662 = r611661 * r611657;
        double r611663 = r611658 + r611662;
        return r611663;
}

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))))