Average Error: 0.0 → 0.0
Time: 19.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r306639 = 0.5;
        double r306640 = re;
        double r306641 = sin(r306640);
        double r306642 = r306639 * r306641;
        double r306643 = 0.0;
        double r306644 = im;
        double r306645 = r306643 - r306644;
        double r306646 = exp(r306645);
        double r306647 = exp(r306644);
        double r306648 = r306646 + r306647;
        double r306649 = r306642 * r306648;
        return r306649;
}
↓
double f(double re, double im) {
        double r306650 = 0.5;
        double r306651 = re;
        double r306652 = sin(r306651);
        double r306653 = r306650 * r306652;
        double r306654 = im;
        double r306655 = -r306654;
        double r306656 = exp(r306655);
        double r306657 = exp(r306654);
        double r306658 = r306656 + r306657;
        double r306659 = r306653 * r306658;
        return r306659;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))