Average Error: 0.0 → 0.0
Time: 5.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{0.0 - im} + e^{im}\right)}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{0.0 - im} + e^{im}\right)}
double f(double re, double im) {
        double r19521 = 0.5;
        double r19522 = re;
        double r19523 = sin(r19522);
        double r19524 = r19521 * r19523;
        double r19525 = 0.0;
        double r19526 = im;
        double r19527 = r19525 - r19526;
        double r19528 = exp(r19527);
        double r19529 = exp(r19526);
        double r19530 = r19528 + r19529;
        double r19531 = r19524 * r19530;
        return r19531;
}
↓
double f(double re, double im) {
        double r19532 = 0.5;
        double r19533 = re;
        double r19534 = sin(r19533);
        double r19535 = r19532 * r19534;
        double r19536 = 0.0;
        double r19537 = im;
        double r19538 = r19536 - r19537;
        double r19539 = exp(r19538);
        double r19540 = exp(r19537);
        double r19541 = r19539 + r19540;
        double r19542 = log(r19541);
        double r19543 = exp(r19542);
        double r19544 = r19535 * r19543;
        return r19544;
}

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 add-exp-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +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))))