Average Error: 0.0 → 0.0
Time: 45.3s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \frac{\sin re}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r17582 = 0.5;
        double r17583 = re;
        double r17584 = sin(r17583);
        double r17585 = r17582 * r17584;
        double r17586 = 0.0;
        double r17587 = im;
        double r17588 = r17586 - r17587;
        double r17589 = exp(r17588);
        double r17590 = exp(r17587);
        double r17591 = r17589 + r17590;
        double r17592 = r17585 * r17591;
        return r17592;
}
↓
double f(double re, double im) {
        double r17593 = 0.5;
        double r17594 = re;
        double r17595 = sin(r17594);
        double r17596 = im;
        double r17597 = exp(r17596);
        double r17598 = r17595 / r17597;
        double r17599 = r17593 * r17598;
        double r17600 = r17593 * r17595;
        double r17601 = r17600 * r17597;
        double r17602 = r17599 + r17601;
        return r17602;
}

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. Taylor expanded around inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))