Average Error: 0.0 → 0.0
Time: 28.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{im}}\right) \cdot \sqrt{e^{im}} + \frac{0.5 \cdot \sin re}{e^{im}}\]
double f(double re, double im) {
        double r1063487 = 0.5;
        double r1063488 = re;
        double r1063489 = sin(r1063488);
        double r1063490 = r1063487 * r1063489;
        double r1063491 = 0.0;
        double r1063492 = im;
        double r1063493 = r1063491 - r1063492;
        double r1063494 = exp(r1063493);
        double r1063495 = exp(r1063492);
        double r1063496 = r1063494 + r1063495;
        double r1063497 = r1063490 * r1063496;
        return r1063497;
}
↓
double f(double re, double im) {
        double r1063498 = 0.5;
        double r1063499 = re;
        double r1063500 = sin(r1063499);
        double r1063501 = r1063498 * r1063500;
        double r1063502 = im;
        double r1063503 = exp(r1063502);
        double r1063504 = sqrt(r1063503);
        double r1063505 = r1063501 * r1063504;
        double r1063506 = r1063505 * r1063504;
        double r1063507 = r1063501 / r1063503;
        double r1063508 = r1063506 + r1063507;
        return r1063508;
}


\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(\left(0.5 \cdot \sin re\right) \cdot \sqrt{e^{im}}\right) \cdot \sqrt{e^{im}} + \frac{0.5 \cdot \sin re}{e^{im}}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied associate-*l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019101 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))