Average Error: 0.0 → 0.0
Time: 17.5s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{e^{0.0} \cdot \left(0.5 \cdot \sin re\right)}{e^{im}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r19558 = 0.5;
        double r19559 = re;
        double r19560 = sin(r19559);
        double r19561 = r19558 * r19560;
        double r19562 = 0.0;
        double r19563 = im;
        double r19564 = r19562 - r19563;
        double r19565 = exp(r19564);
        double r19566 = exp(r19563);
        double r19567 = r19565 + r19566;
        double r19568 = r19561 * r19567;
        return r19568;
}
↓
double f(double re, double im) {
        double r19569 = 0.0;
        double r19570 = exp(r19569);
        double r19571 = 0.5;
        double r19572 = re;
        double r19573 = sin(r19572);
        double r19574 = r19571 * r19573;
        double r19575 = r19570 * r19574;
        double r19576 = im;
        double r19577 = exp(r19576);
        double r19578 = r19575 / r19577;
        double r19579 = r19577 * r19574;
        double r19580 = r19578 + r19579;
        return r19580;
}

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. Simplified0.0

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

  5. Simplified0.0

    \[\leadsto e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + \color{blue}{e^{im} \cdot \left(0.5 \cdot \sin re\right)}\]
  6. Using strategy rm

  7. Applied exp-diff0.0

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

  8. Applied associate-*l/0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))