Average Error: 0.0 → 0.0
Time: 11.4s
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 r81539 = 0.5;
        double r81540 = re;
        double r81541 = sin(r81540);
        double r81542 = r81539 * r81541;
        double r81543 = 0.0;
        double r81544 = im;
        double r81545 = r81543 - r81544;
        double r81546 = exp(r81545);
        double r81547 = exp(r81544);
        double r81548 = r81546 + r81547;
        double r81549 = r81542 * r81548;
        return r81549;
}
↓
double f(double re, double im) {
        double r81550 = 0.0;
        double r81551 = exp(r81550);
        double r81552 = 0.5;
        double r81553 = re;
        double r81554 = sin(r81553);
        double r81555 = r81552 * r81554;
        double r81556 = r81551 * r81555;
        double r81557 = im;
        double r81558 = exp(r81557);
        double r81559 = r81556 / r81558;
        double r81560 = r81558 * r81555;
        double r81561 = r81559 + r81560;
        return r81561;
}

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 2020046 +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))))