Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\frac{\left(0.5 \cdot \sin re\right) \cdot e^{0.0}}{e^{im}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r24484 = 0.5;
        double r24485 = re;
        double r24486 = sin(r24485);
        double r24487 = r24484 * r24486;
        double r24488 = 0.0;
        double r24489 = im;
        double r24490 = r24488 - r24489;
        double r24491 = exp(r24490);
        double r24492 = exp(r24489);
        double r24493 = r24491 + r24492;
        double r24494 = r24487 * r24493;
        return r24494;
}
↓
double f(double re, double im) {
        double r24495 = 0.5;
        double r24496 = re;
        double r24497 = sin(r24496);
        double r24498 = r24495 * r24497;
        double r24499 = 0.0;
        double r24500 = exp(r24499);
        double r24501 = r24498 * r24500;
        double r24502 = im;
        double r24503 = exp(r24502);
        double r24504 = r24501 / r24503;
        double r24505 = r24498 * r24503;
        double r24506 = r24504 + r24505;
        return r24506;
}

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. Using strategy rm

  5. Applied exp-diff0.0

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +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))))