Average Error: 0.0 → 0.0
Time: 5.6s
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 r23481 = 0.5;
        double r23482 = re;
        double r23483 = sin(r23482);
        double r23484 = r23481 * r23483;
        double r23485 = 0.0;
        double r23486 = im;
        double r23487 = r23485 - r23486;
        double r23488 = exp(r23487);
        double r23489 = exp(r23486);
        double r23490 = r23488 + r23489;
        double r23491 = r23484 * r23490;
        return r23491;
}
↓
double f(double re, double im) {
        double r23492 = 0.5;
        double r23493 = re;
        double r23494 = sin(r23493);
        double r23495 = r23492 * r23494;
        double r23496 = 0.0;
        double r23497 = exp(r23496);
        double r23498 = r23495 * r23497;
        double r23499 = im;
        double r23500 = exp(r23499);
        double r23501 = r23498 / r23500;
        double r23502 = r23495 * r23500;
        double r23503 = r23501 + r23502;
        return r23503;
}

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))))