Average Error: 0.0 → 0.0
Time: 5.3s
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 r26508 = 0.5;
        double r26509 = re;
        double r26510 = sin(r26509);
        double r26511 = r26508 * r26510;
        double r26512 = 0.0;
        double r26513 = im;
        double r26514 = r26512 - r26513;
        double r26515 = exp(r26514);
        double r26516 = exp(r26513);
        double r26517 = r26515 + r26516;
        double r26518 = r26511 * r26517;
        return r26518;
}
↓
double f(double re, double im) {
        double r26519 = 0.5;
        double r26520 = re;
        double r26521 = sin(r26520);
        double r26522 = r26519 * r26521;
        double r26523 = 0.0;
        double r26524 = exp(r26523);
        double r26525 = r26522 * r26524;
        double r26526 = im;
        double r26527 = exp(r26526);
        double r26528 = r26525 / r26527;
        double r26529 = r26522 * r26527;
        double r26530 = r26528 + r26529;
        return r26530;
}

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 2020020 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))