Average Error: 0.0 → 0.0
Time: 24.2s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re \cdot 0.5}{e^{im}} + \left(\sin re \cdot 0.5\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\frac{\sin re \cdot 0.5}{e^{im}} + \left(\sin re \cdot 0.5\right) \cdot e^{im}
double f(double re, double im) {
        double r648405 = 0.5;
        double r648406 = re;
        double r648407 = sin(r648406);
        double r648408 = r648405 * r648407;
        double r648409 = 0.0;
        double r648410 = im;
        double r648411 = r648409 - r648410;
        double r648412 = exp(r648411);
        double r648413 = exp(r648410);
        double r648414 = r648412 + r648413;
        double r648415 = r648408 * r648414;
        return r648415;
}
↓
double f(double re, double im) {
        double r648416 = re;
        double r648417 = sin(r648416);
        double r648418 = 0.5;
        double r648419 = r648417 * r648418;
        double r648420 = im;
        double r648421 = exp(r648420);
        double r648422 = r648419 / r648421;
        double r648423 = r648419 * r648421;
        double r648424 = r648422 + r648423;
        return r648424;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019121 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))