Average Error: 0.0 → 0.0
Time: 14.7s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
double f(double re, double im) {
        double r14301 = 0.5;
        double r14302 = re;
        double r14303 = sin(r14302);
        double r14304 = r14301 * r14303;
        double r14305 = 0.0;
        double r14306 = im;
        double r14307 = r14305 - r14306;
        double r14308 = exp(r14307);
        double r14309 = exp(r14306);
        double r14310 = r14308 + r14309;
        double r14311 = r14304 * r14310;
        return r14311;
}
↓
double f(double re, double im) {
        double r14312 = 0.5;
        double r14313 = re;
        double r14314 = sin(r14313);
        double r14315 = r14312 * r14314;
        double r14316 = 0.0;
        double r14317 = im;
        double r14318 = r14316 - r14317;
        double r14319 = exp(r14318);
        double r14320 = exp(r14317);
        double r14321 = r14319 + r14320;
        double r14322 = r14315 * r14321;
        return r14322;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))