Average Error: 0.0 → 0.0
Time: 13.4s
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 r83250 = 0.5;
        double r83251 = re;
        double r83252 = sin(r83251);
        double r83253 = r83250 * r83252;
        double r83254 = 0.0;
        double r83255 = im;
        double r83256 = r83254 - r83255;
        double r83257 = exp(r83256);
        double r83258 = exp(r83255);
        double r83259 = r83257 + r83258;
        double r83260 = r83253 * r83259;
        return r83260;
}
↓
double f(double re, double im) {
        double r83261 = 0.5;
        double r83262 = re;
        double r83263 = sin(r83262);
        double r83264 = r83261 * r83263;
        double r83265 = 0.0;
        double r83266 = im;
        double r83267 = r83265 - r83266;
        double r83268 = exp(r83267);
        double r83269 = exp(r83266);
        double r83270 = r83268 + r83269;
        double r83271 = r83264 * r83270;
        return r83271;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +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))))