Average Error: 0.0 → 0.0
Time: 3.9s
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 r17270 = 0.5;
        double r17271 = re;
        double r17272 = sin(r17271);
        double r17273 = r17270 * r17272;
        double r17274 = 0.0;
        double r17275 = im;
        double r17276 = r17274 - r17275;
        double r17277 = exp(r17276);
        double r17278 = exp(r17275);
        double r17279 = r17277 + r17278;
        double r17280 = r17273 * r17279;
        return r17280;
}
↓
double f(double re, double im) {
        double r17281 = 0.5;
        double r17282 = re;
        double r17283 = sin(r17282);
        double r17284 = r17281 * r17283;
        double r17285 = 0.0;
        double r17286 = im;
        double r17287 = r17285 - r17286;
        double r17288 = exp(r17287);
        double r17289 = exp(r17286);
        double r17290 = r17288 + r17289;
        double r17291 = r17284 * r17290;
        return r17291;
}

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 2020025 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))