Average Error: 0.0 → 0.0
Time: 6.5s
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 r30279 = 0.5;
        double r30280 = re;
        double r30281 = sin(r30280);
        double r30282 = r30279 * r30281;
        double r30283 = 0.0;
        double r30284 = im;
        double r30285 = r30283 - r30284;
        double r30286 = exp(r30285);
        double r30287 = exp(r30284);
        double r30288 = r30286 + r30287;
        double r30289 = r30282 * r30288;
        return r30289;
}
↓
double f(double re, double im) {
        double r30290 = 0.5;
        double r30291 = re;
        double r30292 = sin(r30291);
        double r30293 = r30290 * r30292;
        double r30294 = 0.0;
        double r30295 = im;
        double r30296 = r30294 - r30295;
        double r30297 = exp(r30296);
        double r30298 = exp(r30295);
        double r30299 = r30297 + r30298;
        double r30300 = r30293 * r30299;
        return r30300;
}

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 2020035 +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))))