Average Error: 0.0 → 0.0
Time: 5.6s
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 r29208 = 0.5;
        double r29209 = re;
        double r29210 = sin(r29209);
        double r29211 = r29208 * r29210;
        double r29212 = 0.0;
        double r29213 = im;
        double r29214 = r29212 - r29213;
        double r29215 = exp(r29214);
        double r29216 = exp(r29213);
        double r29217 = r29215 + r29216;
        double r29218 = r29211 * r29217;
        return r29218;
}
↓
double f(double re, double im) {
        double r29219 = 0.5;
        double r29220 = re;
        double r29221 = sin(r29220);
        double r29222 = r29219 * r29221;
        double r29223 = 0.0;
        double r29224 = im;
        double r29225 = r29223 - r29224;
        double r29226 = exp(r29225);
        double r29227 = exp(r29224);
        double r29228 = r29226 + r29227;
        double r29229 = r29222 * r29228;
        return r29229;
}

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 2020027 +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))))