Average Error: 0.0 → 0.0
Time: 5.2s
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 r21188 = 0.5;
        double r21189 = re;
        double r21190 = sin(r21189);
        double r21191 = r21188 * r21190;
        double r21192 = 0.0;
        double r21193 = im;
        double r21194 = r21192 - r21193;
        double r21195 = exp(r21194);
        double r21196 = exp(r21193);
        double r21197 = r21195 + r21196;
        double r21198 = r21191 * r21197;
        return r21198;
}
↓
double f(double re, double im) {
        double r21199 = 0.5;
        double r21200 = re;
        double r21201 = sin(r21200);
        double r21202 = r21199 * r21201;
        double r21203 = 0.0;
        double r21204 = im;
        double r21205 = r21203 - r21204;
        double r21206 = exp(r21205);
        double r21207 = exp(r21204);
        double r21208 = r21206 + r21207;
        double r21209 = r21202 * r21208;
        return r21209;
}

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