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 r32161 = 0.5;
        double r32162 = re;
        double r32163 = sin(r32162);
        double r32164 = r32161 * r32163;
        double r32165 = 0.0;
        double r32166 = im;
        double r32167 = r32165 - r32166;
        double r32168 = exp(r32167);
        double r32169 = exp(r32166);
        double r32170 = r32168 + r32169;
        double r32171 = r32164 * r32170;
        return r32171;
}
↓
double f(double re, double im) {
        double r32172 = 0.5;
        double r32173 = re;
        double r32174 = sin(r32173);
        double r32175 = r32172 * r32174;
        double r32176 = 0.0;
        double r32177 = im;
        double r32178 = r32176 - r32177;
        double r32179 = exp(r32178);
        double r32180 = exp(r32177);
        double r32181 = r32179 + r32180;
        double r32182 = r32175 * r32181;
        return r32182;
}

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 2020062 +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))))