Average Error: 0.0 → 0.0
Time: 6.7s
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 r30075 = 0.5;
        double r30076 = re;
        double r30077 = sin(r30076);
        double r30078 = r30075 * r30077;
        double r30079 = 0.0;
        double r30080 = im;
        double r30081 = r30079 - r30080;
        double r30082 = exp(r30081);
        double r30083 = exp(r30080);
        double r30084 = r30082 + r30083;
        double r30085 = r30078 * r30084;
        return r30085;
}
↓
double f(double re, double im) {
        double r30086 = 0.5;
        double r30087 = re;
        double r30088 = sin(r30087);
        double r30089 = r30086 * r30088;
        double r30090 = 0.0;
        double r30091 = im;
        double r30092 = r30090 - r30091;
        double r30093 = exp(r30092);
        double r30094 = exp(r30091);
        double r30095 = r30093 + r30094;
        double r30096 = r30089 * r30095;
        return r30096;
}

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 2020089 +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))))