Average Error: 0.0 → 0.0
Time: 1.2m
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r4538035 = 0.5;
        double r4538036 = re;
        double r4538037 = sin(r4538036);
        double r4538038 = r4538035 * r4538037;
        double r4538039 = 0.0;
        double r4538040 = im;
        double r4538041 = r4538039 - r4538040;
        double r4538042 = exp(r4538041);
        double r4538043 = exp(r4538040);
        double r4538044 = r4538042 + r4538043;
        double r4538045 = r4538038 * r4538044;
        return r4538045;
}
↓
double f(double re, double im) {
        double r4538046 = 0.5;
        double r4538047 = re;
        double r4538048 = sin(r4538047);
        double r4538049 = r4538046 * r4538048;
        double r4538050 = im;
        double r4538051 = -r4538050;
        double r4538052 = exp(r4538051);
        double r4538053 = exp(r4538050);
        double r4538054 = r4538052 + r4538053;
        double r4538055 = r4538049 * r4538054;
        return r4538055;
}

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

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))