Average Error: 0.0 → 0.0
Time: 13.8s
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 r12974 = 0.5;
        double r12975 = re;
        double r12976 = sin(r12975);
        double r12977 = r12974 * r12976;
        double r12978 = 0.0;
        double r12979 = im;
        double r12980 = r12978 - r12979;
        double r12981 = exp(r12980);
        double r12982 = exp(r12979);
        double r12983 = r12981 + r12982;
        double r12984 = r12977 * r12983;
        return r12984;
}
↓
double f(double re, double im) {
        double r12985 = 0.5;
        double r12986 = re;
        double r12987 = sin(r12986);
        double r12988 = r12985 * r12987;
        double r12989 = 0.0;
        double r12990 = im;
        double r12991 = r12989 - r12990;
        double r12992 = exp(r12991);
        double r12993 = exp(r12990);
        double r12994 = r12992 + r12993;
        double r12995 = r12988 * r12994;
        return r12995;
}

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 2019209 +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))))