Average Error: 0.0 → 0.0
Time: 3.9s
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 r18823 = 0.5;
        double r18824 = re;
        double r18825 = sin(r18824);
        double r18826 = r18823 * r18825;
        double r18827 = 0.0;
        double r18828 = im;
        double r18829 = r18827 - r18828;
        double r18830 = exp(r18829);
        double r18831 = exp(r18828);
        double r18832 = r18830 + r18831;
        double r18833 = r18826 * r18832;
        return r18833;
}
↓
double f(double re, double im) {
        double r18834 = 0.5;
        double r18835 = re;
        double r18836 = sin(r18835);
        double r18837 = r18834 * r18836;
        double r18838 = 0.0;
        double r18839 = im;
        double r18840 = r18838 - r18839;
        double r18841 = exp(r18840);
        double r18842 = exp(r18839);
        double r18843 = r18841 + r18842;
        double r18844 = r18837 * r18843;
        return r18844;
}

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 2020025 +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))))