Average Error: 0.0 → 0.1
Time: 4.0s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}
double f(double re, double im) {
        double r23864 = 0.5;
        double r23865 = re;
        double r23866 = sin(r23865);
        double r23867 = r23864 * r23866;
        double r23868 = 0.0;
        double r23869 = im;
        double r23870 = r23868 - r23869;
        double r23871 = exp(r23870);
        double r23872 = exp(r23869);
        double r23873 = r23871 + r23872;
        double r23874 = r23867 * r23873;
        return r23874;
}
↓
double f(double re, double im) {
        double r23875 = 0.5;
        double r23876 = re;
        double r23877 = sin(r23876);
        double r23878 = r23875 * r23877;
        double r23879 = 0.0;
        double r23880 = im;
        double r23881 = r23879 - r23880;
        double r23882 = exp(r23881);
        double r23883 = r23878 * r23882;
        double r23884 = exp(r23880);
        double r23885 = r23878 * r23884;
        double r23886 = r23883 + r23885;
        return r23886;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}}\]

  4. Final simplification0.1

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot e^{0.0 - im} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Reproduce

herbie shell --seed 2020002 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))