Average Error: 0.0 → 0.0
Time: 7.6s
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 r81086 = 0.5;
        double r81087 = re;
        double r81088 = sin(r81087);
        double r81089 = r81086 * r81088;
        double r81090 = 0.0;
        double r81091 = im;
        double r81092 = r81090 - r81091;
        double r81093 = exp(r81092);
        double r81094 = exp(r81091);
        double r81095 = r81093 + r81094;
        double r81096 = r81089 * r81095;
        return r81096;
}
↓
double f(double re, double im) {
        double r81097 = 0.5;
        double r81098 = re;
        double r81099 = sin(r81098);
        double r81100 = r81097 * r81099;
        double r81101 = 0.0;
        double r81102 = im;
        double r81103 = r81101 - r81102;
        double r81104 = exp(r81103);
        double r81105 = exp(r81102);
        double r81106 = r81104 + r81105;
        double r81107 = r81100 * r81106;
        return r81107;
}

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 2020035 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))