Average Error: 0.0 → 0.0
Time: 32.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot \left(e^{im} + e^{-im}\right)\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(\sin re \cdot \left(e^{im} + e^{-im}\right)\right) \cdot 0.5
double f(double re, double im) {
        double r1004230 = 0.5;
        double r1004231 = re;
        double r1004232 = sin(r1004231);
        double r1004233 = r1004230 * r1004232;
        double r1004234 = 0.0;
        double r1004235 = im;
        double r1004236 = r1004234 - r1004235;
        double r1004237 = exp(r1004236);
        double r1004238 = exp(r1004235);
        double r1004239 = r1004237 + r1004238;
        double r1004240 = r1004233 * r1004239;
        return r1004240;
}
↓
double f(double re, double im) {
        double r1004241 = re;
        double r1004242 = sin(r1004241);
        double r1004243 = im;
        double r1004244 = exp(r1004243);
        double r1004245 = -r1004243;
        double r1004246 = exp(r1004245);
        double r1004247 = r1004244 + r1004246;
        double r1004248 = r1004242 * r1004247;
        double r1004249 = 0.5;
        double r1004250 = r1004248 * r1004249;
        return r1004250;
}

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. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

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