Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
0.5 \cdot \left(\sin re \cdot \left(e^{0.0 - im} + e^{im}\right)\right)
double f(double re, double im) {
        double r28329 = 0.5;
        double r28330 = re;
        double r28331 = sin(r28330);
        double r28332 = r28329 * r28331;
        double r28333 = 0.0;
        double r28334 = im;
        double r28335 = r28333 - r28334;
        double r28336 = exp(r28335);
        double r28337 = exp(r28334);
        double r28338 = r28336 + r28337;
        double r28339 = r28332 * r28338;
        return r28339;
}
↓
double f(double re, double im) {
        double r28340 = 0.5;
        double r28341 = re;
        double r28342 = sin(r28341);
        double r28343 = 0.0;
        double r28344 = im;
        double r28345 = r28343 - r28344;
        double r28346 = exp(r28345);
        double r28347 = exp(r28344);
        double r28348 = r28346 + r28347;
        double r28349 = r28342 * r28348;
        double r28350 = r28340 * r28349;
        return r28350;
}

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 associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +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))))