Average Error: 0.0 → 0.0
Time: 6.4s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{0.0 - im} + e^{im}\right)}\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot e^{\log \left(e^{0.0 - im} + e^{im}\right)}
double f(double re, double im) {
        double r69238 = 0.5;
        double r69239 = re;
        double r69240 = sin(r69239);
        double r69241 = r69238 * r69240;
        double r69242 = 0.0;
        double r69243 = im;
        double r69244 = r69242 - r69243;
        double r69245 = exp(r69244);
        double r69246 = exp(r69243);
        double r69247 = r69245 + r69246;
        double r69248 = r69241 * r69247;
        return r69248;
}
↓
double f(double re, double im) {
        double r69249 = 0.5;
        double r69250 = re;
        double r69251 = sin(r69250);
        double r69252 = r69249 * r69251;
        double r69253 = 0.0;
        double r69254 = im;
        double r69255 = r69253 - r69254;
        double r69256 = exp(r69255);
        double r69257 = exp(r69254);
        double r69258 = r69256 + r69257;
        double r69259 = log(r69258);
        double r69260 = exp(r69259);
        double r69261 = r69252 * r69260;
        return r69261;
}

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 add-exp-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))