Average Error: 0.0 → 0.0
Time: 15.6s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
e^{0.0 - im} \cdot \left(0.5 \cdot \sin re\right) + e^{im} \cdot \left(0.5 \cdot \sin re\right)
double f(double re, double im) {
        double r16353 = 0.5;
        double r16354 = re;
        double r16355 = sin(r16354);
        double r16356 = r16353 * r16355;
        double r16357 = 0.0;
        double r16358 = im;
        double r16359 = r16357 - r16358;
        double r16360 = exp(r16359);
        double r16361 = exp(r16358);
        double r16362 = r16360 + r16361;
        double r16363 = r16356 * r16362;
        return r16363;
}
↓
double f(double re, double im) {
        double r16364 = 0.0;
        double r16365 = im;
        double r16366 = r16364 - r16365;
        double r16367 = exp(r16366);
        double r16368 = 0.5;
        double r16369 = re;
        double r16370 = sin(r16369);
        double r16371 = r16368 * r16370;
        double r16372 = r16367 * r16371;
        double r16373 = exp(r16365);
        double r16374 = r16373 * r16371;
        double r16375 = r16372 + r16374;
        return r16375;
}

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-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))