Average Error: 0.0 → 0.0
Time: 19.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(\sin re \cdot \left(e^{im} + e^{0.0 - im}\right)\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(\sin re \cdot \left(e^{im} + e^{0.0 - im}\right)\right) \cdot 0.5
double f(double re, double im) {
        double r1021340 = 0.5;
        double r1021341 = re;
        double r1021342 = sin(r1021341);
        double r1021343 = r1021340 * r1021342;
        double r1021344 = 0.0;
        double r1021345 = im;
        double r1021346 = r1021344 - r1021345;
        double r1021347 = exp(r1021346);
        double r1021348 = exp(r1021345);
        double r1021349 = r1021347 + r1021348;
        double r1021350 = r1021343 * r1021349;
        return r1021350;
}
↓
double f(double re, double im) {
        double r1021351 = re;
        double r1021352 = sin(r1021351);
        double r1021353 = im;
        double r1021354 = exp(r1021353);
        double r1021355 = 0.0;
        double r1021356 = r1021355 - r1021353;
        double r1021357 = exp(r1021356);
        double r1021358 = r1021354 + r1021357;
        double r1021359 = r1021352 * r1021358;
        double r1021360 = 0.5;
        double r1021361 = r1021359 * r1021360;
        return r1021361;
}

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

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))