Average Error: 14.3 → 0.3
Time: 18.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r506362 = 8.0;
        double r506363 = 3.0;
        double r506364 = r506362 / r506363;
        double r506365 = x;
        double r506366 = 0.5;
        double r506367 = r506365 * r506366;
        double r506368 = sin(r506367);
        double r506369 = r506364 * r506368;
        double r506370 = r506369 * r506368;
        double r506371 = sin(r506365);
        double r506372 = r506370 / r506371;
        return r506372;
}
↓
double f(double x) {
        double r506373 = 8.0;
        double r506374 = 0.5;
        double r506375 = x;
        double r506376 = r506374 * r506375;
        double r506377 = sin(r506376);
        double r506378 = r506373 * r506377;
        double r506379 = 3.0;
        double r506380 = r506378 / r506379;
        double r506381 = r506375 * r506374;
        double r506382 = sin(r506381);
        double r506383 = sin(r506375);
        double r506384 = r506382 / r506383;
        double r506385 = r506380 * r506384;
        return r506385;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.3
Target0.3
Herbie0.3
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.3

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity14.3

    \[\leadsto \frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\color{blue}{1 \cdot \sin x}}\]

  4. Applied times-frac0.5

    \[\leadsto \color{blue}{\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{1} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\]

  5. Simplified0.5

    \[\leadsto \color{blue}{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right)} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
  6. Using strategy rm

  7. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  8. Simplified0.3

    \[\leadsto \frac{\color{blue}{8 \cdot \sin \left(0.5 \cdot x\right)}}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  9. Final simplification0.3

    \[\leadsto \frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8 (sin (* x 0.5))) 3) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8 3) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))