Average Error: 15.0 → 0.3
Time: 9.4s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\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(x \cdot 0.5\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r839492 = 8.0;
        double r839493 = 3.0;
        double r839494 = r839492 / r839493;
        double r839495 = x;
        double r839496 = 0.5;
        double r839497 = r839495 * r839496;
        double r839498 = sin(r839497);
        double r839499 = r839494 * r839498;
        double r839500 = r839499 * r839498;
        double r839501 = sin(r839495);
        double r839502 = r839500 / r839501;
        return r839502;
}
↓
double f(double x) {
        double r839503 = 8.0;
        double r839504 = x;
        double r839505 = 0.5;
        double r839506 = r839504 * r839505;
        double r839507 = sin(r839506);
        double r839508 = r839503 * r839507;
        double r839509 = 3.0;
        double r839510 = r839508 / r839509;
        double r839511 = sin(r839504);
        double r839512 = r839507 / r839511;
        double r839513 = r839510 * r839512;
        return r839513;
}

Error

Bits error versus x

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Results

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Target

Original15.0
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 15.0

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

  3. Applied *-un-lft-identity15.0

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

  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. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 +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)))