Average Error: 15.2 → 0.3
Time: 17.1s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3}
double f(double x) {
        double r358404 = 8.0;
        double r358405 = 3.0;
        double r358406 = r358404 / r358405;
        double r358407 = x;
        double r358408 = 0.5;
        double r358409 = r358407 * r358408;
        double r358410 = sin(r358409);
        double r358411 = r358406 * r358410;
        double r358412 = r358411 * r358410;
        double r358413 = sin(r358407);
        double r358414 = r358412 / r358413;
        return r358414;
}
↓
double f(double x) {
        double r358415 = 0.5;
        double r358416 = x;
        double r358417 = r358415 * r358416;
        double r358418 = sin(r358417);
        double r358419 = 8.0;
        double r358420 = r358418 * r358419;
        double r358421 = sin(r358416);
        double r358422 = r358421 / r358418;
        double r358423 = 3.0;
        double r358424 = r358422 * r358423;
        double r358425 = r358420 / r358424;
        return r358425;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.2
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 15.2

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

  3. Applied associate-/l*0.5

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

  4. Simplified0.5

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

  6. Applied associate-*l/0.3

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

  7. Simplified0.3

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

  9. Applied div-inv0.5

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

  10. Applied associate-/l*0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 +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)))