Average Error: 15.1 → 0.3
Time: 16.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}}\]
\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{8 \cdot \sin \left(x \cdot 0.5\right)}{\left(\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}}
double f(double x) {
        double r502411 = 8.0;
        double r502412 = 3.0;
        double r502413 = r502411 / r502412;
        double r502414 = x;
        double r502415 = 0.5;
        double r502416 = r502414 * r502415;
        double r502417 = sin(r502416);
        double r502418 = r502413 * r502417;
        double r502419 = r502418 * r502417;
        double r502420 = sin(r502414);
        double r502421 = r502419 / r502420;
        return r502421;
}
↓
double f(double x) {
        double r502422 = 8.0;
        double r502423 = x;
        double r502424 = 0.5;
        double r502425 = r502423 * r502424;
        double r502426 = sin(r502425);
        double r502427 = r502422 * r502426;
        double r502428 = sin(r502423);
        double r502429 = r502428 / r502426;
        double r502430 = 3.0;
        double r502431 = cbrt(r502430);
        double r502432 = r502431 * r502431;
        double r502433 = r502429 * r502432;
        double r502434 = r502433 * r502431;
        double r502435 = r502427 / r502434;
        return r502435;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.1
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 15.1

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

  5. Applied associate-*l/0.3

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

  6. Applied associate-/l/0.3

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

  8. Applied add-cube-cbrt0.3

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019235 
(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)))