Average Error: 14.8 → 0.4
Time: 4.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}}\]
\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(0.5 \cdot x\right)} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}}
double f(double x) {
        double r656540 = 8.0;
        double r656541 = 3.0;
        double r656542 = r656540 / r656541;
        double r656543 = x;
        double r656544 = 0.5;
        double r656545 = r656543 * r656544;
        double r656546 = sin(r656545);
        double r656547 = r656542 * r656546;
        double r656548 = r656547 * r656546;
        double r656549 = sin(r656543);
        double r656550 = r656548 / r656549;
        return r656550;
}
↓
double f(double x) {
        double r656551 = 8.0;
        double r656552 = x;
        double r656553 = 0.5;
        double r656554 = r656552 * r656553;
        double r656555 = sin(r656554);
        double r656556 = r656551 * r656555;
        double r656557 = sin(r656552);
        double r656558 = r656553 * r656552;
        double r656559 = sin(r656558);
        double r656560 = r656557 / r656559;
        double r656561 = 3.0;
        double r656562 = cbrt(r656561);
        double r656563 = r656562 * r656562;
        double r656564 = r656560 * r656563;
        double r656565 = r656564 * r656562;
        double r656566 = r656556 / r656565;
        return r656566;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie0.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.8

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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. Applied associate-/l/0.3

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

  9. Applied add-cube-cbrt0.3

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

  10. Applied associate-*r*0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(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)))