Average Error: 14.8 → 1.4
Time: 5.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sqrt[3]{\sin x}}\]
\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{\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)}{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \frac{\sin \left(0.5 \cdot x\right)}{\sqrt[3]{\sin x}}
double f(double x) {
        double r641567 = 8.0;
        double r641568 = 3.0;
        double r641569 = r641567 / r641568;
        double r641570 = x;
        double r641571 = 0.5;
        double r641572 = r641570 * r641571;
        double r641573 = sin(r641572);
        double r641574 = r641569 * r641573;
        double r641575 = r641574 * r641573;
        double r641576 = sin(r641570);
        double r641577 = r641575 / r641576;
        return r641577;
}
↓
double f(double x) {
        double r641578 = 8.0;
        double r641579 = 3.0;
        double r641580 = r641578 / r641579;
        double r641581 = x;
        double r641582 = 0.5;
        double r641583 = r641581 * r641582;
        double r641584 = sin(r641583);
        double r641585 = r641580 * r641584;
        double r641586 = sin(r641581);
        double r641587 = cbrt(r641586);
        double r641588 = r641587 * r641587;
        double r641589 = r641585 / r641588;
        double r641590 = r641582 * r641581;
        double r641591 = sin(r641590);
        double r641592 = r641591 / r641587;
        double r641593 = r641589 * r641592;
        return r641593;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie1.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

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 add-cube-cbrt15.4

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

  4. Applied times-frac1.4

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

  5. Simplified1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2020062 +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)))