Average Error: 14.6 → 0.3
Time: 14.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r471755 = 8.0;
        double r471756 = 3.0;
        double r471757 = r471755 / r471756;
        double r471758 = x;
        double r471759 = 0.5;
        double r471760 = r471758 * r471759;
        double r471761 = sin(r471760);
        double r471762 = r471757 * r471761;
        double r471763 = r471762 * r471761;
        double r471764 = sin(r471758);
        double r471765 = r471763 / r471764;
        return r471765;
}
↓
double f(double x) {
        double r471766 = 0.5;
        double r471767 = x;
        double r471768 = r471766 * r471767;
        double r471769 = sin(r471768);
        double r471770 = 8.0;
        double r471771 = r471769 * r471770;
        double r471772 = 3.0;
        double r471773 = r471771 / r471772;
        double r471774 = r471767 * r471766;
        double r471775 = sin(r471774);
        double r471776 = sin(r471767);
        double r471777 = r471775 / r471776;
        double r471778 = r471773 * r471777;
        return r471778;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.6
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 14.6

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

  3. Applied *-un-lft-identity14.6

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

  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. Simplified0.5

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

  7. Applied associate-*l/0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 
(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)))