Average Error: 14.2 → 0.3
Time: 32.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]
\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 \frac{\sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}
double f(double x) {
        double r549743 = 8.0;
        double r549744 = 3.0;
        double r549745 = r549743 / r549744;
        double r549746 = x;
        double r549747 = 0.5;
        double r549748 = r549746 * r549747;
        double r549749 = sin(r549748);
        double r549750 = r549745 * r549749;
        double r549751 = r549750 * r549749;
        double r549752 = sin(r549746);
        double r549753 = r549751 / r549752;
        return r549753;
}
↓
double f(double x) {
        double r549754 = 8.0;
        double r549755 = x;
        double r549756 = 0.5;
        double r549757 = r549755 * r549756;
        double r549758 = sin(r549757);
        double r549759 = 3.0;
        double r549760 = r549758 / r549759;
        double r549761 = r549754 * r549760;
        double r549762 = sin(r549755);
        double r549763 = r549762 / r549758;
        double r549764 = r549761 / r549763;
        return r549764;
}

Error

Bits error versus x

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Results

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Target

Original14.2
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 14.2

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

  5. Applied div-inv0.5

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

  6. Applied associate-*l*0.5

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"

  :herbie-target
  (/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))