Average Error: 14.9 → 0.3
Time: 4.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{1 \cdot \left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3\right)}\]
\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 \sin \left(x \cdot 0.5\right)}{1 \cdot \left(\frac{\sin x}{\sin \left(0.5 \cdot x\right)} \cdot 3\right)}
double f(double x) {
        double r564703 = 8.0;
        double r564704 = 3.0;
        double r564705 = r564703 / r564704;
        double r564706 = x;
        double r564707 = 0.5;
        double r564708 = r564706 * r564707;
        double r564709 = sin(r564708);
        double r564710 = r564705 * r564709;
        double r564711 = r564710 * r564709;
        double r564712 = sin(r564706);
        double r564713 = r564711 / r564712;
        return r564713;
}
↓
double f(double x) {
        double r564714 = 8.0;
        double r564715 = x;
        double r564716 = 0.5;
        double r564717 = r564715 * r564716;
        double r564718 = sin(r564717);
        double r564719 = r564714 * r564718;
        double r564720 = 1.0;
        double r564721 = sin(r564715);
        double r564722 = r564716 * r564715;
        double r564723 = sin(r564722);
        double r564724 = r564721 / r564723;
        double r564725 = 3.0;
        double r564726 = r564724 * r564725;
        double r564727 = r564720 * r564726;
        double r564728 = r564719 / r564727;
        return r564728;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.9
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 14.9

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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 *-un-lft-identity0.3

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

  10. Applied *-un-lft-identity0.3

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

  11. Applied times-frac0.3

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

  12. Applied associate-*l*0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 
(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)))