Average Error: 15.3 → 0.3
Time: 5.4s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{1}{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}} \cdot 3}\]
\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)}{\frac{1}{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}} \cdot 3}
double f(double x) {
        double r751633 = 8.0;
        double r751634 = 3.0;
        double r751635 = r751633 / r751634;
        double r751636 = x;
        double r751637 = 0.5;
        double r751638 = r751636 * r751637;
        double r751639 = sin(r751638);
        double r751640 = r751635 * r751639;
        double r751641 = r751640 * r751639;
        double r751642 = sin(r751636);
        double r751643 = r751641 / r751642;
        return r751643;
}
↓
double f(double x) {
        double r751644 = 8.0;
        double r751645 = x;
        double r751646 = 0.5;
        double r751647 = r751645 * r751646;
        double r751648 = sin(r751647);
        double r751649 = r751644 * r751648;
        double r751650 = 1.0;
        double r751651 = r751646 * r751645;
        double r751652 = sin(r751651);
        double r751653 = sin(r751645);
        double r751654 = r751652 / r751653;
        double r751655 = r751650 / r751654;
        double r751656 = 3.0;
        double r751657 = r751655 * r751656;
        double r751658 = r751649 / r751657;
        return r751658;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.3
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 15.3

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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 clear-num0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020083 
(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)))