Average Error: 15.0 → 0.3
Time: 10.0s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{-8 \cdot \sin \left(x \cdot 0.5\right)}{-3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\frac{-8 \cdot \sin \left(x \cdot 0.5\right)}{-3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r465683 = 8.0;
        double r465684 = 3.0;
        double r465685 = r465683 / r465684;
        double r465686 = x;
        double r465687 = 0.5;
        double r465688 = r465686 * r465687;
        double r465689 = sin(r465688);
        double r465690 = r465685 * r465689;
        double r465691 = r465690 * r465689;
        double r465692 = sin(r465686);
        double r465693 = r465691 / r465692;
        return r465693;
}
↓
double f(double x) {
        double r465694 = 8.0;
        double r465695 = x;
        double r465696 = 0.5;
        double r465697 = r465695 * r465696;
        double r465698 = sin(r465697);
        double r465699 = r465694 * r465698;
        double r465700 = -r465699;
        double r465701 = 3.0;
        double r465702 = -r465701;
        double r465703 = r465700 / r465702;
        double r465704 = sin(r465695);
        double r465705 = r465696 * r465695;
        double r465706 = sin(r465705);
        double r465707 = r465704 / r465706;
        double r465708 = r465703 / r465707;
        return r465708;
}

Error

Bits error versus x

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Results

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Target

Original15.0
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 15.0

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

  8. Applied frac-2neg0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020034 +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)))