Average Error: 15.2 → 0.3
Time: 20.3s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}\]
\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{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}
double f(double x) {
        double r26342716 = 8.0;
        double r26342717 = 3.0;
        double r26342718 = r26342716 / r26342717;
        double r26342719 = x;
        double r26342720 = 0.5;
        double r26342721 = r26342719 * r26342720;
        double r26342722 = sin(r26342721);
        double r26342723 = r26342718 * r26342722;
        double r26342724 = r26342723 * r26342722;
        double r26342725 = sin(r26342719);
        double r26342726 = r26342724 / r26342725;
        return r26342726;
}
↓
double f(double x) {
        double r26342727 = 0.5;
        double r26342728 = x;
        double r26342729 = r26342727 * r26342728;
        double r26342730 = sin(r26342729);
        double r26342731 = sin(r26342728);
        double r26342732 = r26342730 / r26342731;
        double r26342733 = 8.0;
        double r26342734 = r26342730 * r26342733;
        double r26342735 = 3.0;
        double r26342736 = r26342734 / r26342735;
        double r26342737 = r26342732 * r26342736;
        return r26342737;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.2
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 15.2

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

  3. Applied *-un-lft-identity15.2

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

  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. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))