Average Error: 14.8 → 0.3
Time: 16.6s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\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) \cdot 8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r539682 = 8.0;
        double r539683 = 3.0;
        double r539684 = r539682 / r539683;
        double r539685 = x;
        double r539686 = 0.5;
        double r539687 = r539685 * r539686;
        double r539688 = sin(r539687);
        double r539689 = r539684 * r539688;
        double r539690 = r539689 * r539688;
        double r539691 = sin(r539685);
        double r539692 = r539690 / r539691;
        return r539692;
}
↓
double f(double x) {
        double r539693 = 0.5;
        double r539694 = x;
        double r539695 = r539693 * r539694;
        double r539696 = sin(r539695);
        double r539697 = 8.0;
        double r539698 = r539696 * r539697;
        double r539699 = 3.0;
        double r539700 = r539698 / r539699;
        double r539701 = r539694 * r539693;
        double r539702 = sin(r539701);
        double r539703 = sin(r539694);
        double r539704 = r539702 / r539703;
        double r539705 = r539700 * r539704;
        return r539705;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.8
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 14.8

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

  3. Applied *-un-lft-identity14.8

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

  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. Simplified0.5

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

  7. Applied associate-*l/0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(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)))