Average Error: 15.0 → 0.3
Time: 42.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r31128703 = 8.0;
        double r31128704 = 3.0;
        double r31128705 = r31128703 / r31128704;
        double r31128706 = x;
        double r31128707 = 0.5;
        double r31128708 = r31128706 * r31128707;
        double r31128709 = sin(r31128708);
        double r31128710 = r31128705 * r31128709;
        double r31128711 = r31128710 * r31128709;
        double r31128712 = sin(r31128706);
        double r31128713 = r31128711 / r31128712;
        return r31128713;
}
↓
double f(double x) {
        double r31128714 = 0.5;
        double r31128715 = x;
        double r31128716 = r31128714 * r31128715;
        double r31128717 = sin(r31128716);
        double r31128718 = 8.0;
        double r31128719 = r31128717 * r31128718;
        double r31128720 = 3.0;
        double r31128721 = r31128719 / r31128720;
        double r31128722 = sin(r31128715);
        double r31128723 = r31128722 / r31128717;
        double r31128724 = r31128721 / r31128723;
        return r31128724;
}

Error

Bits error versus x

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Your Program's Arguments

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. Using strategy rm

  5. Applied associate-*l/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(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)))