Average Error: 15.2 → 0.3
Time: 17.1s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot 3}\]
\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{\sin x}{\sin \left(x \cdot 0.5\right)} \cdot 3}
double f(double x) {
        double r39034973 = 8.0;
        double r39034974 = 3.0;
        double r39034975 = r39034973 / r39034974;
        double r39034976 = x;
        double r39034977 = 0.5;
        double r39034978 = r39034976 * r39034977;
        double r39034979 = sin(r39034978);
        double r39034980 = r39034975 * r39034979;
        double r39034981 = r39034980 * r39034979;
        double r39034982 = sin(r39034976);
        double r39034983 = r39034981 / r39034982;
        return r39034983;
}
↓
double f(double x) {
        double r39034984 = 8.0;
        double r39034985 = x;
        double r39034986 = 0.5;
        double r39034987 = r39034985 * r39034986;
        double r39034988 = sin(r39034987);
        double r39034989 = r39034984 * r39034988;
        double r39034990 = sin(r39034985);
        double r39034991 = r39034990 / r39034988;
        double r39034992 = 3.0;
        double r39034993 = r39034991 * r39034992;
        double r39034994 = r39034989 / r39034993;
        return r39034994;
}

Error

Bits error versus x

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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 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. Applied associate-/l/0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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)))