Average Error: 14.8 → 0.3
Time: 16.3s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\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 r369962 = 8.0;
        double r369963 = 3.0;
        double r369964 = r369962 / r369963;
        double r369965 = x;
        double r369966 = 0.5;
        double r369967 = r369965 * r369966;
        double r369968 = sin(r369967);
        double r369969 = r369964 * r369968;
        double r369970 = r369969 * r369968;
        double r369971 = sin(r369965);
        double r369972 = r369970 / r369971;
        return r369972;
}
↓
double f(double x) {
        double r369973 = 0.5;
        double r369974 = x;
        double r369975 = r369973 * r369974;
        double r369976 = sin(r369975);
        double r369977 = 8.0;
        double r369978 = r369976 * r369977;
        double r369979 = 3.0;
        double r369980 = r369978 / r369979;
        double r369981 = r369974 * r369973;
        double r369982 = sin(r369981);
        double r369983 = sin(r369974);
        double r369984 = r369982 / r369983;
        double r369985 = r369980 * r369984;
        return r369985;
}

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)))