Average Error: 14.8 → 0.4
Time: 14.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}\]
\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{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}
double f(double x) {
        double r498046 = 8.0;
        double r498047 = 3.0;
        double r498048 = r498046 / r498047;
        double r498049 = x;
        double r498050 = 0.5;
        double r498051 = r498049 * r498050;
        double r498052 = sin(r498051);
        double r498053 = r498048 * r498052;
        double r498054 = r498053 * r498052;
        double r498055 = sin(r498049);
        double r498056 = r498054 / r498055;
        return r498056;
}
↓
double f(double x) {
        double r498057 = 8.0;
        double r498058 = 0.5;
        double r498059 = x;
        double r498060 = r498058 * r498059;
        double r498061 = sin(r498060);
        double r498062 = r498057 * r498061;
        double r498063 = 3.0;
        double r498064 = r498062 / r498063;
        double r498065 = 1.0;
        double r498066 = sin(r498059);
        double r498067 = r498059 * r498058;
        double r498068 = sin(r498067);
        double r498069 = r498066 / r498068;
        double r498070 = exp(r498069);
        double r498071 = log(r498070);
        double r498072 = r498065 / r498071;
        double r498073 = r498064 * r498072;
        return r498073;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
Target0.3
Herbie0.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

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 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. Simplified0.3

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

  8. Applied div-inv0.3

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

  10. Applied add-log-exp0.4

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

  11. Final simplification0.4

    \[\leadsto \frac{8 \cdot \sin \left(0.5 \cdot x\right)}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}\]

Reproduce

herbie shell --seed 2019323 
(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)))