Average Error: 14.8 → 0.4
Time: 18.5s
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 r402833 = 8.0;
        double r402834 = 3.0;
        double r402835 = r402833 / r402834;
        double r402836 = x;
        double r402837 = 0.5;
        double r402838 = r402836 * r402837;
        double r402839 = sin(r402838);
        double r402840 = r402835 * r402839;
        double r402841 = r402840 * r402839;
        double r402842 = sin(r402836);
        double r402843 = r402841 / r402842;
        return r402843;
}
↓
double f(double x) {
        double r402844 = 8.0;
        double r402845 = 0.5;
        double r402846 = x;
        double r402847 = r402845 * r402846;
        double r402848 = sin(r402847);
        double r402849 = r402844 * r402848;
        double r402850 = 3.0;
        double r402851 = r402849 / r402850;
        double r402852 = 1.0;
        double r402853 = sin(r402846);
        double r402854 = r402846 * r402845;
        double r402855 = sin(r402854);
        double r402856 = r402853 / r402855;
        double r402857 = exp(r402856);
        double r402858 = log(r402857);
        double r402859 = r402852 / r402858;
        double r402860 = r402851 * r402859;
        return r402860;
}

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)))