Average Error: 14.6 → 0.4
Time: 18.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}\right)\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}\right)\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r462775 = 8.0;
        double r462776 = 3.0;
        double r462777 = r462775 / r462776;
        double r462778 = x;
        double r462779 = 0.5;
        double r462780 = r462778 * r462779;
        double r462781 = sin(r462780);
        double r462782 = r462777 * r462781;
        double r462783 = r462782 * r462781;
        double r462784 = sin(r462778);
        double r462785 = r462783 / r462784;
        return r462785;
}
↓
double f(double x) {
        double r462786 = x;
        double r462787 = 0.5;
        double r462788 = r462786 * r462787;
        double r462789 = sin(r462788);
        double r462790 = 3.0;
        double r462791 = 8.0;
        double r462792 = r462790 / r462791;
        double r462793 = r462789 / r462792;
        double r462794 = expm1(r462793);
        double r462795 = log1p(r462794);
        double r462796 = sin(r462786);
        double r462797 = r462789 / r462796;
        double r462798 = r462795 * r462797;
        return r462798;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
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 14.6

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

  3. Applied *-un-lft-identity14.6

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

  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. Simplified0.3

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

  7. Applied pow10.3

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

  9. Applied log1p-expm1-u0.4

    \[\leadsto {\color{blue}{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}\right)\right)\right)}}^{1} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  10. Simplified0.4

    \[\leadsto {\left(\mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}\right)}\right)\right)}^{1} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  11. Final simplification0.4

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin \left(x \cdot 0.5\right)}{\frac{3}{8}}\right)\right) \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))