Average Error: 14.9 → 0.3
Time: 29.2s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\frac{3.0}{8.0}}\]
\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\frac{3.0}{8.0}}
double f(double x) {
        double r18837041 = 8.0;
        double r18837042 = 3.0;
        double r18837043 = r18837041 / r18837042;
        double r18837044 = x;
        double r18837045 = 0.5;
        double r18837046 = r18837044 * r18837045;
        double r18837047 = sin(r18837046);
        double r18837048 = r18837043 * r18837047;
        double r18837049 = r18837048 * r18837047;
        double r18837050 = sin(r18837044);
        double r18837051 = r18837049 / r18837050;
        return r18837051;
}
↓
double f(double x) {
        double r18837052 = x;
        double r18837053 = 0.5;
        double r18837054 = r18837052 * r18837053;
        double r18837055 = sin(r18837054);
        double r18837056 = sin(r18837052);
        double r18837057 = r18837055 / r18837056;
        double r18837058 = 3.0;
        double r18837059 = 8.0;
        double r18837060 = r18837058 / r18837059;
        double r18837061 = r18837055 / r18837060;
        double r18837062 = r18837057 * r18837061;
        return r18837062;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.3
Herbie0.3
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.9

    \[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity14.9

    \[\leadsto \frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\color{blue}{1 \cdot \sin x}}\]

  4. Applied times-frac0.5

    \[\leadsto \color{blue}{\frac{\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)}{1} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\]

  5. Simplified0.3

    \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right)}{\frac{3.0}{8.0}}} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]

  6. Final simplification0.3

    \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\frac{3.0}{8.0}}\]

Reproduce

herbie shell --seed 2019158 +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)))