Average Error: 15.2 → 0.3
Time: 19.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r38111286 = 8.0;
        double r38111287 = 3.0;
        double r38111288 = r38111286 / r38111287;
        double r38111289 = x;
        double r38111290 = 0.5;
        double r38111291 = r38111289 * r38111290;
        double r38111292 = sin(r38111291);
        double r38111293 = r38111288 * r38111292;
        double r38111294 = r38111293 * r38111292;
        double r38111295 = sin(r38111289);
        double r38111296 = r38111294 / r38111295;
        return r38111296;
}
↓
double f(double x) {
        double r38111297 = 0.5;
        double r38111298 = x;
        double r38111299 = r38111297 * r38111298;
        double r38111300 = sin(r38111299);
        double r38111301 = 8.0;
        double r38111302 = r38111300 * r38111301;
        double r38111303 = 3.0;
        double r38111304 = r38111302 / r38111303;
        double r38111305 = sin(r38111298);
        double r38111306 = r38111305 / r38111300;
        double r38111307 = r38111304 / r38111306;
        return r38111307;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
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 15.2

    \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(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)))