Average Error: 14.5 → 0.4
Time: 18.1s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\left(\sin \left(0.5 \cdot x\right) \cdot \frac{1}{\sin x}\right) \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8\right)}{3}\]
\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{\left(\sin \left(0.5 \cdot x\right) \cdot \frac{1}{\sin x}\right) \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8\right)}{3}
double f(double x) {
        double r27191286 = 8.0;
        double r27191287 = 3.0;
        double r27191288 = r27191286 / r27191287;
        double r27191289 = x;
        double r27191290 = 0.5;
        double r27191291 = r27191289 * r27191290;
        double r27191292 = sin(r27191291);
        double r27191293 = r27191288 * r27191292;
        double r27191294 = r27191293 * r27191292;
        double r27191295 = sin(r27191289);
        double r27191296 = r27191294 / r27191295;
        return r27191296;
}
↓
double f(double x) {
        double r27191297 = 0.5;
        double r27191298 = x;
        double r27191299 = r27191297 * r27191298;
        double r27191300 = sin(r27191299);
        double r27191301 = 1.0;
        double r27191302 = sin(r27191298);
        double r27191303 = r27191301 / r27191302;
        double r27191304 = r27191300 * r27191303;
        double r27191305 = 8.0;
        double r27191306 = r27191300 * r27191305;
        double r27191307 = r27191304 * r27191306;
        double r27191308 = 3.0;
        double r27191309 = r27191307 / r27191308;
        return r27191309;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
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 14.5

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

  3. Applied *-un-lft-identity14.5

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

  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 associate-*l/0.3

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

  9. Applied div-inv0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 +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)))