Average Error: 15.0 → 0.3
Time: 20.2s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{\frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r29561219 = 8.0;
        double r29561220 = 3.0;
        double r29561221 = r29561219 / r29561220;
        double r29561222 = x;
        double r29561223 = 0.5;
        double r29561224 = r29561222 * r29561223;
        double r29561225 = sin(r29561224);
        double r29561226 = r29561221 * r29561225;
        double r29561227 = r29561226 * r29561225;
        double r29561228 = sin(r29561222);
        double r29561229 = r29561227 / r29561228;
        return r29561229;
}
↓
double f(double x) {
        double r29561230 = 0.5;
        double r29561231 = x;
        double r29561232 = r29561230 * r29561231;
        double r29561233 = sin(r29561232);
        double r29561234 = 8.0;
        double r29561235 = r29561233 * r29561234;
        double r29561236 = 3.0;
        double r29561237 = r29561235 / r29561236;
        double r29561238 = sin(r29561231);
        double r29561239 = r29561238 / r29561233;
        double r29561240 = r29561237 / r29561239;
        return r29561240;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
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 15.0

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

  3. Applied associate-/l*0.5

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

  5. Applied associate-*l/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(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)))