Average Error: 14.4 → 0.4
Time: 43.6s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\sin x} \cdot \frac{8.0}{\frac{1}{\frac{\sin \left(x \cdot 0.5\right)}{3.0}}}\]
\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{8.0}{\frac{1}{\frac{\sin \left(x \cdot 0.5\right)}{3.0}}}
double f(double x) {
        double r27720037 = 8.0;
        double r27720038 = 3.0;
        double r27720039 = r27720037 / r27720038;
        double r27720040 = x;
        double r27720041 = 0.5;
        double r27720042 = r27720040 * r27720041;
        double r27720043 = sin(r27720042);
        double r27720044 = r27720039 * r27720043;
        double r27720045 = r27720044 * r27720043;
        double r27720046 = sin(r27720040);
        double r27720047 = r27720045 / r27720046;
        return r27720047;
}
↓
double f(double x) {
        double r27720048 = x;
        double r27720049 = 0.5;
        double r27720050 = r27720048 * r27720049;
        double r27720051 = sin(r27720050);
        double r27720052 = sin(r27720048);
        double r27720053 = r27720051 / r27720052;
        double r27720054 = 8.0;
        double r27720055 = 1.0;
        double r27720056 = 3.0;
        double r27720057 = r27720051 / r27720056;
        double r27720058 = r27720055 / r27720057;
        double r27720059 = r27720054 / r27720058;
        double r27720060 = r27720053 * r27720059;
        return r27720060;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.4
Target0.3
Herbie0.4
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.4

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

  3. Applied *-un-lft-identity14.4

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

  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. Simplified0.5

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

  7. Applied clear-num0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019165 
(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)))