Average Error: 15.1 → 0.3
Time: 16.2s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8.0\right)}{3.0}\]
\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{\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8.0\right)}{3.0}
double f(double x) {
        double r30683021 = 8.0;
        double r30683022 = 3.0;
        double r30683023 = r30683021 / r30683022;
        double r30683024 = x;
        double r30683025 = 0.5;
        double r30683026 = r30683024 * r30683025;
        double r30683027 = sin(r30683026);
        double r30683028 = r30683023 * r30683027;
        double r30683029 = r30683028 * r30683027;
        double r30683030 = sin(r30683024);
        double r30683031 = r30683029 / r30683030;
        return r30683031;
}
↓
double f(double x) {
        double r30683032 = 0.5;
        double r30683033 = x;
        double r30683034 = r30683032 * r30683033;
        double r30683035 = sin(r30683034);
        double r30683036 = sin(r30683033);
        double r30683037 = r30683035 / r30683036;
        double r30683038 = 8.0;
        double r30683039 = r30683035 * r30683038;
        double r30683040 = r30683037 * r30683039;
        double r30683041 = 3.0;
        double r30683042 = r30683040 / r30683041;
        return r30683042;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
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 15.1

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

  3. Applied *-un-lft-identity15.1

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

  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

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

  7. Applied associate-*l/0.3

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

  8. Applied associate-*l/0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(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)))