Average Error: 15.2 → 0.4
Time: 8.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \log \left(e^{\frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\right)\]
\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{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \log \left(e^{\frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\right)
double f(double x) {
        double r623130 = 8.0;
        double r623131 = 3.0;
        double r623132 = r623130 / r623131;
        double r623133 = x;
        double r623134 = 0.5;
        double r623135 = r623133 * r623134;
        double r623136 = sin(r623135);
        double r623137 = r623132 * r623136;
        double r623138 = r623137 * r623136;
        double r623139 = sin(r623133);
        double r623140 = r623138 / r623139;
        return r623140;
}
↓
double f(double x) {
        double r623141 = 0.5;
        double r623142 = x;
        double r623143 = r623141 * r623142;
        double r623144 = sin(r623143);
        double r623145 = 8.0;
        double r623146 = r623144 * r623145;
        double r623147 = 3.0;
        double r623148 = r623146 / r623147;
        double r623149 = r623142 * r623141;
        double r623150 = sin(r623149);
        double r623151 = sin(r623142);
        double r623152 = r623150 / r623151;
        double r623153 = exp(r623152);
        double r623154 = log(r623153);
        double r623155 = r623148 * r623154;
        return r623155;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
Target0.3
Herbie0.4
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 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 *-un-lft-identity15.2

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

  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. Simplified0.5

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

  7. Applied associate-*r/0.3

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

  9. Applied add-log-exp0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8 (sin (* x 0.5))) 3) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8 3) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))