Average Error: 14.6 → 0.4
Time: 9.2s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3} \cdot \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}\]
\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 \frac{1}{\log \left(e^{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\right)}
double f(double x) {
        double r755216 = 8.0;
        double r755217 = 3.0;
        double r755218 = r755216 / r755217;
        double r755219 = x;
        double r755220 = 0.5;
        double r755221 = r755219 * r755220;
        double r755222 = sin(r755221);
        double r755223 = r755218 * r755222;
        double r755224 = r755223 * r755222;
        double r755225 = sin(r755219);
        double r755226 = r755224 / r755225;
        return r755226;
}
↓
double f(double x) {
        double r755227 = 0.5;
        double r755228 = x;
        double r755229 = r755227 * r755228;
        double r755230 = sin(r755229);
        double r755231 = 8.0;
        double r755232 = r755230 * r755231;
        double r755233 = 3.0;
        double r755234 = r755232 / r755233;
        double r755235 = 1.0;
        double r755236 = sin(r755228);
        double r755237 = r755228 * r755227;
        double r755238 = sin(r755237);
        double r755239 = r755236 / r755238;
        double r755240 = exp(r755239);
        double r755241 = log(r755240);
        double r755242 = r755235 / r755241;
        double r755243 = r755234 * r755242;
        return r755243;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
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 14.6

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

  3. Applied *-un-lft-identity14.6

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

  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 clear-num0.3

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

  11. Applied add-log-exp0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020043 +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)))