Average Error: 14.9 → 0.3
Time: 4.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3} \cdot \log \left(e^{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}}\right)\]
\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{8 \cdot \sin \left(x \cdot 0.5\right)}{3} \cdot \log \left(e^{\frac{\sin \left(0.5 \cdot x\right)}{\sin x}}\right)
double f(double x) {
        double r582287 = 8.0;
        double r582288 = 3.0;
        double r582289 = r582287 / r582288;
        double r582290 = x;
        double r582291 = 0.5;
        double r582292 = r582290 * r582291;
        double r582293 = sin(r582292);
        double r582294 = r582289 * r582293;
        double r582295 = r582294 * r582293;
        double r582296 = sin(r582290);
        double r582297 = r582295 / r582296;
        return r582297;
}
↓
double f(double x) {
        double r582298 = 8.0;
        double r582299 = x;
        double r582300 = 0.5;
        double r582301 = r582299 * r582300;
        double r582302 = sin(r582301);
        double r582303 = r582298 * r582302;
        double r582304 = 3.0;
        double r582305 = r582303 / r582304;
        double r582306 = r582300 * r582299;
        double r582307 = sin(r582306);
        double r582308 = sin(r582299);
        double r582309 = r582307 / r582308;
        double r582310 = exp(r582309);
        double r582311 = log(r582310);
        double r582312 = r582305 * r582311;
        return r582312;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
Target0.3
Herbie0.3
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.9

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

  3. Applied *-un-lft-identity14.9

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

  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

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

  6. Simplified0.5

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

  8. Applied associate-*l/0.3

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

  10. Applied add-log-exp0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020036 
(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)))