Average Error: 15.0 → 0.3
Time: 9.4s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\]
\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 \frac{\sin \left(x \cdot 0.5\right)}{\sin x}
double f(double x) {
        double r714230 = 8.0;
        double r714231 = 3.0;
        double r714232 = r714230 / r714231;
        double r714233 = x;
        double r714234 = 0.5;
        double r714235 = r714233 * r714234;
        double r714236 = sin(r714235);
        double r714237 = r714232 * r714236;
        double r714238 = r714237 * r714236;
        double r714239 = sin(r714233);
        double r714240 = r714238 / r714239;
        return r714240;
}
↓
double f(double x) {
        double r714241 = 8.0;
        double r714242 = x;
        double r714243 = 0.5;
        double r714244 = r714242 * r714243;
        double r714245 = sin(r714244);
        double r714246 = r714241 * r714245;
        double r714247 = 3.0;
        double r714248 = r714246 / r714247;
        double r714249 = sin(r714242);
        double r714250 = r714245 / r714249;
        double r714251 = r714248 * r714250;
        return r714251;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.0
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 15.0

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

  3. Applied *-un-lft-identity15.0

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

  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. Using strategy rm

  7. Applied *-un-lft-identity0.5

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

  8. Applied *-un-lft-identity0.5

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

  9. Applied times-frac0.5

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 
(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)))