Average Error: 14.8 → 0.5
Time: 18.3s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\left(\frac{8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right) \cdot \sin \left(x \cdot 0.5\right)\]
\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\left(\frac{8}{3} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}\right) \cdot \sin \left(x \cdot 0.5\right)
double f(double x) {
        double r373693 = 8.0;
        double r373694 = 3.0;
        double r373695 = r373693 / r373694;
        double r373696 = x;
        double r373697 = 0.5;
        double r373698 = r373696 * r373697;
        double r373699 = sin(r373698);
        double r373700 = r373695 * r373699;
        double r373701 = r373700 * r373699;
        double r373702 = sin(r373696);
        double r373703 = r373701 / r373702;
        return r373703;
}
↓
double f(double x) {
        double r373704 = 8.0;
        double r373705 = 3.0;
        double r373706 = r373704 / r373705;
        double r373707 = x;
        double r373708 = 0.5;
        double r373709 = r373707 * r373708;
        double r373710 = sin(r373709);
        double r373711 = sin(r373707);
        double r373712 = r373710 / r373711;
        double r373713 = r373706 * r373712;
        double r373714 = r373713 * r373710;
        return r373714;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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Target

Original14.8
Target0.3
Herbie0.5
\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.8

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

  3. Applied *-un-lft-identity14.8

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

  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 associate-*l/0.3

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

  8. Simplified0.3

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

  10. Applied *-un-lft-identity0.3

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

  11. Applied times-frac0.5

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

  12. Applied associate-*l*0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019325 +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)))