Average Error: 15.1 → 0.3
Time: 20.7s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}\]
\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)}{\sin x} \cdot \frac{\sin \left(0.5 \cdot x\right) \cdot 8}{3}
double f(double x) {
        double r26723883 = 8.0;
        double r26723884 = 3.0;
        double r26723885 = r26723883 / r26723884;
        double r26723886 = x;
        double r26723887 = 0.5;
        double r26723888 = r26723886 * r26723887;
        double r26723889 = sin(r26723888);
        double r26723890 = r26723885 * r26723889;
        double r26723891 = r26723890 * r26723889;
        double r26723892 = sin(r26723886);
        double r26723893 = r26723891 / r26723892;
        return r26723893;
}
↓
double f(double x) {
        double r26723894 = 0.5;
        double r26723895 = x;
        double r26723896 = r26723894 * r26723895;
        double r26723897 = sin(r26723896);
        double r26723898 = sin(r26723895);
        double r26723899 = r26723897 / r26723898;
        double r26723900 = 8.0;
        double r26723901 = r26723897 * r26723900;
        double r26723902 = 3.0;
        double r26723903 = r26723901 / r26723902;
        double r26723904 = r26723899 * r26723903;
        return r26723904;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original15.1
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 15.1

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

  3. Applied *-un-lft-identity15.1

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

  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. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"

  :herbie-target
  (/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))