Average Error: 14.7 → 0.3
Time: 23.9s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\sin \left(x \cdot 0.5\right)}{\frac{\frac{\sin x}{8}}{\sin \left(x \cdot 0.5\right)} \cdot 3}\]
\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(x \cdot 0.5\right)}{\frac{\frac{\sin x}{8}}{\sin \left(x \cdot 0.5\right)} \cdot 3}
double f(double x) {
        double r494944 = 8.0;
        double r494945 = 3.0;
        double r494946 = r494944 / r494945;
        double r494947 = x;
        double r494948 = 0.5;
        double r494949 = r494947 * r494948;
        double r494950 = sin(r494949);
        double r494951 = r494946 * r494950;
        double r494952 = r494951 * r494950;
        double r494953 = sin(r494947);
        double r494954 = r494952 / r494953;
        return r494954;
}
↓
double f(double x) {
        double r494955 = x;
        double r494956 = 0.5;
        double r494957 = r494955 * r494956;
        double r494958 = sin(r494957);
        double r494959 = sin(r494955);
        double r494960 = 8.0;
        double r494961 = r494959 / r494960;
        double r494962 = r494961 / r494958;
        double r494963 = 3.0;
        double r494964 = r494962 * r494963;
        double r494965 = r494958 / r494964;
        return r494965;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.7
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 14.7

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

  2. Simplified14.7

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

  4. Applied associate-/l*0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(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)))