Average Error: 14.4 → 0.3
Time: 12.5s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{8 \cdot \sin \left(x \cdot \frac{1}{2}\right)}{3}}{\frac{\sin x}{\sin \left(\frac{1}{2} \cdot x\right)}}\]
\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{\frac{8 \cdot \sin \left(x \cdot \frac{1}{2}\right)}{3}}{\frac{\sin x}{\sin \left(\frac{1}{2} \cdot x\right)}}
double f(double x) {
        double r415937 = 8.0;
        double r415938 = 3.0;
        double r415939 = r415937 / r415938;
        double r415940 = x;
        double r415941 = 0.5;
        double r415942 = r415940 * r415941;
        double r415943 = sin(r415942);
        double r415944 = r415939 * r415943;
        double r415945 = r415944 * r415943;
        double r415946 = sin(r415940);
        double r415947 = r415945 / r415946;
        return r415947;
}
↓
double f(double x) {
        double r415948 = 8.0;
        double r415949 = x;
        double r415950 = 1.0;
        double r415951 = 2.0;
        double r415952 = r415950 / r415951;
        double r415953 = r415949 * r415952;
        double r415954 = sin(r415953);
        double r415955 = r415948 * r415954;
        double r415956 = 3.0;
        double r415957 = r415955 / r415956;
        double r415958 = sin(r415949);
        double r415959 = r415952 * r415949;
        double r415960 = sin(r415959);
        double r415961 = r415958 / r415960;
        double r415962 = r415957 / r415961;
        return r415962;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original14.4
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 14.4

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

  2. Simplified14.4

    \[\leadsto \color{blue}{\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)\right) \cdot \sin \left(x \cdot \frac{1}{2}\right)}{\sin x}}\]
  3. Using strategy rm

  4. Applied associate-/l*0.5

    \[\leadsto \color{blue}{\frac{\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)}{\frac{\sin x}{\sin \left(x \cdot \frac{1}{2}\right)}}}\]

  5. Simplified0.5

    \[\leadsto \frac{\frac{8}{3} \cdot \sin \left(x \cdot \frac{1}{2}\right)}{\color{blue}{\frac{\sin x}{\sin \left(\frac{1}{2} \cdot x\right)}}}\]
  6. Using strategy rm

  7. Applied associate-*l/0.3

    \[\leadsto \frac{\color{blue}{\frac{8 \cdot \sin \left(x \cdot \frac{1}{2}\right)}{3}}}{\frac{\sin x}{\sin \left(\frac{1}{2} \cdot x\right)}}\]

  8. Final simplification0.3

    \[\leadsto \frac{\frac{8 \cdot \sin \left(x \cdot \frac{1}{2}\right)}{3}}{\frac{\sin x}{\sin \left(\frac{1}{2} \cdot x\right)}}\]

Reproduce

herbie shell --seed 2019303 
(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)))