Average Error: 15.1 → 0.3
Time: 20.8s
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 r23465071 = 8.0;
        double r23465072 = 3.0;
        double r23465073 = r23465071 / r23465072;
        double r23465074 = x;
        double r23465075 = 0.5;
        double r23465076 = r23465074 * r23465075;
        double r23465077 = sin(r23465076);
        double r23465078 = r23465073 * r23465077;
        double r23465079 = r23465078 * r23465077;
        double r23465080 = sin(r23465074);
        double r23465081 = r23465079 / r23465080;
        return r23465081;
}
↓
double f(double x) {
        double r23465082 = 0.5;
        double r23465083 = x;
        double r23465084 = r23465082 * r23465083;
        double r23465085 = sin(r23465084);
        double r23465086 = sin(r23465083);
        double r23465087 = r23465085 / r23465086;
        double r23465088 = 8.0;
        double r23465089 = r23465085 * r23465088;
        double r23465090 = 3.0;
        double r23465091 = r23465089 / r23465090;
        double r23465092 = r23465087 * r23465091;
        return r23465092;
}

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)))