Average Error: 15.1 → 0.3
Time: 20.4s
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 r27237051 = 8.0;
        double r27237052 = 3.0;
        double r27237053 = r27237051 / r27237052;
        double r27237054 = x;
        double r27237055 = 0.5;
        double r27237056 = r27237054 * r27237055;
        double r27237057 = sin(r27237056);
        double r27237058 = r27237053 * r27237057;
        double r27237059 = r27237058 * r27237057;
        double r27237060 = sin(r27237054);
        double r27237061 = r27237059 / r27237060;
        return r27237061;
}
↓
double f(double x) {
        double r27237062 = 0.5;
        double r27237063 = x;
        double r27237064 = r27237062 * r27237063;
        double r27237065 = sin(r27237064);
        double r27237066 = sin(r27237063);
        double r27237067 = r27237065 / r27237066;
        double r27237068 = 8.0;
        double r27237069 = r27237065 * r27237068;
        double r27237070 = 3.0;
        double r27237071 = r27237069 / r27237070;
        double r27237072 = r27237067 * r27237071;
        return r27237072;
}

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 2019192 +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)))