Average Error: 14.8 → 0.3
Time: 4.8s
Precision: 64
\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\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{8 \cdot \frac{\sin \left(0.5 \cdot x\right)}{3}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r674040 = 8.0;
        double r674041 = 3.0;
        double r674042 = r674040 / r674041;
        double r674043 = x;
        double r674044 = 0.5;
        double r674045 = r674043 * r674044;
        double r674046 = sin(r674045);
        double r674047 = r674042 * r674046;
        double r674048 = r674047 * r674046;
        double r674049 = sin(r674043);
        double r674050 = r674048 / r674049;
        return r674050;
}
↓
double f(double x) {
        double r674051 = 8.0;
        double r674052 = 0.5;
        double r674053 = x;
        double r674054 = r674052 * r674053;
        double r674055 = sin(r674054);
        double r674056 = 3.0;
        double r674057 = r674055 / r674056;
        double r674058 = r674051 * r674057;
        double r674059 = sin(r674053);
        double r674060 = r674059 / r674055;
        double r674061 = r674058 / r674060;
        return r674061;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.8
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 14.8

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

  3. Applied associate-/l*0.5

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

  4. Simplified0.5

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

  6. Applied div-inv0.5

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

  7. Applied associate-*l*0.5

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))