Average Error: 14.4 → 0.3
Time: 18.5s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]
\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}
↓
\frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}
double f(double x) {
        double r31699110 = 8.0;
        double r31699111 = 3.0;
        double r31699112 = r31699110 / r31699111;
        double r31699113 = x;
        double r31699114 = 0.5;
        double r31699115 = r31699113 * r31699114;
        double r31699116 = sin(r31699115);
        double r31699117 = r31699112 * r31699116;
        double r31699118 = r31699117 * r31699116;
        double r31699119 = sin(r31699113);
        double r31699120 = r31699118 / r31699119;
        return r31699120;
}
↓
double f(double x) {
        double r31699121 = 0.5;
        double r31699122 = x;
        double r31699123 = r31699121 * r31699122;
        double r31699124 = sin(r31699123);
        double r31699125 = 8.0;
        double r31699126 = r31699124 * r31699125;
        double r31699127 = 3.0;
        double r31699128 = r31699126 / r31699127;
        double r31699129 = sin(r31699122);
        double r31699130 = r31699129 / r31699124;
        double r31699131 = r31699128 / r31699130;
        return r31699131;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.4
Target0.3
Herbie0.3
\[\frac{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

Derivation

  1. Initial program 14.4

    \[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.5

    \[\leadsto \color{blue}{\frac{\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}\]
  4. Using strategy rm

  5. Applied associate-*l/0.3

    \[\leadsto \frac{\color{blue}{\frac{8.0 \cdot \sin \left(x \cdot 0.5\right)}{3.0}}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}\]

  6. Final simplification0.3

    \[\leadsto \frac{\frac{\sin \left(0.5 \cdot x\right) \cdot 8.0}{3.0}}{\frac{\sin x}{\sin \left(0.5 \cdot x\right)}}\]

Reproduce

herbie shell --seed 2019165 
(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)))