Average Error: 14.9 → 0.3
Time: 18.0s
Precision: 64
\[\frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x}\]
↓
\[\frac{\frac{\sin \left(0.5 \cdot x\right)}{\sin x} \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8.0\right)}{3.0}\]
\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)}{\sin x} \cdot \left(\sin \left(0.5 \cdot x\right) \cdot 8.0\right)}{3.0}
double f(double x) {
        double r32858523 = 8.0;
        double r32858524 = 3.0;
        double r32858525 = r32858523 / r32858524;
        double r32858526 = x;
        double r32858527 = 0.5;
        double r32858528 = r32858526 * r32858527;
        double r32858529 = sin(r32858528);
        double r32858530 = r32858525 * r32858529;
        double r32858531 = r32858530 * r32858529;
        double r32858532 = sin(r32858526);
        double r32858533 = r32858531 / r32858532;
        return r32858533;
}
↓
double f(double x) {
        double r32858534 = 0.5;
        double r32858535 = x;
        double r32858536 = r32858534 * r32858535;
        double r32858537 = sin(r32858536);
        double r32858538 = sin(r32858535);
        double r32858539 = r32858537 / r32858538;
        double r32858540 = 8.0;
        double r32858541 = r32858537 * r32858540;
        double r32858542 = r32858539 * r32858541;
        double r32858543 = 3.0;
        double r32858544 = r32858542 / r32858543;
        return r32858544;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.9
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 14.9

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

  3. Applied *-un-lft-identity14.9

    \[\leadsto \frac{\left(\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\color{blue}{1 \cdot \sin x}}\]

  4. Applied times-frac0.5

    \[\leadsto \color{blue}{\frac{\frac{8.0}{3.0} \cdot \sin \left(x \cdot 0.5\right)}{1} \cdot \frac{\sin \left(x \cdot 0.5\right)}{\sin x}}\]

  5. Simplified0.5

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

  7. Applied associate-*l/0.3

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

  8. Applied associate-*l/0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(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)))