Average Error: 10.9 → 1.2
Time: 6.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r622857 = x;
        double r622858 = y;
        double r622859 = z;
        double r622860 = t;
        double r622861 = r622859 - r622860;
        double r622862 = r622858 * r622861;
        double r622863 = a;
        double r622864 = r622859 - r622863;
        double r622865 = r622862 / r622864;
        double r622866 = r622857 + r622865;
        return r622866;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r622867 = x;
        double r622868 = y;
        double r622869 = z;
        double r622870 = a;
        double r622871 = r622869 - r622870;
        double r622872 = t;
        double r622873 = r622869 - r622872;
        double r622874 = r622871 / r622873;
        double r622875 = r622868 / r622874;
        double r622876 = r622867 + r622875;
        return r622876;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  2. Using strategy rm

  3. Applied associate-/l*1.2

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]

  4. Final simplification1.2

    \[\leadsto x + \frac{y}{\frac{z - a}{z - t}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))