Average Error: 10.8 → 1.3
Time: 3.4s
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 r577840 = x;
        double r577841 = y;
        double r577842 = z;
        double r577843 = t;
        double r577844 = r577842 - r577843;
        double r577845 = r577841 * r577844;
        double r577846 = a;
        double r577847 = r577842 - r577846;
        double r577848 = r577845 / r577847;
        double r577849 = r577840 + r577848;
        return r577849;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r577850 = x;
        double r577851 = y;
        double r577852 = z;
        double r577853 = a;
        double r577854 = r577852 - r577853;
        double r577855 = t;
        double r577856 = r577852 - r577855;
        double r577857 = r577854 / r577856;
        double r577858 = r577851 / r577857;
        double r577859 = r577850 + r577858;
        return r577859;
}

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

Original10.8
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 
(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))))