Average Error: 10.8 → 1.3
Time: 14.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{1}{\frac{z - t}{a - t}}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{1}{\frac{z - t}{a - t}}}
double f(double x, double y, double z, double t, double a) {
        double r454786 = x;
        double r454787 = y;
        double r454788 = z;
        double r454789 = t;
        double r454790 = r454788 - r454789;
        double r454791 = r454787 * r454790;
        double r454792 = a;
        double r454793 = r454792 - r454789;
        double r454794 = r454791 / r454793;
        double r454795 = r454786 + r454794;
        return r454795;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r454796 = x;
        double r454797 = y;
        double r454798 = 1.0;
        double r454799 = z;
        double r454800 = t;
        double r454801 = r454799 - r454800;
        double r454802 = a;
        double r454803 = r454802 - r454800;
        double r454804 = r454801 / r454803;
        double r454805 = r454798 / r454804;
        double r454806 = r454797 / r454805;
        double r454807 = r454796 + r454806;
        return r454807;
}

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
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.2

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied clear-num1.3

    \[\leadsto x + \frac{y}{\color{blue}{\frac{1}{\frac{z - t}{a - t}}}}\]

  6. Final simplification1.3

    \[\leadsto x + \frac{y}{\frac{1}{\frac{z - t}{a - t}}}\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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