Average Error: 10.5 → 1.1
Time: 16.1s
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 r422000 = x;
        double r422001 = y;
        double r422002 = z;
        double r422003 = t;
        double r422004 = r422002 - r422003;
        double r422005 = r422001 * r422004;
        double r422006 = a;
        double r422007 = r422002 - r422006;
        double r422008 = r422005 / r422007;
        double r422009 = r422000 + r422008;
        return r422009;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r422010 = x;
        double r422011 = y;
        double r422012 = z;
        double r422013 = a;
        double r422014 = r422012 - r422013;
        double r422015 = t;
        double r422016 = r422012 - r422015;
        double r422017 = r422014 / r422016;
        double r422018 = r422011 / r422017;
        double r422019 = r422010 + r422018;
        return r422019;
}

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

Original10.5
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

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, A"
  :precision binary64

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

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