Average Error: 9.9 → 1.1
Time: 21.2s
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 r41802208 = x;
        double r41802209 = y;
        double r41802210 = z;
        double r41802211 = t;
        double r41802212 = r41802210 - r41802211;
        double r41802213 = r41802209 * r41802212;
        double r41802214 = a;
        double r41802215 = r41802210 - r41802214;
        double r41802216 = r41802213 / r41802215;
        double r41802217 = r41802208 + r41802216;
        return r41802217;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r41802218 = x;
        double r41802219 = y;
        double r41802220 = z;
        double r41802221 = a;
        double r41802222 = r41802220 - r41802221;
        double r41802223 = t;
        double r41802224 = r41802220 - r41802223;
        double r41802225 = r41802222 / r41802224;
        double r41802226 = r41802219 / r41802225;
        double r41802227 = r41802218 + r41802226;
        return r41802227;
}

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

Original9.9
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 9.9

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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