Average Error: 11.3 → 1.2
Time: 52.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r27838386 = x;
        double r27838387 = y;
        double r27838388 = z;
        double r27838389 = t;
        double r27838390 = r27838388 - r27838389;
        double r27838391 = r27838387 * r27838390;
        double r27838392 = a;
        double r27838393 = r27838392 - r27838389;
        double r27838394 = r27838391 / r27838393;
        double r27838395 = r27838386 + r27838394;
        return r27838395;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27838396 = x;
        double r27838397 = y;
        double r27838398 = a;
        double r27838399 = t;
        double r27838400 = r27838398 - r27838399;
        double r27838401 = z;
        double r27838402 = r27838401 - r27838399;
        double r27838403 = r27838400 / r27838402;
        double r27838404 = r27838397 / r27838403;
        double r27838405 = r27838396 + r27838404;
        return r27838405;
}

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

Original11.3
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.3

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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