Average Error: 9.9 → 1.2
Time: 16.4s
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 r27859632 = x;
        double r27859633 = y;
        double r27859634 = z;
        double r27859635 = t;
        double r27859636 = r27859634 - r27859635;
        double r27859637 = r27859633 * r27859636;
        double r27859638 = a;
        double r27859639 = r27859634 - r27859638;
        double r27859640 = r27859637 / r27859639;
        double r27859641 = r27859632 + r27859640;
        return r27859641;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27859642 = x;
        double r27859643 = y;
        double r27859644 = z;
        double r27859645 = a;
        double r27859646 = r27859644 - r27859645;
        double r27859647 = t;
        double r27859648 = r27859644 - r27859647;
        double r27859649 = r27859646 / r27859648;
        double r27859650 = r27859643 / r27859649;
        double r27859651 = r27859642 + r27859650;
        return r27859651;
}

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

Derivation

  1. Initial program 9.9

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019164 
(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))))