Average Error: 10.3 → 1.2
Time: 18.8s
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 r29035533 = x;
        double r29035534 = y;
        double r29035535 = z;
        double r29035536 = t;
        double r29035537 = r29035535 - r29035536;
        double r29035538 = r29035534 * r29035537;
        double r29035539 = a;
        double r29035540 = r29035535 - r29035539;
        double r29035541 = r29035538 / r29035540;
        double r29035542 = r29035533 + r29035541;
        return r29035542;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29035543 = x;
        double r29035544 = y;
        double r29035545 = z;
        double r29035546 = a;
        double r29035547 = r29035545 - r29035546;
        double r29035548 = t;
        double r29035549 = r29035545 - r29035548;
        double r29035550 = r29035547 / r29035549;
        double r29035551 = r29035544 / r29035550;
        double r29035552 = r29035543 + r29035551;
        return r29035552;
}

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

Original10.3
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.3

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019163 
(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))))