Average Error: 10.5 → 1.1
Time: 3.5s
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 r1279682 = x;
        double r1279683 = y;
        double r1279684 = z;
        double r1279685 = t;
        double r1279686 = r1279684 - r1279685;
        double r1279687 = r1279683 * r1279686;
        double r1279688 = a;
        double r1279689 = r1279684 - r1279688;
        double r1279690 = r1279687 / r1279689;
        double r1279691 = r1279682 + r1279690;
        return r1279691;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1279692 = x;
        double r1279693 = y;
        double r1279694 = z;
        double r1279695 = a;
        double r1279696 = r1279694 - r1279695;
        double r1279697 = t;
        double r1279698 = r1279694 - r1279697;
        double r1279699 = r1279696 / r1279698;
        double r1279700 = r1279693 / r1279699;
        double r1279701 = r1279692 + r1279700;
        return r1279701;
}

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 2020034 +o rules:numerics
(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))))