Average Error: 11.2 → 1.1
Time: 4.8s
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 r619534 = x;
        double r619535 = y;
        double r619536 = z;
        double r619537 = t;
        double r619538 = r619536 - r619537;
        double r619539 = r619535 * r619538;
        double r619540 = a;
        double r619541 = r619536 - r619540;
        double r619542 = r619539 / r619541;
        double r619543 = r619534 + r619542;
        return r619543;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r619544 = x;
        double r619545 = y;
        double r619546 = z;
        double r619547 = a;
        double r619548 = r619546 - r619547;
        double r619549 = t;
        double r619550 = r619546 - r619549;
        double r619551 = r619548 / r619550;
        double r619552 = r619545 / r619551;
        double r619553 = r619544 + r619552;
        return r619553;
}

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

Original11.2
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.2

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019322 
(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))))