Average Error: 10.7 → 1.2
Time: 24.1s
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 r30104431 = x;
        double r30104432 = y;
        double r30104433 = z;
        double r30104434 = t;
        double r30104435 = r30104433 - r30104434;
        double r30104436 = r30104432 * r30104435;
        double r30104437 = a;
        double r30104438 = r30104433 - r30104437;
        double r30104439 = r30104436 / r30104438;
        double r30104440 = r30104431 + r30104439;
        return r30104440;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30104441 = x;
        double r30104442 = y;
        double r30104443 = z;
        double r30104444 = a;
        double r30104445 = r30104443 - r30104444;
        double r30104446 = t;
        double r30104447 = r30104443 - r30104446;
        double r30104448 = r30104445 / r30104447;
        double r30104449 = r30104442 / r30104448;
        double r30104450 = r30104441 + r30104449;
        return r30104450;
}

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

Original10.7
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019170 
(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))))