Average Error: 10.7 → 1.1
Time: 11.7s
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 r343618 = x;
        double r343619 = y;
        double r343620 = z;
        double r343621 = t;
        double r343622 = r343620 - r343621;
        double r343623 = r343619 * r343622;
        double r343624 = a;
        double r343625 = r343620 - r343624;
        double r343626 = r343623 / r343625;
        double r343627 = r343618 + r343626;
        return r343627;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r343628 = x;
        double r343629 = y;
        double r343630 = z;
        double r343631 = a;
        double r343632 = r343630 - r343631;
        double r343633 = t;
        double r343634 = r343630 - r343633;
        double r343635 = r343632 / r343634;
        double r343636 = r343629 / r343635;
        double r343637 = r343628 + r343636;
        return r343637;
}

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

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2019294 
(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))))