Average Error: 11.2 → 1.2
Time: 13.8s
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 r516618 = x;
        double r516619 = y;
        double r516620 = z;
        double r516621 = t;
        double r516622 = r516620 - r516621;
        double r516623 = r516619 * r516622;
        double r516624 = a;
        double r516625 = r516620 - r516624;
        double r516626 = r516623 / r516625;
        double r516627 = r516618 + r516626;
        return r516627;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r516628 = x;
        double r516629 = y;
        double r516630 = z;
        double r516631 = a;
        double r516632 = r516630 - r516631;
        double r516633 = t;
        double r516634 = r516630 - r516633;
        double r516635 = r516632 / r516634;
        double r516636 = r516629 / r516635;
        double r516637 = r516628 + r516636;
        return r516637;
}

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

Derivation

  1. Initial program 11.2

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019174 
(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))))