Average Error: 10.9 → 1.2
Time: 3.4s
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 r613746 = x;
        double r613747 = y;
        double r613748 = z;
        double r613749 = t;
        double r613750 = r613748 - r613749;
        double r613751 = r613747 * r613750;
        double r613752 = a;
        double r613753 = r613748 - r613752;
        double r613754 = r613751 / r613753;
        double r613755 = r613746 + r613754;
        return r613755;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r613756 = x;
        double r613757 = y;
        double r613758 = z;
        double r613759 = a;
        double r613760 = r613758 - r613759;
        double r613761 = t;
        double r613762 = r613758 - r613761;
        double r613763 = r613760 / r613762;
        double r613764 = r613757 / r613763;
        double r613765 = r613756 + r613764;
        return r613765;
}

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

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2020047 
(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))))