Average Error: 10.9 → 1.2
Time: 10.7s
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 r498998 = x;
        double r498999 = y;
        double r499000 = z;
        double r499001 = t;
        double r499002 = r499000 - r499001;
        double r499003 = r498999 * r499002;
        double r499004 = a;
        double r499005 = r499000 - r499004;
        double r499006 = r499003 / r499005;
        double r499007 = r498998 + r499006;
        return r499007;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r499008 = x;
        double r499009 = y;
        double r499010 = z;
        double r499011 = a;
        double r499012 = r499010 - r499011;
        double r499013 = t;
        double r499014 = r499010 - r499013;
        double r499015 = r499012 / r499014;
        double r499016 = r499009 / r499015;
        double r499017 = r499008 + r499016;
        return r499017;
}

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 +o rules:numerics
(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))))