Average Error: 10.7 → 1.3
Time: 2.7s
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 r574995 = x;
        double r574996 = y;
        double r574997 = z;
        double r574998 = t;
        double r574999 = r574997 - r574998;
        double r575000 = r574996 * r574999;
        double r575001 = a;
        double r575002 = r574997 - r575001;
        double r575003 = r575000 / r575002;
        double r575004 = r574995 + r575003;
        return r575004;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r575005 = x;
        double r575006 = y;
        double r575007 = z;
        double r575008 = a;
        double r575009 = r575007 - r575008;
        double r575010 = t;
        double r575011 = r575007 - r575010;
        double r575012 = r575009 / r575011;
        double r575013 = r575006 / r575012;
        double r575014 = r575005 + r575013;
        return r575014;
}

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
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020024 
(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))))