Average Error: 11.0 → 1.3
Time: 3.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r601140 = x;
        double r601141 = y;
        double r601142 = z;
        double r601143 = t;
        double r601144 = r601142 - r601143;
        double r601145 = r601141 * r601144;
        double r601146 = a;
        double r601147 = r601142 - r601146;
        double r601148 = r601145 / r601147;
        double r601149 = r601140 + r601148;
        return r601149;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r601150 = x;
        double r601151 = y;
        double r601152 = z;
        double r601153 = a;
        double r601154 = r601152 - r601153;
        double r601155 = 1.0;
        double r601156 = t;
        double r601157 = r601152 - r601156;
        double r601158 = r601155 / r601157;
        double r601159 = r601154 * r601158;
        double r601160 = r601151 / r601159;
        double r601161 = r601150 + r601160;
        return r601161;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied div-inv1.3

    \[\leadsto x + \frac{y}{\color{blue}{\left(z - a\right) \cdot \frac{1}{z - t}}}\]

  6. Final simplification1.3

    \[\leadsto x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\]

Reproduce

herbie shell --seed 2020001 
(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))))