Average Error: 1.5 → 1.3
Time: 3.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r622171 = x;
        double r622172 = y;
        double r622173 = z;
        double r622174 = t;
        double r622175 = r622173 - r622174;
        double r622176 = a;
        double r622177 = r622173 - r622176;
        double r622178 = r622175 / r622177;
        double r622179 = r622172 * r622178;
        double r622180 = r622171 + r622179;
        return r622180;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r622181 = x;
        double r622182 = y;
        double r622183 = z;
        double r622184 = a;
        double r622185 = r622183 - r622184;
        double r622186 = t;
        double r622187 = r622183 - r622186;
        double r622188 = r622185 / r622187;
        double r622189 = r622182 / r622188;
        double r622190 = r622181 + r622189;
        return r622190;
}

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

Original1.5
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.5

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

  3. Applied associate-*r/10.8

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

  5. Applied associate-/l*1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))