Average Error: 11.0 → 1.1
Time: 3.8s
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 r527204 = x;
        double r527205 = y;
        double r527206 = z;
        double r527207 = t;
        double r527208 = r527206 - r527207;
        double r527209 = r527205 * r527208;
        double r527210 = a;
        double r527211 = r527206 - r527210;
        double r527212 = r527209 / r527211;
        double r527213 = r527204 + r527212;
        return r527213;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r527214 = x;
        double r527215 = y;
        double r527216 = z;
        double r527217 = a;
        double r527218 = r527216 - r527217;
        double r527219 = t;
        double r527220 = r527216 - r527219;
        double r527221 = r527218 / r527220;
        double r527222 = r527215 / r527221;
        double r527223 = r527214 + r527222;
        return r527223;
}

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
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020081 +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))))