Average Error: 10.6 → 1.3
Time: 3.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r620218 = x;
        double r620219 = y;
        double r620220 = z;
        double r620221 = t;
        double r620222 = r620220 - r620221;
        double r620223 = r620219 * r620222;
        double r620224 = a;
        double r620225 = r620224 - r620221;
        double r620226 = r620223 / r620225;
        double r620227 = r620218 + r620226;
        return r620227;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r620228 = x;
        double r620229 = y;
        double r620230 = a;
        double r620231 = t;
        double r620232 = r620230 - r620231;
        double r620233 = z;
        double r620234 = r620233 - r620231;
        double r620235 = r620232 / r620234;
        double r620236 = r620229 / r620235;
        double r620237 = r620228 + r620236;
        return r620237;
}

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

Original10.6
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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