Average Error: 10.8 → 1.1
Time: 3.4s
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 r614073 = x;
        double r614074 = y;
        double r614075 = z;
        double r614076 = t;
        double r614077 = r614075 - r614076;
        double r614078 = r614074 * r614077;
        double r614079 = a;
        double r614080 = r614079 - r614076;
        double r614081 = r614078 / r614080;
        double r614082 = r614073 + r614081;
        return r614082;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r614083 = x;
        double r614084 = y;
        double r614085 = a;
        double r614086 = t;
        double r614087 = r614085 - r614086;
        double r614088 = z;
        double r614089 = r614088 - r614086;
        double r614090 = r614087 / r614089;
        double r614091 = r614084 / r614090;
        double r614092 = r614083 + r614091;
        return r614092;
}

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

Original10.8
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020025 
(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))))