Average Error: 10.5 → 1.1
Time: 5.3s
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 r548295 = x;
        double r548296 = y;
        double r548297 = z;
        double r548298 = t;
        double r548299 = r548297 - r548298;
        double r548300 = r548296 * r548299;
        double r548301 = a;
        double r548302 = r548297 - r548301;
        double r548303 = r548300 / r548302;
        double r548304 = r548295 + r548303;
        return r548304;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r548305 = x;
        double r548306 = y;
        double r548307 = z;
        double r548308 = a;
        double r548309 = r548307 - r548308;
        double r548310 = t;
        double r548311 = r548307 - r548310;
        double r548312 = r548309 / r548311;
        double r548313 = r548306 / r548312;
        double r548314 = r548305 + r548313;
        return r548314;
}

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

Original10.5
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2020034 
(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))))