Average Error: 11.7 → 1.3
Time: 3.6s
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 r547050 = x;
        double r547051 = y;
        double r547052 = z;
        double r547053 = t;
        double r547054 = r547052 - r547053;
        double r547055 = r547051 * r547054;
        double r547056 = a;
        double r547057 = r547052 - r547056;
        double r547058 = r547055 / r547057;
        double r547059 = r547050 + r547058;
        return r547059;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r547060 = x;
        double r547061 = y;
        double r547062 = z;
        double r547063 = a;
        double r547064 = r547062 - r547063;
        double r547065 = t;
        double r547066 = r547062 - r547065;
        double r547067 = r547064 / r547066;
        double r547068 = r547061 / r547067;
        double r547069 = r547060 + r547068;
        return r547069;
}

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

Original11.7
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.7

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019353 
(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))))