Average Error: 10.8 → 1.3
Time: 3.9s
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 r633973 = x;
        double r633974 = y;
        double r633975 = z;
        double r633976 = t;
        double r633977 = r633975 - r633976;
        double r633978 = r633974 * r633977;
        double r633979 = a;
        double r633980 = r633975 - r633979;
        double r633981 = r633978 / r633980;
        double r633982 = r633973 + r633981;
        return r633982;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r633983 = x;
        double r633984 = y;
        double r633985 = z;
        double r633986 = a;
        double r633987 = r633985 - r633986;
        double r633988 = t;
        double r633989 = r633985 - r633988;
        double r633990 = r633987 / r633989;
        double r633991 = r633984 / r633990;
        double r633992 = r633983 + r633991;
        return r633992;
}

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

Derivation

  1. Initial program 10.8

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2020036 
(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))))