Average Error: 1.3 → 1.2
Time: 19.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r31104810 = x;
        double r31104811 = y;
        double r31104812 = z;
        double r31104813 = t;
        double r31104814 = r31104812 - r31104813;
        double r31104815 = a;
        double r31104816 = r31104812 - r31104815;
        double r31104817 = r31104814 / r31104816;
        double r31104818 = r31104811 * r31104817;
        double r31104819 = r31104810 + r31104818;
        return r31104819;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31104820 = x;
        double r31104821 = y;
        double r31104822 = z;
        double r31104823 = a;
        double r31104824 = r31104822 - r31104823;
        double r31104825 = t;
        double r31104826 = r31104822 - r31104825;
        double r31104827 = r31104824 / r31104826;
        double r31104828 = r31104821 / r31104827;
        double r31104829 = r31104820 + r31104828;
        return r31104829;
}

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

Original1.3
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied associate-*r/10.7

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

  5. Applied associate-/l*1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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