Average Error: 10.8 → 10.8
Time: 13.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y \cdot \left(z - t\right)}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r452868 = x;
        double r452869 = y;
        double r452870 = z;
        double r452871 = t;
        double r452872 = r452870 - r452871;
        double r452873 = r452869 * r452872;
        double r452874 = a;
        double r452875 = r452870 - r452874;
        double r452876 = r452873 / r452875;
        double r452877 = r452868 + r452876;
        return r452877;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r452878 = x;
        double r452879 = y;
        double r452880 = z;
        double r452881 = t;
        double r452882 = r452880 - r452881;
        double r452883 = r452879 * r452882;
        double r452884 = a;
        double r452885 = r452880 - r452884;
        double r452886 = r452883 / r452885;
        double r452887 = r452878 + r452886;
        return r452887;
}

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
Target1.2
Herbie10.8
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.8379621231086494e-19 or 3.355115332728058e-103 < y

    1. Initial program 18.7

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

    3. Applied associate-/l*0.7

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

    if -2.8379621231086494e-19 < y < 3.355115332728058e-103

    1. Initial program 0.4

      \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.8

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

Reproduce

herbie shell --seed 2019297 
(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))))