Average Error: 11.0 → 1.3
Time: 3.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r550838 = x;
        double r550839 = y;
        double r550840 = z;
        double r550841 = t;
        double r550842 = r550840 - r550841;
        double r550843 = r550839 * r550842;
        double r550844 = a;
        double r550845 = r550840 - r550844;
        double r550846 = r550843 / r550845;
        double r550847 = r550838 + r550846;
        return r550847;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r550848 = x;
        double r550849 = y;
        double r550850 = z;
        double r550851 = a;
        double r550852 = r550850 - r550851;
        double r550853 = 1.0;
        double r550854 = t;
        double r550855 = r550850 - r550854;
        double r550856 = r550853 / r550855;
        double r550857 = r550852 * r550856;
        double r550858 = r550849 / r550857;
        double r550859 = r550848 + r550858;
        return r550859;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

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

  5. Applied div-inv1.3

    \[\leadsto x + \frac{y}{\color{blue}{\left(z - a\right) \cdot \frac{1}{z - t}}}\]

  6. Final simplification1.3

    \[\leadsto x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\]

Reproduce

herbie shell --seed 2020001 
(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))))