Average Error: 1.4 → 1.3
Time: 4.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}}\]
x + y \cdot \frac{z - t}{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 r678840 = x;
        double r678841 = y;
        double r678842 = z;
        double r678843 = t;
        double r678844 = r678842 - r678843;
        double r678845 = a;
        double r678846 = r678842 - r678845;
        double r678847 = r678844 / r678846;
        double r678848 = r678841 * r678847;
        double r678849 = r678840 + r678848;
        return r678849;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r678850 = x;
        double r678851 = y;
        double r678852 = z;
        double r678853 = a;
        double r678854 = r678852 - r678853;
        double r678855 = 1.0;
        double r678856 = t;
        double r678857 = r678852 - r678856;
        double r678858 = r678855 / r678857;
        double r678859 = r678854 * r678858;
        double r678860 = r678851 / r678859;
        double r678861 = r678850 + r678860;
        return r678861;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.5

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied un-div-inv1.3

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

  7. Applied div-inv1.3

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

  8. 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:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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