Average Error: 1.4 → 1.3
Time: 9.0s
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 r563845 = x;
        double r563846 = y;
        double r563847 = z;
        double r563848 = t;
        double r563849 = r563847 - r563848;
        double r563850 = a;
        double r563851 = r563847 - r563850;
        double r563852 = r563849 / r563851;
        double r563853 = r563846 * r563852;
        double r563854 = r563845 + r563853;
        return r563854;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r563855 = x;
        double r563856 = y;
        double r563857 = z;
        double r563858 = a;
        double r563859 = r563857 - r563858;
        double r563860 = t;
        double r563861 = r563857 - r563860;
        double r563862 = r563859 / r563861;
        double r563863 = r563856 / r563862;
        double r563864 = r563855 + r563863;
        return r563864;
}

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 pow11.4

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

  5. Applied clear-num1.5

    \[\leadsto {\left(x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\right)}^{1}\]
  6. Using strategy rm

  7. Applied un-div-inv1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2020045 
(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)))))