Average Error: 10.4 → 1.4
Time: 23.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}
double f(double x, double y, double z, double t, double a) {
        double r21275846 = x;
        double r21275847 = y;
        double r21275848 = z;
        double r21275849 = t;
        double r21275850 = r21275848 - r21275849;
        double r21275851 = r21275847 * r21275850;
        double r21275852 = a;
        double r21275853 = r21275852 - r21275849;
        double r21275854 = r21275851 / r21275853;
        double r21275855 = r21275846 + r21275854;
        return r21275855;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r21275856 = x;
        double r21275857 = 1.0;
        double r21275858 = a;
        double r21275859 = t;
        double r21275860 = r21275858 - r21275859;
        double r21275861 = z;
        double r21275862 = r21275861 - r21275859;
        double r21275863 = r21275860 / r21275862;
        double r21275864 = y;
        double r21275865 = r21275863 / r21275864;
        double r21275866 = r21275857 / r21275865;
        double r21275867 = r21275856 + r21275866;
        return r21275867;
}

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

Original10.4
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.3

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

  5. Applied clear-num1.4

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y}}}\]

  6. Final simplification1.4

    \[\leadsto x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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