Average Error: 1.3 → 1.3
Time: 5.7s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \frac{z - t}{a - t}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \frac{z - t}{a - t}
double f(double x, double y, double z, double t, double a) {
        double r685807 = x;
        double r685808 = y;
        double r685809 = z;
        double r685810 = t;
        double r685811 = r685809 - r685810;
        double r685812 = a;
        double r685813 = r685812 - r685810;
        double r685814 = r685811 / r685813;
        double r685815 = r685808 * r685814;
        double r685816 = r685807 + r685815;
        return r685816;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r685817 = x;
        double r685818 = y;
        double r685819 = z;
        double r685820 = t;
        double r685821 = r685819 - r685820;
        double r685822 = a;
        double r685823 = r685822 - r685820;
        double r685824 = r685821 / r685823;
        double r685825 = r685818 * r685824;
        double r685826 = r685817 + r685825;
        return r685826;
}

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

Original1.3
Target0.5
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.3

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

  2. Final simplification1.3

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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