Average Error: 9.9 → 1.2
Time: 20.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r26352841 = x;
        double r26352842 = y;
        double r26352843 = z;
        double r26352844 = t;
        double r26352845 = r26352843 - r26352844;
        double r26352846 = r26352842 * r26352845;
        double r26352847 = a;
        double r26352848 = r26352843 - r26352847;
        double r26352849 = r26352846 / r26352848;
        double r26352850 = r26352841 + r26352849;
        return r26352850;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26352851 = x;
        double r26352852 = y;
        double r26352853 = z;
        double r26352854 = a;
        double r26352855 = r26352853 - r26352854;
        double r26352856 = t;
        double r26352857 = r26352853 - r26352856;
        double r26352858 = r26352855 / r26352857;
        double r26352859 = r26352852 / r26352858;
        double r26352860 = r26352851 + r26352859;
        return r26352860;
}

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

Original9.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 9.9

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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