Average Error: 10.7 → 1.2
Time: 9.7s
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 r786634 = x;
        double r786635 = y;
        double r786636 = z;
        double r786637 = t;
        double r786638 = r786636 - r786637;
        double r786639 = r786635 * r786638;
        double r786640 = a;
        double r786641 = r786636 - r786640;
        double r786642 = r786639 / r786641;
        double r786643 = r786634 + r786642;
        return r786643;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r786644 = x;
        double r786645 = y;
        double r786646 = z;
        double r786647 = a;
        double r786648 = r786646 - r786647;
        double r786649 = t;
        double r786650 = r786646 - r786649;
        double r786651 = r786648 / r786650;
        double r786652 = r786645 / r786651;
        double r786653 = r786644 + r786652;
        return r786653;
}

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

Original10.7
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019350 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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