Average Error: 10.9 → 1.1
Time: 9.9s
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 r476633 = x;
        double r476634 = y;
        double r476635 = z;
        double r476636 = t;
        double r476637 = r476635 - r476636;
        double r476638 = r476634 * r476637;
        double r476639 = a;
        double r476640 = r476635 - r476639;
        double r476641 = r476638 / r476640;
        double r476642 = r476633 + r476641;
        return r476642;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r476643 = x;
        double r476644 = y;
        double r476645 = z;
        double r476646 = a;
        double r476647 = r476645 - r476646;
        double r476648 = t;
        double r476649 = r476645 - r476648;
        double r476650 = r476647 / r476649;
        double r476651 = r476644 / r476650;
        double r476652 = r476643 + r476651;
        return r476652;
}

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

Original10.9
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020046 
(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))))