Average Error: 10.9 → 1.1
Time: 5.2s
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 r418743 = x;
        double r418744 = y;
        double r418745 = z;
        double r418746 = t;
        double r418747 = r418745 - r418746;
        double r418748 = r418744 * r418747;
        double r418749 = a;
        double r418750 = r418745 - r418749;
        double r418751 = r418748 / r418750;
        double r418752 = r418743 + r418751;
        return r418752;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r418753 = x;
        double r418754 = y;
        double r418755 = z;
        double r418756 = a;
        double r418757 = r418755 - r418756;
        double r418758 = t;
        double r418759 = r418755 - r418758;
        double r418760 = r418757 / r418759;
        double r418761 = r418754 / r418760;
        double r418762 = r418753 + r418761;
        return r418762;
}

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))))