Average Error: 11.7 → 1.3
Time: 3.6s
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 r813691 = x;
        double r813692 = y;
        double r813693 = z;
        double r813694 = t;
        double r813695 = r813693 - r813694;
        double r813696 = r813692 * r813695;
        double r813697 = a;
        double r813698 = r813693 - r813697;
        double r813699 = r813696 / r813698;
        double r813700 = r813691 + r813699;
        return r813700;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r813701 = x;
        double r813702 = y;
        double r813703 = z;
        double r813704 = a;
        double r813705 = r813703 - r813704;
        double r813706 = t;
        double r813707 = r813703 - r813706;
        double r813708 = r813705 / r813707;
        double r813709 = r813702 / r813708;
        double r813710 = r813701 + r813709;
        return r813710;
}

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

Original11.7
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.7

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019353 
(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))))