Average Error: 11.0 → 1.3
Time: 10.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r451688 = x;
        double r451689 = y;
        double r451690 = z;
        double r451691 = t;
        double r451692 = r451690 - r451691;
        double r451693 = r451689 * r451692;
        double r451694 = a;
        double r451695 = r451694 - r451691;
        double r451696 = r451693 / r451695;
        double r451697 = r451688 + r451696;
        return r451697;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r451698 = x;
        double r451699 = y;
        double r451700 = a;
        double r451701 = z;
        double r451702 = t;
        double r451703 = r451701 - r451702;
        double r451704 = r451700 / r451703;
        double r451705 = r451702 / r451703;
        double r451706 = r451704 - r451705;
        double r451707 = r451699 / r451706;
        double r451708 = r451698 + r451707;
        return r451708;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied div-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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