Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Average Error: 10.7 → 0.5

Time: 12.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -4.42328525588315658 \cdot 10^{240} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 9.4807877995094137 \cdot 10^{304}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r711998 = x;
        double r711999 = y;
        double r712000 = z;
        double r712001 = t;
        double r712002 = r712000 - r712001;
        double r712003 = r711999 * r712002;
        double r712004 = a;
        double r712005 = r712004 - r712001;
        double r712006 = r712003 / r712005;
        double r712007 = r711998 + r712006;
        return r712007;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r712008 = y;
        double r712009 = z;
        double r712010 = t;
        double r712011 = r712009 - r712010;
        double r712012 = r712008 * r712011;
        double r712013 = a;
        double r712014 = r712013 - r712010;
        double r712015 = r712012 / r712014;
        double r712016 = -4.4232852558831566e+240;
        bool r712017 = r712015 <= r712016;
        double r712018 = 9.480787799509414e+304;
        bool r712019 = r712015 <= r712018;
        double r712020 = !r712019;
        bool r712021 = r712017 || r712020;
        double r712022 = r712008 / r712014;
        double r712023 = x;
        double r712024 = fma(r712022, r712011, r712023);
        double r712025 = r712023 + r712015;
        double r712026 = r712021 ? r712024 : r712025;
        return r712026;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.7
Target	1.3
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- a t)) < -4.4232852558831566e+240 or 9.480787799509414e+304 < (/ (* y (- z t)) (- a t))

   1. Initial program 58.3

      \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]

   2. Simplified 1.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]

   if -4.4232852558831566e+240 < (/ (* y (- z t)) (- a t)) < 9.480787799509414e+304

   1. Initial program 0.2

      \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -4.42328525588315658 \cdot 10^{240} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 9.4807877995094137 \cdot 10^{304}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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))))