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

Average Error: 10.9 → 0.4

Time: 8.4s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.88083214181031576 \cdot 10^{280} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 8.6295076012176389 \cdot 10^{282}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r544165 = x;
        double r544166 = y;
        double r544167 = z;
        double r544168 = t;
        double r544169 = r544167 - r544168;
        double r544170 = r544166 * r544169;
        double r544171 = a;
        double r544172 = r544167 - r544171;
        double r544173 = r544170 / r544172;
        double r544174 = r544165 + r544173;
        return r544174;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r544175 = y;
        double r544176 = z;
        double r544177 = t;
        double r544178 = r544176 - r544177;
        double r544179 = r544175 * r544178;
        double r544180 = a;
        double r544181 = r544176 - r544180;
        double r544182 = r544179 / r544181;
        double r544183 = -1.8808321418103158e+280;
        bool r544184 = r544182 <= r544183;
        double r544185 = 8.629507601217639e+282;
        bool r544186 = r544182 <= r544185;
        double r544187 = !r544186;
        bool r544188 = r544184 || r544187;
        double r544189 = r544175 / r544181;
        double r544190 = x;
        double r544191 = fma(r544189, r544178, r544190);
        double r544192 = r544190 + r544182;
        double r544193 = r544188 ? r544191 : r544192;
        return r544193;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.9
Target	1.1
Herbie	0.4

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -1.8808321418103158e+280 or 8.629507601217639e+282 < (/ (* y (- z t)) (- z a))

   1. Initial program 60.3

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

   2. Simplified 1.1

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

   if -1.8808321418103158e+280 < (/ (* y (- z t)) (- z a)) < 8.629507601217639e+282

   1. Initial program 0.2

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.88083214181031576 \cdot 10^{280} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 8.6295076012176389 \cdot 10^{282}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))))