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

Average Error: 10.9 → 0.4

Time: 10.7s

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 r599413 = x;
        double r599414 = y;
        double r599415 = z;
        double r599416 = t;
        double r599417 = r599415 - r599416;
        double r599418 = r599414 * r599417;
        double r599419 = a;
        double r599420 = r599415 - r599419;
        double r599421 = r599418 / r599420;
        double r599422 = r599413 + r599421;
        return r599422;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r599423 = y;
        double r599424 = z;
        double r599425 = t;
        double r599426 = r599424 - r599425;
        double r599427 = r599423 * r599426;
        double r599428 = a;
        double r599429 = r599424 - r599428;
        double r599430 = r599427 / r599429;
        double r599431 = -1.8808321418103158e+280;
        bool r599432 = r599430 <= r599431;
        double r599433 = 8.629507601217639e+282;
        bool r599434 = r599430 <= r599433;
        double r599435 = !r599434;
        bool r599436 = r599432 || r599435;
        double r599437 = r599423 / r599429;
        double r599438 = x;
        double r599439 = fma(r599437, r599426, r599438);
        double r599440 = r599438 + r599430;
        double r599441 = r599436 ? r599439 : r599440;
        return r599441;
}

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))))