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

Average Error: 10.7 → 0.5

Time: 11.6s

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 r738513 = x;
        double r738514 = y;
        double r738515 = z;
        double r738516 = t;
        double r738517 = r738515 - r738516;
        double r738518 = r738514 * r738517;
        double r738519 = a;
        double r738520 = r738519 - r738516;
        double r738521 = r738518 / r738520;
        double r738522 = r738513 + r738521;
        return r738522;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r738523 = y;
        double r738524 = z;
        double r738525 = t;
        double r738526 = r738524 - r738525;
        double r738527 = r738523 * r738526;
        double r738528 = a;
        double r738529 = r738528 - r738525;
        double r738530 = r738527 / r738529;
        double r738531 = -4.4232852558831566e+240;
        bool r738532 = r738530 <= r738531;
        double r738533 = 9.480787799509414e+304;
        bool r738534 = r738530 <= r738533;
        double r738535 = !r738534;
        bool r738536 = r738532 || r738535;
        double r738537 = r738523 / r738529;
        double r738538 = x;
        double r738539 = fma(r738537, r738526, r738538);
        double r738540 = r738538 + r738530;
        double r738541 = r738536 ? r738539 : r738540;
        return r738541;
}

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))))