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

Average Error: 10.7 → 0.4

Time: 27.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 2.886184098505586518165870377542885099677 \cdot 10^{246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r111559400 = x;
        double r111559401 = y;
        double r111559402 = z;
        double r111559403 = t;
        double r111559404 = r111559402 - r111559403;
        double r111559405 = r111559401 * r111559404;
        double r111559406 = a;
        double r111559407 = r111559402 - r111559406;
        double r111559408 = r111559405 / r111559407;
        double r111559409 = r111559400 + r111559408;
        return r111559409;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r111559410 = y;
        double r111559411 = z;
        double r111559412 = t;
        double r111559413 = r111559411 - r111559412;
        double r111559414 = r111559410 * r111559413;
        double r111559415 = a;
        double r111559416 = r111559411 - r111559415;
        double r111559417 = r111559414 / r111559416;
        double r111559418 = -inf.0;
        bool r111559419 = r111559417 <= r111559418;
        double r111559420 = x;
        double r111559421 = r111559416 / r111559413;
        double r111559422 = r111559410 / r111559421;
        double r111559423 = r111559420 + r111559422;
        double r111559424 = 2.8861840985055865e+246;
        bool r111559425 = r111559417 <= r111559424;
        double r111559426 = r111559420 + r111559417;
        double r111559427 = r111559425 ? r111559426 : r111559423;
        double r111559428 = r111559419 ? r111559423 : r111559427;
        return r111559428;
}

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	1.4
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)) < -inf.0 or 2.8861840985055865e+246 < (/ (* y (- z t)) (- z a))

   1. Initial program 59.0

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

   3. Applied associate-/l* 1.2

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

   if -inf.0 < (/ (* y (- z t)) (- z a)) < 2.8861840985055865e+246

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{z - a} \le 2.886184098505586518165870377542885099677 \cdot 10^{246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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