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

Average Error: 10.4 → 0.5

Time: 16.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 4.575129148191398110691261007157626695296 \cdot 10^{204}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r426821 = x;
        double r426822 = y;
        double r426823 = z;
        double r426824 = t;
        double r426825 = r426823 - r426824;
        double r426826 = r426822 * r426825;
        double r426827 = a;
        double r426828 = r426823 - r426827;
        double r426829 = r426826 / r426828;
        double r426830 = r426821 + r426829;
        return r426830;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r426831 = y;
        double r426832 = z;
        double r426833 = t;
        double r426834 = r426832 - r426833;
        double r426835 = r426831 * r426834;
        double r426836 = a;
        double r426837 = r426832 - r426836;
        double r426838 = r426835 / r426837;
        double r426839 = -inf.0;
        bool r426840 = r426838 <= r426839;
        double r426841 = 4.575129148191398e+204;
        bool r426842 = r426838 <= r426841;
        double r426843 = !r426842;
        bool r426844 = r426840 || r426843;
        double r426845 = r426831 / r426837;
        double r426846 = x;
        double r426847 = fma(r426845, r426834, r426846);
        double r426848 = r426846 + r426838;
        double r426849 = r426844 ? r426847 : r426848;
        return r426849;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.4
Target	1.3
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 4.575129148191398e+204 < (/ (* y (- z t)) (- z a))

   1. Initial program 54.6

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

   2. Simplified 1.8

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

   if -inf.0 < (/ (* y (- z t)) (- z a)) < 4.575129148191398e+204

   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 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 4.575129148191398110691261007157626695296 \cdot 10^{204}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 +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))))