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

Average Error: 10.5 → 0.7

Time: 17.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.539770865773377012647932284333126840637 \cdot 10^{177}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r378635 = x;
        double r378636 = y;
        double r378637 = z;
        double r378638 = t;
        double r378639 = r378637 - r378638;
        double r378640 = r378636 * r378639;
        double r378641 = a;
        double r378642 = r378637 - r378641;
        double r378643 = r378640 / r378642;
        double r378644 = r378635 + r378643;
        return r378644;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r378645 = y;
        double r378646 = z;
        double r378647 = t;
        double r378648 = r378646 - r378647;
        double r378649 = r378645 * r378648;
        double r378650 = a;
        double r378651 = r378646 - r378650;
        double r378652 = r378649 / r378651;
        double r378653 = -inf.0;
        bool r378654 = r378652 <= r378653;
        double r378655 = 6.539770865773377e+177;
        bool r378656 = r378652 <= r378655;
        double r378657 = !r378656;
        bool r378658 = r378654 || r378657;
        double r378659 = r378645 / r378651;
        double r378660 = x;
        double r378661 = fma(r378659, r378648, r378660);
        double r378662 = r378660 + r378652;
        double r378663 = r378658 ? r378661 : r378662;
        return r378663;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.5
Target	1.5
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -inf.0 or 6.539770865773377e+177 < (/ (* y (- z t)) (- z a))

   1. Initial program 51.1

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

   2. Simplified 2.6

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

   if -inf.0 < (/ (* y (- z t)) (- z a)) < 6.539770865773377e+177

   1. Initial program 0.3

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 6.539770865773377012647932284333126840637 \cdot 10^{177}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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))))