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

Average Error: 10.5 → 0.7

Time: 21.0s

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 r380676 = x;
        double r380677 = y;
        double r380678 = z;
        double r380679 = t;
        double r380680 = r380678 - r380679;
        double r380681 = r380677 * r380680;
        double r380682 = a;
        double r380683 = r380678 - r380682;
        double r380684 = r380681 / r380683;
        double r380685 = r380676 + r380684;
        return r380685;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r380686 = y;
        double r380687 = z;
        double r380688 = t;
        double r380689 = r380687 - r380688;
        double r380690 = r380686 * r380689;
        double r380691 = a;
        double r380692 = r380687 - r380691;
        double r380693 = r380690 / r380692;
        double r380694 = -inf.0;
        bool r380695 = r380693 <= r380694;
        double r380696 = 6.539770865773377e+177;
        bool r380697 = r380693 <= r380696;
        double r380698 = !r380697;
        bool r380699 = r380695 || r380698;
        double r380700 = r380686 / r380692;
        double r380701 = x;
        double r380702 = fma(r380700, r380689, r380701);
        double r380703 = r380701 + r380693;
        double r380704 = r380699 ? r380702 : r380703;
        return r380704;
}

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))))