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

Average Error: 10.8 → 0.6

Time: 19.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -1.435703423329415845082578000340298383955 \cdot 10^{218} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.302610413147462264895587144625997761847 \cdot 10^{289}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r438746 = x;
        double r438747 = y;
        double r438748 = z;
        double r438749 = t;
        double r438750 = r438748 - r438749;
        double r438751 = r438747 * r438750;
        double r438752 = a;
        double r438753 = r438752 - r438749;
        double r438754 = r438751 / r438753;
        double r438755 = r438746 + r438754;
        return r438755;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r438756 = y;
        double r438757 = z;
        double r438758 = t;
        double r438759 = r438757 - r438758;
        double r438760 = r438756 * r438759;
        double r438761 = a;
        double r438762 = r438761 - r438758;
        double r438763 = r438760 / r438762;
        double r438764 = -1.4357034233294158e+218;
        bool r438765 = r438763 <= r438764;
        double r438766 = 1.3026104131474623e+289;
        bool r438767 = r438763 <= r438766;
        double r438768 = !r438767;
        bool r438769 = r438765 || r438768;
        double r438770 = r438756 / r438762;
        double r438771 = x;
        double r438772 = fma(r438770, r438759, r438771);
        double r438773 = r438771 + r438763;
        double r438774 = r438769 ? r438772 : r438773;
        return r438774;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.8
Target	1.2
Herbie	0.6

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- a t)) < -1.4357034233294158e+218 or 1.3026104131474623e+289 < (/ (* y (- z t)) (- a t))

   1. Initial program 55.3

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

   2. Simplified 2.2

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

   if -1.4357034233294158e+218 < (/ (* y (- z t)) (- a t)) < 1.3026104131474623e+289

   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 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -1.435703423329415845082578000340298383955 \cdot 10^{218} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.302610413147462264895587144625997761847 \cdot 10^{289}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 +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))))