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

Average Error: 10.9 → 0.4

Time: 4.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.88083214181031576 \cdot 10^{280} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 8.6295076012176389 \cdot 10^{282}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r526186 = x;
        double r526187 = y;
        double r526188 = z;
        double r526189 = t;
        double r526190 = r526188 - r526189;
        double r526191 = r526187 * r526190;
        double r526192 = a;
        double r526193 = r526188 - r526192;
        double r526194 = r526191 / r526193;
        double r526195 = r526186 + r526194;
        return r526195;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r526196 = y;
        double r526197 = z;
        double r526198 = t;
        double r526199 = r526197 - r526198;
        double r526200 = r526196 * r526199;
        double r526201 = a;
        double r526202 = r526197 - r526201;
        double r526203 = r526200 / r526202;
        double r526204 = -1.8808321418103158e+280;
        bool r526205 = r526203 <= r526204;
        double r526206 = 8.629507601217639e+282;
        bool r526207 = r526203 <= r526206;
        double r526208 = !r526207;
        bool r526209 = r526205 || r526208;
        double r526210 = r526196 / r526202;
        double r526211 = x;
        double r526212 = fma(r526210, r526199, r526211);
        double r526213 = r526211 + r526203;
        double r526214 = r526209 ? r526212 : r526213;
        return r526214;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.9
Target	1.1
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)) < -1.8808321418103158e+280 or 8.629507601217639e+282 < (/ (* y (- z t)) (- z a))

   1. Initial program 60.3

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

   2. Simplified 1.1

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

   if -1.8808321418103158e+280 < (/ (* y (- z t)) (- z a)) < 8.629507601217639e+282

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -1.88083214181031576 \cdot 10^{280} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 8.6295076012176389 \cdot 10^{282}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))))