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

Average Error: 1.4 → 0.4

Time: 9.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -8.8421123940869923 \cdot 10^{-4} \lor \neg \left(y \le 1.5536369793631163 \cdot 10^{-59}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r639244 = x;
        double r639245 = y;
        double r639246 = z;
        double r639247 = t;
        double r639248 = r639246 - r639247;
        double r639249 = a;
        double r639250 = r639249 - r639247;
        double r639251 = r639248 / r639250;
        double r639252 = r639245 * r639251;
        double r639253 = r639244 + r639252;
        return r639253;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r639254 = y;
        double r639255 = -0.0008842112394086992;
        bool r639256 = r639254 <= r639255;
        double r639257 = 1.5536369793631163e-59;
        bool r639258 = r639254 <= r639257;
        double r639259 = !r639258;
        bool r639260 = r639256 || r639259;
        double r639261 = x;
        double r639262 = z;
        double r639263 = t;
        double r639264 = r639262 - r639263;
        double r639265 = a;
        double r639266 = r639265 - r639263;
        double r639267 = r639264 / r639266;
        double r639268 = r639254 * r639267;
        double r639269 = r639261 + r639268;
        double r639270 = r639264 * r639254;
        double r639271 = r639270 / r639266;
        double r639272 = r639271 + r639261;
        double r639273 = r639260 ? r639269 : r639272;
        return r639273;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	1.4
Target	0.4
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if y < -0.0008842112394086992 or 1.5536369793631163e-59 < y

   1. Initial program 0.5

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

   if -0.0008842112394086992 < y < 1.5536369793631163e-59

   1. Initial program 2.3

      \[x + y \cdot \frac{z - t}{a - t}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 2.3

      \[\leadsto x + \color{blue}{\left(1 \cdot y\right)} \cdot \frac{z - t}{a - t}\]

   4. Applied associate-*l* 2.3

      \[\leadsto x + \color{blue}{1 \cdot \left(y \cdot \frac{z - t}{a - t}\right)}\]

   5. Simplified 3.3

      \[\leadsto x + 1 \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{y}{a - t}\right)}\]
   6. Using strategy rm

   7. Applied associate-*r/ 0.3

      \[\leadsto x + 1 \cdot \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.8421123940869923 \cdot 10^{-4} \lor \neg \left(y \le 1.5536369793631163 \cdot 10^{-59}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

  (+ x (* y (/ (- z t) (- a t)))))