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

Average Error: 10.6 → 0.4

Time: 2.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -5.214740867201422251548963035487610456322 \cdot 10^{-31} \lor \neg \left(t \le 1558841615728887808\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r633435 = x;
        double r633436 = y;
        double r633437 = z;
        double r633438 = r633436 - r633437;
        double r633439 = t;
        double r633440 = r633438 * r633439;
        double r633441 = a;
        double r633442 = r633441 - r633437;
        double r633443 = r633440 / r633442;
        double r633444 = r633435 + r633443;
        return r633444;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r633445 = t;
        double r633446 = -5.214740867201422e-31;
        bool r633447 = r633445 <= r633446;
        double r633448 = 1.5588416157288878e+18;
        bool r633449 = r633445 <= r633448;
        double r633450 = !r633449;
        bool r633451 = r633447 || r633450;
        double r633452 = x;
        double r633453 = y;
        double r633454 = z;
        double r633455 = r633453 - r633454;
        double r633456 = a;
        double r633457 = r633456 - r633454;
        double r633458 = r633455 / r633457;
        double r633459 = r633458 * r633445;
        double r633460 = r633452 + r633459;
        double r633461 = r633455 * r633445;
        double r633462 = r633461 / r633457;
        double r633463 = r633452 + r633462;
        double r633464 = r633451 ? r633460 : r633463;
        return r633464;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.6
Target	0.5
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if t < -5.214740867201422e-31 or 1.5588416157288878e+18 < t

   1. Initial program 22.0

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

   3. Applied associate-/l* 2.0

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
   4. Using strategy rm

   5. Applied associate-/r/ 0.4

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

   if -5.214740867201422e-31 < t < 1.5588416157288878e+18

   1. Initial program 0.3

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.214740867201422251548963035487610456322 \cdot 10^{-31} \lor \neg \left(t \le 1558841615728887808\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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