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

Average Error: 10.7 → 1.1

Time: 5.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -8.7537559398872107 \cdot 10^{-143} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 3.1147786030260667 \cdot 10^{225}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r802474 = x;
        double r802475 = y;
        double r802476 = z;
        double r802477 = t;
        double r802478 = r802476 - r802477;
        double r802479 = r802475 * r802478;
        double r802480 = a;
        double r802481 = r802476 - r802480;
        double r802482 = r802479 / r802481;
        double r802483 = r802474 + r802482;
        return r802483;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r802484 = y;
        double r802485 = z;
        double r802486 = t;
        double r802487 = r802485 - r802486;
        double r802488 = r802484 * r802487;
        double r802489 = a;
        double r802490 = r802485 - r802489;
        double r802491 = r802488 / r802490;
        double r802492 = -8.75375593988721e-143;
        bool r802493 = r802491 <= r802492;
        double r802494 = 3.114778603026067e+225;
        bool r802495 = r802491 <= r802494;
        double r802496 = !r802495;
        bool r802497 = r802493 || r802496;
        double r802498 = x;
        double r802499 = r802490 / r802487;
        double r802500 = r802484 / r802499;
        double r802501 = r802498 + r802500;
        double r802502 = r802498 + r802491;
        double r802503 = r802497 ? r802501 : r802502;
        return r802503;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.7
Target	1.4
Herbie	1.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) (- z a)) < -8.75375593988721e-143 or 3.114778603026067e+225 < (/ (* y (- z t)) (- z a))

   1. Initial program 23.6

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

   3. Applied associate-/l* 2.0

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

   if -8.75375593988721e-143 < (/ (* y (- z t)) (- z a)) < 3.114778603026067e+225

   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 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \le -8.7537559398872107 \cdot 10^{-143} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \le 3.1147786030260667 \cdot 10^{225}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))))