Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Average Error: 7.2 → 3.4

Time: 19.3s

Precision: 64

Math

\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.1409575287436362 \cdot 10^{+77}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 1.2840647236389548 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r30561483 = x;
        double r30561484 = y;
        double r30561485 = z;
        double r30561486 = r30561484 * r30561485;
        double r30561487 = r30561486 - r30561483;
        double r30561488 = t;
        double r30561489 = r30561488 * r30561485;
        double r30561490 = r30561489 - r30561483;
        double r30561491 = r30561487 / r30561490;
        double r30561492 = r30561483 + r30561491;
        double r30561493 = 1.0;
        double r30561494 = r30561483 + r30561493;
        double r30561495 = r30561492 / r30561494;
        return r30561495;
}

↓

double f(double x, double y, double z, double t) {
        double r30561496 = z;
        double r30561497 = -1.1409575287436362e+77;
        bool r30561498 = r30561496 <= r30561497;
        double r30561499 = x;
        double r30561500 = y;
        double r30561501 = t;
        double r30561502 = r30561500 / r30561501;
        double r30561503 = r30561499 + r30561502;
        double r30561504 = 1.0;
        double r30561505 = r30561499 + r30561504;
        double r30561506 = r30561503 / r30561505;
        double r30561507 = 1.2840647236389548e+57;
        bool r30561508 = r30561496 <= r30561507;
        double r30561509 = 1.0;
        double r30561510 = r30561501 * r30561496;
        double r30561511 = r30561510 - r30561499;
        double r30561512 = r30561500 * r30561496;
        double r30561513 = r30561512 - r30561499;
        double r30561514 = r30561511 / r30561513;
        double r30561515 = r30561509 / r30561514;
        double r30561516 = r30561499 + r30561515;
        double r30561517 = r30561516 / r30561505;
        double r30561518 = r30561508 ? r30561517 : r30561506;
        double r30561519 = r30561498 ? r30561506 : r30561518;
        return r30561519;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.2
Target	0.4
Herbie	3.4

\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

1. Split input into 2 regimes

2. if z < -1.1409575287436362e+77 or 1.2840647236389548e+57 < z

   1. Initial program 18.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]

   2. Taylor expanded around inf 7.7

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1.0}\]

   if -1.1409575287436362e+77 < z < 1.2840647236389548e+57

   1. Initial program 0.7

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
   2. Using strategy rm

   3. Applied clear-num 0.8

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}}{x + 1.0}\]
   4. Using strategy rm

   5. Applied +-commutative 0.8

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{t \cdot z - x}{y \cdot z - x}} + x}}{x + 1.0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 3.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1409575287436362 \cdot 10^{+77}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \mathbf{elif}\;z \le 1.2840647236389548 \cdot 10^{+57}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))