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

Average Error: 7.6 → 3.8

Time: 20.1s

Precision: 64

Math

\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.160115839689408068409085936108477411806 \cdot 10^{172}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 3.641116230673848176898687453531338972974 \cdot 10^{130}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{t \cdot z - x}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r46410300 = x;
        double r46410301 = y;
        double r46410302 = z;
        double r46410303 = r46410301 * r46410302;
        double r46410304 = r46410303 - r46410300;
        double r46410305 = t;
        double r46410306 = r46410305 * r46410302;
        double r46410307 = r46410306 - r46410300;
        double r46410308 = r46410304 / r46410307;
        double r46410309 = r46410300 + r46410308;
        double r46410310 = 1.0;
        double r46410311 = r46410300 + r46410310;
        double r46410312 = r46410309 / r46410311;
        return r46410312;
}

↓

double f(double x, double y, double z, double t) {
        double r46410313 = z;
        double r46410314 = -1.160115839689408e+172;
        bool r46410315 = r46410313 <= r46410314;
        double r46410316 = x;
        double r46410317 = y;
        double r46410318 = t;
        double r46410319 = r46410317 / r46410318;
        double r46410320 = r46410316 + r46410319;
        double r46410321 = 1.0;
        double r46410322 = r46410316 + r46410321;
        double r46410323 = r46410320 / r46410322;
        double r46410324 = 3.641116230673848e+130;
        bool r46410325 = r46410313 <= r46410324;
        double r46410326 = 1.0;
        double r46410327 = r46410317 * r46410313;
        double r46410328 = r46410327 - r46410316;
        double r46410329 = r46410318 * r46410313;
        double r46410330 = r46410329 - r46410316;
        double r46410331 = r46410328 / r46410330;
        double r46410332 = r46410316 + r46410331;
        double r46410333 = r46410322 / r46410332;
        double r46410334 = r46410326 / r46410333;
        double r46410335 = r46410325 ? r46410334 : r46410323;
        double r46410336 = r46410315 ? r46410323 : r46410335;
        return r46410336;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.6
Target	0.4
Herbie	3.8

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

Derivation

1. Split input into 2 regimes

2. if z < -1.160115839689408e+172 or 3.641116230673848e+130 < z

   1. Initial program 22.4

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

   2. Taylor expanded around inf 7.4

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]

   if -1.160115839689408e+172 < z < 3.641116230673848e+130

   1. Initial program 2.6

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
   2. Using strategy rm

   3. Applied clear-num 2.6

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

4. Final simplification 3.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.160115839689408068409085936108477411806 \cdot 10^{172}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 3.641116230673848176898687453531338972974 \cdot 10^{130}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{t \cdot z - x}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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)))