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

Average Error: 7.4 → 4.0

Time: 24.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -4.898559820385924943383218878329955525278 \cdot 10^{110}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 4.989921171097169236254159654900191065389 \cdot 10^{193}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r19434423 = x;
        double r19434424 = y;
        double r19434425 = z;
        double r19434426 = r19434424 * r19434425;
        double r19434427 = r19434426 - r19434423;
        double r19434428 = t;
        double r19434429 = r19434428 * r19434425;
        double r19434430 = r19434429 - r19434423;
        double r19434431 = r19434427 / r19434430;
        double r19434432 = r19434423 + r19434431;
        double r19434433 = 1.0;
        double r19434434 = r19434423 + r19434433;
        double r19434435 = r19434432 / r19434434;
        return r19434435;
}

↓

double f(double x, double y, double z, double t) {
        double r19434436 = z;
        double r19434437 = -4.898559820385925e+110;
        bool r19434438 = r19434436 <= r19434437;
        double r19434439 = x;
        double r19434440 = y;
        double r19434441 = t;
        double r19434442 = r19434440 / r19434441;
        double r19434443 = r19434439 + r19434442;
        double r19434444 = 1.0;
        double r19434445 = r19434439 + r19434444;
        double r19434446 = r19434443 / r19434445;
        double r19434447 = 4.989921171097169e+193;
        bool r19434448 = r19434436 <= r19434447;
        double r19434449 = 1.0;
        double r19434450 = r19434441 * r19434436;
        double r19434451 = r19434450 - r19434439;
        double r19434452 = r19434440 * r19434436;
        double r19434453 = r19434452 - r19434439;
        double r19434454 = r19434451 / r19434453;
        double r19434455 = r19434449 / r19434454;
        double r19434456 = r19434439 + r19434455;
        double r19434457 = r19434456 / r19434445;
        double r19434458 = r19434448 ? r19434457 : r19434446;
        double r19434459 = r19434438 ? r19434446 : r19434458;
        return r19434459;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.4
Target	0.4
Herbie	4.0

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

Derivation

1. Split input into 2 regimes

2. if z < -4.898559820385925e+110 or 4.989921171097169e+193 < z

   1. Initial program 22.1

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

   2. Taylor expanded around inf 8.1

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

   if -4.898559820385925e+110 < z < 4.989921171097169e+193

   1. Initial program 2.7

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

   3. Applied clear-num 2.7

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

   4. Taylor expanded around 0 2.7

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

4. Final simplification 4.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.898559820385924943383218878329955525278 \cdot 10^{110}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 4.989921171097169236254159654900191065389 \cdot 10^{193}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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)))