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

Average Error: 7.4 → 4.0

Time: 19.1s

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 r46968529 = x;
        double r46968530 = y;
        double r46968531 = z;
        double r46968532 = r46968530 * r46968531;
        double r46968533 = r46968532 - r46968529;
        double r46968534 = t;
        double r46968535 = r46968534 * r46968531;
        double r46968536 = r46968535 - r46968529;
        double r46968537 = r46968533 / r46968536;
        double r46968538 = r46968529 + r46968537;
        double r46968539 = 1.0;
        double r46968540 = r46968529 + r46968539;
        double r46968541 = r46968538 / r46968540;
        return r46968541;
}

↓

double f(double x, double y, double z, double t) {
        double r46968542 = z;
        double r46968543 = -4.898559820385925e+110;
        bool r46968544 = r46968542 <= r46968543;
        double r46968545 = x;
        double r46968546 = y;
        double r46968547 = t;
        double r46968548 = r46968546 / r46968547;
        double r46968549 = r46968545 + r46968548;
        double r46968550 = 1.0;
        double r46968551 = r46968545 + r46968550;
        double r46968552 = r46968549 / r46968551;
        double r46968553 = 4.989921171097169e+193;
        bool r46968554 = r46968542 <= r46968553;
        double r46968555 = 1.0;
        double r46968556 = r46968547 * r46968542;
        double r46968557 = r46968556 - r46968545;
        double r46968558 = r46968546 * r46968542;
        double r46968559 = r46968558 - r46968545;
        double r46968560 = r46968557 / r46968559;
        double r46968561 = r46968555 / r46968560;
        double r46968562 = r46968545 + r46968561;
        double r46968563 = r46968562 / r46968551;
        double r46968564 = r46968554 ? r46968563 : r46968552;
        double r46968565 = r46968544 ? r46968552 : r46968564;
        return r46968565;
}

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)))