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

Average Error: 7.2 → 3.4

Time: 23.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -7.150582175885458915277202527443364197416 \cdot 10^{54} \lor \neg \left(z \le 6.043915376694697440989411808244092375242 \cdot 10^{86}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r457568 = x;
        double r457569 = y;
        double r457570 = z;
        double r457571 = r457569 * r457570;
        double r457572 = r457571 - r457568;
        double r457573 = t;
        double r457574 = r457573 * r457570;
        double r457575 = r457574 - r457568;
        double r457576 = r457572 / r457575;
        double r457577 = r457568 + r457576;
        double r457578 = 1.0;
        double r457579 = r457568 + r457578;
        double r457580 = r457577 / r457579;
        return r457580;
}

↓

double f(double x, double y, double z, double t) {
        double r457581 = z;
        double r457582 = -7.150582175885459e+54;
        bool r457583 = r457581 <= r457582;
        double r457584 = 6.043915376694697e+86;
        bool r457585 = r457581 <= r457584;
        double r457586 = !r457585;
        bool r457587 = r457583 || r457586;
        double r457588 = x;
        double r457589 = y;
        double r457590 = t;
        double r457591 = r457589 / r457590;
        double r457592 = r457588 + r457591;
        double r457593 = 1.0;
        double r457594 = r457588 + r457593;
        double r457595 = r457592 / r457594;
        double r457596 = 1.0;
        double r457597 = r457590 * r457581;
        double r457598 = r457597 - r457588;
        double r457599 = r457589 * r457581;
        double r457600 = r457599 - r457588;
        double r457601 = r457598 / r457600;
        double r457602 = r457596 / r457601;
        double r457603 = r457588 + r457602;
        double r457604 = r457603 / r457594;
        double r457605 = r457587 ? r457595 : r457604;
        return r457605;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.2
Target	0.3
Herbie	3.4

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

Derivation

1. Split input into 2 regimes

2. if z < -7.150582175885459e+54 or 6.043915376694697e+86 < z

   1. Initial program 18.2

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

   2. Taylor expanded around inf 7.8

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

   if -7.150582175885459e+54 < z < 6.043915376694697e+86

   1. Initial program 0.7

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

   3. Applied clear-num 0.8

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

4. Final simplification 3.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.150582175885458915277202527443364197416 \cdot 10^{54} \lor \neg \left(z \le 6.043915376694697440989411808244092375242 \cdot 10^{86}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))