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

Average Error: 7.3 → 2.1

Time: 13.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 8.3183219701519654 \cdot 10^{263}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r748209 = x;
        double r748210 = y;
        double r748211 = z;
        double r748212 = r748210 * r748211;
        double r748213 = r748212 - r748209;
        double r748214 = t;
        double r748215 = r748214 * r748211;
        double r748216 = r748215 - r748209;
        double r748217 = r748213 / r748216;
        double r748218 = r748209 + r748217;
        double r748219 = 1.0;
        double r748220 = r748209 + r748219;
        double r748221 = r748218 / r748220;
        return r748221;
}

↓

double f(double x, double y, double z, double t) {
        double r748222 = x;
        double r748223 = y;
        double r748224 = z;
        double r748225 = r748223 * r748224;
        double r748226 = r748225 - r748222;
        double r748227 = t;
        double r748228 = r748227 * r748224;
        double r748229 = r748228 - r748222;
        double r748230 = r748226 / r748229;
        double r748231 = r748222 + r748230;
        double r748232 = 1.0;
        double r748233 = r748222 + r748232;
        double r748234 = r748231 / r748233;
        double r748235 = -inf.0;
        bool r748236 = r748234 <= r748235;
        double r748237 = 8.318321970151965e+263;
        bool r748238 = r748234 <= r748237;
        double r748239 = !r748238;
        bool r748240 = r748236 || r748239;
        double r748241 = r748223 / r748227;
        double r748242 = r748222 + r748241;
        double r748243 = r748242 / r748233;
        double r748244 = r748240 ? r748243 : r748234;
        return r748244;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.3
Target	0.4
Herbie	2.1

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

Derivation

1. Split input into 2 regimes

2. if (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < -inf.0 or 8.318321970151965e+263 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))

   1. Initial program 61.3

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

   2. Taylor expanded around inf 14.0

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

   if -inf.0 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < 8.318321970151965e+263

   1. Initial program 0.7

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 8.3183219701519654 \cdot 10^{263}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))