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

Average Error: 7.2 → 3.4

Time: 21.0s

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 r443952 = x;
        double r443953 = y;
        double r443954 = z;
        double r443955 = r443953 * r443954;
        double r443956 = r443955 - r443952;
        double r443957 = t;
        double r443958 = r443957 * r443954;
        double r443959 = r443958 - r443952;
        double r443960 = r443956 / r443959;
        double r443961 = r443952 + r443960;
        double r443962 = 1.0;
        double r443963 = r443952 + r443962;
        double r443964 = r443961 / r443963;
        return r443964;
}

↓

double f(double x, double y, double z, double t) {
        double r443965 = z;
        double r443966 = -7.150582175885459e+54;
        bool r443967 = r443965 <= r443966;
        double r443968 = 6.043915376694697e+86;
        bool r443969 = r443965 <= r443968;
        double r443970 = !r443969;
        bool r443971 = r443967 || r443970;
        double r443972 = x;
        double r443973 = y;
        double r443974 = t;
        double r443975 = r443973 / r443974;
        double r443976 = r443972 + r443975;
        double r443977 = 1.0;
        double r443978 = r443972 + r443977;
        double r443979 = r443976 / r443978;
        double r443980 = 1.0;
        double r443981 = r443974 * r443965;
        double r443982 = r443981 - r443972;
        double r443983 = r443973 * r443965;
        double r443984 = r443983 - r443972;
        double r443985 = r443982 / r443984;
        double r443986 = r443980 / r443985;
        double r443987 = r443972 + r443986;
        double r443988 = r443987 / r443978;
        double r443989 = r443971 ? r443979 : r443988;
        return r443989;
}

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)))