Average Error: 7.1 → 3.5
Time: 14.9s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.114676354067779218146434366254066316571 \cdot 10^{166} \lor \neg \left(z \le 6.158470310373082749921667144051634464626 \cdot 10^{144}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.114676354067779218146434366254066316571 \cdot 10^{166} \lor \neg \left(z \le 6.158470310373082749921667144051634464626 \cdot 10^{144}\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}
double f(double x, double y, double z, double t) {
        double r592056 = x;
        double r592057 = y;
        double r592058 = z;
        double r592059 = r592057 * r592058;
        double r592060 = r592059 - r592056;
        double r592061 = t;
        double r592062 = r592061 * r592058;
        double r592063 = r592062 - r592056;
        double r592064 = r592060 / r592063;
        double r592065 = r592056 + r592064;
        double r592066 = 1.0;
        double r592067 = r592056 + r592066;
        double r592068 = r592065 / r592067;
        return r592068;
}
↓
double f(double x, double y, double z, double t) {
        double r592069 = z;
        double r592070 = -8.114676354067779e+166;
        bool r592071 = r592069 <= r592070;
        double r592072 = 6.158470310373083e+144;
        bool r592073 = r592069 <= r592072;
        double r592074 = !r592073;
        bool r592075 = r592071 || r592074;
        double r592076 = x;
        double r592077 = y;
        double r592078 = t;
        double r592079 = r592077 / r592078;
        double r592080 = r592076 + r592079;
        double r592081 = 1.0;
        double r592082 = r592076 + r592081;
        double r592083 = r592080 / r592082;
        double r592084 = r592077 * r592069;
        double r592085 = r592084 - r592076;
        double r592086 = r592078 * r592069;
        double r592087 = r592086 - r592076;
        double r592088 = r592085 / r592087;
        double r592089 = r592076 + r592088;
        double r592090 = r592089 / r592082;
        double r592091 = r592075 ? r592083 : r592090;
        return r592091;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.1
Target0.2
Herbie3.5
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.114676354067779e+166 or 6.158470310373083e+144 < z

    1. Initial program 21.5

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

    2. Taylor expanded around inf 6.9

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

    if -8.114676354067779e+166 < z < 6.158470310373083e+144

    1. Initial program 2.4

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.114676354067779218146434366254066316571 \cdot 10^{166} \lor \neg \left(z \le 6.158470310373082749921667144051634464626 \cdot 10^{144}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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)))