Average Error: 7.5 → 3.3
Time: 4.9s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\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}
double f(double x, double y, double z, double t) {
        double r671131 = x;
        double r671132 = y;
        double r671133 = z;
        double r671134 = r671132 * r671133;
        double r671135 = r671134 - r671131;
        double r671136 = t;
        double r671137 = r671136 * r671133;
        double r671138 = r671137 - r671131;
        double r671139 = r671135 / r671138;
        double r671140 = r671131 + r671139;
        double r671141 = 1.0;
        double r671142 = r671131 + r671141;
        double r671143 = r671140 / r671142;
        return r671143;
}
↓
double f(double x, double y, double z, double t) {
        double r671144 = z;
        double r671145 = -1.6579298446565844e+132;
        bool r671146 = r671144 <= r671145;
        double r671147 = 5.589683021273789e+76;
        bool r671148 = r671144 <= r671147;
        double r671149 = !r671148;
        bool r671150 = r671146 || r671149;
        double r671151 = x;
        double r671152 = y;
        double r671153 = t;
        double r671154 = r671152 / r671153;
        double r671155 = r671151 + r671154;
        double r671156 = 1.0;
        double r671157 = r671151 + r671156;
        double r671158 = r671155 / r671157;
        double r671159 = 1.0;
        double r671160 = r671153 * r671144;
        double r671161 = r671160 - r671151;
        double r671162 = r671152 * r671144;
        double r671163 = r671162 - r671151;
        double r671164 = r671161 / r671163;
        double r671165 = r671159 / r671164;
        double r671166 = r671151 + r671165;
        double r671167 = r671166 / r671157;
        double r671168 = r671150 ? r671158 : r671167;
        return r671168;
}

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

Original7.5
Target0.4
Herbie3.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.6579298446565844e+132 or 5.589683021273789e+76 < z

    1. Initial program 20.5

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

    2. Taylor expanded around inf 7.6

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

    if -1.6579298446565844e+132 < z < 5.589683021273789e+76

    1. Initial program 1.3

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

    3. Applied clear-num1.3

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.6579298446565844 \cdot 10^{132} \lor \neg \left(z \le 5.5896830212737893 \cdot 10^{76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +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)))