Average Error: 2.9 → 2.6
Time: 6.8s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 3.500414053322566554674071078271460628078 \cdot 10^{149} \lor \neg \left(x \le 3.253127234732810282842347103578009613163 \cdot 10^{245}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;x \le 3.500414053322566554674071078271460628078 \cdot 10^{149} \lor \neg \left(x \le 3.253127234732810282842347103578009613163 \cdot 10^{245}\right):\\
\;\;\;\;\frac{x}{y - z \cdot t}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r458179 = x;
        double r458180 = y;
        double r458181 = z;
        double r458182 = t;
        double r458183 = r458181 * r458182;
        double r458184 = r458180 - r458183;
        double r458185 = r458179 / r458184;
        return r458185;
}
↓
double f(double x, double y, double z, double t) {
        double r458186 = x;
        double r458187 = 3.5004140533225666e+149;
        bool r458188 = r458186 <= r458187;
        double r458189 = 3.2531272347328103e+245;
        bool r458190 = r458186 <= r458189;
        double r458191 = !r458190;
        bool r458192 = r458188 || r458191;
        double r458193 = y;
        double r458194 = z;
        double r458195 = t;
        double r458196 = r458194 * r458195;
        double r458197 = r458193 - r458196;
        double r458198 = r458186 / r458197;
        double r458199 = 1.0;
        double r458200 = r458193 / r458186;
        double r458201 = r458195 / r458186;
        double r458202 = r458201 * r458194;
        double r458203 = r458200 - r458202;
        double r458204 = r458199 / r458203;
        double r458205 = r458192 ? r458198 : r458204;
        return r458205;
}

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

Original2.9
Target1.6
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 3.5004140533225666e+149 or 3.2531272347328103e+245 < x

    1. Initial program 2.4

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

    if 3.5004140533225666e+149 < x < 3.2531272347328103e+245

    1. Initial program 8.4

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

    3. Applied clear-num8.6

      \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}}\]

    4. Simplified8.6

      \[\leadsto \frac{1}{\color{blue}{\frac{y - t \cdot z}{x}}}\]
    5. Using strategy rm

    6. Applied div-sub8.6

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} - \frac{t \cdot z}{x}}}\]

    7. Simplified4.5

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 3.500414053322566554674071078271460628078 \cdot 10^{149} \lor \neg \left(x \le 3.253127234732810282842347103578009613163 \cdot 10^{245}\right):\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.13783064348764444e131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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