Average Error: 2.7 → 1.6
Time: 7.8s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le 2.100739535547299830719442701131869475522 \cdot 10^{286}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le 2.100739535547299830719442701131869475522 \cdot 10^{286}:\\
\;\;\;\;\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 r570248 = x;
        double r570249 = y;
        double r570250 = z;
        double r570251 = t;
        double r570252 = r570250 * r570251;
        double r570253 = r570249 - r570252;
        double r570254 = r570248 / r570253;
        return r570254;
}
↓
double f(double x, double y, double z, double t) {
        double r570255 = z;
        double r570256 = t;
        double r570257 = r570255 * r570256;
        double r570258 = 2.1007395355473e+286;
        bool r570259 = r570257 <= r570258;
        double r570260 = x;
        double r570261 = y;
        double r570262 = r570261 - r570257;
        double r570263 = r570260 / r570262;
        double r570264 = 1.0;
        double r570265 = r570261 / r570260;
        double r570266 = r570256 / r570260;
        double r570267 = r570266 * r570255;
        double r570268 = r570265 - r570267;
        double r570269 = r570264 / r570268;
        double r570270 = r570259 ? r570263 : r570269;
        return r570270;
}

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

Original2.7
Target1.6
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < 2.1007395355473e+286

    1. Initial program 1.4

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

    if 2.1007395355473e+286 < (* z t)

    1. Initial program 18.1

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

    3. Applied clear-num18.1

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

    4. Simplified18.1

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

    6. Applied div-sub21.3

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

    7. Simplified4.0

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le 2.100739535547299830719442701131869475522 \cdot 10^{286}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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))))