Average Error: 2.7 → 1.6
Time: 8.4s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y - z \cdot t = -\infty:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;y - z \cdot t = -\infty:\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r470328 = x;
        double r470329 = y;
        double r470330 = z;
        double r470331 = t;
        double r470332 = r470330 * r470331;
        double r470333 = r470329 - r470332;
        double r470334 = r470328 / r470333;
        return r470334;
}
↓
double f(double x, double y, double z, double t) {
        double r470335 = y;
        double r470336 = z;
        double r470337 = t;
        double r470338 = r470336 * r470337;
        double r470339 = r470335 - r470338;
        double r470340 = -inf.0;
        bool r470341 = r470339 <= r470340;
        double r470342 = 1.0;
        double r470343 = x;
        double r470344 = r470335 / r470343;
        double r470345 = r470337 / r470343;
        double r470346 = r470345 * r470336;
        double r470347 = r470344 - r470346;
        double r470348 = r470342 / r470347;
        double r470349 = r470343 / r470339;
        double r470350 = r470341 ? r470348 : r470349;
        return r470350;
}

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 (- y (* z t)) < -inf.0

    1. Initial program 21.0

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

    3. Applied clear-num21.0

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

    4. Simplified21.0

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

    6. Applied div-sub23.8

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

    7. Simplified3.7

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

    if -inf.0 < (- y (* z t))

    1. Initial program 1.4

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \cdot t = -\infty:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))))