Average Error: 2.9 → 0.8
Time: 13.6s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.870437953213253477696033415768704282134 \cdot 10^{286}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.870437953213253477696033415768704282134 \cdot 10^{286}\right):\\
\;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r543588 = x;
        double r543589 = y;
        double r543590 = z;
        double r543591 = t;
        double r543592 = r543590 * r543591;
        double r543593 = r543589 - r543592;
        double r543594 = r543588 / r543593;
        return r543594;
}
↓
double f(double x, double y, double z, double t) {
        double r543595 = z;
        double r543596 = t;
        double r543597 = r543595 * r543596;
        double r543598 = -inf.0;
        bool r543599 = r543597 <= r543598;
        double r543600 = 1.8704379532132535e+286;
        bool r543601 = r543597 <= r543600;
        double r543602 = !r543601;
        bool r543603 = r543599 || r543602;
        double r543604 = 1.0;
        double r543605 = y;
        double r543606 = x;
        double r543607 = r543605 / r543606;
        double r543608 = r543595 / r543606;
        double r543609 = r543608 * r543596;
        double r543610 = r543607 - r543609;
        double r543611 = r543604 / r543610;
        double r543612 = r543605 - r543597;
        double r543613 = r543606 / r543612;
        double r543614 = r543603 ? r543611 : r543613;
        return r543614;
}

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
Target1.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < -inf.0 or 1.8704379532132535e+286 < (* z t)

    1. Initial program 20.1

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

    3. Applied clear-num20.0

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

    5. Applied div-sub24.0

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

    6. Simplified5.0

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

    if -inf.0 < (* z t) < 1.8704379532132535e+286

    1. Initial program 0.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t = -\infty \lor \neg \left(z \cdot t \le 1.870437953213253477696033415768704282134 \cdot 10^{286}\right):\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

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