Average Error: 2.9 → 0.8
Time: 13.2s
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 r591537 = x;
        double r591538 = y;
        double r591539 = z;
        double r591540 = t;
        double r591541 = r591539 * r591540;
        double r591542 = r591538 - r591541;
        double r591543 = r591537 / r591542;
        return r591543;
}
↓
double f(double x, double y, double z, double t) {
        double r591544 = z;
        double r591545 = t;
        double r591546 = r591544 * r591545;
        double r591547 = -inf.0;
        bool r591548 = r591546 <= r591547;
        double r591549 = 1.8704379532132535e+286;
        bool r591550 = r591546 <= r591549;
        double r591551 = !r591550;
        bool r591552 = r591548 || r591551;
        double r591553 = 1.0;
        double r591554 = y;
        double r591555 = x;
        double r591556 = r591554 / r591555;
        double r591557 = r591544 / r591555;
        double r591558 = r591557 * r591545;
        double r591559 = r591556 - r591558;
        double r591560 = r591553 / r591559;
        double r591561 = r591554 - r591546;
        double r591562 = r591555 / r591561;
        double r591563 = r591552 ? r591560 : r591562;
        return r591563;
}

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))))