Average Error: 3.0 → 1.9
Time: 14.5s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t = -\infty:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t = -\infty:\\
\;\;\;\;\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 r570545 = x;
        double r570546 = y;
        double r570547 = z;
        double r570548 = t;
        double r570549 = r570547 * r570548;
        double r570550 = r570546 - r570549;
        double r570551 = r570545 / r570550;
        return r570551;
}
↓
double f(double x, double y, double z, double t) {
        double r570552 = z;
        double r570553 = t;
        double r570554 = r570552 * r570553;
        double r570555 = -inf.0;
        bool r570556 = r570554 <= r570555;
        double r570557 = 1.0;
        double r570558 = y;
        double r570559 = x;
        double r570560 = r570558 / r570559;
        double r570561 = r570552 / r570559;
        double r570562 = r570561 * r570553;
        double r570563 = r570560 - r570562;
        double r570564 = r570557 / r570563;
        double r570565 = r570558 - r570554;
        double r570566 = r570559 / r570565;
        double r570567 = r570556 ? r570564 : r570566;
        return r570567;
}

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

Original3.0
Target1.7
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.137830643487644440407921345820165445823 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

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

    1. Initial program 20.9

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

    3. Applied clear-num20.9

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

    5. Applied div-sub24.4

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

    6. Simplified4.3

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

    if -inf.0 < (* z t)

    1. Initial program 1.7

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

  4. Final simplification1.9

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

Reproduce

herbie shell --seed 2019303 
(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))))