Average Error: 2.8 → 1.8
Time: 14.4s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot t \le 2.01586935138895613 \cdot 10^{253}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot t \le 2.01586935138895613 \cdot 10^{253}:\\
\;\;\;\;\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 r478778 = x;
        double r478779 = y;
        double r478780 = z;
        double r478781 = t;
        double r478782 = r478780 * r478781;
        double r478783 = r478779 - r478782;
        double r478784 = r478778 / r478783;
        return r478784;
}
↓
double f(double x, double y, double z, double t) {
        double r478785 = z;
        double r478786 = t;
        double r478787 = r478785 * r478786;
        double r478788 = 2.015869351388956e+253;
        bool r478789 = r478787 <= r478788;
        double r478790 = x;
        double r478791 = y;
        double r478792 = r478791 - r478787;
        double r478793 = r478790 / r478792;
        double r478794 = 1.0;
        double r478795 = r478791 / r478790;
        double r478796 = r478786 / r478790;
        double r478797 = r478796 * r478785;
        double r478798 = r478795 - r478797;
        double r478799 = r478794 / r478798;
        double r478800 = r478789 ? r478793 : r478799;
        return r478800;
}

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

Original2.8
Target1.8
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z t) < 2.015869351388956e+253

    1. Initial program 1.5

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

    if 2.015869351388956e+253 < (* z t)

    1. Initial program 15.3

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

    3. Applied clear-num15.5

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

    4. Simplified15.5

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

    6. Applied div-sub19.7

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

    7. Simplified4.9

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \le 2.01586935138895613 \cdot 10^{253}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{x} \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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