Average Error: 2.8 → 2.3
Time: 12.3s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 8.17808007950012565 \cdot 10^{41}:\\ \;\;\;\;x \cdot \frac{1}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \end{array}\]
\frac{x}{y - z \cdot t}
↓
\begin{array}{l}
\mathbf{if}\;x \le 8.17808007950012565 \cdot 10^{41}:\\
\;\;\;\;x \cdot \frac{1}{y - z \cdot t}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r880536 = x;
        double r880537 = y;
        double r880538 = z;
        double r880539 = t;
        double r880540 = r880538 * r880539;
        double r880541 = r880537 - r880540;
        double r880542 = r880536 / r880541;
        return r880542;
}
↓
double f(double x, double y, double z, double t) {
        double r880543 = x;
        double r880544 = 8.178080079500126e+41;
        bool r880545 = r880543 <= r880544;
        double r880546 = 1.0;
        double r880547 = y;
        double r880548 = z;
        double r880549 = t;
        double r880550 = r880548 * r880549;
        double r880551 = r880547 - r880550;
        double r880552 = r880546 / r880551;
        double r880553 = r880543 * r880552;
        double r880554 = r880547 / r880543;
        double r880555 = r880549 / r880543;
        double r880556 = r880548 * r880555;
        double r880557 = r880554 - r880556;
        double r880558 = r880546 / r880557;
        double r880559 = r880545 ? r880553 : r880558;
        return r880559;
}

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
Target1.9
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 8.178080079500126e+41

    1. Initial program 2.0

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

    3. Applied div-inv2.1

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

    if 8.178080079500126e+41 < x

    1. Initial program 5.9

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

    3. Applied clear-num6.1

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

    5. Applied div-sub6.1

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

    6. Simplified3.1

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 8.17808007950012565 \cdot 10^{41}:\\ \;\;\;\;x \cdot \frac{1}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - z \cdot \frac{t}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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))))