Average Error: 16.6 → 15.0
Time: 10.7s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.71592468019581054 \cdot 10^{-24} \lor \neg \left(t \le 3.5522884658024391 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y \cdot z}}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.71592468019581054 \cdot 10^{-24} \lor \neg \left(t \le 3.5522884658024391 \cdot 10^{-40}\right):\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{t}{y \cdot z}}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1525 = x;
        double r1526 = y;
        double r1527 = z;
        double r1528 = r1526 * r1527;
        double r1529 = t;
        double r1530 = r1528 / r1529;
        double r1531 = r1525 + r1530;
        double r1532 = a;
        double r1533 = 1.0;
        double r1534 = r1532 + r1533;
        double r1535 = b;
        double r1536 = r1526 * r1535;
        double r1537 = r1536 / r1529;
        double r1538 = r1534 + r1537;
        double r1539 = r1531 / r1538;
        return r1539;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1540 = t;
        double r1541 = -9.71592468019581e-24;
        bool r1542 = r1540 <= r1541;
        double r1543 = 3.552288465802439e-40;
        bool r1544 = r1540 <= r1543;
        double r1545 = !r1544;
        bool r1546 = r1542 || r1545;
        double r1547 = x;
        double r1548 = y;
        double r1549 = z;
        double r1550 = r1549 / r1540;
        double r1551 = r1548 * r1550;
        double r1552 = r1547 + r1551;
        double r1553 = a;
        double r1554 = 1.0;
        double r1555 = r1553 + r1554;
        double r1556 = b;
        double r1557 = r1548 * r1556;
        double r1558 = r1557 / r1540;
        double r1559 = r1555 + r1558;
        double r1560 = r1552 / r1559;
        double r1561 = 1.0;
        double r1562 = r1548 * r1549;
        double r1563 = r1540 / r1562;
        double r1564 = r1561 / r1563;
        double r1565 = r1547 + r1564;
        double r1566 = r1540 / r1557;
        double r1567 = r1561 / r1566;
        double r1568 = r1555 + r1567;
        double r1569 = r1565 / r1568;
        double r1570 = r1546 ? r1560 : r1569;
        return r1570;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original16.6
Target13.4
Herbie15.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.71592468019581e-24 or 3.552288465802439e-40 < t

    1. Initial program 11.3

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity11.3

      \[\leadsto \frac{x + \frac{y \cdot z}{\color{blue}{1 \cdot t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    4. Applied times-frac8.4

      \[\leadsto \frac{x + \color{blue}{\frac{y}{1} \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    5. Simplified8.4

      \[\leadsto \frac{x + \color{blue}{y} \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    if -9.71592468019581e-24 < t < 3.552288465802439e-40

    1. Initial program 23.3

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    2. Using strategy rm

    3. Applied clear-num23.4

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{1}{\frac{t}{y \cdot b}}}}\]
    4. Using strategy rm

    5. Applied clear-num23.4

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{t}{y \cdot z}}}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification15.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.71592468019581054 \cdot 10^{-24} \lor \neg \left(t \le 3.5522884658024391 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y \cdot z}}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1) (/ (* y b) t))))