Average Error: 16.9 → 15.0
Time: 5.5s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7447485.11014015507:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{elif}\;y \le 3.23958624363235925 \cdot 10^{-134}:\\ \;\;\;\;\left(x + \frac{1}{\frac{t}{y \cdot z}}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7447485.11014015507:\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\

\mathbf{elif}\;y \le 3.23958624363235925 \cdot 10^{-134}:\\
\;\;\;\;\left(x + \frac{1}{\frac{t}{y \cdot z}}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r742533 = x;
        double r742534 = y;
        double r742535 = z;
        double r742536 = r742534 * r742535;
        double r742537 = t;
        double r742538 = r742536 / r742537;
        double r742539 = r742533 + r742538;
        double r742540 = a;
        double r742541 = 1.0;
        double r742542 = r742540 + r742541;
        double r742543 = b;
        double r742544 = r742534 * r742543;
        double r742545 = r742544 / r742537;
        double r742546 = r742542 + r742545;
        double r742547 = r742539 / r742546;
        return r742547;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r742548 = y;
        double r742549 = -7447485.110140155;
        bool r742550 = r742548 <= r742549;
        double r742551 = x;
        double r742552 = z;
        double r742553 = t;
        double r742554 = r742552 / r742553;
        double r742555 = r742548 * r742554;
        double r742556 = r742551 + r742555;
        double r742557 = a;
        double r742558 = 1.0;
        double r742559 = r742557 + r742558;
        double r742560 = cbrt(r742553);
        double r742561 = r742560 * r742560;
        double r742562 = r742548 / r742561;
        double r742563 = b;
        double r742564 = r742563 / r742560;
        double r742565 = r742562 * r742564;
        double r742566 = r742559 + r742565;
        double r742567 = r742556 / r742566;
        double r742568 = 3.2395862436323592e-134;
        bool r742569 = r742548 <= r742568;
        double r742570 = 1.0;
        double r742571 = r742548 * r742552;
        double r742572 = r742553 / r742571;
        double r742573 = r742570 / r742572;
        double r742574 = r742551 + r742573;
        double r742575 = r742548 * r742563;
        double r742576 = r742575 / r742553;
        double r742577 = r742559 + r742576;
        double r742578 = r742570 / r742577;
        double r742579 = r742574 * r742578;
        double r742580 = r742553 / r742552;
        double r742581 = r742548 / r742580;
        double r742582 = r742551 + r742581;
        double r742583 = r742582 / r742577;
        double r742584 = r742569 ? r742579 : r742583;
        double r742585 = r742550 ? r742567 : r742584;
        return r742585;
}

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

Original16.9
Target13.6
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 3 regimes

  2. if y < -7447485.110140155

    1. Initial program 31.0

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

    3. Applied add-cube-cbrt31.2

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}}\]

    4. Applied times-frac29.5

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity29.5

      \[\leadsto \frac{x + \frac{y \cdot z}{\color{blue}{1 \cdot t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\]

    7. Applied times-frac24.8

      \[\leadsto \frac{x + \color{blue}{\frac{y}{1} \cdot \frac{z}{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\]

    8. Simplified24.8

      \[\leadsto \frac{x + \color{blue}{y} \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\]

    if -7447485.110140155 < y < 3.2395862436323592e-134

    1. Initial program 3.4

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

    3. Applied clear-num3.4

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

    5. Applied div-inv3.5

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

    if 3.2395862436323592e-134 < y

    1. Initial program 22.6

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

    3. Applied associate-/l*21.5

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

  4. Final simplification15.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7447485.11014015507:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{elif}\;y \le 3.23958624363235925 \cdot 10^{-134}:\\ \;\;\;\;\left(x + \frac{1}{\frac{t}{y \cdot z}}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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))))