Average Error: 17.0 → 13.5
Time: 4.7s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.02232426222707281 \cdot 10^{93}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{elif}\;t \le 2.881100886802703 \cdot 10^{35}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.02232426222707281 \cdot 10^{93}:\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\

\mathbf{elif}\;t \le 2.881100886802703 \cdot 10^{35}:\\
\;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r711661 = x;
        double r711662 = y;
        double r711663 = z;
        double r711664 = r711662 * r711663;
        double r711665 = t;
        double r711666 = r711664 / r711665;
        double r711667 = r711661 + r711666;
        double r711668 = a;
        double r711669 = 1.0;
        double r711670 = r711668 + r711669;
        double r711671 = b;
        double r711672 = r711662 * r711671;
        double r711673 = r711672 / r711665;
        double r711674 = r711670 + r711673;
        double r711675 = r711667 / r711674;
        return r711675;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r711676 = t;
        double r711677 = -5.022324262227073e+93;
        bool r711678 = r711676 <= r711677;
        double r711679 = x;
        double r711680 = y;
        double r711681 = z;
        double r711682 = r711681 / r711676;
        double r711683 = r711680 * r711682;
        double r711684 = r711679 + r711683;
        double r711685 = a;
        double r711686 = 1.0;
        double r711687 = r711685 + r711686;
        double r711688 = 1.0;
        double r711689 = r711676 / r711680;
        double r711690 = b;
        double r711691 = r711689 / r711690;
        double r711692 = r711688 / r711691;
        double r711693 = r711687 + r711692;
        double r711694 = r711684 / r711693;
        double r711695 = 2.881100886802703e+35;
        bool r711696 = r711676 <= r711695;
        double r711697 = r711680 * r711681;
        double r711698 = r711688 / r711676;
        double r711699 = r711697 * r711698;
        double r711700 = r711679 + r711699;
        double r711701 = r711680 * r711690;
        double r711702 = r711676 / r711701;
        double r711703 = r711688 / r711702;
        double r711704 = r711687 + r711703;
        double r711705 = r711700 / r711704;
        double r711706 = r711676 / r711681;
        double r711707 = r711680 / r711706;
        double r711708 = r711679 + r711707;
        double r711709 = r711708 / r711693;
        double r711710 = r711696 ? r711705 : r711709;
        double r711711 = r711678 ? r711694 : r711710;
        return r711711;
}

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

Original17.0
Target13.6
Herbie13.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -5.022324262227073e+93

    1. Initial program 11.8

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

    3. Applied clear-num11.8

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

    5. Applied associate-/r*8.2

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

    7. Applied *-un-lft-identity8.2

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

    8. Applied times-frac2.3

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

    9. Simplified2.3

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

    if -5.022324262227073e+93 < t < 2.881100886802703e+35

    1. Initial program 20.4

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

    3. Applied clear-num20.5

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

    5. Applied div-inv20.5

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

    if 2.881100886802703e+35 < t

    1. Initial program 11.7

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

    3. Applied clear-num11.7

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

    5. Applied associate-/r*8.1

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

    7. Applied associate-/l*3.4

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

  4. Final simplification13.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.02232426222707281 \cdot 10^{93}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{elif}\;t \le 2.881100886802703 \cdot 10^{35}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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))))