Average Error: 16.6 → 15.0
Time: 4.1s
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 r964730 = x;
        double r964731 = y;
        double r964732 = z;
        double r964733 = r964731 * r964732;
        double r964734 = t;
        double r964735 = r964733 / r964734;
        double r964736 = r964730 + r964735;
        double r964737 = a;
        double r964738 = 1.0;
        double r964739 = r964737 + r964738;
        double r964740 = b;
        double r964741 = r964731 * r964740;
        double r964742 = r964741 / r964734;
        double r964743 = r964739 + r964742;
        double r964744 = r964736 / r964743;
        return r964744;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r964745 = t;
        double r964746 = -9.71592468019581e-24;
        bool r964747 = r964745 <= r964746;
        double r964748 = 3.552288465802439e-40;
        bool r964749 = r964745 <= r964748;
        double r964750 = !r964749;
        bool r964751 = r964747 || r964750;
        double r964752 = x;
        double r964753 = y;
        double r964754 = z;
        double r964755 = r964754 / r964745;
        double r964756 = r964753 * r964755;
        double r964757 = r964752 + r964756;
        double r964758 = a;
        double r964759 = 1.0;
        double r964760 = r964758 + r964759;
        double r964761 = b;
        double r964762 = r964753 * r964761;
        double r964763 = r964762 / r964745;
        double r964764 = r964760 + r964763;
        double r964765 = r964757 / r964764;
        double r964766 = 1.0;
        double r964767 = r964753 * r964754;
        double r964768 = r964745 / r964767;
        double r964769 = r964766 / r964768;
        double r964770 = r964752 + r964769;
        double r964771 = r964745 / r964762;
        double r964772 = r964766 / r964771;
        double r964773 = r964760 + r964772;
        double r964774 = r964770 / r964773;
        double r964775 = r964751 ? r964765 : r964774;
        return r964775;
}

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))))