Average Error: 16.0 → 15.1
Time: 4.8s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \le 2.3906737161539997 \cdot 10^{274}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \le 2.3906737161539997 \cdot 10^{274}:\\
\;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\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 r531857 = x;
        double r531858 = y;
        double r531859 = z;
        double r531860 = r531858 * r531859;
        double r531861 = t;
        double r531862 = r531860 / r531861;
        double r531863 = r531857 + r531862;
        double r531864 = a;
        double r531865 = 1.0;
        double r531866 = r531864 + r531865;
        double r531867 = b;
        double r531868 = r531858 * r531867;
        double r531869 = r531868 / r531861;
        double r531870 = r531866 + r531869;
        double r531871 = r531863 / r531870;
        return r531871;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r531872 = x;
        double r531873 = y;
        double r531874 = z;
        double r531875 = r531873 * r531874;
        double r531876 = t;
        double r531877 = r531875 / r531876;
        double r531878 = r531872 + r531877;
        double r531879 = a;
        double r531880 = 1.0;
        double r531881 = r531879 + r531880;
        double r531882 = b;
        double r531883 = r531873 * r531882;
        double r531884 = r531883 / r531876;
        double r531885 = r531881 + r531884;
        double r531886 = r531878 / r531885;
        double r531887 = 2.3906737161539997e+274;
        bool r531888 = r531886 <= r531887;
        double r531889 = 1.0;
        double r531890 = r531889 / r531876;
        double r531891 = r531875 * r531890;
        double r531892 = r531872 + r531891;
        double r531893 = r531892 / r531885;
        double r531894 = r531876 / r531874;
        double r531895 = r531873 / r531894;
        double r531896 = r531872 + r531895;
        double r531897 = r531896 / r531885;
        double r531898 = r531888 ? r531893 : r531897;
        return r531898;
}

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

Original16.0
Target13.3
Herbie15.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) < 2.3906737161539997e+274

    1. Initial program 8.6

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

    3. Applied div-inv8.6

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

    if 2.3906737161539997e+274 < (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

    1. Initial program 59.9

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

    3. Applied associate-/l*53.6

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

  4. Final simplification15.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \le 2.3906737161539997 \cdot 10^{274}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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))))