Average Error: 16.6 → 12.8
Time: 8.5s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\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 r819947 = x;
        double r819948 = y;
        double r819949 = z;
        double r819950 = r819948 * r819949;
        double r819951 = t;
        double r819952 = r819950 / r819951;
        double r819953 = r819947 + r819952;
        double r819954 = a;
        double r819955 = 1.0;
        double r819956 = r819954 + r819955;
        double r819957 = b;
        double r819958 = r819948 * r819957;
        double r819959 = r819958 / r819951;
        double r819960 = r819956 + r819959;
        double r819961 = r819953 / r819960;
        return r819961;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r819962 = t;
        double r819963 = -2.5546346162075872e+39;
        bool r819964 = r819962 <= r819963;
        double r819965 = 2.1879920080466582e+39;
        bool r819966 = r819962 <= r819965;
        double r819967 = !r819966;
        bool r819968 = r819964 || r819967;
        double r819969 = x;
        double r819970 = y;
        double r819971 = z;
        double r819972 = r819971 / r819962;
        double r819973 = r819970 * r819972;
        double r819974 = r819969 + r819973;
        double r819975 = a;
        double r819976 = 1.0;
        double r819977 = r819975 + r819976;
        double r819978 = 1.0;
        double r819979 = r819962 / r819970;
        double r819980 = b;
        double r819981 = r819979 / r819980;
        double r819982 = r819978 / r819981;
        double r819983 = r819977 + r819982;
        double r819984 = r819974 / r819983;
        double r819985 = r819970 * r819971;
        double r819986 = r819985 / r819962;
        double r819987 = r819969 + r819986;
        double r819988 = r819970 * r819980;
        double r819989 = r819962 / r819988;
        double r819990 = r819978 / r819989;
        double r819991 = r819977 + r819990;
        double r819992 = r819987 / r819991;
        double r819993 = r819968 ? r819984 : r819992;
        return r819993;
}

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
Target13.1
Herbie12.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.5546346162075872e+39 or 2.1879920080466582e+39 < 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*8.6

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

    7. Applied *-un-lft-identity8.6

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

    8. Applied times-frac3.4

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

    9. Simplified3.4

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

    if -2.5546346162075872e+39 < t < 2.1879920080466582e+39

    1. Initial program 20.7

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

    3. Applied clear-num20.7

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

  4. Final simplification12.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))))