Average Error: 17.2 → 15.6
Time: 26.1s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.04643155897004219 \cdot 10^{24}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{elif}\;y \le 5.7911477760190765 \cdot 10^{45}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{b}{t} \cdot y + \left(a + 1\right)}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.04643155897004219 \cdot 10^{24}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\

\mathbf{elif}\;y \le 5.7911477760190765 \cdot 10^{45}:\\
\;\;\;\;\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 \cdot z}{t}}{\frac{b}{t} \cdot y + \left(a + 1\right)}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r528950 = x;
        double r528951 = y;
        double r528952 = z;
        double r528953 = r528951 * r528952;
        double r528954 = t;
        double r528955 = r528953 / r528954;
        double r528956 = r528950 + r528955;
        double r528957 = a;
        double r528958 = 1.0;
        double r528959 = r528957 + r528958;
        double r528960 = b;
        double r528961 = r528951 * r528960;
        double r528962 = r528961 / r528954;
        double r528963 = r528959 + r528962;
        double r528964 = r528956 / r528963;
        return r528964;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r528965 = y;
        double r528966 = -1.0464315589700422e+24;
        bool r528967 = r528965 <= r528966;
        double r528968 = x;
        double r528969 = t;
        double r528970 = z;
        double r528971 = r528969 / r528970;
        double r528972 = r528965 / r528971;
        double r528973 = r528968 + r528972;
        double r528974 = a;
        double r528975 = 1.0;
        double r528976 = r528974 + r528975;
        double r528977 = b;
        double r528978 = r528965 * r528977;
        double r528979 = 1.0;
        double r528980 = r528979 / r528969;
        double r528981 = r528978 * r528980;
        double r528982 = r528976 + r528981;
        double r528983 = r528973 / r528982;
        double r528984 = 5.791147776019076e+45;
        bool r528985 = r528965 <= r528984;
        double r528986 = r528965 * r528970;
        double r528987 = r528986 * r528980;
        double r528988 = r528968 + r528987;
        double r528989 = r528978 / r528969;
        double r528990 = r528976 + r528989;
        double r528991 = r528988 / r528990;
        double r528992 = r528986 / r528969;
        double r528993 = r528968 + r528992;
        double r528994 = r528977 / r528969;
        double r528995 = r528994 * r528965;
        double r528996 = r528995 + r528976;
        double r528997 = r528993 / r528996;
        double r528998 = r528985 ? r528991 : r528997;
        double r528999 = r528967 ? r528983 : r528998;
        return r528999;
}

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

Original17.2
Target13.7
Herbie15.6
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.0464315589700422e+24

    1. Initial program 32.1

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

    3. Applied div-inv32.1

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

    5. Applied associate-/l*28.3

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

    if -1.0464315589700422e+24 < y < 5.791147776019076e+45

    1. Initial program 5.1

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

    3. Applied div-inv5.1

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

    if 5.791147776019076e+45 < y

    1. Initial program 34.1

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

    3. Applied div-inv34.1

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

    5. Applied pow134.1

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

    6. Applied pow134.1

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

    7. Applied pow134.1

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

    8. Applied pow-prod-down34.1

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

    9. Applied pow-prod-down34.1

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

    10. Simplified30.3

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

  4. Final simplification15.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.04643155897004219 \cdot 10^{24}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{elif}\;y \le 5.7911477760190765 \cdot 10^{45}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{b}{t} \cdot y + \left(a + 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))