Average Error: 16.3 → 12.5
Time: 24.1s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -15.16109420821437225868066889233887195587:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4597803625745355781306336193547547443200:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + \frac{y \cdot b}{t}}{x + \frac{y \cdot z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -15.16109420821437225868066889233887195587:\\
\;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\

\mathbf{elif}\;t \le 4597803625745355781306336193547547443200:\\
\;\;\;\;\frac{1}{\frac{\left(a + 1\right) + \frac{y \cdot b}{t}}{x + \frac{y \cdot z}{t}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r117559987 = x;
        double r117559988 = y;
        double r117559989 = z;
        double r117559990 = r117559988 * r117559989;
        double r117559991 = t;
        double r117559992 = r117559990 / r117559991;
        double r117559993 = r117559987 + r117559992;
        double r117559994 = a;
        double r117559995 = 1.0;
        double r117559996 = r117559994 + r117559995;
        double r117559997 = b;
        double r117559998 = r117559988 * r117559997;
        double r117559999 = r117559998 / r117559991;
        double r117560000 = r117559996 + r117559999;
        double r117560001 = r117559993 / r117560000;
        return r117560001;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r117560002 = t;
        double r117560003 = -15.161094208214372;
        bool r117560004 = r117560002 <= r117560003;
        double r117560005 = x;
        double r117560006 = y;
        double r117560007 = cbrt(r117560002);
        double r117560008 = r117560007 * r117560007;
        double r117560009 = r117560006 / r117560008;
        double r117560010 = z;
        double r117560011 = r117560010 / r117560007;
        double r117560012 = r117560009 * r117560011;
        double r117560013 = r117560005 + r117560012;
        double r117560014 = a;
        double r117560015 = 1.0;
        double r117560016 = r117560014 + r117560015;
        double r117560017 = b;
        double r117560018 = r117560017 / r117560007;
        double r117560019 = r117560009 * r117560018;
        double r117560020 = r117560016 + r117560019;
        double r117560021 = r117560013 / r117560020;
        double r117560022 = 4.597803625745356e+39;
        bool r117560023 = r117560002 <= r117560022;
        double r117560024 = 1.0;
        double r117560025 = r117560006 * r117560017;
        double r117560026 = r117560025 / r117560002;
        double r117560027 = r117560016 + r117560026;
        double r117560028 = r117560006 * r117560010;
        double r117560029 = r117560028 / r117560002;
        double r117560030 = r117560005 + r117560029;
        double r117560031 = r117560027 / r117560030;
        double r117560032 = r117560024 / r117560031;
        double r117560033 = r117560023 ? r117560032 : r117560021;
        double r117560034 = r117560004 ? r117560021 : r117560033;
        return r117560034;
}

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

Original16.3
Target12.9
Herbie12.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -15.161094208214372 or 4.597803625745356e+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 add-cube-cbrt11.9

      \[\leadsto \frac{x + \frac{y \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    4. Applied times-frac8.1

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt8.1

      \[\leadsto \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y \cdot b}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}}\]

    7. Applied times-frac3.6

      \[\leadsto \frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}}\]

    if -15.161094208214372 < t < 4.597803625745356e+39

    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

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

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -15.16109420821437225868066889233887195587:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4597803625745355781306336193547547443200:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + \frac{y \cdot b}{t}}{x + \frac{y \cdot z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}}{\left(a + 1\right) + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{b}{\sqrt[3]{t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(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))))