Average Error: 16.5 → 12.8
Time: 14.3s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -11426198898.5786876678466796875:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \le 6.399239486311505375772837011137183856531 \cdot 10^{-56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{\frac{y}{t}}{\frac{1}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -11426198898.5786876678466796875:\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

\mathbf{elif}\;y \le 6.399239486311505375772837011137183856531 \cdot 10^{-56}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{\frac{y}{t}}{\frac{1}{b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r443128 = x;
        double r443129 = y;
        double r443130 = z;
        double r443131 = r443129 * r443130;
        double r443132 = t;
        double r443133 = r443131 / r443132;
        double r443134 = r443128 + r443133;
        double r443135 = a;
        double r443136 = 1.0;
        double r443137 = r443135 + r443136;
        double r443138 = b;
        double r443139 = r443129 * r443138;
        double r443140 = r443139 / r443132;
        double r443141 = r443137 + r443140;
        double r443142 = r443134 / r443141;
        return r443142;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r443143 = y;
        double r443144 = -11426198898.578688;
        bool r443145 = r443143 <= r443144;
        double r443146 = x;
        double r443147 = z;
        double r443148 = t;
        double r443149 = r443147 / r443148;
        double r443150 = r443143 * r443149;
        double r443151 = r443146 + r443150;
        double r443152 = a;
        double r443153 = 1.0;
        double r443154 = r443152 + r443153;
        double r443155 = b;
        double r443156 = r443155 / r443148;
        double r443157 = r443143 * r443156;
        double r443158 = r443154 + r443157;
        double r443159 = r443151 / r443158;
        double r443160 = 6.399239486311505e-56;
        bool r443161 = r443143 <= r443160;
        double r443162 = r443143 * r443147;
        double r443163 = r443162 / r443148;
        double r443164 = r443146 + r443163;
        double r443165 = r443143 / r443148;
        double r443166 = 1.0;
        double r443167 = r443166 / r443155;
        double r443168 = r443165 / r443167;
        double r443169 = r443154 + r443168;
        double r443170 = r443164 / r443169;
        double r443171 = r443148 / r443147;
        double r443172 = r443143 / r443171;
        double r443173 = r443146 + r443172;
        double r443174 = r443148 / r443155;
        double r443175 = r443143 / r443174;
        double r443176 = r443154 + r443175;
        double r443177 = r443173 / r443176;
        double r443178 = r443161 ? r443170 : r443177;
        double r443179 = r443145 ? r443159 : r443178;
        return r443179;
}

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

Original16.5
Target13.5
Herbie12.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -11426198898.578688

    1. Initial program 30.6

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

    3. Applied associate-/l*27.9

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

    5. Applied *-un-lft-identity27.9

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

    6. Applied times-frac23.2

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

    7. Simplified23.2

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

    9. Applied div-inv23.2

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

    10. Simplified23.2

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

    if -11426198898.578688 < y < 6.399239486311505e-56

    1. Initial program 3.7

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

    3. Applied associate-/l*8.0

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

    5. Applied div-inv8.0

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

    6. Applied associate-/r*3.7

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

    if 6.399239486311505e-56 < y

    1. Initial program 26.3

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

    3. Applied associate-/l*23.5

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

    5. Applied associate-/l*19.5

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

  4. Final simplification12.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -11426198898.5786876678466796875:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \le 6.399239486311505375772837011137183856531 \cdot 10^{-56}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{\frac{y}{t}}{\frac{1}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))