Average Error: 16.4 → 15.9
Time: 12.8s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -954416122714153287680:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + y \cdot \frac{b}{t}}{x + y \cdot \frac{z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -954416122714153287680:\\
\;\;\;\;\frac{1}{\frac{\left(a + 1\right) + y \cdot \frac{b}{t}}{x + y \cdot \frac{z}{t}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{\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 r441114 = x;
        double r441115 = y;
        double r441116 = z;
        double r441117 = r441115 * r441116;
        double r441118 = t;
        double r441119 = r441117 / r441118;
        double r441120 = r441114 + r441119;
        double r441121 = a;
        double r441122 = 1.0;
        double r441123 = r441121 + r441122;
        double r441124 = b;
        double r441125 = r441115 * r441124;
        double r441126 = r441125 / r441118;
        double r441127 = r441123 + r441126;
        double r441128 = r441120 / r441127;
        return r441128;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r441129 = y;
        double r441130 = -9.544161227141533e+20;
        bool r441131 = r441129 <= r441130;
        double r441132 = 1.0;
        double r441133 = a;
        double r441134 = 1.0;
        double r441135 = r441133 + r441134;
        double r441136 = b;
        double r441137 = t;
        double r441138 = r441136 / r441137;
        double r441139 = r441129 * r441138;
        double r441140 = r441135 + r441139;
        double r441141 = x;
        double r441142 = z;
        double r441143 = r441142 / r441137;
        double r441144 = r441129 * r441143;
        double r441145 = r441141 + r441144;
        double r441146 = r441140 / r441145;
        double r441147 = r441132 / r441146;
        double r441148 = r441137 / r441142;
        double r441149 = r441148 / r441129;
        double r441150 = r441132 / r441149;
        double r441151 = r441141 + r441150;
        double r441152 = r441129 * r441136;
        double r441153 = r441152 / r441137;
        double r441154 = r441135 + r441153;
        double r441155 = r441151 / r441154;
        double r441156 = r441131 ? r441147 : r441155;
        return r441156;
}

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

Original16.4
Target13.2
Herbie15.9
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -9.544161227141533e+20

    1. Initial program 30.0

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

    3. Applied associate-/l*26.3

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

    5. Applied *-un-lft-identity26.3

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

    6. Applied times-frac21.7

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

    7. Simplified21.7

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

    9. Applied div-inv21.7

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

    10. Simplified21.6

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

    12. Applied clear-num21.8

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

    if -9.544161227141533e+20 < y

    1. Initial program 12.4

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

    3. Applied associate-/l*14.1

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

    5. Applied clear-num14.1

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

  4. Final simplification15.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -954416122714153287680:\\ \;\;\;\;\frac{1}{\frac{\left(a + 1\right) + y \cdot \frac{b}{t}}{x + y \cdot \frac{z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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))))