Average Error: 16.4 → 15.9
Time: 12.0s
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 r482654 = x;
        double r482655 = y;
        double r482656 = z;
        double r482657 = r482655 * r482656;
        double r482658 = t;
        double r482659 = r482657 / r482658;
        double r482660 = r482654 + r482659;
        double r482661 = a;
        double r482662 = 1.0;
        double r482663 = r482661 + r482662;
        double r482664 = b;
        double r482665 = r482655 * r482664;
        double r482666 = r482665 / r482658;
        double r482667 = r482663 + r482666;
        double r482668 = r482660 / r482667;
        return r482668;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r482669 = y;
        double r482670 = -9.544161227141533e+20;
        bool r482671 = r482669 <= r482670;
        double r482672 = 1.0;
        double r482673 = a;
        double r482674 = 1.0;
        double r482675 = r482673 + r482674;
        double r482676 = b;
        double r482677 = t;
        double r482678 = r482676 / r482677;
        double r482679 = r482669 * r482678;
        double r482680 = r482675 + r482679;
        double r482681 = x;
        double r482682 = z;
        double r482683 = r482682 / r482677;
        double r482684 = r482669 * r482683;
        double r482685 = r482681 + r482684;
        double r482686 = r482680 / r482685;
        double r482687 = r482672 / r482686;
        double r482688 = r482677 / r482682;
        double r482689 = r482688 / r482669;
        double r482690 = r482672 / r482689;
        double r482691 = r482681 + r482690;
        double r482692 = r482669 * r482676;
        double r482693 = r482692 / r482677;
        double r482694 = r482675 + r482693;
        double r482695 = r482691 / r482694;
        double r482696 = r482671 ? r482687 : r482695;
        return r482696;
}

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))))