Average Error: 16.8 → 13.9
Time: 15.7s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1453.204980965323557029478251934051513672:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \le 7.363181675657233677189530241484786519983 \cdot 10^{-181}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1453.204980965323557029478251934051513672:\\
\;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\

\mathbf{elif}\;t \le 7.363181675657233677189530241484786519983 \cdot 10^{-181}:\\
\;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\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 r49405471 = x;
        double r49405472 = y;
        double r49405473 = z;
        double r49405474 = r49405472 * r49405473;
        double r49405475 = t;
        double r49405476 = r49405474 / r49405475;
        double r49405477 = r49405471 + r49405476;
        double r49405478 = a;
        double r49405479 = 1.0;
        double r49405480 = r49405478 + r49405479;
        double r49405481 = b;
        double r49405482 = r49405472 * r49405481;
        double r49405483 = r49405482 / r49405475;
        double r49405484 = r49405480 + r49405483;
        double r49405485 = r49405477 / r49405484;
        return r49405485;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r49405486 = t;
        double r49405487 = -1453.2049809653236;
        bool r49405488 = r49405486 <= r49405487;
        double r49405489 = x;
        double r49405490 = y;
        double r49405491 = r49405490 / r49405486;
        double r49405492 = z;
        double r49405493 = r49405491 * r49405492;
        double r49405494 = r49405489 + r49405493;
        double r49405495 = a;
        double r49405496 = 1.0;
        double r49405497 = r49405495 + r49405496;
        double r49405498 = b;
        double r49405499 = r49405498 / r49405486;
        double r49405500 = r49405490 * r49405499;
        double r49405501 = r49405497 + r49405500;
        double r49405502 = r49405494 / r49405501;
        double r49405503 = 7.363181675657234e-181;
        bool r49405504 = r49405486 <= r49405503;
        double r49405505 = r49405490 * r49405492;
        double r49405506 = r49405505 / r49405486;
        double r49405507 = r49405489 + r49405506;
        double r49405508 = 1.0;
        double r49405509 = r49405490 * r49405498;
        double r49405510 = r49405509 / r49405486;
        double r49405511 = r49405497 + r49405510;
        double r49405512 = r49405508 / r49405511;
        double r49405513 = r49405507 * r49405512;
        double r49405514 = r49405492 / r49405486;
        double r49405515 = r49405490 * r49405514;
        double r49405516 = r49405489 + r49405515;
        double r49405517 = r49405486 / r49405498;
        double r49405518 = r49405490 / r49405517;
        double r49405519 = r49405497 + r49405518;
        double r49405520 = r49405516 / r49405519;
        double r49405521 = r49405504 ? r49405513 : r49405520;
        double r49405522 = r49405488 ? r49405502 : r49405521;
        return r49405522;
}

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

Original16.8
Target13.2
Herbie13.9
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1453.2049809653236

    1. Initial program 11.1

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

    3. Applied associate-/l*8.4

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

    5. Applied associate-/r/8.5

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

    7. Applied *-un-lft-identity8.5

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

    8. Applied times-frac3.8

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

    9. Simplified3.8

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

    if -1453.2049809653236 < t < 7.363181675657234e-181

    1. Initial program 25.3

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

    3. Applied div-inv25.3

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

    if 7.363181675657234e-181 < t

    1. Initial program 13.3

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

    3. Applied *-un-lft-identity13.3

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

    4. Applied times-frac12.7

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

    5. Simplified12.7

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

    7. Applied associate-/l*10.7

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

  4. Final simplification13.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1453.204980965323557029478251934051513672:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \le 7.363181675657233677189530241484786519983 \cdot 10^{-181}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))))