Average Error: 16.6 → 12.8
Time: 8.6s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r410436 = x;
        double r410437 = y;
        double r410438 = z;
        double r410439 = r410437 * r410438;
        double r410440 = t;
        double r410441 = r410439 / r410440;
        double r410442 = r410436 + r410441;
        double r410443 = a;
        double r410444 = 1.0;
        double r410445 = r410443 + r410444;
        double r410446 = b;
        double r410447 = r410437 * r410446;
        double r410448 = r410447 / r410440;
        double r410449 = r410445 + r410448;
        double r410450 = r410442 / r410449;
        return r410450;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r410451 = t;
        double r410452 = -2.5546346162075872e+39;
        bool r410453 = r410451 <= r410452;
        double r410454 = 2.1879920080466582e+39;
        bool r410455 = r410451 <= r410454;
        double r410456 = !r410455;
        bool r410457 = r410453 || r410456;
        double r410458 = x;
        double r410459 = y;
        double r410460 = z;
        double r410461 = r410460 / r410451;
        double r410462 = r410459 * r410461;
        double r410463 = r410458 + r410462;
        double r410464 = a;
        double r410465 = 1.0;
        double r410466 = r410464 + r410465;
        double r410467 = 1.0;
        double r410468 = r410451 / r410459;
        double r410469 = b;
        double r410470 = r410468 / r410469;
        double r410471 = r410467 / r410470;
        double r410472 = r410466 + r410471;
        double r410473 = r410463 / r410472;
        double r410474 = r410459 * r410460;
        double r410475 = r410474 / r410451;
        double r410476 = r410458 + r410475;
        double r410477 = r410459 * r410469;
        double r410478 = r410451 / r410477;
        double r410479 = r410467 / r410478;
        double r410480 = r410466 + r410479;
        double r410481 = r410476 / r410480;
        double r410482 = r410457 ? r410473 : r410481;
        return r410482;
}

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

Original16.6
Target13.1
Herbie12.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.5546346162075872e+39 or 2.1879920080466582e+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 clear-num11.7

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

    5. Applied associate-/r*8.6

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

    7. Applied *-un-lft-identity8.6

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

    8. Applied times-frac3.4

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

    9. Simplified3.4

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

    if -2.5546346162075872e+39 < t < 2.1879920080466582e+39

    1. Initial program 20.7

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

    3. Applied clear-num20.7

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

  4. Final simplification12.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.55463461620758721 \cdot 10^{39} \lor \neg \left(t \le 2.18799200804665815 \cdot 10^{39}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{\frac{t}{y}}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))))