Average Error: 16.6 → 13.4
Time: 5.8s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.00157721529175776 \cdot 10^{-36} \lor \neg \left(y \le 8.0593349417547793 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{y}{\frac{\sqrt[3]{t}}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.00157721529175776 \cdot 10^{-36} \lor \neg \left(y \le 8.0593349417547793 \cdot 10^{-133}\right):\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{y}{\frac{\sqrt[3]{t}}{z}}}{\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 r843374 = x;
        double r843375 = y;
        double r843376 = z;
        double r843377 = r843375 * r843376;
        double r843378 = t;
        double r843379 = r843377 / r843378;
        double r843380 = r843374 + r843379;
        double r843381 = a;
        double r843382 = 1.0;
        double r843383 = r843381 + r843382;
        double r843384 = b;
        double r843385 = r843375 * r843384;
        double r843386 = r843385 / r843378;
        double r843387 = r843383 + r843386;
        double r843388 = r843380 / r843387;
        return r843388;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r843389 = y;
        double r843390 = -1.0015772152917578e-36;
        bool r843391 = r843389 <= r843390;
        double r843392 = 8.05933494175478e-133;
        bool r843393 = r843389 <= r843392;
        double r843394 = !r843393;
        bool r843395 = r843391 || r843394;
        double r843396 = x;
        double r843397 = t;
        double r843398 = z;
        double r843399 = r843397 / r843398;
        double r843400 = r843389 / r843399;
        double r843401 = r843396 + r843400;
        double r843402 = a;
        double r843403 = 1.0;
        double r843404 = r843402 + r843403;
        double r843405 = b;
        double r843406 = r843397 / r843405;
        double r843407 = r843389 / r843406;
        double r843408 = r843404 + r843407;
        double r843409 = r843401 / r843408;
        double r843410 = 1.0;
        double r843411 = cbrt(r843397);
        double r843412 = r843411 * r843411;
        double r843413 = r843410 / r843412;
        double r843414 = r843411 / r843398;
        double r843415 = r843389 / r843414;
        double r843416 = r843413 * r843415;
        double r843417 = r843396 + r843416;
        double r843418 = r843389 * r843405;
        double r843419 = r843418 / r843397;
        double r843420 = r843404 + r843419;
        double r843421 = r843417 / r843420;
        double r843422 = r843395 ? r843409 : r843421;
        return r843422;
}

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
Herbie13.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.0015772152917578e-36 or 8.05933494175478e-133 < y

    1. Initial program 25.0

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

    3. Applied associate-/l*22.8

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

    5. Applied associate-/l*19.5

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

    if -1.0015772152917578e-36 < y < 8.05933494175478e-133

    1. Initial program 2.5

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

    3. Applied associate-/l*7.0

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

    5. Applied *-un-lft-identity7.0

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

    6. Applied add-cube-cbrt7.2

      \[\leadsto \frac{x + \frac{y}{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{1 \cdot z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    7. Applied times-frac7.2

      \[\leadsto \frac{x + \frac{y}{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \frac{\sqrt[3]{t}}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    8. Applied *-un-lft-identity7.2

      \[\leadsto \frac{x + \frac{\color{blue}{1 \cdot y}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \frac{\sqrt[3]{t}}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    9. Applied times-frac3.1

      \[\leadsto \frac{x + \color{blue}{\frac{1}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1}} \cdot \frac{y}{\frac{\sqrt[3]{t}}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]

    10. Simplified3.1

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

  4. Final simplification13.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.00157721529175776 \cdot 10^{-36} \lor \neg \left(y \le 8.0593349417547793 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{y}{\frac{\sqrt[3]{t}}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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))))