Average Error: 16.6 → 13.3
Time: 16.8s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\
\;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\

\mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r544391 = x;
        double r544392 = y;
        double r544393 = z;
        double r544394 = r544392 * r544393;
        double r544395 = t;
        double r544396 = r544394 / r544395;
        double r544397 = r544391 + r544396;
        double r544398 = a;
        double r544399 = 1.0;
        double r544400 = r544398 + r544399;
        double r544401 = b;
        double r544402 = r544392 * r544401;
        double r544403 = r544402 / r544395;
        double r544404 = r544400 + r544403;
        double r544405 = r544397 / r544404;
        return r544405;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r544406 = t;
        double r544407 = -1.282223415085258e+46;
        bool r544408 = r544406 <= r544407;
        double r544409 = x;
        double r544410 = y;
        double r544411 = r544410 / r544406;
        double r544412 = z;
        double r544413 = r544411 * r544412;
        double r544414 = r544409 + r544413;
        double r544415 = b;
        double r544416 = r544415 * r544411;
        double r544417 = a;
        double r544418 = r544416 + r544417;
        double r544419 = 1.0;
        double r544420 = r544418 + r544419;
        double r544421 = r544414 / r544420;
        double r544422 = 4.427619810627215e+72;
        bool r544423 = r544406 <= r544422;
        double r544424 = r544410 * r544412;
        double r544425 = r544424 / r544406;
        double r544426 = r544409 + r544425;
        double r544427 = r544417 + r544419;
        double r544428 = r544410 * r544415;
        double r544429 = r544428 / r544406;
        double r544430 = r544427 + r544429;
        double r544431 = r544426 / r544430;
        double r544432 = r544412 / r544406;
        double r544433 = r544410 * r544432;
        double r544434 = r544433 + r544409;
        double r544435 = r544434 / r544420;
        double r544436 = r544423 ? r544431 : r544435;
        double r544437 = r544408 ? r544421 : r544436;
        return r544437;
}

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
Target12.8
Herbie13.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.282223415085258e+46

    1. Initial program 11.5

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

    2. Simplified3.3

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

    if -1.282223415085258e+46 < t < 4.427619810627215e+72

    1. Initial program 20.4

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

    if 4.427619810627215e+72 < t

    1. Initial program 10.6

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

    2. Simplified3.0

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

    4. Applied div-inv3.0

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

    5. Applied associate-*l*3.0

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

    6. Simplified3.0

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

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.282223415085258012742835684889144208601 \cdot 10^{46}:\\ \;\;\;\;\frac{x + \frac{y}{t} \cdot z}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \mathbf{elif}\;t \le 4.427619810627214919217705553013839297329 \cdot 10^{72}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{\left(b \cdot \frac{y}{t} + a\right) + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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))))