Average Error: 16.1 → 13.7
Time: 21.4s
Precision: 64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le -2.258728505456341409539353559607828206977 \cdot 10^{282}:\\ \;\;\;\;\frac{1}{1 + \left(a + b \cdot \frac{y}{t}\right)} \cdot \left(\frac{y}{t} \cdot z + x\right)\\ \mathbf{elif}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le 5.849243555943348130308357181547556512187 \cdot 10^{226}:\\ \;\;\;\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le -2.258728505456341409539353559607828206977 \cdot 10^{282}:\\
\;\;\;\;\frac{1}{1 + \left(a + b \cdot \frac{y}{t}\right)} \cdot \left(\frac{y}{t} \cdot z + x\right)\\

\mathbf{elif}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le 5.849243555943348130308357181547556512187 \cdot 10^{226}:\\
\;\;\;\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r35342445 = x;
        double r35342446 = y;
        double r35342447 = z;
        double r35342448 = r35342446 * r35342447;
        double r35342449 = t;
        double r35342450 = r35342448 / r35342449;
        double r35342451 = r35342445 + r35342450;
        double r35342452 = a;
        double r35342453 = 1.0;
        double r35342454 = r35342452 + r35342453;
        double r35342455 = b;
        double r35342456 = r35342446 * r35342455;
        double r35342457 = r35342456 / r35342449;
        double r35342458 = r35342454 + r35342457;
        double r35342459 = r35342451 / r35342458;
        return r35342459;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r35342460 = z;
        double r35342461 = y;
        double r35342462 = r35342460 * r35342461;
        double r35342463 = t;
        double r35342464 = r35342462 / r35342463;
        double r35342465 = x;
        double r35342466 = r35342464 + r35342465;
        double r35342467 = b;
        double r35342468 = r35342467 * r35342461;
        double r35342469 = r35342468 / r35342463;
        double r35342470 = a;
        double r35342471 = 1.0;
        double r35342472 = r35342470 + r35342471;
        double r35342473 = r35342469 + r35342472;
        double r35342474 = r35342466 / r35342473;
        double r35342475 = -2.2587285054563414e+282;
        bool r35342476 = r35342474 <= r35342475;
        double r35342477 = 1.0;
        double r35342478 = r35342461 / r35342463;
        double r35342479 = r35342467 * r35342478;
        double r35342480 = r35342470 + r35342479;
        double r35342481 = r35342471 + r35342480;
        double r35342482 = r35342477 / r35342481;
        double r35342483 = r35342478 * r35342460;
        double r35342484 = r35342483 + r35342465;
        double r35342485 = r35342482 * r35342484;
        double r35342486 = 5.849243555943348e+226;
        bool r35342487 = r35342474 <= r35342486;
        double r35342488 = r35342460 / r35342463;
        double r35342489 = r35342461 * r35342488;
        double r35342490 = r35342489 + r35342465;
        double r35342491 = r35342490 / r35342481;
        double r35342492 = r35342487 ? r35342474 : r35342491;
        double r35342493 = r35342476 ? r35342485 : r35342492;
        return r35342493;
}

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

Original16.1
Target12.9
Herbie13.7
\[\begin{array}{l} \mathbf{if}\;t \lt -1.365908536631008841640163147697088508132 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.036967103737245906066829435890093573122 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) < -2.2587285054563414e+282

    1. Initial program 53.7

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

    2. Simplified35.1

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

    4. Applied div-inv35.2

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

    if -2.2587285054563414e+282 < (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) < 5.849243555943348e+226

    1. Initial program 6.1

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

    if 5.849243555943348e+226 < (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

    1. Initial program 54.5

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

    2. Simplified44.2

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

    4. Applied div-inv44.2

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

    5. Applied associate-*l*45.0

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

    6. Simplified45.0

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

  4. Final simplification13.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le -2.258728505456341409539353559607828206977 \cdot 10^{282}:\\ \;\;\;\;\frac{1}{1 + \left(a + b \cdot \frac{y}{t}\right)} \cdot \left(\frac{y}{t} \cdot z + x\right)\\ \mathbf{elif}\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)} \le 5.849243555943348130308357181547556512187 \cdot 10^{226}:\\ \;\;\;\;\frac{\frac{z \cdot y}{t} + x}{\frac{b \cdot y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t} + x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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))))