\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.078370184907716 \cdot 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \mathbf{elif}\;z \le 5.495362439678872 \cdot 10^{+155}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \end{array}\]

\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}

↓

\begin{array}{l}
\mathbf{if}\;z \le -1.078370184907716 \cdot 10^{+153}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\

\mathbf{elif}\;z \le 5.495362439678872 \cdot 10^{+155}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r12010527 = x;
        double r12010528 = y;
        double r12010529 = z;
        double r12010530 = r12010528 * r12010529;
        double r12010531 = t;
        double r12010532 = r12010530 / r12010531;
        double r12010533 = r12010527 + r12010532;
        double r12010534 = a;
        double r12010535 = 1.0;
        double r12010536 = r12010534 + r12010535;
        double r12010537 = b;
        double r12010538 = r12010528 * r12010537;
        double r12010539 = r12010538 / r12010531;
        double r12010540 = r12010536 + r12010539;
        double r12010541 = r12010533 / r12010540;
        return r12010541;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r12010542 = z;
        double r12010543 = -1.078370184907716e+153;
        bool r12010544 = r12010542 <= r12010543;
        double r12010545 = y;
        double r12010546 = t;
        double r12010547 = r12010545 / r12010546;
        double r12010548 = x;
        double r12010549 = fma(r12010547, r12010542, r12010548);
        double r12010550 = b;
        double r12010551 = 1.0;
        double r12010552 = a;
        double r12010553 = r12010551 + r12010552;
        double r12010554 = fma(r12010547, r12010550, r12010553);
        double r12010555 = r12010549 / r12010554;
        double r12010556 = 5.495362439678872e+155;
        bool r12010557 = r12010542 <= r12010556;
        double r12010558 = r12010546 / r12010542;
        double r12010559 = r12010545 / r12010558;
        double r12010560 = r12010548 + r12010559;
        double r12010561 = r12010550 * r12010545;
        double r12010562 = r12010561 / r12010546;
        double r12010563 = r12010562 + r12010553;
        double r12010564 = r12010560 / r12010563;
        double r12010565 = r12010557 ? r12010564 : r12010555;
        double r12010566 = r12010544 ? r12010555 : r12010565;
        return r12010566;
}

Original	16.2
Target	13.1
Herbie	14.8

Derivation

Split input into 2 regimes
if z < -1.078370184907716e+153 or 5.495362439678872e+155 < z
1. Initial program 28.2
  \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]
2. Simplified21.5
  \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, a + 1.0\right)}}\]
if -1.078370184907716e+153 < z < 5.495362439678872e+155
1. Initial program 12.5
  \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]
2. Using strategy rm
3. Applied associate-/l*12.8
  \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]
Recombined 2 regimes into one program.
Final simplification14.8
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.078370184907716 \cdot 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \mathbf{elif}\;z \le 5.495362439678872 \cdot 10^{+155}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

Error

Target

Derivation

`if z < -1.078370184907716e+153 or 5.495362439678872e+155 < z`

`if -1.078370184907716e+153 < z < 5.495362439678872e+155`

Reproduce