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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -4.849517237759767 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \mathbf{elif}\;t \le 5.653415297019765 \cdot 10^{-74}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{t}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;t \le -4.849517237759767 \cdot 10^{+56}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\

\mathbf{elif}\;t \le 5.653415297019765 \cdot 10^{-74}:\\
\;\;\;\;\frac{x + \frac{z \cdot y}{t}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, 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 r30418675 = x;
        double r30418676 = y;
        double r30418677 = z;
        double r30418678 = r30418676 * r30418677;
        double r30418679 = t;
        double r30418680 = r30418678 / r30418679;
        double r30418681 = r30418675 + r30418680;
        double r30418682 = a;
        double r30418683 = 1.0;
        double r30418684 = r30418682 + r30418683;
        double r30418685 = b;
        double r30418686 = r30418676 * r30418685;
        double r30418687 = r30418686 / r30418679;
        double r30418688 = r30418684 + r30418687;
        double r30418689 = r30418681 / r30418688;
        return r30418689;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r30418690 = t;
        double r30418691 = -4.849517237759767e+56;
        bool r30418692 = r30418690 <= r30418691;
        double r30418693 = z;
        double r30418694 = r30418693 / r30418690;
        double r30418695 = y;
        double r30418696 = x;
        double r30418697 = fma(r30418694, r30418695, r30418696);
        double r30418698 = r30418695 / r30418690;
        double r30418699 = b;
        double r30418700 = 1.0;
        double r30418701 = a;
        double r30418702 = r30418700 + r30418701;
        double r30418703 = fma(r30418698, r30418699, r30418702);
        double r30418704 = r30418697 / r30418703;
        double r30418705 = 5.653415297019765e-74;
        bool r30418706 = r30418690 <= r30418705;
        double r30418707 = r30418693 * r30418695;
        double r30418708 = r30418707 / r30418690;
        double r30418709 = r30418696 + r30418708;
        double r30418710 = r30418699 * r30418695;
        double r30418711 = r30418710 / r30418690;
        double r30418712 = r30418711 + r30418702;
        double r30418713 = r30418709 / r30418712;
        double r30418714 = r30418706 ? r30418713 : r30418704;
        double r30418715 = r30418692 ? r30418704 : r30418714;
        return r30418715;
}

Original	15.9
Target	13.2
Herbie	12.7

Derivation

Split input into 2 regimes
if t < -4.849517237759767e+56 or 5.653415297019765e-74 < t
1. Initial program 10.7
  \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]
2. Simplified5.0
  \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, a + 1.0\right)}}\]
3. Using strategy rm
4. Applied div-inv5.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z, x\right) \cdot \frac{1}{\mathsf{fma}\left(\frac{y}{t}, b, a + 1.0\right)}}\]
5. Using strategy rm
6. Applied associate-*r/5.0
  \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right) \cdot 1}{\mathsf{fma}\left(\frac{y}{t}, b, a + 1.0\right)}}\]
7. Simplified4.7
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}}{\mathsf{fma}\left(\frac{y}{t}, b, a + 1.0\right)}\]
if -4.849517237759767e+56 < t < 5.653415297019765e-74
1. Initial program 21.7
  \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1.0\right) + \frac{y \cdot b}{t}}\]
Recombined 2 regimes into one program.
Final simplification12.7
\[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.849517237759767 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \mathbf{elif}\;t \le 5.653415297019765 \cdot 10^{-74}:\\ \;\;\;\;\frac{x + \frac{z \cdot y}{t}}{\frac{b \cdot y}{t} + \left(1.0 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{t}, y, x\right)}{\mathsf{fma}\left(\frac{y}{t}, b, 1.0 + a\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +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 t < -4.849517237759767e+56 or 5.653415297019765e-74 < t`

`if -4.849517237759767e+56 < t < 5.653415297019765e-74`

Reproduce