Average Error: 16.5 → 13.2
Time: 5.3s
Precision: binary64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.6031014728832484 \cdot 10^{96} \lor \neg \left(y \le 9.53884126376018804 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{1}{\frac{a + \left(1 + y \cdot \frac{b}{t}\right)}{x + y \cdot \frac{z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.6031014728832484 \cdot 10^{96} \lor \neg \left(y \le 9.53884126376018804 \cdot 10^{-56}\right):\\
\;\;\;\;\frac{1}{\frac{a + \left(1 + y \cdot \frac{b}{t}\right)}{x + y \cdot \frac{z}{t}}}\\

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

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (x + ((double) (((double) (y * z)) / t)))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) / t))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((y <= -6.603101472883248e+96) || !(y <= 9.538841263760188e-56))) {
		VAR = ((double) (1.0 / ((double) (((double) (a + ((double) (1.0 + ((double) (y * ((double) (b / t)))))))) / ((double) (x + ((double) (y * ((double) (z / t))))))))));
	} else {
		VAR = ((double) (((double) (x + ((double) (((double) (y * z)) / t)))) * ((double) (1.0 / ((double) (a + ((double) (1.0 + ((double) (b * ((double) (y / t))))))))))));
	}
	return VAR;
}

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

Original16.5
Target13.5
Herbie13.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.6031014728832484e96 or 9.53884126376018804e-56 < y

    1. Initial program 29.5

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

    3. Applied clear-num29.7

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

    4. Simplified22.4

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

    if -6.6031014728832484e96 < y < 9.53884126376018804e-56

    1. Initial program 5.3

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

    3. Applied add-cube-cbrt5.5

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

    4. Applied associate-/r*5.5

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

    5. Simplified5.3

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

    7. Applied div-inv5.3

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

    8. Simplified5.3

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

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.6031014728832484 \cdot 10^{96} \lor \neg \left(y \le 9.53884126376018804 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{1}{\frac{a + \left(1 + y \cdot \frac{b}{t}\right)}{x + y \cdot \frac{z}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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) (* 1.0 (* (+ 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))))