Average Error: 17.0 → 17.6
Time: 6.5s
Precision: binary64
\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 6.07389619857644002 \cdot 10^{-286}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \le 5.4179398585709244 \cdot 10^{-202}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left({a}^{3} + {1}^{3}\right) \cdot t + \left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot \left(y \cdot b\right)} \cdot \left(\left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot t\right)\\ \mathbf{elif}\;t \le 1.4424782413980692 \cdot 10^{287}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}
↓
\begin{array}{l}
\mathbf{if}\;t \le 6.07389619857644002 \cdot 10^{-286}:\\
\;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

\mathbf{elif}\;t \le 5.4179398585709244 \cdot 10^{-202}:\\
\;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left({a}^{3} + {1}^{3}\right) \cdot t + \left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot \left(y \cdot b\right)} \cdot \left(\left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot t\right)\\

\mathbf{elif}\;t \le 1.4424782413980692 \cdot 10^{287}:\\
\;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\

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

\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 ((t <= 6.07389619857644e-286)) {
		VAR = ((double) (((double) (x + ((double) (((double) (y * z)) * ((double) (1.0 / t)))))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) / t))))));
	} else {
		double VAR_1;
		if ((t <= 5.417939858570924e-202)) {
			VAR_1 = ((double) (((double) (((double) (x + ((double) (((double) (y * z)) / t)))) / ((double) (((double) (((double) (((double) pow(a, 3.0)) + ((double) pow(1.0, 3.0)))) * t)) + ((double) (((double) (((double) (a * a)) + ((double) (((double) (1.0 * 1.0)) - ((double) (a * 1.0)))))) * ((double) (y * b)))))))) * ((double) (((double) (((double) (a * a)) + ((double) (((double) (1.0 * 1.0)) - ((double) (a * 1.0)))))) * t))));
		} else {
			double VAR_2;
			if ((t <= 1.4424782413980692e+287)) {
				VAR_2 = ((double) (((double) (x + ((double) (y / ((double) (t / z)))))) / ((double) (((double) (a + 1.0)) + ((double) (((double) (y * b)) / t))))));
			} else {
				VAR_2 = ((double) (((double) (x + ((double) (((double) (y * z)) / t)))) / ((double) (((double) (a + 1.0)) + ((double) (y / ((double) (t / b))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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

Original17.0
Target13.6
Herbie17.6
\[\begin{array}{l} \mathbf{if}\;t \lt -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t \lt 3.0369671037372459 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if t < 6.07389619857644002e-286

    1. Initial program 17.9

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

    3. Applied div-inv17.9

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

    if 6.07389619857644002e-286 < t < 5.4179398585709244e-202

    1. Initial program 30.1

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

    3. Applied flip3-+41.5

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

    4. Applied frac-add41.5

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

    5. Applied associate-/r/43.4

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

    if 5.4179398585709244e-202 < t < 1.4424782413980692e287

    1. Initial program 14.0

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

    3. Applied associate-/l*13.3

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

    if 1.4424782413980692e287 < t

    1. Initial program 12.1

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

    3. Applied associate-/l*7.4

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{y}{\frac{t}{b}}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification17.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 6.07389619857644002 \cdot 10^{-286}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \le 5.4179398585709244 \cdot 10^{-202}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left({a}^{3} + {1}^{3}\right) \cdot t + \left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot \left(y \cdot b\right)} \cdot \left(\left(a \cdot a + \left(1 \cdot 1 - a \cdot 1\right)\right) \cdot t\right)\\ \mathbf{elif}\;t \le 1.4424782413980692 \cdot 10^{287}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(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))))