Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Average Accuracy: 75.3% → 87.1%

Time: 25.0s

Precision: binary64

Cost: 4556

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{t_1}\\ \mathbf{elif}\;t_2 \leq 10^{-20}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -2e-38)
     (/ (+ x (/ 1.0 (/ (/ t y) z))) t_1)
     (if (<= t_2 1e-20)
       (/ (+ x (/ y (/ t z))) (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_2 INFINITY)
         (/ (+ x (/ z (/ t y))) (+ (/ y (/ t b)) (+ a 1.0)))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -2e-38) {
		tmp = (x + (1.0 / ((t / y) / z))) / t_1;
	} else if (t_2 <= 1e-20) {
		tmp = (x + (y / (t / z))) / ((b * (y / t)) + (a + 1.0));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (x + (z / (t / y))) / ((y / (t / b)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -2e-38) {
		tmp = (x + (1.0 / ((t / y) / z))) / t_1;
	} else if (t_2 <= 1e-20) {
		tmp = (x + (y / (t / z))) / ((b * (y / t)) + (a + 1.0));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (z / (t / y))) / ((y / (t / b)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

↓

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -2e-38:
		tmp = (x + (1.0 / ((t / y) / z))) / t_1
	elif t_2 <= 1e-20:
		tmp = (x + (y / (t / z))) / ((b * (y / t)) + (a + 1.0))
	elif t_2 <= math.inf:
		tmp = (x + (z / (t / y))) / ((y / (t / b)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -2e-38)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(t / y) / z))) / t_1);
	elseif (t_2 <= 1e-20)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(y / Float64(t / b)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -2e-38)
		tmp = (x + (1.0 / ((t / y) / z))) / t_1;
	elseif (t_2 <= 1e-20)
		tmp = (x + (y / (t / z))) / ((b * (y / t)) + (a + 1.0));
	elseif (t_2 <= Inf)
		tmp = (x + (z / (t / y))) / ((y / (t / b)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-38], N[(N[(x + N[(1.0 / N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e-20], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Target

Original	75.3%
Target	79.8%
Herbie	87.1%

\[\begin{array}{l} \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999999999e-38

   1. Initial program 83.1%

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

   2. Applied egg-rr 83.0%

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

      [Start] 83.1	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      clear-num [=>] 83.0	\[ \frac{x + \color{blue}{\frac{1}{\frac{t}{y \cdot z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      inv-pow [=>] 83.0	\[ \frac{x + \color{blue}{{\left(\frac{t}{y \cdot z}\right)}^{-1}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Simplified 91.3%

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

      [Start] 83.0	\[ \frac{x + {\left(\frac{t}{y \cdot z}\right)}^{-1}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      unpow-1 [=>] 83.0	\[ \frac{x + \color{blue}{\frac{1}{\frac{t}{y \cdot z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/r* [=>] 91.3	\[ \frac{x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if -1.9999999999999999e-38 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.99999999999999945e-21

   1. Initial program 83.2%

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

   2. Simplified 87.1%

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

      [Start] 83.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 83.2	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 81.2	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 87.1	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in z around 0 88.2%

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

   4. Simplified 89.8%

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

      [Start] 88.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
      associate-/l* [=>] 89.8	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]

   if 9.99999999999999945e-21 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 80.7%

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

   2. Simplified 84.6%

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

      [Start] 80.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 80.7	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 89.5	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 84.6	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Applied egg-rr 89.4%

      \[\leadsto \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{\frac{t}{b}}}} \]
      Step-by-step derivation

      [Start] 84.6	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
      associate-*l/ [=>] 89.5	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y \cdot b}{t}}} \]
      associate-/l* [=>] 89.4	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{\frac{t}{b}}}} \]

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

   2. Simplified 4.7%

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

      [Start] 0.0	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 0.0	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 0.2	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 4.7	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in t around 0 95.6%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{y}}{z}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{-20}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	85.6%
Cost	2244

\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2
Accuracy	46.7%
Cost	1768

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 3
Accuracy	46.8%
Cost	1768

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-275}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 4
Accuracy	63.1%
Cost	1629

\[\begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 96000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{+89} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5
Accuracy	62.8%
Cost	1629

\[\begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-113}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 96000000:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{+89} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6
Accuracy	67.6%
Cost	1488

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+88}:\\ \;\;\;\;\frac{x + y \cdot \left(z \cdot \frac{1}{t}\right)}{a + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;\frac{z \cdot \frac{y}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	82.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-56} \lor \neg \left(t \leq 4.7 \cdot 10^{-140}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 8
Accuracy	54.1%
Cost	1245

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{a + 1}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 410:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+89} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9
Accuracy	54.0%
Cost	1245

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1150:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+86} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10
Accuracy	58.3%
Cost	1245

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 120:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{+89} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 11
Accuracy	42.5%
Cost	1116

\[\begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-278}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+32}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12
Accuracy	68.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-48} \lor \neg \left(t \leq 9.6 \cdot 10^{-163}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 13
Accuracy	55.5%
Cost	850

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-13} \lor \neg \left(t \leq 1.6 \cdot 10^{-110}\right) \land \left(t \leq 3.95 \cdot 10^{+89} \lor \neg \left(t \leq 4.8 \cdot 10^{+110}\right)\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14
Accuracy	41.7%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15
Accuracy	19.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023159 
(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))))