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

Average Error: 26.23% → 14.05%

Time: 27.3s

Precision: binary64

Cost: 4556

Math

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

↓

\[\begin{array}{l} t_1 := \frac{b \cdot y}{t} + \left(1 + a\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-281}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{elif}\;t_2 \leq 10^{+250}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}\\ \end{array} \]

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 (+ (/ (* b y) t) (+ 1.0 a))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -1e-281)
     (/ (+ x (* z (* y (/ 1.0 t)))) t_1)
     (if (<= t_2 0.0)
       (/ (+ z (/ (* t x) y)) b)
       (if (<= t_2 1e+250) t_2 (+ (/ z b) (* x (/ (/ t y) 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 = ((b * y) / t) + (1.0 + a);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -1e-281) {
		tmp = (x + (z * (y * (1.0 / t)))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z + ((t * x) / y)) / b;
	} else if (t_2 <= 1e+250) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (x * ((t / y) / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((b * y) / t) + (1.0d0 + a)
    t_2 = (x + ((y * z) / t)) / t_1
    if (t_2 <= (-1d-281)) then
        tmp = (x + (z * (y * (1.0d0 / t)))) / t_1
    else if (t_2 <= 0.0d0) then
        tmp = (z + ((t * x) / y)) / b
    else if (t_2 <= 1d+250) then
        tmp = t_2
    else
        tmp = (z / b) + (x * ((t / y) / b))
    end if
    code = tmp
end function

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 = ((b * y) / t) + (1.0 + a);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -1e-281) {
		tmp = (x + (z * (y * (1.0 / t)))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z + ((t * x) / y)) / b;
	} else if (t_2 <= 1e+250) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (x * ((t / y) / 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 = ((b * y) / t) + (1.0 + a)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -1e-281:
		tmp = (x + (z * (y * (1.0 / t)))) / t_1
	elif t_2 <= 0.0:
		tmp = (z + ((t * x) / y)) / b
	elif t_2 <= 1e+250:
		tmp = t_2
	else:
		tmp = (z / b) + (x * ((t / y) / 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(b * y) / t) + Float64(1.0 + a))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e-281)
		tmp = Float64(Float64(x + Float64(z * Float64(y * Float64(1.0 / t)))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z + Float64(Float64(t * x) / y)) / b);
	elseif (t_2 <= 1e+250)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(x * Float64(Float64(t / y) / 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 = ((b * y) / t) + (1.0 + a);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -1e-281)
		tmp = (x + (z * (y * (1.0 / t)))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = (z + ((t * x) / y)) / b;
	elseif (t_2 <= 1e+250)
		tmp = t_2;
	else
		tmp = (z / b) + (x * ((t / y) / 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[(b * y), $MachinePrecision] / t), $MachinePrecision] + N[(1.0 + a), $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, -1e-281], N[(N[(x + N[(z * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(z + N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 1e+250], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(x * N[(N[(t / y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	26.23%
Target	20.91%
Herbie	14.05%

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

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))) < -1e-281

   1. Initial program 11.99

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

   2. Applied egg-rr 10.87

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

   if -1e-281 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 44.28

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

   2. Taylor expanded in b around inf 51.8

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

   3. Simplified 51.25

      \[\leadsto \color{blue}{\frac{t}{\frac{y \cdot b}{x + y \cdot \frac{z}{t}}}} \]
      Proof

      [Start] 51.8	\[ \frac{t \cdot \left(\frac{y \cdot z}{t} + x\right)}{y \cdot b} \]
      associate-/l* [=>] 50.47	\[ \color{blue}{\frac{t}{\frac{y \cdot b}{\frac{y \cdot z}{t} + x}}} \]
      +-commutative [=>] 50.47	\[ \frac{t}{\frac{y \cdot b}{\color{blue}{x + \frac{y \cdot z}{t}}}} \]
      associate-*r/ [<=] 51.25	\[ \frac{t}{\frac{y \cdot b}{x + \color{blue}{y \cdot \frac{z}{t}}}} \]

   4. Taylor expanded in t around 0 42.37

      \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \frac{z}{b}} \]

   5. Simplified 39.22

      \[\leadsto \color{blue}{\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}} \]
      Proof

      [Start] 42.37	\[ \frac{t \cdot x}{y \cdot b} + \frac{z}{b} \]
      +-commutative [=>] 42.37	\[ \color{blue}{\frac{z}{b} + \frac{t \cdot x}{y \cdot b}} \]
      *-commutative [=>] 42.37	\[ \frac{z}{b} + \frac{\color{blue}{x \cdot t}}{y \cdot b} \]
      associate-*r/ [<=] 47.2	\[ \frac{z}{b} + \color{blue}{x \cdot \frac{t}{y \cdot b}} \]
      associate-/r* [=>] 39.22	\[ \frac{z}{b} + x \cdot \color{blue}{\frac{\frac{t}{y}}{b}} \]

   6. Taylor expanded in b around 0 34.48

      \[\leadsto \color{blue}{\frac{\frac{t \cdot x}{y} + z}{b}} \]

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999992e249

   1. Initial program 0.66

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

   if 9.9999999999999992e249 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 91.09

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

   2. Taylor expanded in b around inf 99.66

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

   3. Simplified 98.15

      \[\leadsto \color{blue}{\frac{t}{\frac{y \cdot b}{x + y \cdot \frac{z}{t}}}} \]
      Proof

      [Start] 99.66	\[ \frac{t \cdot \left(\frac{y \cdot z}{t} + x\right)}{y \cdot b} \]
      associate-/l* [=>] 99.87	\[ \color{blue}{\frac{t}{\frac{y \cdot b}{\frac{y \cdot z}{t} + x}}} \]
      +-commutative [=>] 99.87	\[ \frac{t}{\frac{y \cdot b}{\color{blue}{x + \frac{y \cdot z}{t}}}} \]
      associate-*r/ [<=] 98.15	\[ \frac{t}{\frac{y \cdot b}{x + \color{blue}{y \cdot \frac{z}{t}}}} \]

   4. Taylor expanded in t around 0 27.95

      \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \frac{z}{b}} \]

   5. Simplified 24.86

      \[\leadsto \color{blue}{\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}} \]
      Proof

      [Start] 27.95	\[ \frac{t \cdot x}{y \cdot b} + \frac{z}{b} \]
      +-commutative [=>] 27.95	\[ \color{blue}{\frac{z}{b} + \frac{t \cdot x}{y \cdot b}} \]
      *-commutative [=>] 27.95	\[ \frac{z}{b} + \frac{\color{blue}{x \cdot t}}{y \cdot b} \]
      associate-*r/ [<=] 26.25	\[ \frac{z}{b} + \color{blue}{x \cdot \frac{t}{y \cdot b}} \]
      associate-/r* [=>] 24.86	\[ \frac{z}{b} + x \cdot \color{blue}{\frac{\frac{t}{y}}{b}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 14.05

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{b \cdot y}{t} + \left(1 + a\right)} \leq -1 \cdot 10^{-281}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{\frac{b \cdot y}{t} + \left(1 + a\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{b \cdot y}{t} + \left(1 + a\right)} \leq 0:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{b \cdot y}{t} + \left(1 + a\right)} \leq 10^{+250}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{b \cdot y}{t} + \left(1 + a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}\\ \end{array} \]

Alternatives

Alternative 1
Error	10.33%
Cost	5712

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{b \cdot y}{t} + \left(1 + a\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-239}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t_1 \leq 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}\\ \end{array} \]

Alternative 2
Error	19.69%
Cost	2256

\[\begin{array}{l} t_1 := 1 + \left(a + b \cdot \frac{y}{t}\right)\\ t_2 := \frac{x}{t_1} + \frac{y}{t} \cdot \frac{z}{t_1}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-237}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	20.83%
Cost	1617

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-237} \lor \neg \left(t \leq 1.05 \cdot 10^{-68}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \end{array} \]

Alternative 4
Error	21.01%
Cost	1617

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{t_1}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-237} \lor \neg \left(t \leq 1.05 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{t_1}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \end{array} \]

Alternative 5
Error	32.08%
Cost	1364

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{1 + a}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-68}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + a}\\ \mathbf{elif}\;t \leq 90000000000:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	48.12%
Cost	1236

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{1 + a}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	43.2%
Cost	1236

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{1 + a}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+15}:\\ \;\;\;\;\frac{z + \frac{t \cdot x}{y}}{b}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	44.25%
Cost	1236

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{1 + a}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 52000000000:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{\frac{t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	43.32%
Cost	1236

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{1 + a}\\ t_2 := \frac{x}{1 + a}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	31.48%
Cost	1101

\[\begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-29} \lor \neg \left(t \leq 2.3 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \end{array} \]

Alternative 11
Error	57.82%
Cost	985

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+22} \lor \neg \left(a \leq 1.75 \cdot 10^{+105}\right) \land a \leq 1.6 \cdot 10^{+135}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12
Error	43.97%
Cost	972

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	43.47%
Cost	972

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	40.26%
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq 530000000000:\\ \;\;\;\;\frac{t \cdot x}{b \cdot y} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + a}\\ \end{array} \]

Alternative 15
Error	44.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-31} \lor \neg \left(t \leq 6.2 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{x}{1 + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 16
Error	58.36%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 17
Error	79.8%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023115 
(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))))