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

Average Accuracy: 73.4% → 89.3%

Time: 33.4s

Precision: binary64

Cost: 8388

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)\right)}{z}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-144}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

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 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ y (/ (* t (+ a (fma y (/ b t) 1.0))) z))
     (if (<= t_1 -2e-122)
       t_1
       (if (<= t_1 1e-144)
         (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ y (/ t b)))))
         (if (<= t_1 2e+263) t_1 (/ (+ z (/ t (/ y x))) 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 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / ((t * (a + fma(y, (b / t), 1.0))) / z);
	} else if (t_1 <= -2e-122) {
		tmp = t_1;
	} else if (t_1 <= 1e-144) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 2e+263) {
		tmp = t_1;
	} else {
		tmp = (z + (t / (y / x))) / 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(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(Float64(t * Float64(a + fma(y, Float64(b / t), 1.0))) / z));
	elseif (t_1 <= -2e-122)
		tmp = t_1;
	elseif (t_1 <= 1e-144)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 2e+263)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	end
	return 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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(N[(t * N[(a + N[(y * N[(b / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-122], t$95$1, If[LessEqual[t$95$1, 1e-144], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], t$95$1, N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]

Target

Original	73.4%
Target	78.5%
Herbie	89.3%

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

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))) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 35.2%

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

      [Start] 0.0	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 35.2	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 35.2	\[ \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      associate-/l* [=>] 35.2	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \color{blue}{\frac{y}{\frac{t}{b}}}\right)} \]

   3. Taylor expanded in x around 0 41.5%

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

   4. Simplified 79.4%

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

      [Start] 41.5	\[ \frac{y \cdot z}{t \cdot \left(\frac{y \cdot b}{t} + \left(1 + a\right)\right)} \]
      associate-/l* [=>] 82.2	\[ \color{blue}{\frac{y}{\frac{t \cdot \left(\frac{y \cdot b}{t} + \left(1 + a\right)\right)}{z}}} \]
      associate-+r+ [=>] 82.2	\[ \frac{y}{\frac{t \cdot \color{blue}{\left(\left(\frac{y \cdot b}{t} + 1\right) + a\right)}}{z}} \]
      associate-*r/ [<=] 79.4	\[ \frac{y}{\frac{t \cdot \left(\left(\color{blue}{y \cdot \frac{b}{t}} + 1\right) + a\right)}{z}} \]
      fma-udef [<=] 79.4	\[ \frac{y}{\frac{t \cdot \left(\color{blue}{\mathsf{fma}\left(y, \frac{b}{t}, 1\right)} + a\right)}{z}} \]
      +-commutative [<=] 79.4	\[ \frac{y}{\frac{t \cdot \color{blue}{\left(a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)\right)}}{z}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000012e-122 or 9.9999999999999995e-145 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e263

   1. Initial program 99.6%

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

   if -2.00000000000000012e-122 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 9.9999999999999995e-145

   1. Initial program 75.1%

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

   2. Simplified 80.8%

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

      [Start] 75.1	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 75.3	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 75.3	\[ \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      associate-/l* [=>] 80.8	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \color{blue}{\frac{y}{\frac{t}{b}}}\right)} \]

   if 2.00000000000000003e263 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.9%

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

   2. Taylor expanded in b around inf 0.4%

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

   3. Simplified 2.6%

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

      [Start] 0.4	\[ \frac{t \cdot \left(\frac{y \cdot z}{t} + x\right)}{y \cdot b} \]
      associate-/l* [=>] 0.1	\[ \color{blue}{\frac{t}{\frac{y \cdot b}{\frac{y \cdot z}{t} + x}}} \]
      +-commutative [=>] 0.1	\[ \frac{t}{\frac{y \cdot b}{\color{blue}{x + \frac{y \cdot z}{t}}}} \]
      associate-/l* [=>] 2.2	\[ \frac{t}{\frac{y \cdot b}{x + \color{blue}{\frac{y}{\frac{t}{z}}}}} \]
      associate-/r/ [=>] 2.4	\[ \color{blue}{\frac{t}{y \cdot b} \cdot \left(x + \frac{y}{\frac{t}{z}}\right)} \]
      associate-/l* [<=] 0.4	\[ \frac{t}{y \cdot b} \cdot \left(x + \color{blue}{\frac{y \cdot z}{t}}\right) \]
      associate-*l/ [<=] 2.6	\[ \frac{t}{y \cdot b} \cdot \left(x + \color{blue}{\frac{y}{t} \cdot z}\right) \]
      *-commutative [=>] 2.6	\[ \frac{t}{y \cdot b} \cdot \left(x + \color{blue}{z \cdot \frac{y}{t}}\right) \]

   4. Taylor expanded in t around 0 73.5%

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

   5. Taylor expanded in b around 0 73.5%

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

   6. Simplified 76.5%

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

      [Start] 73.5	\[ \frac{\frac{t \cdot x}{y} + z}{b} \]
      +-commutative [=>] 73.5	\[ \frac{\color{blue}{z + \frac{t \cdot x}{y}}}{b} \]
      associate-/l* [=>] 76.5	\[ \frac{z + \color{blue}{\frac{t}{\frac{y}{x}}}}{b} \]

3. Recombined 4 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{-144}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	87.1%
Cost	14788

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-59}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + \mathsf{fma}\left(\frac{y}{t}, b, a\right)}\\ \mathbf{elif}\;t_1 \leq 10^{-144}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 2
Accuracy	89.3%
Cost	5712

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := \frac{y}{\frac{t}{b}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t \cdot \left(t_2 + \left(a + 1\right)\right)}{z}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-144}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + t_2\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]

Alternative 3
Accuracy	66.6%
Cost	2016

\[\begin{array}{l} t_1 := 1 + y \cdot \frac{b}{t}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{t_1}\\ t_3 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{a + t_1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+85}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Accuracy	66.6%
Cost	2016

\[\begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ t_2 := 1 + y \cdot \frac{b}{t}\\ t_3 := \frac{y}{\frac{t}{b}}\\ t_4 := \frac{t_1}{1 + t_3}\\ t_5 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_3 + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{t_1}{t_2}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{a + t_2}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+85}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Accuracy	66.4%
Cost	1888

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{1}{\frac{t}{z}}}{a + 1}\\ \end{array} \]

Alternative 6
Accuracy	66.5%
Cost	1888

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-178}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{a + 1}\\ \end{array} \]

Alternative 7
Accuracy	66.6%
Cost	1888

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{\frac{t}{z}}{y}}}{a + 1}\\ \end{array} \]

Alternative 8
Accuracy	55.2%
Cost	1628

\[\begin{array}{l} t_1 := \frac{1}{b} \cdot \left(z + \frac{x}{\frac{y}{t}}\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+66}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{a}\\ \end{array} \]

Alternative 9
Accuracy	55.0%
Cost	1628

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+66}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{b} \cdot \left(z + \frac{x}{\frac{y}{t}}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{a}\\ \end{array} \]

Alternative 10
Accuracy	57.4%
Cost	1368

\[\begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	81.8%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-124} \lor \neg \left(t \leq 3.7 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b} + \frac{z}{b}\\ \end{array} \]

Alternative 12
Accuracy	55.8%
Cost	1236

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ t_2 := \frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-113}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	63.3%
Cost	1233

\[\begin{array}{l} t_1 := \frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot t}{y \cdot b} + \frac{z}{b}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-16} \lor \neg \left(t \leq 8.8 \cdot 10^{+27}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14
Accuracy	50.3%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{if}\;a \leq -5:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-72}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15
Accuracy	68.6%
Cost	1100

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;b \leq -9 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.09 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	41.8%
Cost	588

\[\begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-307}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 17
Accuracy	55.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 18
Accuracy	41.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 19
Accuracy	20.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023133 
(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))))