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

Average Accuracy: 74.2% → 87.7%

Time: 21.3s

Precision: binary64

Cost: 10828

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 3.8 \cdot 10^{+214}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{b}{\frac{t}{y}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{1}{1 + \mathsf{fma}\left(b, \frac{y}{t}, a\right)}\\ \end{array} \]

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) (/ z (+ a (fma (/ y t) b 1.0))))
     (if (<= t_1 -5e-245)
       t_1
       (if (<= t_1 3.8e+214)
         (/ (+ x (/ z (/ t y))) (+ (/ b (/ t y)) (+ a 1.0)))
         (+ (/ z b) (* x (/ 1.0 (+ 1.0 (fma b (/ y t) a))))))))))

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) * (z / (a + fma((y / t), b, 1.0)));
	} else if (t_1 <= -5e-245) {
		tmp = t_1;
	} else if (t_1 <= 3.8e+214) {
		tmp = (x + (z / (t / y))) / ((b / (t / y)) + (a + 1.0));
	} else {
		tmp = (z / b) + (x * (1.0 / (1.0 + fma(b, (y / t), a))));
	}
	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(Float64(y / t) * Float64(z / Float64(a + fma(Float64(y / t), b, 1.0))));
	elseif (t_1 <= -5e-245)
		tmp = t_1;
	elseif (t_1 <= 3.8e+214)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(b / Float64(t / y)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(x * Float64(1.0 / Float64(1.0 + fma(b, Float64(y / t), a)))));
	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[(N[(y / t), $MachinePrecision] * N[(z / N[(a + N[(N[(y / t), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-245], t$95$1, If[LessEqual[t$95$1, 3.8e+214], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(x * N[(1.0 / N[(1.0 + N[(b * N[(y / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	74.2%
Target	79.0%
Herbie	87.7%

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

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 36.6%

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

      [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* [=>] 36.6	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 36.6	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in x around 0 35.9%

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

   4. Simplified 73.5%

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

      [Start] 35.9	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} \]
      times-frac [=>] 73.5	\[ \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(\frac{y \cdot b}{t} + a\right)}} \]
      associate-+r+ [=>] 73.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\left(1 + \frac{y \cdot b}{t}\right) + a}} \]
      associate-*l/ [<=] 73.5	\[ \frac{y}{t} \cdot \frac{z}{\left(1 + \color{blue}{\frac{y}{t} \cdot b}\right) + a} \]
      +-commutative [=>] 73.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\left(\frac{y}{t} \cdot b + 1\right)} + a} \]
      fma-udef [<=] 73.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\mathsf{fma}\left(\frac{y}{t}, b, 1\right)} + a} \]
      +-commutative [<=] 73.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.9999999999999997e-245

   1. Initial program 99.6%

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

   if -4.9999999999999997e-245 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 3.79999999999999997e214

   1. Initial program 83.7%

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

   2. Simplified 84.0%

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

      [Start] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 83.7	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 79.2	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 84.0	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Applied egg-rr 84.3%

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

      [Start] 84.0	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
      *-commutative [=>] 84.0	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{b \cdot \frac{y}{t}}} \]
      clear-num [=>] 84.0	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \color{blue}{\frac{1}{\frac{t}{y}}}} \]
      un-div-inv [=>] 84.3	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{b}{\frac{t}{y}}}} \]

   if 3.79999999999999997e214 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 16.7%

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

   2. Simplified 32.5%

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

      [Start] 16.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 16.7	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 26.4	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 32.5	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in x around 0 29.4%

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

   4. Applied egg-rr 29.4%

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

      [Start] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{x}{1 + \left(\frac{y \cdot b}{t} + a\right)} \]
      clear-num [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \color{blue}{\frac{1}{\frac{1 + \left(\frac{y \cdot b}{t} + a\right)}{x}}} \]
      associate-/r/ [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \color{blue}{\frac{1}{1 + \left(\frac{y \cdot b}{t} + a\right)} \cdot x} \]
      *-un-lft-identity [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{\color{blue}{1 \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)}} \cdot x \]
      *-un-lft-identity [<=] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{\color{blue}{1 + \left(\frac{y \cdot b}{t} + a\right)}} \cdot x \]
      div-inv [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{1 + \left(\color{blue}{\left(y \cdot b\right) \cdot \frac{1}{t}} + a\right)} \cdot x \]
      *-commutative [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{1 + \left(\color{blue}{\left(b \cdot y\right)} \cdot \frac{1}{t} + a\right)} \cdot x \]
      associate-*l* [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{1 + \left(\color{blue}{b \cdot \left(y \cdot \frac{1}{t}\right)} + a\right)} \cdot x \]
      div-inv [<=] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{1 + \left(b \cdot \color{blue}{\frac{y}{t}} + a\right)} \cdot x \]
      fma-def [=>] 29.4	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} + \frac{1}{1 + \color{blue}{\mathsf{fma}\left(b, \frac{y}{t}, a\right)}} \cdot x \]

   5. Taylor expanded in y around inf 80.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-245}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 3.8 \cdot 10^{+214}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{b}{\frac{t}{y}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + x \cdot \frac{1}{1 + \mathsf{fma}\left(b, \frac{y}{t}, a\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.2%
Cost	8388

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+306}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{b}{\frac{t}{y}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2
Accuracy	85.8%
Cost	2244

\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+306}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{b}{\frac{t}{y}} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3
Accuracy	45.5%
Cost	1769

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+99}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+32} \lor \neg \left(b \leq 7.5 \cdot 10^{+212}\right) \land b \leq 2.5 \cdot 10^{+253}:\\ \;\;\;\;\frac{\frac{t}{y}}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4
Accuracy	77.9%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+228}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+105}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5
Accuracy	79.5%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+233}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6
Accuracy	46.8%
Cost	1240

\[\begin{array}{l} t_1 := \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;b \leq -9 \cdot 10^{+141}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+216}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+253}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7
Accuracy	46.8%
Cost	1240

\[\begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+103}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+214}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+256}:\\ \;\;\;\;\frac{\frac{t}{y}}{\frac{b}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 8
Accuracy	61.4%
Cost	1234

\[\begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-70} \lor \neg \left(t \leq -9.5 \cdot 10^{-94} \lor \neg \left(t \leq -1.9 \cdot 10^{-204}\right) \land t \leq 5.8 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9
Accuracy	62.3%
Cost	1232

\[\begin{array}{l} t_1 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{if}\;b \leq -9 \cdot 10^{+220}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 62000000000:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+211}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	42.3%
Cost	1116

\[\begin{array}{l} \mathbf{if}\;a \leq -6800000:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-267}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4800000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 11
Accuracy	42.4%
Cost	1116

\[\begin{array}{l} t_1 := x - x \cdot a\\ \mathbf{if}\;a \leq -6800000:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-266}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-207}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5600000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12
Accuracy	55.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -23.5 \lor \neg \left(t \leq 1.1 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13
Accuracy	42.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -6800000:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 5800000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14
Accuracy	20.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(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))))