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

Average Accuracy: 73.9% → 88.5%

Time: 26.9s

Precision: binary64

Cost: 5584

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{t_1}{\left(2 + \left(a + y \cdot \frac{b}{t}\right)\right) + -1}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{\frac{z}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (/ z b)
     (if (<= t_2 -5e-302)
       t_2
       (if (<= t_2 5e+278)
         (/ t_1 (+ (+ 2.0 (+ a (* y (/ b t)))) -1.0))
         (if (<= t_2 INFINITY)
           (/ (/ z (+ a (+ 1.0 (/ b (/ t y))))) (/ t y))
           (/ 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 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z / b;
	} else if (t_2 <= -5e-302) {
		tmp = t_2;
	} else if (t_2 <= 5e+278) {
		tmp = t_1 / ((2.0 + (a + (y * (b / t)))) + -1.0);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (z / (a + (1.0 + (b / (t / y))))) / (t / y);
	} 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 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z / b;
	} else if (t_2 <= -5e-302) {
		tmp = t_2;
	} else if (t_2 <= 5e+278) {
		tmp = t_1 / ((2.0 + (a + (y * (b / t)))) + -1.0);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (z / (a + (1.0 + (b / (t / y))))) / (t / y);
	} 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 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z / b
	elif t_2 <= -5e-302:
		tmp = t_2
	elif t_2 <= 5e+278:
		tmp = t_1 / ((2.0 + (a + (y * (b / t)))) + -1.0)
	elif t_2 <= math.inf:
		tmp = (z / (a + (1.0 + (b / (t / y))))) / (t / y)
	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(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z / b);
	elseif (t_2 <= -5e-302)
		tmp = t_2;
	elseif (t_2 <= 5e+278)
		tmp = Float64(t_1 / Float64(Float64(2.0 + Float64(a + Float64(y * Float64(b / t)))) + -1.0));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(z / Float64(a + Float64(1.0 + Float64(b / Float64(t / y))))) / Float64(t / y));
	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 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z / b;
	elseif (t_2 <= -5e-302)
		tmp = t_2;
	elseif (t_2 <= 5e+278)
		tmp = t_1 / ((2.0 + (a + (y * (b / t)))) + -1.0);
	elseif (t_2 <= Inf)
		tmp = (z / (a + (1.0 + (b / (t / y))))) / (t / y);
	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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z / b), $MachinePrecision], If[LessEqual[t$95$2, -5e-302], t$95$2, If[LessEqual[t$95$2, 5e+278], N[(t$95$1 / N[(N[(2.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(z / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Target

Original	73.9%
Target	79.3%
Herbie	88.5%

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

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 or +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 18.5%

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

      [Start] 0.0	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      +-commutative [=>] 0.0	\[ \frac{\color{blue}{\frac{y \cdot z}{t} + x}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 11.4	\[ \frac{\color{blue}{\frac{y}{t} \cdot z} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      fma-def [=>] 11.4	\[ \frac{\color{blue}{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      +-commutative [=>] 11.4	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{\frac{y \cdot b}{t} + \left(a + 1\right)}} \]
      associate-+r+ [=>] 11.4	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{\left(\frac{y \cdot b}{t} + a\right) + 1}} \]
      +-commutative [=>] 11.4	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{1 + \left(\frac{y \cdot b}{t} + a\right)}} \]
      associate-*l/ [<=] 18.5	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + \left(\color{blue}{\frac{y}{t} \cdot b} + a\right)} \]
      fma-def [=>] 18.5	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{1 + \color{blue}{\mathsf{fma}\left(\frac{y}{t}, b, a\right)}} \]

   3. Taylor expanded in y around inf 81.8%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -5.00000000000000033e-302

   1. Initial program 99.1%

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

   if -5.00000000000000033e-302 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.00000000000000029e278

   1. Initial program 83.7%

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

   2. Applied egg-rr 85.6%

      \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\color{blue}{\left(2 + \left(a + \frac{b}{t} \cdot y\right)\right) - 1}} \]
      Proof

      [Start] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      expm1-log1p-u [=>] 66.3	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot b}{t}\right)\right)}} \]
      expm1-udef [=>] 66.3	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot b}{t}\right)} - 1\right)}} \]
      log1p-udef [=>] 66.3	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(e^{\color{blue}{\log \left(1 + \frac{y \cdot b}{t}\right)}} - 1\right)} \]
      add-exp-log [<=] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(\color{blue}{\left(1 + \frac{y \cdot b}{t}\right)} - 1\right)} \]
      associate-+r- [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\color{blue}{\left(\left(a + 1\right) + \left(1 + \frac{y \cdot b}{t}\right)\right) - 1}} \]
      +-commutative [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(\color{blue}{\left(1 + a\right)} + \left(1 + \frac{y \cdot b}{t}\right)\right) - 1} \]
      associate-+r+ [<=] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\color{blue}{\left(1 + \left(a + \left(1 + \frac{y \cdot b}{t}\right)\right)\right)} - 1} \]
      associate-+l+ [<=] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(1 + \color{blue}{\left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\right) - 1} \]
      +-commutative [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(1 + \left(\color{blue}{\left(1 + a\right)} + \frac{y \cdot b}{t}\right)\right) - 1} \]
      associate-+l+ [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(1 + \color{blue}{\left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right) - 1} \]
      associate-+r+ [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\color{blue}{\left(\left(1 + 1\right) + \left(a + \frac{y \cdot b}{t}\right)\right)} - 1} \]
      metadata-eval [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(\color{blue}{2} + \left(a + \frac{y \cdot b}{t}\right)\right) - 1} \]
      *-commutative [=>] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(2 + \left(a + \frac{\color{blue}{b \cdot y}}{t}\right)\right) - 1} \]
      associate-/l* [=>] 87.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(2 + \left(a + \color{blue}{\frac{b}{\frac{t}{y}}}\right)\right) - 1} \]
      associate-/r/ [=>] 85.6	\[ \frac{x + \frac{y \cdot z}{t}}{\left(2 + \left(a + \color{blue}{\frac{b}{t} \cdot y}\right)\right) - 1} \]

   if 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 15.8%

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

   2. Applied egg-rr 46.3%

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

      [Start] 15.8	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 44.0	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/r/ [=>] 46.3	\[ \frac{x + \color{blue}{\frac{y}{t} \cdot z}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Taylor expanded in x around 0 35.1%

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

   4. Simplified 64.6%

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

      [Start] 35.1	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} \]
      times-frac [=>] 64.6	\[ \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(\frac{y \cdot b}{t} + a\right)}} \]
      associate-+r+ [=>] 64.6	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\left(1 + \frac{y \cdot b}{t}\right) + a}} \]
      +-commutative [<=] 64.6	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]

   5. Applied egg-rr 65.5%

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

      [Start] 64.6	\[ \frac{y}{t} \cdot \frac{z}{a + \left(1 + \frac{y \cdot b}{t}\right)} \]
      *-commutative [=>] 64.6	\[ \color{blue}{\frac{z}{a + \left(1 + \frac{y \cdot b}{t}\right)} \cdot \frac{y}{t}} \]
      clear-num [=>] 64.5	\[ \frac{z}{a + \left(1 + \frac{y \cdot b}{t}\right)} \cdot \color{blue}{\frac{1}{\frac{t}{y}}} \]
      un-div-inv [=>] 65.3	\[ \color{blue}{\frac{\frac{z}{a + \left(1 + \frac{y \cdot b}{t}\right)}}{\frac{t}{y}}} \]
      *-commutative [=>] 65.3	\[ \frac{\frac{z}{a + \left(1 + \frac{\color{blue}{b \cdot y}}{t}\right)}}{\frac{t}{y}} \]
      associate-/l* [=>] 65.5	\[ \frac{\frac{z}{a + \left(1 + \color{blue}{\frac{b}{\frac{t}{y}}}\right)}}{\frac{t}{y}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(2 + \left(a + y \cdot \frac{b}{t}\right)\right) + -1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{\frac{z}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	86.4%
Cost	4556

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2
Accuracy	75.5%
Cost	1485

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+195} \lor \neg \left(y \leq 4.5 \cdot 10^{+84}\right) \land y \leq 8.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 3
Accuracy	77.1%
Cost	1484

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+195}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+161}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \end{array} \]

Alternative 4
Accuracy	77.2%
Cost	1484

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+195}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+162}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \end{array} \]

Alternative 5
Accuracy	61.7%
Cost	1364

\[\begin{array}{l} t_1 := \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{if}\;t \leq -9 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-143}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	63.4%
Cost	1232

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7
Accuracy	64.6%
Cost	1232

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 8
Accuracy	64.5%
Cost	1232

\[\begin{array}{l} t_1 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+190}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9
Accuracy	64.5%
Cost	1232

\[\begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+177}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10
Accuracy	56.4%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1.06:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1950000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	57.4%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -2.2:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 9.8:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	57.0%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -12.2:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 72000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{a}\\ \end{array} \]

Alternative 13
Accuracy	42.5%
Cost	848

\[\begin{array}{l} t_1 := x - x \cdot a\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.75:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14
Accuracy	42.4%
Cost	720

\[\begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-67}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15
Accuracy	55.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+119}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 16
Accuracy	43.0%
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 17
Accuracy	20.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023136 
(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))))