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

Average Accuracy: 74.0% → 89.6%

Time: 23.0s

Precision: binary64

Cost: 8388

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z (+ a (fma (/ y t) b 1.0))))
     (if (<= t_2 -5e-304)
       (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
       (if (or (<= t_2 0.0) (not (<= t_2 2e+296)))
         (+ (/ z b) (* (/ t y) (/ x b)))
         t_2)))))

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 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (a + fma((y / t), b, 1.0)));
	} else if (t_2 <= -5e-304) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+296)) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = t_2;
	}
	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(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + fma(Float64(y / t), b, 1.0))));
	elseif (t_2 <= -5e-304)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif ((t_2 <= 0.0) || !(t_2 <= 2e+296))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)));
	else
		tmp = t_2;
	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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-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$2, -5e-304], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2e+296]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Target

Original	74.0%
Target	79.2%
Herbie	89.6%

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

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 35.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}} \]
      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/ [<=] 35.7	\[ \frac{\color{blue}{\frac{y}{t} \cdot z} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      fma-def [=>] 35.7	\[ \frac{\color{blue}{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 35.7	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      +-commutative [=>] 35.7	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \color{blue}{\left(\frac{y \cdot b}{t} + 1\right)}} \]
      associate-*l/ [<=] 35.7	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \left(\color{blue}{\frac{y}{t} \cdot b} + 1\right)} \]
      fma-def [=>] 35.7	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \color{blue}{\mathsf{fma}\left(\frac{y}{t}, b, 1\right)}} \]

   3. Taylor expanded in z around inf 37.8%

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

   4. Simplified 77.5%

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

      [Start] 37.8	\[ \frac{y \cdot z}{t \cdot \left(1 + \left(\frac{y \cdot b}{t} + a\right)\right)} \]
      times-frac [=>] 77.5	\[ \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + \left(\frac{y \cdot b}{t} + a\right)}} \]
      associate-+r+ [=>] 77.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\left(1 + \frac{y \cdot b}{t}\right) + a}} \]
      associate-*l/ [<=] 77.5	\[ \frac{y}{t} \cdot \frac{z}{\left(1 + \color{blue}{\frac{y}{t} \cdot b}\right) + a} \]
      +-commutative [<=] 77.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\left(\frac{y}{t} \cdot b + 1\right)} + a} \]
      fma-def [=>] 77.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{\mathsf{fma}\left(\frac{y}{t}, b, 1\right)} + a} \]
      +-commutative [<=] 77.5	\[ \frac{y}{t} \cdot \frac{z}{\color{blue}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.99999999999999965e-304

   1. Initial program 99.4%

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

   2. Simplified 94.9%

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

      [Start] 99.4	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 94.9	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\frac{y}{\frac{t}{b}}}} \]

   if -4.99999999999999965e-304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or 1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 29.2%

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

   2. Simplified 41.1%

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

      [Start] 29.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      +-commutative [=>] 29.2	\[ \frac{\color{blue}{\frac{y \cdot z}{t} + x}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 30.6	\[ \frac{\color{blue}{\frac{y}{t} \cdot z} + x}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      fma-def [=>] 30.6	\[ \frac{\color{blue}{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 30.6	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      +-commutative [=>] 30.6	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \color{blue}{\left(\frac{y \cdot b}{t} + 1\right)}} \]
      associate-*l/ [<=] 41.1	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \left(\color{blue}{\frac{y}{t} \cdot b} + 1\right)} \]
      fma-def [=>] 41.1	\[ \frac{\mathsf{fma}\left(\frac{y}{t}, z, x\right)}{a + \color{blue}{\mathsf{fma}\left(\frac{y}{t}, b, 1\right)}} \]

   3. Taylor expanded in b around inf 25.7%

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

   4. Taylor expanded in t around 0 68.5%

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

   5. Simplified 75.1%

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

      [Start] 68.5	\[ \frac{t \cdot x}{y \cdot b} + \frac{z}{b} \]
      +-commutative [=>] 68.5	\[ \color{blue}{\frac{z}{b} + \frac{t \cdot x}{y \cdot b}} \]
      times-frac [=>] 75.1	\[ \frac{z}{b} + \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} \]

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.99999999999999996e296

   1. Initial program 99.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(\frac{y}{t}, b, 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.0%
Cost	5713

\[\begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{\left(a + 1\right) + t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t_1\right)\right)}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\frac{t_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Accuracy	55.3%
Cost	1368

\[\begin{array}{l} t_1 := \frac{x}{1 + \frac{y \cdot b}{t}}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -150:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-161}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	81.2%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+150} \lor \neg \left(y \leq 5 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 4
Accuracy	40.1%
Cost	1248

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-171}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5
Accuracy	40.3%
Cost	1248

\[\begin{array}{l} t_1 := x - x \cdot a\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-235}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6
Accuracy	65.8%
Cost	1232

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ t_2 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	67.8%
Cost	1232

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	59.6%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+28} \lor \neg \left(y \leq 7 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9
Accuracy	64.6%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+28} \lor \neg \left(y \leq 6.2 \cdot 10^{+143}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 10
Accuracy	56.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 11
Accuracy	43.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -0.00052:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1.16:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12
Accuracy	21.0%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023146 
(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))))