Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Average Accuracy: 84.6% → 96.0%

Time: 19.4s

Precision: binary64

Cost: 4176

Math

\[\frac{x - y \cdot z}{t - a \cdot z} \]

↓

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y}{\frac{t_1}{z}} - \frac{x}{t_1}\\ t_3 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t))
        (t_2 (- (/ y (/ t_1 z)) (/ x t_1)))
        (t_3 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_3 -2e-295)
     t_2
     (if (<= t_3 0.0)
       (/ y (- a (/ t z)))
       (if (<= t_3 2e+131) t_3 (if (<= t_3 INFINITY) t_2 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (y / (t_1 / z)) - (x / t_1);
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -2e-295) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_3 <= 2e+131) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (y / (t_1 / z)) - (x / t_1);
	double t_3 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_3 <= -2e-295) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = y / (a - (t / z));
	} else if (t_3 <= 2e+131) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

↓

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = (y / (t_1 / z)) - (x / t_1)
	t_3 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_3 <= -2e-295:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = y / (a - (t / z))
	elif t_3 <= 2e+131:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(y / Float64(t_1 / z)) - Float64(x / t_1))
	t_3 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_3 <= -2e-295)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (t_3 <= 2e+131)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (x - (y * z)) / (t - (a * z));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = (y / (t_1 / z)) - (x / t_1);
	t_3 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_3 <= -2e-295)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = y / (a - (t / z));
	elseif (t_3 <= 2e+131)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-295], t$95$2, If[LessEqual[t$95$3, 0.0], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+131], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]

Target

Original	84.6%
Target	97.0%
Herbie	96.0%

\[\begin{array}{l} \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -2.00000000000000012e-295 or 1.9999999999999998e131 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 91.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]

   2. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Proof

      [Start] 91.0	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 91.0	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 91.0	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 91.0	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 91.0	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 91.0	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 91.0	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 91.0	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 91.0	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 91.0	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 91.0	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 91.0	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}} \]
      Proof

      [Start] 91.0	\[ \frac{y \cdot z - x}{z \cdot a - t} \]
      div-sub [=>] 91.0	\[ \color{blue}{\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}} \]
      associate-/l* [=>] 99.1	\[ \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}}} - \frac{x}{z \cdot a - t} \]

   if -2.00000000000000012e-295 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 50.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]

   2. Simplified 50.5%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Proof

      [Start] 50.5	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 50.5	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 50.5	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 50.5	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 50.5	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 50.5	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 50.5	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 50.5	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 50.5	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 50.5	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 50.5	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 50.5	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a \cdot z - t}} \]

   4. Simplified 50.5%

      \[\leadsto \color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}} \]
      Proof

      [Start] 50.5	\[ \frac{y \cdot z}{a \cdot z - t} \]
      associate-/l* [=>] 50.5	\[ \color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}} \]

   5. Taylor expanded in a around 0 86.9%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]

   6. Simplified 86.9%

      \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]
      Proof

      [Start] 86.9	\[ \frac{y}{a + -1 \cdot \frac{t}{z}} \]
      neg-mul-1 [<=] 86.9	\[ \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]
      sub-neg [<=] 86.9	\[ \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.9999999999999998e131

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]

   2. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Proof

      [Start] 0.0	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 0.0	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 0.0	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 0.0	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 0.0	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 0.0	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 0.0	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 0.0	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 0.0	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 0.0	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 0.0	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 0.0	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	94.2%
Cost	9868

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{y}{\frac{t_1}{z}} - \frac{x}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{a}{y} + \frac{\frac{a}{y} \cdot \frac{x}{y} - \frac{t}{y}}{z}\right)}^{-1}\\ \end{array} \]

Alternative 2
Accuracy	73.7%
Cost	1372

\[\begin{array}{l} t_1 := \frac{-x}{z \cdot a - t}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ t_3 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+213}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	53.4%
Cost	1044

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4
Accuracy	53.7%
Cost	1044

\[\begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5
Accuracy	54.0%
Cost	1044

\[\begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 6
Accuracy	54.0%
Cost	1044

\[\begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-36}:\\ \;\;\;\;\frac{-y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+75}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Accuracy	73.1%
Cost	976

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	90.6%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+197}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+163}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 9
Accuracy	65.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-68} \lor \neg \left(z \leq 9.2 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 10
Accuracy	72.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-31} \lor \neg \left(z \leq 10^{-102}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 11
Accuracy	54.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 12
Accuracy	36.0%
Cost	192

\[\frac{x}{t} \]

Reproduce

herbie shell --seed 2023160 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))