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

Average Accuracy: 83.0% → 92.2%

Time: 15.9s

Precision: binary64

Cost: 2248

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;t_1 \leq 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

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 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 (- INFINITY))
     (* z (/ y (- (* z a) t)))
     (if (<= t_1 1e+287) t_1 (/ (- y (/ x z)) 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 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (y / ((z * a) - t));
	} else if (t_1 <= 1e+287) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / 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 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / ((z * a) - t));
	} else if (t_1 <= 1e+287) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / 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 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / ((z * a) - t))
	elif t_1 <= 1e+287:
		tmp = t_1
	else:
		tmp = (y - (x / z)) / 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(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (t_1 <= 1e+287)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / 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 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / ((z * a) - t));
	elseif (t_1 <= 1e+287)
		tmp = t_1;
	else
		tmp = (y - (x / z)) / 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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+287], t$95$1, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Target

Original	83.0%
Target	97.2%
Herbie	92.2%

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

Derivation

1. Split input into 3 regimes

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

   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	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 0.0	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 0.0	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 0.0	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 0.0	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 0.0	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 0.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      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 y around inf 0.0%

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

   4. Simplified 99.3%

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

      [Start] 0.0	\[ \frac{y \cdot z}{a \cdot z - t} \]
      associate-/l* [=>] 99.5	\[ \color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}} \]
      *-commutative [=>] 99.5	\[ \frac{y}{\frac{\color{blue}{z \cdot a} - t}{z}} \]
      associate-/r/ [=>] 99.3	\[ \color{blue}{\frac{y}{z \cdot a - t} \cdot z} \]
      *-commutative [<=] 99.3	\[ \frac{y}{\color{blue}{a \cdot z} - t} \cdot z \]

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.0000000000000001e287

   1. Initial program 93.0%

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

   if 1.0000000000000001e287 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 7.8%

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

   2. Simplified 7.8%

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

      [Start] 7.8	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 7.8	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 7.8	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 7.8	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 7.8	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 7.8	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 7.8	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 7.8	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 7.8	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 7.8	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 7.8	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 7.8	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in z around inf 56.5%

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

   4. Simplified 73.8%

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

      [Start] 56.5	\[ \left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]
      +-commutative [=>] 56.5	\[ \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z} \]
      associate--l+ [=>] 56.5	\[ \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right)} \]
      associate-/r* [=>] 55.8	\[ \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]
      associate-*r/ [=>] 55.8	\[ \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{y \cdot t}{{a}^{2} \cdot z}\right) \]
      associate-/r* [=>] 54.3	\[ \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{y \cdot t}{{a}^{2}}}{z}}\right) \]
      associate-*r/ [=>] 54.3	\[ \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}}\right) \]
      div-sub [<=] 54.3	\[ \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{y \cdot t}{{a}^{2}}}{z}} \]
      distribute-lft-out-- [=>] 54.3	\[ \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}\right)}}{z} \]
      associate-*r/ [<=] 54.3	\[ \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]
      mul-1-neg [=>] 54.3	\[ \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}\right)} \]
      unsub-neg [=>] 54.3	\[ \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{y \cdot t}{{a}^{2}}}{z}} \]

   5. Taylor expanded in x around inf 81.1%

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

   6. Taylor expanded in y around 0 82.6%

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

   7. Simplified 81.7%

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

      [Start] 82.6	\[ -1 \cdot \frac{x}{a \cdot z} + \frac{y}{a} \]
      +-commutative [=>] 82.6	\[ \color{blue}{\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}} \]
      mul-1-neg [=>] 82.6	\[ \frac{y}{a} + \color{blue}{\left(-\frac{x}{a \cdot z}\right)} \]
      sub-neg [<=] 82.6	\[ \color{blue}{\frac{y}{a} - \frac{x}{a \cdot z}} \]
      associate-/l/ [<=] 81.7	\[ \frac{y}{a} - \color{blue}{\frac{\frac{x}{z}}{a}} \]
      div-sub [<=] 81.7	\[ \color{blue}{\frac{y - \frac{x}{z}}{a}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+287}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	50.1%
Cost	1968

\[\begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ t_2 := \frac{\frac{x}{-z}}{a}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.68:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-113}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{-y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2
Accuracy	50.9%
Cost	1704

\[\begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ t_2 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.15:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;\frac{-y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3
Accuracy	69.0%
Cost	1636

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	58.0%
Cost	1505

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x}{-z}}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+32} \lor \neg \left(z \leq 3.2 \cdot 10^{+66}\right) \land z \leq 2.45 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5
Accuracy	67.5%
Cost	1504

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	70.1%
Cost	1500

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t}\\ t_3 := \frac{y - \frac{x}{z}}{a}\\ t_4 := z \cdot \frac{y}{t_1}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-86}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{t_1}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+92}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	70.2%
Cost	1500

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ t_2 := z \cdot a - t\\ t_3 := z \cdot \frac{y}{t_2}\\ t_4 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{t_2}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Accuracy	51.5%
Cost	1440

\[\begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ t_2 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.034:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9
Accuracy	39.4%
Cost	1176

\[\begin{array}{l} t_1 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 10
Accuracy	45.1%
Cost	721

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+162} \lor \neg \left(t \leq -9 \cdot 10^{-88}\right) \land t \leq 10^{+77}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11
Accuracy	34.3%
Cost	192

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

Reproduce

herbie shell --seed 2023136 
(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))))