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

Average Accuracy: 85.1% → 90.9%

Time: 20.2s

Precision: binary64

Cost: 3404

Math

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

↓

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

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 (/ (- x (* y z)) (- t (* z a))))
        (t_2 (<= t_1 0.0))
        (t_3 (- (* z a) t)))
   (if t_2
     t_1
     (if t_2
       (/ y (- a (/ t z)))
       (if (<= t_1 INFINITY) (- (/ y (/ t_3 z)) (/ x t_3)) (/ 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 = (x - (y * z)) / (t - (z * a));
	int t_2 = t_1 <= 0.0;
	double t_3 = (z * a) - t;
	double tmp;
	if (t_2) {
		tmp = t_1;
	} else if (t_2) {
		tmp = y / (a - (t / z));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / (t_3 / z)) - (x / t_3);
	} 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 = (x - (y * z)) / (t - (z * a));
	boolean t_2 = t_1 <= 0.0;
	double t_3 = (z * a) - t;
	double tmp;
	if (t_2) {
		tmp = t_1;
	} else if (t_2) {
		tmp = y / (a - (t / z));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / (t_3 / z)) - (x / t_3);
	} 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 = (x - (y * z)) / (t - (z * a))
	t_2 = t_1 <= 0.0
	t_3 = (z * a) - t
	tmp = 0
	if t_2:
		tmp = t_1
	elif t_2:
		tmp = y / (a - (t / z))
	elif t_1 <= math.inf:
		tmp = (y / (t_3 / z)) - (x / t_3)
	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(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	t_2 = t_1 <= 0.0
	t_3 = Float64(Float64(z * a) - t)
	tmp = 0.0
	if (t_2)
		tmp = t_1;
	elseif (t_2)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / Float64(t_3 / z)) - Float64(x / t_3));
	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 = (x - (y * z)) / (t - (z * a));
	t_2 = t_1 <= 0.0;
	t_3 = (z * a) - t;
	tmp = 0.0;
	if (t_2)
		tmp = t_1;
	elseif (t_2)
		tmp = y / (a - (t / z));
	elseif (t_1 <= Inf)
		tmp = (y / (t_3 / z)) - (x / t_3);
	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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = LessEqual[t$95$1, 0.0]}, Block[{t$95$3 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, If[t$95$2, t$95$1, If[t$95$2, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(y / N[(t$95$3 / z), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Target

Original	85.1%
Target	97.2%
Herbie	90.9%

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 87.3%

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

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

   1. Initial program 83.7%

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

   2. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Step-by-step derivation

      [Start] 83.7	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 83.7	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 83.7	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 83.7	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 83.7	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 83.7	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 83.7	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 83.7	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 83.7	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 83.7	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 83.7	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 83.7	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Taylor expanded in y around inf 43.7%

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

   4. Simplified 45.7%

      \[\leadsto \color{blue}{y \cdot \frac{z}{a \cdot z - t}} \]
      Step-by-step derivation

      [Start] 43.7	\[ \frac{y \cdot z}{a \cdot z - t} \]
      *-commutative [=>] 43.7	\[ \frac{y \cdot z}{\color{blue}{z \cdot a} - t} \]
      associate-*r/ [<=] 45.7	\[ \color{blue}{y \cdot \frac{z}{z \cdot a - t}} \]
      *-commutative [<=] 45.7	\[ y \cdot \frac{z}{\color{blue}{a \cdot z} - t} \]

   5. Applied egg-rr 45.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}}} \]
      Step-by-step derivation

      [Start] 45.7	\[ y \cdot \frac{z}{a \cdot z - t} \]
      clear-num [=>] 45.7	\[ y \cdot \color{blue}{\frac{1}{\frac{a \cdot z - t}{z}}} \]
      un-div-inv [=>] 45.8	\[ \color{blue}{\frac{y}{\frac{a \cdot z - t}{z}}} \]
      *-commutative [=>] 45.8	\[ \frac{y}{\frac{\color{blue}{z \cdot a} - t}{z}} \]

   6. Taylor expanded in z around 0 56.1%

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

   7. Simplified 56.1%

      \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]
      Step-by-step derivation

      [Start] 56.1	\[ \frac{y}{a + -1 \cdot \frac{t}{z}} \]
      neg-mul-1 [<=] 56.1	\[ \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]
      sub-neg [<=] 56.1	\[ \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.4%

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

   2. Simplified 92.4%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Step-by-step derivation

      [Start] 92.4	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      +-commutative [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{\left(-a \cdot z\right) + t}} \]
      neg-sub0 [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{\left(0 - a \cdot z\right)} + t} \]
      associate-+l- [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{0 - \left(a \cdot z - t\right)}} \]
      sub0-neg [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{-\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 92.4	\[ \frac{x - y \cdot z}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      sub-neg [=>] 92.4	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      +-commutative [=>] 92.4	\[ \frac{\color{blue}{\left(-y \cdot z\right) + x}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-sub0 [=>] 92.4	\[ \frac{\color{blue}{\left(0 - y \cdot z\right)} + x}{-1 \cdot \left(a \cdot z - t\right)} \]
      associate-+l- [=>] 92.4	\[ \frac{\color{blue}{0 - \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      sub0-neg [=>] 92.4	\[ \frac{\color{blue}{-\left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      neg-mul-1 [=>] 92.4	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{-1 \cdot \left(a \cdot z - t\right)} \]
      times-frac [=>] 92.4	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 92.4	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 92.4	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 92.4	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}} - \frac{x}{z \cdot a - t}} \]
      Step-by-step derivation

      [Start] 92.4	\[ \frac{y \cdot z - x}{z \cdot a - t} \]
      div-sub [=>] 91.3	\[ \color{blue}{\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}} \]
      associate-/l* [=>] 97.6	\[ \color{blue}{\frac{y}{\frac{z \cdot a - t}{z}}} - \frac{x}{z \cdot a - t} \]

   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%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a - t}} \]
      Step-by-step derivation

      [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 91.8%

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

Alternatives

Alternative 1
Accuracy	89.3%
Cost	3020

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

Alternative 2
Accuracy	52.9%
Cost	1108

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;y \leq 5.8 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-287}:\\ \;\;\;\;\frac{-\frac{x}{z}}{a}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-125}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	52.9%
Cost	1040

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;y \leq 8.6 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	52.9%
Cost	1040

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;y \leq 3.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	52.9%
Cost	1040

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;y \leq 1.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{1}{\frac{-t}{y \cdot z - x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-108}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	35.0%
Cost	912

\[\begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq 6.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4500:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Accuracy	35.0%
Cost	912

\[\begin{array}{l} t_1 := \frac{z}{\frac{t}{-y}}\\ \mathbf{if}\;z \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5800:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8
Accuracy	35.0%
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-120}:\\ \;\;\;\;\frac{z}{\frac{t}{-y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 10^{-58}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 12500:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9
Accuracy	53.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{-61} \lor \neg \left(z \leq 3900\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]

Alternative 10
Accuracy	52.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-47}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 11
Accuracy	35.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq 4.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6200:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 12
Accuracy	35.2%
Cost	192

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

Reproduce

herbie shell --seed 2023159 
(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))))