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

Average Error: 10.1 → 3.2

Time: 15.9s

Precision: binary64

Cost: 3792

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-322}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(1 + \frac{\frac{t}{z}}{a}\right)\\ \end{array} \]

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))
     (/ y (/ (- (* z a) t) z))
     (if (<= t_1 -5e-322)
       t_1
       (if (<= t_1 0.0)
         (- (/ y a) (/ (/ x a) z))
         (if (<= t_1 1e+307) t_1 (* (/ y a) (+ 1.0 (/ (/ t 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 = y / (((z * a) - t) / z);
	} else if (t_1 <= -5e-322) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = (y / a) * (1.0 + ((t / 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 = y / (((z * a) - t) / z);
	} else if (t_1 <= -5e-322) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (y / a) - ((x / a) / z);
	} else if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = (y / a) * (1.0 + ((t / 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 = y / (((z * a) - t) / z)
	elif t_1 <= -5e-322:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (y / a) - ((x / a) / z)
	elif t_1 <= 1e+307:
		tmp = t_1
	else:
		tmp = (y / a) * (1.0 + ((t / 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(y / Float64(Float64(Float64(z * a) - t) / z));
	elseif (t_1 <= -5e-322)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * Float64(1.0 + Float64(Float64(t / 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 = y / (((z * a) - t) / z);
	elseif (t_1 <= -5e-322)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (y / a) - ((x / a) / z);
	elseif (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = (y / a) * (1.0 + ((t / 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[(y / N[(N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-322], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], t$95$1, N[(N[(y / a), $MachinePrecision] * N[(1.0 + N[(N[(t / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	10.1
Target	1.7
Herbie	3.2

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot a - t}} \]
      Proof
      (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 z a) t)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) x)) (-.f64 (*.f64 z a) t)): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 a z)) t)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 y z) x)) (*.f64 -1 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 y z) x))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 y z) (neg.f64 x)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 x) (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> remove-double-neg_binary64 x) (neg.f64 (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 a z) (neg.f64 t))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 t) (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 t)) (neg.f64 (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (+.f64 (Rewrite=> remove-double-neg_binary64 t) (neg.f64 (*.f64 a z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= sub-neg_binary64 (-.f64 t (*.f64 a z)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in y around inf 64.0

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

   4. Simplified 0.3

      \[\leadsto \color{blue}{\frac{z}{a \cdot z - t} \cdot y} \]
      Proof
      (*.f64 (/.f64 z (-.f64 (*.f64 a z) t)) y): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 z (/.f64 (-.f64 (*.f64 a z) t) y))): 54 points increase in error, 38 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z y) (-.f64 (*.f64 a z) t))): 55 points increase in error, 43 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y z)) (-.f64 (*.f64 a z) t)): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 0.2

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -4.99006e-322 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.99999999999999986e306

   1. Initial program 0.2

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

   if -4.99006e-322 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 23.7

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

   2. Simplified 23.7

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot a - t}} \]
      Proof
      (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 z a) t)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) x)) (-.f64 (*.f64 z a) t)): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 a z)) t)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 y z) x)) (*.f64 -1 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 y z) x))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 y z) (neg.f64 x)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 x) (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> remove-double-neg_binary64 x) (neg.f64 (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 a z) (neg.f64 t))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 t) (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 t)) (neg.f64 (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (+.f64 (Rewrite=> remove-double-neg_binary64 t) (neg.f64 (*.f64 a z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= sub-neg_binary64 (-.f64 t (*.f64 a z)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 28.5

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

   4. Simplified 16.8

      \[\leadsto \color{blue}{\frac{y}{a} + \frac{\frac{y}{a} \cdot \frac{t}{a} - \frac{x}{a}}{z}} \]
      Proof
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (*.f64 (/.f64 y a) (/.f64 t a)) (/.f64 x a)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y t) (*.f64 a a))) (/.f64 x a)) z)): 20 points increase in error, 4 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (/.f64 (*.f64 y t) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 x a)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) (neg.f64 (/.f64 x a)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x a)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 x a)) (/.f64 (*.f64 y t) (pow.f64 a 2)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (*.f64 -1 (/.f64 x a)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (*.f64 -1 (/.f64 x a)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 y t) (pow.f64 a 2)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 -1 (/.f64 x a)) (*.f64 -1 (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))) z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> unsub-neg_binary64 (-.f64 (/.f64 y a) (/.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 y a) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 x a) z) (/.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 y a) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 x (*.f64 a z))) (/.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) z))): 14 points increase in error, 10 points decrease in error
      (-.f64 (/.f64 y a) (-.f64 (/.f64 x (*.f64 a z)) (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 3 points increase in error, 8 points decrease in error
      (Rewrite=> associate--r-_binary64 (+.f64 (-.f64 (/.f64 y a) (/.f64 x (*.f64 a z))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 y a) (neg.f64 (/.f64 x (*.f64 a z))))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (/.f64 x (*.f64 a z))) (/.f64 y a))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x (*.f64 a z)))) (/.f64 y a)) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (*.f64 -1 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in y around 0 27.0

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

   6. Simplified 16.3

      \[\leadsto \frac{y}{a} + \color{blue}{\frac{\frac{-x}{a}}{z}} \]
      Proof
      (/.f64 (/.f64 (neg.f64 x) a) z): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 x)) a) z): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 -1 x) (*.f64 a z))): 49 points increase in error, 40 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 x (*.f64 a z)))): 0 points increase in error, 0 points decrease in error

   if 9.99999999999999986e306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 63.8

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

   2. Simplified 63.8

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot a - t}} \]
      Proof
      (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 z a) t)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y z) x)) (-.f64 (*.f64 z a) t)): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 a z)) t)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 y z) x)) (*.f64 -1 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 y z) x))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 y z) (neg.f64 x)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 x) (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (*.f64 y z)))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> remove-double-neg_binary64 x) (neg.f64 (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x (*.f64 y z))) (*.f64 -1 (-.f64 (*.f64 a z) t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 (*.f64 a z) t)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 a z) (neg.f64 t))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (neg.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 t) (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite=> distribute-neg-in_binary64 (+.f64 (neg.f64 (neg.f64 t)) (neg.f64 (*.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (+.f64 (Rewrite=> remove-double-neg_binary64 t) (neg.f64 (*.f64 a z)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x (*.f64 y z)) (Rewrite<= sub-neg_binary64 (-.f64 t (*.f64 a z)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 25.2

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

   4. Simplified 13.3

      \[\leadsto \color{blue}{\frac{y}{a} + \frac{\frac{y}{a} \cdot \frac{t}{a} - \frac{x}{a}}{z}} \]
      Proof
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (*.f64 (/.f64 y a) (/.f64 t a)) (/.f64 x a)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y t) (*.f64 a a))) (/.f64 x a)) z)): 20 points increase in error, 4 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (-.f64 (/.f64 (*.f64 y t) (Rewrite<= unpow2_binary64 (pow.f64 a 2))) (/.f64 x a)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) (neg.f64 (/.f64 x a)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x a)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 x a)) (/.f64 (*.f64 y t) (pow.f64 a 2)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (*.f64 -1 (/.f64 x a)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (+.f64 (*.f64 -1 (/.f64 x a)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 y t) (pow.f64 a 2)))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 -1 (/.f64 x a)) (*.f64 -1 (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))))) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 y a) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))) z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> unsub-neg_binary64 (-.f64 (/.f64 y a) (/.f64 (-.f64 (/.f64 x a) (/.f64 (*.f64 y t) (pow.f64 a 2))) z))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 y a) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (/.f64 x a) z) (/.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 y a) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 x (*.f64 a z))) (/.f64 (/.f64 (*.f64 y t) (pow.f64 a 2)) z))): 14 points increase in error, 10 points decrease in error
      (-.f64 (/.f64 y a) (-.f64 (/.f64 x (*.f64 a z)) (Rewrite<= associate-/r*_binary64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 3 points increase in error, 8 points decrease in error
      (Rewrite=> associate--r-_binary64 (+.f64 (-.f64 (/.f64 y a) (/.f64 x (*.f64 a z))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 y a) (neg.f64 (/.f64 x (*.f64 a z))))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (/.f64 x (*.f64 a z))) (/.f64 y a))) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 x (*.f64 a z)))) (/.f64 y a)) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 x (*.f64 a z))) (/.f64 y a)) (*.f64 -1 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z))))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in y around inf 9.6

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

   6. Simplified 8.7

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(1 + \frac{\frac{t}{z}}{a}\right)} \]
      Proof
      (*.f64 (/.f64 y a) (+.f64 1 (/.f64 (/.f64 t z) a))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 y a) (+.f64 1 (Rewrite=> associate-/l/_binary64 (/.f64 t (*.f64 a z))))): 7 points increase in error, 17 points decrease in error
      (*.f64 (/.f64 y a) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 t (*.f64 a z)) 1))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 y a) (+.f64 (/.f64 t (*.f64 a z)) (Rewrite<= metadata-eval (neg.f64 -1)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 y a) (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 t (*.f64 a z)) -1))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y a) (/.f64 t (*.f64 a z))) (*.f64 (/.f64 y a) -1))): 3 points increase in error, 2 points decrease in error
      (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y t) (*.f64 a (*.f64 a z)))) (*.f64 (/.f64 y a) -1)): 31 points increase in error, 11 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 a a) z))) (*.f64 (/.f64 y a) -1)): 15 points increase in error, 4 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 a 2)) z)) (*.f64 (/.f64 y a) -1)): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y -1) a))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (Rewrite<= associate-*r/_binary64 (*.f64 y (/.f64 -1 a)))): 19 points increase in error, 3 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (*.f64 y (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) a))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (*.f64 y (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 a))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (Rewrite=> *-commutative_binary64 (*.f64 (neg.f64 (/.f64 1 a)) y))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> cancel-sign-sub_binary64 (+.f64 (/.f64 (*.f64 y t) (*.f64 (pow.f64 a 2) z)) (*.f64 (/.f64 1 a) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 t y)) (*.f64 (pow.f64 a 2) z)) (*.f64 (/.f64 1 a) y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 t (*.f64 (pow.f64 a 2) z)) y)) (*.f64 (/.f64 1 a) y)): 6 points increase in error, 16 points decrease in error
      (Rewrite<= distribute-rgt-in_binary64 (*.f64 y (+.f64 (/.f64 t (*.f64 (pow.f64 a 2) z)) (/.f64 1 a)))): 4 points increase in error, 2 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 3.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -5 \cdot 10^{-322}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+307}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(1 + \frac{\frac{t}{z}}{a}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.1
Cost	3404

\[\begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t_1} - \frac{y}{\frac{t_1}{z}}\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{-322}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 2
Error	20.5
Cost	1504

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -1.326087997355754 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6666415030706505 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -5.6201730598367596 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.24387497720412 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3582859300696995 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 4.4804673252140417 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3787404827315 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.907052763534918 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.5
Cost	1504

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -1.326087997355754 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6666415030706505 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -5.6201730598367596 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.24387497720412 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3582859300696995 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 4.4804673252140417 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t} - \frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.3787404827315 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.907052763534918 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	37.4
Cost	1440

\[\begin{array}{l} t_1 := y \cdot \frac{-z}{t}\\ \mathbf{if}\;a \leq -3.42119026625898 \cdot 10^{+230}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -4.892100330510754 \cdot 10^{+147}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;a \leq -3.6947706394969627 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq 4.970412288747455 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.69391989161264 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq 3.722260101656925 \cdot 10^{-44}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5
Error	28.7
Cost	1440

\[\begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -9.9873216686308 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq -7.093115502997947 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.0337132441218047 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 2.3608568955277423 \cdot 10^{-14}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq 26450045369257.875:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;t \leq 3.780623481393505 \cdot 10^{+78}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq 5.114197621311976 \cdot 10^{+144}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;t \leq 8.226207345533928 \cdot 10^{+231}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	37.0
Cost	1176

\[\begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -3.42119026625898 \cdot 10^{+230}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -4.892100330510754 \cdot 10^{+147}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;a \leq -3.6947706394969627 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.722260101656925 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Error	20.9
Cost	972

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -2.0509166705494974 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.69391989161264 \cdot 10^{-46}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.1719813428439755 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	20.2
Cost	972

\[\begin{array}{l} t_1 := \frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{if}\;a \leq -2.0509166705494974 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.69391989161264 \cdot 10^{-46}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.1719813428439755 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{\frac{z \cdot a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.8
Cost	712

\[\begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -2.0509166705494974 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.083657806743804 \cdot 10^{-28}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	29.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4412619779503693 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4804673252140417 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 11
Error	42.3
Cost	192

\[\frac{y}{a} \]

Reproduce

herbie shell --seed 2022294 
(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))))