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

Average Accuracy: 83.2% → 96.2%

Time: 15.2s

Precision: binary64

Cost: 2760.00

Math

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

↓

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ t_3 := y \cdot z - x\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-138}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y}} - \frac{x}{t_1}\\ \mathbf{elif}\;t_2 \leq 10^{+306}:\\ \;\;\;\;\frac{1}{a \cdot \frac{z}{t_3} - \frac{t}{t_3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

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 (/ (- x (* y z)) (- t (* z a))))
        (t_3 (- (* y z) x)))
   (if (<= t_2 -1e-138)
     (- (/ z (/ t_1 y)) (/ x t_1))
     (if (<= t_2 1e+306)
       (/ 1.0 (- (* a (/ z t_3)) (/ t t_3)))
       (/ y (- a (/ t z)))))))

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 = (x - (y * z)) / (t - (z * a));
	double t_3 = (y * z) - x;
	double tmp;
	if (t_2 <= -1e-138) {
		tmp = (z / (t_1 / y)) - (x / t_1);
	} else if (t_2 <= 1e+306) {
		tmp = 1.0 / ((a * (z / t_3)) - (t / t_3));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x - (y * z)) / (t - (a * z))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = (x - (y * z)) / (t - (z * a))
    t_3 = (y * z) - x
    if (t_2 <= (-1d-138)) then
        tmp = (z / (t_1 / y)) - (x / t_1)
    else if (t_2 <= 1d+306) then
        tmp = 1.0d0 / ((a * (z / t_3)) - (t / t_3))
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

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 = (x - (y * z)) / (t - (z * a));
	double t_3 = (y * z) - x;
	double tmp;
	if (t_2 <= -1e-138) {
		tmp = (z / (t_1 / y)) - (x / t_1);
	} else if (t_2 <= 1e+306) {
		tmp = 1.0 / ((a * (z / t_3)) - (t / t_3));
	} else {
		tmp = y / (a - (t / z));
	}
	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 = (x - (y * z)) / (t - (z * a))
	t_3 = (y * z) - x
	tmp = 0
	if t_2 <= -1e-138:
		tmp = (z / (t_1 / y)) - (x / t_1)
	elif t_2 <= 1e+306:
		tmp = 1.0 / ((a * (z / t_3)) - (t / t_3))
	else:
		tmp = y / (a - (t / z))
	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(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	t_3 = Float64(Float64(y * z) - x)
	tmp = 0.0
	if (t_2 <= -1e-138)
		tmp = Float64(Float64(z / Float64(t_1 / y)) - Float64(x / t_1));
	elseif (t_2 <= 1e+306)
		tmp = Float64(1.0 / Float64(Float64(a * Float64(z / t_3)) - Float64(t / t_3)));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	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 = (x - (y * z)) / (t - (z * a));
	t_3 = (y * z) - x;
	tmp = 0.0;
	if (t_2 <= -1e-138)
		tmp = (z / (t_1 / y)) - (x / t_1);
	elseif (t_2 <= 1e+306)
		tmp = 1.0 / ((a * (z / t_3)) - (t / t_3));
	else
		tmp = y / (a - (t / z));
	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[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-138], N[(N[(z / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+306], N[(1.0 / N[(N[(a * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision] - N[(t / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	83.2%
Target	97.4%
Herbie	96.2%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000007e-138

   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	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 91.0	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 91.0	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 91.0	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 91.0	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 91.0	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 91.0	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      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 90.8%

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

   4. Applied egg-rr 94.4%

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

   if -1.00000000000000007e-138 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000002e306

   1. Initial program 89.9%

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

   2. Simplified 89.9%

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

      [Start] 89.9	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 89.9	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 89.9	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 89.9	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 89.9	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 89.9	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 89.9	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 89.9	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 89.9	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 89.9	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 89.9	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 89.9	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 89.7%

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

   4. Applied egg-rr 89.2%

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

   5. Applied egg-rr 96.7%

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

   if 1.00000000000000002e306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.3%

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

   2. Simplified 0.3%

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

      [Start] 0.3	\[ \frac{x - y \cdot z}{t - a \cdot z} \]
      sub-neg [=>] 0.3	\[ \frac{\color{blue}{x + \left(-y \cdot z\right)}}{t - a \cdot z} \]
      remove-double-neg [<=] 0.3	\[ \frac{\color{blue}{\left(-\left(-x\right)\right)} + \left(-y \cdot z\right)}{t - a \cdot z} \]
      distribute-neg-in [<=] 0.3	\[ \frac{\color{blue}{-\left(\left(-x\right) + y \cdot z\right)}}{t - a \cdot z} \]
      +-commutative [<=] 0.3	\[ \frac{-\color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{t - a \cdot z} \]
      sub-neg [<=] 0.3	\[ \frac{-\color{blue}{\left(y \cdot z - x\right)}}{t - a \cdot z} \]
      neg-mul-1 [=>] 0.3	\[ \frac{\color{blue}{-1 \cdot \left(y \cdot z - x\right)}}{t - a \cdot z} \]
      sub-neg [=>] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{t + \left(-a \cdot z\right)}} \]
      remove-double-neg [<=] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{\left(-\left(-t\right)\right)} + \left(-a \cdot z\right)} \]
      distribute-neg-in [<=] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-\left(\left(-t\right) + a \cdot z\right)}} \]
      +-commutative [<=] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z + \left(-t\right)\right)}} \]
      sub-neg [<=] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{-\color{blue}{\left(a \cdot z - t\right)}} \]
      neg-mul-1 [=>] 0.3	\[ \frac{-1 \cdot \left(y \cdot z - x\right)}{\color{blue}{-1 \cdot \left(a \cdot z - t\right)}} \]
      times-frac [=>] 0.3	\[ \color{blue}{\frac{-1}{-1} \cdot \frac{y \cdot z - x}{a \cdot z - t}} \]
      metadata-eval [=>] 0.3	\[ \color{blue}{1} \cdot \frac{y \cdot z - x}{a \cdot z - t} \]
      *-lft-identity [=>] 0.3	\[ \color{blue}{\frac{y \cdot z - x}{a \cdot z - t}} \]
      *-commutative [=>] 0.3	\[ \frac{y \cdot z - x}{\color{blue}{z \cdot a} - t} \]

   3. Applied egg-rr 0.3%

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

   4. Applied egg-rr 0.3%

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

   5. Applied egg-rr 0.3%

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

   6. Taylor expanded in y around inf 99.8%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-138}:\\ \;\;\;\;\frac{z}{\frac{z \cdot a - t}{y}} - \frac{x}{z \cdot a - t}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+306}:\\ \;\;\;\;\frac{1}{a \cdot \frac{z}{y \cdot z - x} - \frac{t}{y \cdot z - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.5%
Cost	3794.00

\[\begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -1 \cdot 10^{-314} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+306}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	94.9%
Cost	3021.00

\[\begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-314}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y}} - \frac{x}{t_1}\\ \mathbf{elif}\;\neg \left(t_2 \leq 0\right) \land t_2 \leq 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]

Alternative 3
Accuracy	58.2%
Cost	1108.00

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 410000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	71.2%
Cost	1040.00

\[\begin{array}{l} t_1 := \frac{-x}{z \cdot a - t}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-277}:\\ \;\;\;\;\frac{y \cdot z - x}{-t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	62.7%
Cost	976.00

\[\begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 10^{-25}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	52.1%
Cost	912.00

\[\begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+75}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7
Accuracy	71.1%
Cost	777.00

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+72} \lor \neg \left(z \leq 4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot a - t}\\ \end{array} \]

Alternative 8
Accuracy	52.3%
Cost	456.00

\[\begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+42}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9
Accuracy	32.8%
Cost	192.00

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

Reproduce

herbie shell --seed 2023096 
(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))))