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

Percentage Accurate: 85.4% → 91.7%

Time: 5.1s

Alternatives: 8

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+265}:\\ \;\;\;\;\frac{\frac{x}{y} - z}{t\_1} \cdot y\\ \mathbf{elif}\;t\_2 \leq 10^{+289}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 -1e+265)
     (* (/ (- (/ x y) z) t_1) y)
     (if (<= t_2 1e+289) t_2 (/ (- y (/ x z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -1e+265) {
		tmp = (((x / y) - z) / t_1) * y;
	} else if (t_2 <= 1e+289) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x - (y * z)) / t_1
    if (t_2 <= (-1d+265)) then
        tmp = (((x / y) - z) / t_1) * y
    else if (t_2 <= 1d+289) then
        tmp = t_2
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -1e+265) {
		tmp = (((x / y) - z) / t_1) * y;
	} else if (t_2 <= 1e+289) {
		tmp = t_2;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x - (y * z)) / t_1
	tmp = 0
	if t_2 <= -1e+265:
		tmp = (((x / y) - z) / t_1) * y
	elif t_2 <= 1e+289:
		tmp = t_2
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= -1e+265)
		tmp = Float64(Float64(Float64(Float64(x / y) - z) / t_1) * y);
	elseif (t_2 <= 1e+289)
		tmp = t_2;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_2 <= -1e+265)
		tmp = (((x / y) - z) / t_1) * y;
	elseif (t_2 <= 1e+289)
		tmp = t_2;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+265], N[(N[(N[(N[(x / y), $MachinePrecision] - z), $MachinePrecision] / t$95$1), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$2, 1e+289], t$95$2, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000007e265

   1. Initial program 68.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{z}{t - a \cdot z} + \frac{x}{y \cdot \left(t - a \cdot z\right)}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/r* N/A

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

      5. associate-*r/ N/A

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

      6. div-add-rev N/A

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

      7. metadata-eval N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. *-lft-identity N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -1.00000000000000007e265 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.0000000000000001e289

   1. Initial program 96.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if 1.0000000000000001e289 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 44.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 15.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{y - \frac{x}{z}}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 85.3%

      \[\leadsto \frac{y - \frac{x}{z}}{a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{if}\;t\_1 \leq 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* a z)))))
   (if (<= t_1 1e+289) t_1 (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (a * z));
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (a * z))
    if (t_1 <= 1d+289) then
        tmp = t_1
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (a * z));
	double tmp;
	if (t_1 <= 1e+289) {
		tmp = t_1;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (a * z))
	tmp = 0
	if t_1 <= 1e+289:
		tmp = t_1
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
	tmp = 0.0
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (a * z));
	tmp = 0.0;
	if (t_1 <= 1e+289)
		tmp = t_1;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+289], t$95$1, N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.0000000000000001e289

   1. Initial program 93.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if 1.0000000000000001e289 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 44.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 15.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{y - \frac{x}{z}}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 85.3%

      \[\leadsto \frac{y - \frac{x}{z}}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+67} \lor \neg \left(a \leq 1.12 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e+67) (not (<= a 1.12e+85)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e+67) || !(a <= 1.12e+85)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	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
    real(8) :: tmp
    if ((a <= (-7.5d+67)) .or. (.not. (a <= 1.12d+85))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e+67) || !(a <= 1.12e+85)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e+67) or not (a <= 1.12e+85):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e+67) || !(a <= 1.12e+85))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e+67) || ~((a <= 1.12e+85)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e+67], N[Not[LessEqual[a, 1.12e+85]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5000000000000005e67 or 1.11999999999999993e85 < a

   1. Initial program 80.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 45.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{y - \frac{x}{z}}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.9%

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

   if -7.5000000000000005e67 < a < 1.11999999999999993e85

   1. Initial program 92.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 74.2

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

   5. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+67} \lor \neg \left(a \leq 1.12 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+84} \lor \neg \left(y \leq 1.35 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(z, a, -t\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e+84) (not (<= y 1.35e+23)))
   (* (/ y (fma z a (- t))) z)
   (/ x (- t (* a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e+84) || !(y <= 1.35e+23)) {
		tmp = (y / fma(z, a, -t)) * z;
	} else {
		tmp = x / (t - (a * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e+84) || !(y <= 1.35e+23))
		tmp = Float64(Float64(y / fma(z, a, Float64(-t))) * z);
	else
		tmp = Float64(x / Float64(t - Float64(a * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e+84], N[Not[LessEqual[y, 1.35e+23]], $MachinePrecision]], N[(N[(y / N[(z * a + (-t)), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000001e84 or 1.3499999999999999e23 < y

   1. Initial program 77.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \frac{z \cdot y}{\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(a\right)\right) \cdot z\right)}\right)} \]

      7. mul-1-neg N/A

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

      8. associate-*r* N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. associate-*r* N/A

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

      12. mul-1-neg N/A

          \[\leadsto \frac{z \cdot y}{\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot z\right)\right) + \left(\mathsf{neg}\left(t\right)\right)} \]

      13. distribute-lft-neg-out N/A

          \[\leadsto \frac{z \cdot y}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right) \cdot z} + \left(\mathsf{neg}\left(t\right)\right)} \]

      14. mul-1-neg N/A

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

      15. distribute-lft-neg-in N/A

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

      16. metadata-eval N/A

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

      17. *-lft-identity N/A

          \[\leadsto \frac{z \cdot y}{\color{blue}{a} \cdot z + \left(\mathsf{neg}\left(t\right)\right)} \]

      18. lower-fma.f64 N/A

          \[\leadsto \frac{z \cdot y}{\color{blue}{\mathsf{fma}\left(a, z, \mathsf{neg}\left(t\right)\right)}} \]

      19. lower-neg.f64 56.2

          \[\leadsto \frac{z \cdot y}{\mathsf{fma}\left(a, z, \color{blue}{-t}\right)} \]

   5. Applied rewrites 56.2%

      \[\leadsto \color{blue}{\frac{z \cdot y}{\mathsf{fma}\left(a, z, -t\right)}} \]
   6. Step-by-step derivation

   7. Applied rewrites 68.2%

      \[\leadsto \color{blue}{\frac{y}{\mathsf{fma}\left(z, a, -t\right)} \cdot z} \]

   if -5.0000000000000001e84 < y < 1.3499999999999999e23

   1. Initial program 96.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+84} \lor \neg \left(y \leq 1.35 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(z, a, -t\right)} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+64} \lor \neg \left(z \leq 8.8 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.18e+64) (not (<= z 8.8e+142))) (/ y a) (/ (- x (* z y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.18e+64) || !(z <= 8.8e+142)) {
		tmp = y / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	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
    real(8) :: tmp
    if ((z <= (-1.18d+64)) .or. (.not. (z <= 8.8d+142))) then
        tmp = y / a
    else
        tmp = (x - (z * y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.18e+64) || !(z <= 8.8e+142)) {
		tmp = y / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.18e+64) or not (z <= 8.8e+142):
		tmp = y / a
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.18e+64) || !(z <= 8.8e+142))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.18e+64) || ~((z <= 8.8e+142)))
		tmp = y / a;
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.18e+64], N[Not[LessEqual[z, 8.8e+142]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.18000000000000006e64 or 8.79999999999999947e142 < z

   1. Initial program 61.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 66.1

         \[\leadsto \color{blue}{\frac{y}{a}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -1.18000000000000006e64 < z < 8.79999999999999947e142

   1. Initial program 98.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

      \[\leadsto \color{blue}{\frac{x - z \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+64} \lor \neg \left(z \leq 8.8 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+61} \lor \neg \left(z \leq 6.2 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+61) (not (<= z 6.2e+115))) (/ y a) (/ x (- t (* a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+61) || !(z <= 6.2e+115)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (a * 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
    real(8) :: tmp
    if ((z <= (-8.8d+61)) .or. (.not. (z <= 6.2d+115))) then
        tmp = y / a
    else
        tmp = x / (t - (a * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+61) || !(z <= 6.2e+115)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (a * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+61) or not (z <= 6.2e+115):
		tmp = y / a
	else:
		tmp = x / (t - (a * z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+61) || !(z <= 6.2e+115))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(a * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e+61) || ~((z <= 6.2e+115)))
		tmp = y / a;
	else
		tmp = x / (t - (a * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+61], N[Not[LessEqual[z, 6.2e+115]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e61 or 6.2000000000000001e115 < z

   1. Initial program 62.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 64.0

         \[\leadsto \color{blue}{\frac{y}{a}} \]

   5. Applied rewrites 64.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -8.8000000000000001e61 < z < 6.2000000000000001e115

   1. Initial program 98.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+61} \lor \neg \left(z \leq 6.2 \cdot 10^{+115}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+39} \lor \neg \left(z \leq 170\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+39) (not (<= z 170.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+39) || !(z <= 170.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	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
    real(8) :: tmp
    if ((z <= (-5.2d+39)) .or. (.not. (z <= 170.0d0))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+39) || !(z <= 170.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+39) or not (z <= 170.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+39) || !(z <= 170.0))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+39) || ~((z <= 170.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+39], N[Not[LessEqual[z, 170.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e39 or 170 < z

   1. Initial program 71.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 54.3

         \[\leadsto \color{blue}{\frac{y}{a}} \]

   5. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -5.2e39 < z < 170

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{x}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 55.8

         \[\leadsto \color{blue}{\frac{x}{t}} \]

   5. Applied rewrites 55.8%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+39} \lor \neg \left(z \leq 170\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

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

C

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

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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\frac{x}{t}} \]
4. Step-by-step derivation

   1. lower-/.f64 39.3

      \[\leadsto \color{blue}{\frac{x}{t}} \]

5. Applied rewrites 39.3%

   \[\leadsto \color{blue}{\frac{x}{t}} \]
6. Add Preprocessing

Developer Target 1: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024332 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

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