Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.4% → 97.4%

Time: 9.1s

Alternatives: 8

Speedup: 0.4×

• 27.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+278}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, z \cdot \frac{-t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+278)))
     (fma (/ y (pow (cbrt a) 2.0)) (/ x (cbrt a)) (* z (/ (- t) a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+278)) {
		tmp = fma((y / pow(cbrt(a), 2.0)), (x / cbrt(a)), (z * (-t / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+278))
		tmp = fma(Float64(y / (cbrt(a) ^ 2.0)), Float64(x / cbrt(a)), Float64(z * Float64(Float64(-t) / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+278]], $MachinePrecision]], N[(N[(y / N[Power[N[Power[a, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(x / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision] + N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 5.00000000000000029e278 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 57.6%

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

      2. *-commutative 57.6%

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

      3. add-cube-cbrt 57.6%

         \[\leadsto \frac{y \cdot x}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      4. times-frac 70.7%

         \[\leadsto \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{x}{\sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      5. fma-neg 74.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right)} \]

      6. pow2 74.3%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 94.3%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{z \cdot \frac{t}{a}}\right) \]

   4. Applied egg-rr 94.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -z \cdot \frac{t}{a}\right)} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000029e278

   1. Initial program 98.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+278}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, z \cdot \frac{-t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1000000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-131} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-92}\right) \land x \cdot y \leq 3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1000000000000.0)
   (/ x (/ a y))
   (if (or (<= (* x y) 2e-131)
           (and (not (<= (* x y) 5e-92)) (<= (* x y) 3e+18)))
     (* t (/ (- z) a))
     (* y (/ x a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1000000000000.0) {
		tmp = x / (a / y);
	} else if (((x * y) <= 2e-131) || (!((x * y) <= 5e-92) && ((x * y) <= 3e+18))) {
		tmp = t * (-z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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) :: tmp
    if ((x * y) <= (-1000000000000.0d0)) then
        tmp = x / (a / y)
    else if (((x * y) <= 2d-131) .or. (.not. ((x * y) <= 5d-92)) .and. ((x * y) <= 3d+18)) then
        tmp = t * (-z / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1000000000000.0) {
		tmp = x / (a / y);
	} else if (((x * y) <= 2e-131) || (!((x * y) <= 5e-92) && ((x * y) <= 3e+18))) {
		tmp = t * (-z / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1000000000000.0:
		tmp = x / (a / y)
	elif ((x * y) <= 2e-131) or (not ((x * y) <= 5e-92) and ((x * y) <= 3e+18)):
		tmp = t * (-z / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1000000000000.0)
		tmp = Float64(x / Float64(a / y));
	elseif ((Float64(x * y) <= 2e-131) || (!(Float64(x * y) <= 5e-92) && (Float64(x * y) <= 3e+18)))
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1000000000000.0)
		tmp = x / (a / y);
	elseif (((x * y) <= 2e-131) || (~(((x * y) <= 5e-92)) && ((x * y) <= 3e+18)))
		tmp = t * (-z / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1000000000000.0], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 2e-131], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-92]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 3e+18]]], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e12

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 80.0%

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

   5. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. un-div-inv 80.1%

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

   7. Applied egg-rr 80.1%

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

   if -1e12 < (*.f64 x y) < 2e-131 or 5.00000000000000011e-92 < (*.f64 x y) < 3e18

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. associate-/l* 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. distribute-neg-frac2 77.1%

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

   5. Simplified 77.1%

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

   if 2e-131 < (*.f64 x y) < 5.00000000000000011e-92 or 3e18 < (*.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. associate-*r/ 83.2%

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

   5. Simplified 83.2%

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

      1. clear-num 82.1%

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

      2. un-div-inv 82.1%

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

   7. Applied egg-rr 82.1%

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

      1. associate-/r/ 86.2%

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

   9. Applied egg-rr 86.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1000000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-131} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-92}\right) \land x \cdot y \leq 3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1000000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-92} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1000000000000.0)
   (/ x (/ a y))
   (if (<= (* x y) 2e-131)
     (* t (/ (- z) a))
     (if (or (<= (* x y) 5e-92) (not (<= (* x y) 3e+18)))
       (* y (/ x a))
       (* z (/ (- t) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1000000000000.0) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e-131) {
		tmp = t * (-z / a);
	} else if (((x * y) <= 5e-92) || !((x * y) <= 3e+18)) {
		tmp = y * (x / a);
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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) :: tmp
    if ((x * y) <= (-1000000000000.0d0)) then
        tmp = x / (a / y)
    else if ((x * y) <= 2d-131) then
        tmp = t * (-z / a)
    else if (((x * y) <= 5d-92) .or. (.not. ((x * y) <= 3d+18))) then
        tmp = y * (x / a)
    else
        tmp = z * (-t / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1000000000000.0) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e-131) {
		tmp = t * (-z / a);
	} else if (((x * y) <= 5e-92) || !((x * y) <= 3e+18)) {
		tmp = y * (x / a);
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1000000000000.0:
		tmp = x / (a / y)
	elif (x * y) <= 2e-131:
		tmp = t * (-z / a)
	elif ((x * y) <= 5e-92) or not ((x * y) <= 3e+18):
		tmp = y * (x / a)
	else:
		tmp = z * (-t / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1000000000000.0)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 2e-131)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif ((Float64(x * y) <= 5e-92) || !(Float64(x * y) <= 3e+18))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(z * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1000000000000.0)
		tmp = x / (a / y);
	elseif ((x * y) <= 2e-131)
		tmp = t * (-z / a);
	elseif (((x * y) <= 5e-92) || ~(((x * y) <= 3e+18)))
		tmp = y * (x / a);
	else
		tmp = z * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1000000000000.0], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-131], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 5e-92], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3e+18]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1e12

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 80.0%

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

   5. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. un-div-inv 80.1%

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

   7. Applied egg-rr 80.1%

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

   if -1e12 < (*.f64 x y) < 2e-131

   1. Initial program 91.0%

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

   3. Taylor expanded in x around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/l* 81.3%

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

      3. distribute-rgt-neg-in 81.3%

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

      4. distribute-neg-frac2 81.3%

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

   5. Simplified 81.3%

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

   if 2e-131 < (*.f64 x y) < 5.00000000000000011e-92 or 3e18 < (*.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. associate-*r/ 83.2%

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

   5. Simplified 83.2%

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

      1. clear-num 82.1%

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

      2. un-div-inv 82.1%

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

   7. Applied egg-rr 82.1%

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

      1. associate-/r/ 86.2%

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

   9. Applied egg-rr 86.2%

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

   if 5.00000000000000011e-92 < (*.f64 x y) < 3e18

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-*r/ 69.0%

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

      3. neg-mul-1 69.0%

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

      4. distribute-rgt-neg-in 69.0%

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

      5. distribute-frac-neg 69.0%

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

   5. Simplified 69.0%

      \[\leadsto \color{blue}{z \cdot \frac{-t}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1000000000000:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-92} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+291} \lor \neg \left(t\_1 \leq 1.2 \cdot 10^{+255}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -2e+291) (not (<= t_1 1.2e+255)))
     (* y (/ (- x (* t (/ z y))) a))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+291) || !(t_1 <= 1.2e+255)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-2d+291)) .or. (.not. (t_1 <= 1.2d+255))) then
        tmp = y * ((x - (t * (z / y))) / a)
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+291) || !(t_1 <= 1.2e+255)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -2e+291) or not (t_1 <= 1.2e+255):
		tmp = y * ((x - (t * (z / y))) / a)
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -2e+291) || !(t_1 <= 1.2e+255))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -2e+291) || ~((t_1 <= 1.2e+255)))
		tmp = y * ((x - (t * (z / y))) / a);
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+291], N[Not[LessEqual[t$95$1, 1.2e+255]], $MachinePrecision]], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e291 or 1.20000000000000003e255 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. unsub-neg 66.2%

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

      3. associate-/l* 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

      3. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

   9. Taylor expanded in y around inf 71.1%

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

       1. +-commutative 71.1%

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

       2. mul-1-neg 71.1%

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

       3. sub-neg 71.1%

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

       4. associate-/l/ 72.9%

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

       5. div-sub 77.4%

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

       6. associate-/l* 84.4%

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

   11. Simplified 84.4%

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

   if -1.9999999999999999e291 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.20000000000000003e255

   1. Initial program 98.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+291} \lor \neg \left(x \cdot y - z \cdot t \leq 1.2 \cdot 10^{+255}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+291}:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -2e+291)
     (* y (/ (- x (* t (/ z y))) a))
     (if (<= t_1 5e+278) (/ t_1 a) (* (/ t a) (- (* x (/ y t)) z))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+291) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 5e+278) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-2d+291)) then
        tmp = y * ((x - (t * (z / y))) / a)
    else if (t_1 <= 5d+278) then
        tmp = t_1 / a
    else
        tmp = (t / a) * ((x * (y / t)) - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+291) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 5e+278) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -2e+291:
		tmp = y * ((x - (t * (z / y))) / a)
	elif t_1 <= 5e+278:
		tmp = t_1 / a
	else:
		tmp = (t / a) * ((x * (y / t)) - z)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+291)
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	elseif (t_1 <= 5e+278)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(t / a) * Float64(Float64(x * Float64(y / t)) - z));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -2e+291)
		tmp = y * ((x - (t * (z / y))) / a);
	elseif (t_1 <= 5e+278)
		tmp = t_1 / a;
	else
		tmp = (t / a) * ((x * (y / t)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+291], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], N[(t$95$1 / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e291

   1. Initial program 68.7%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. associate-/l* 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in y around inf 77.8%

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

       1. +-commutative 77.8%

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

       2. mul-1-neg 77.8%

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

       3. sub-neg 77.8%

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

       4. associate-/l/ 77.8%

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

       5. div-sub 81.1%

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

       6. associate-/l* 84.2%

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

   11. Simplified 84.2%

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

   if -1.9999999999999999e291 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000029e278

   1. Initial program 98.5%

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

   if 5.00000000000000029e278 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 63.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 56.9%

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

      2. *-commutative 56.9%

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

      3. add-cube-cbrt 56.9%

         \[\leadsto \frac{y \cdot x}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      4. times-frac 68.9%

         \[\leadsto \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{x}{\sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      5. fma-neg 72.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right)} \]

      6. pow2 72.1%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 93.3%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{z \cdot \frac{t}{a}}\right) \]

   4. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -z \cdot \frac{t}{a}\right)} \]

   5. Taylor expanded in t around inf 81.4%

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

      1. times-frac 87.3%

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

      2. associate-*l/ 90.9%

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

      3. div-sub 90.9%

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

      4. fma-neg 90.9%

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

      5. associate-*r/ 66.5%

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

      6. associate-*l/ 90.5%

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

      7. fma-define 90.5%

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

      8. unsub-neg 90.5%

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

   7. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+291}:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 -2e+291)
     (- (* x (/ y a)) (* z (/ t a)))
     (if (<= t_1 5e+278) (/ t_1 a) (* (/ t a) (- (* x (/ y t)) z))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+291) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+278) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-2d+291)) then
        tmp = (x * (y / a)) - (z * (t / a))
    else if (t_1 <= 5d+278) then
        tmp = t_1 / a
    else
        tmp = (t / a) * ((x * (y / t)) - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+291) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+278) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -2e+291:
		tmp = (x * (y / a)) - (z * (t / a))
	elif t_1 <= 5e+278:
		tmp = t_1 / a
	else:
		tmp = (t / a) * ((x * (y / t)) - z)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+291)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	elseif (t_1 <= 5e+278)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(t / a) * Float64(Float64(x * Float64(y / t)) - z));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -2e+291)
		tmp = (x * (y / a)) - (z * (t / a));
	elseif (t_1 <= 5e+278)
		tmp = t_1 / a;
	else
		tmp = (t / a) * ((x * (y / t)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+291], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], N[(t$95$1 / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e291

   1. Initial program 68.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 65.3%

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

      2. associate-/l* 77.8%

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

      3. associate-/l* 93.2%

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

   4. Applied egg-rr 93.2%

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

   if -1.9999999999999999e291 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000029e278

   1. Initial program 98.5%

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

   if 5.00000000000000029e278 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 63.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 56.9%

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

      2. *-commutative 56.9%

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

      3. add-cube-cbrt 56.9%

         \[\leadsto \frac{y \cdot x}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      4. times-frac 68.9%

         \[\leadsto \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{x}{\sqrt[3]{a}}} - \frac{z \cdot t}{a} \]

      5. fma-neg 72.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right)} \]

      6. pow2 72.1%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 93.3%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{z \cdot \frac{t}{a}}\right) \]

   4. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -z \cdot \frac{t}{a}\right)} \]

   5. Taylor expanded in t around inf 81.4%

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

      1. times-frac 87.3%

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

      2. associate-*l/ 90.9%

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

      3. div-sub 90.9%

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

      4. fma-neg 90.9%

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

      5. associate-*r/ 66.5%

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

      6. associate-*l/ 90.5%

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

      7. fma-define 90.5%

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

      8. unsub-neg 90.5%

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

   7. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) (- INFINITY))
   (* z (/ (- t) a))
   (if (<= (* z t) 5e+280) (/ (- (* x y) (* z t)) a) (* t (/ (- z) a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 5e+280) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 5e+280) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t * (-z / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -math.inf:
		tmp = z * (-t / a)
	elif (z * t) <= 5e+280:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t * (-z / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (Float64(z * t) <= 5e+280)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(t * Float64(Float64(-z) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -Inf)
		tmp = z * (-t / a);
	elseif ((z * t) <= 5e+280)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t * (-z / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+280], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -inf.0

   1. Initial program 52.5%

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

   3. Taylor expanded in x around 0 52.5%

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

      1. *-commutative 52.5%

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

      2. associate-*r/ 93.6%

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

      3. neg-mul-1 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. distribute-frac-neg 93.6%

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

   5. Simplified 93.6%

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

   if -inf.0 < (*.f64 z t) < 5.0000000000000002e280

   1. Initial program 95.3%

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

   if 5.0000000000000002e280 < (*.f64 z t)

   1. Initial program 59.8%

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

   3. Taylor expanded in x around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. associate-/l* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. distribute-neg-frac2 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ x \cdot \frac{y}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* x (/ y a)))

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this 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
    code = x * (y / a)
end function

Java

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

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return x * (y / a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(x * Float64(y / a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = x * (y / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.7%

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

3. Taylor expanded in x around inf 53.9%

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

   1. associate-*r/ 53.0%

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

5. Simplified 53.0%

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

6. Final simplification 53.0%

   \[\leadsto x \cdot \frac{y}{a} \]
7. Add Preprocessing

Developer target: 92.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	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 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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