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

Percentage Accurate: 91.5% → 94.9%

Time: 8.7s

Alternatives: 9

Speedup: 0.6×

• 28.8% 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: 91.5% 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: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;x \cdot \frac{y}{a} + z \cdot \frac{-1}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(x \cdot \frac{y}{t} - z\right)}{a}\\ \end{array} \end{array} \]

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 (<= t_1 4e+305)
     (/ t_1 a)
     (if (<= t_1 INFINITY)
       (+ (* x (/ y a)) (* z (/ -1.0 (/ a t))))
       (/ (* t (- (* x (/ y 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 4e+305) {
		tmp = t_1 / a;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x * (y / a)) + (z * (-1.0 / (a / t)));
	} else {
		tmp = (t * ((x * (y / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 4e+305) {
		tmp = t_1 / a;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) + (z * (-1.0 / (a / t)));
	} else {
		tmp = (t * ((x * (y / t)) - z)) / 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 <= 4e+305:
		tmp = t_1 / a
	elif t_1 <= math.inf:
		tmp = (x * (y / a)) + (z * (-1.0 / (a / t)))
	else:
		tmp = (t * ((x * (y / t)) - z)) / 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 <= 4e+305)
		tmp = Float64(t_1 / a);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x * Float64(y / a)) + Float64(z * Float64(-1.0 / Float64(a / t))));
	else
		tmp = Float64(Float64(t * Float64(Float64(x * Float64(y / t)) - 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 4e+305)
		tmp = t_1 / a;
	elseif (t_1 <= Inf)
		tmp = (x * (y / a)) + (z * (-1.0 / (a / t)));
	else
		tmp = (t * ((x * (y / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+305], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-1.0 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 96.8%

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

   if 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 57.8%

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

      1. div-sub 52.8%

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

      2. associate-/l* 57.3%

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

      3. associate-/l* 89.8%

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

   4. Applied egg-rr 89.8%

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

      1. clear-num 89.8%

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

      2. inv-pow 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. unpow-1 89.8%

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

   8. Simplified 89.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 66.7%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq \infty:\\ \;\;\;\;x \cdot \frac{y}{a} + z \cdot \frac{-1}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(x \cdot \frac{y}{t} - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(x \cdot \frac{y}{t} - z\right)}{a}\\ \end{array} \end{array} \]

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 (<= t_1 4e+305)
     (/ t_1 a)
     (if (<= t_1 INFINITY)
       (- (* x (/ y a)) (* z (/ t a)))
       (/ (* t (- (* x (/ y 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 4e+305) {
		tmp = t_1 / a;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = (t * ((x * (y / 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 4e+305) {
		tmp = t_1 / a;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else {
		tmp = (t * ((x * (y / t)) - z)) / 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 <= 4e+305:
		tmp = t_1 / a
	elif t_1 <= math.inf:
		tmp = (x * (y / a)) - (z * (t / a))
	else:
		tmp = (t * ((x * (y / t)) - z)) / 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 <= 4e+305)
		tmp = Float64(t_1 / a);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(Float64(t * Float64(Float64(x * Float64(y / t)) - 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 4e+305)
		tmp = t_1 / a;
	elseif (t_1 <= Inf)
		tmp = (x * (y / a)) - (z * (t / a));
	else
		tmp = (t * ((x * (y / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+305], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 96.8%

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

   if 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 57.8%

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

      1. div-sub 52.8%

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

      2. associate-/l* 57.3%

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

      3. associate-/l* 89.8%

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

   4. Applied egg-rr 89.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 66.7%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

Alternative 3: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1 - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 a))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 4e+305)
     (/ t_2 a)
     (if (<= t_2 INFINITY) (- t_1 (* z (/ t a))) t_1))))

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 / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= 4e+305) {
		tmp = t_2 / a;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1 - (z * (t / a));
	} else {
		tmp = t_1;
	}
	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 t_1 = x * (y / a);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= 4e+305) {
		tmp = t_2 / a;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 - (z * (t / a));
	} else {
		tmp = t_1;
	}
	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 / a)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= 4e+305:
		tmp = t_2 / a
	elif t_2 <= math.inf:
		tmp = t_1 - (z * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= 4e+305)
		tmp = Float64(t_2 / a);
	elseif (t_2 <= Inf)
		tmp = Float64(t_1 - Float64(z * Float64(t / a)));
	else
		tmp = t_1;
	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 / a);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= 4e+305)
		tmp = t_2 / a;
	elseif (t_2 <= Inf)
		tmp = t_1 - (z * (t / a));
	else
		tmp = t_1;
	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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e+305], N[(t$95$2 / a), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(t$95$1 - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 3.9999999999999998e305

   1. Initial program 96.8%

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

   if 3.9999999999999998e305 < (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 57.8%

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

      1. div-sub 52.8%

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

      2. associate-/l* 57.3%

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

      3. associate-/l* 89.8%

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

   4. Applied egg-rr 89.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 66.7%

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

      1. associate-*r/ 66.7%

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

   5. Simplified 66.7%

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

Alternative 4: 70.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -2e+169)
   (/ 1.0 (/ (/ a x) y))
   (if (<= (* x y) 4e-103) (/ (* z t) (- a)) (/ (* 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) {
	double tmp;
	if ((x * y) <= -2e+169) {
		tmp = 1.0 / ((a / x) / y);
	} else if ((x * y) <= 4e-103) {
		tmp = (z * t) / -a;
	} else {
		tmp = (x * y) / 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) <= (-2d+169)) then
        tmp = 1.0d0 / ((a / x) / y)
    else if ((x * y) <= 4d-103) then
        tmp = (z * t) / -a
    else
        tmp = (x * y) / 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) <= -2e+169) {
		tmp = 1.0 / ((a / x) / y);
	} else if ((x * y) <= 4e-103) {
		tmp = (z * t) / -a;
	} else {
		tmp = (x * y) / 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) <= -2e+169:
		tmp = 1.0 / ((a / x) / y)
	elif (x * y) <= 4e-103:
		tmp = (z * t) / -a
	else:
		tmp = (x * y) / 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) <= -2e+169)
		tmp = Float64(1.0 / Float64(Float64(a / x) / y));
	elseif (Float64(x * y) <= 4e-103)
		tmp = Float64(Float64(z * t) / Float64(-a));
	else
		tmp = Float64(Float64(x * y) / 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) <= -2e+169)
		tmp = 1.0 / ((a / x) / y);
	elseif ((x * y) <= 4e-103)
		tmp = (z * t) / -a;
	else
		tmp = (x * y) / 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], -2e+169], N[(1.0 / N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-103], N[(N[(z * t), $MachinePrecision] / (-a)), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999987e169

   1. Initial program 82.5%

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

   3. Taylor expanded in t around inf 77.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. fma-neg 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in t around 0 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*r/ 92.1%

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

   10. Simplified 92.1%

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

       1. associate-*r/ 85.0%

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

       2. clear-num 85.0%

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

       3. *-commutative 85.0%

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

       4. associate-/r* 92.1%

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

   12. Applied egg-rr 92.1%

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

   if -1.99999999999999987e169 < (*.f64 x y) < 3.99999999999999983e-103

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. *-commutative 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

   5. Simplified 80.1%

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

   if 3.99999999999999983e-103 < (*.f64 x y)

   1. Initial program 88.5%

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

   3. Taylor expanded in x around inf 67.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -2e+169)
   (* y (/ x a))
   (if (<= (* x y) 4e-103) (/ (* z t) (- a)) (/ (* 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) {
	double tmp;
	if ((x * y) <= -2e+169) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-103) {
		tmp = (z * t) / -a;
	} else {
		tmp = (x * y) / 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) <= (-2d+169)) then
        tmp = y * (x / a)
    else if ((x * y) <= 4d-103) then
        tmp = (z * t) / -a
    else
        tmp = (x * y) / 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) <= -2e+169) {
		tmp = y * (x / a);
	} else if ((x * y) <= 4e-103) {
		tmp = (z * t) / -a;
	} else {
		tmp = (x * y) / 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) <= -2e+169:
		tmp = y * (x / a)
	elif (x * y) <= 4e-103:
		tmp = (z * t) / -a
	else:
		tmp = (x * y) / 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) <= -2e+169)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 4e-103)
		tmp = Float64(Float64(z * t) / Float64(-a));
	else
		tmp = Float64(Float64(x * y) / 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) <= -2e+169)
		tmp = y * (x / a);
	elseif ((x * y) <= 4e-103)
		tmp = (z * t) / -a;
	else
		tmp = (x * y) / 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], -2e+169], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-103], N[(N[(z * t), $MachinePrecision] / (-a)), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999987e169

   1. Initial program 82.5%

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

   3. Taylor expanded in t around inf 77.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. fma-neg 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in t around 0 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*r/ 92.1%

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

   10. Simplified 92.1%

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

   if -1.99999999999999987e169 < (*.f64 x y) < 3.99999999999999983e-103

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. *-commutative 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

   5. Simplified 80.1%

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

   if 3.99999999999999983e-103 < (*.f64 x y)

   1. Initial program 88.5%

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

   3. Taylor expanded in x around inf 67.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{z \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-116}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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) -2e+169)
   (* y (/ x a))
   (if (<= (* x y) 5e-116) (* (- t) (/ z a)) (/ (* 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) {
	double tmp;
	if ((x * y) <= -2e+169) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-116) {
		tmp = -t * (z / a);
	} else {
		tmp = (x * y) / 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) <= (-2d+169)) then
        tmp = y * (x / a)
    else if ((x * y) <= 5d-116) then
        tmp = -t * (z / a)
    else
        tmp = (x * y) / 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) <= -2e+169) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-116) {
		tmp = -t * (z / a);
	} else {
		tmp = (x * y) / 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) <= -2e+169:
		tmp = y * (x / a)
	elif (x * y) <= 5e-116:
		tmp = -t * (z / a)
	else:
		tmp = (x * y) / 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) <= -2e+169)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e-116)
		tmp = Float64(Float64(-t) * Float64(z / a));
	else
		tmp = Float64(Float64(x * y) / 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) <= -2e+169)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e-116)
		tmp = -t * (z / a);
	else
		tmp = (x * y) / 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], -2e+169], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-116], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999987e169

   1. Initial program 82.5%

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

   3. Taylor expanded in t around inf 77.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

      1. div-inv 80.5%

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

      2. fma-neg 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in t around 0 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*r/ 92.1%

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

   10. Simplified 92.1%

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

   if -1.99999999999999987e169 < (*.f64 x y) < 5.0000000000000003e-116

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-/l* 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

      4. distribute-neg-frac2 77.7%

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

   5. Simplified 77.7%

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

   if 5.0000000000000003e-116 < (*.f64 x y)

   1. Initial program 88.7%

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

   3. Taylor expanded in x around inf 66.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-116}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

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 (<= (* z t) (- INFINITY)) (* (- t) (/ z a)) (/ (- (* x y) (* 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 ((z * t) <= -((double) INFINITY)) {
		tmp = -t * (z / a);
	} else {
		tmp = ((x * y) - (z * t)) / 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 = -t * (z / a);
	} else {
		tmp = ((x * y) - (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 (z * t) <= -math.inf:
		tmp = -t * (z / a)
	else:
		tmp = ((x * y) - (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(z * t) <= Float64(-Inf))
		tmp = Float64(Float64(-t) * Float64(z / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * 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 ((z * t) <= -Inf)
		tmp = -t * (z / a);
	else
		tmp = ((x * y) - (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[(z * t), $MachinePrecision], (-Infinity)], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 36.5%

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

   3. Taylor expanded in x around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. associate-/l* 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. distribute-neg-frac2 80.3%

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

   5. Simplified 80.3%

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

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

   1. Initial program 94.9%

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

4. Final simplification 94.1%

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

Alternative 8: 51.1% accurate, 1.8× speedup

Math

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

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 (* 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) {
	return y * (x / 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 = y * (x / 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 y * (x / a);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 91.5%

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

3. Taylor expanded in t around inf 87.8%

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

   1. associate-/l* 83.8%

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

5. Simplified 83.8%

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

   1. div-inv 83.8%

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

   2. fma-neg 83.8%

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

7. Applied egg-rr 83.8%

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

8. Taylor expanded in t around 0 46.7%

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

   1. *-commutative 46.7%

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

   2. associate-*r/ 47.5%

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

10. Simplified 47.5%

    \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]
11. Add Preprocessing

Alternative 9: 51.4% 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 91.5%

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

3. Taylor expanded in x around inf 46.7%

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

   1. associate-*r/ 44.9%

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

5. Simplified 44.9%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer Target 1: 91.2% 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 2024146 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

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