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

Percentage Accurate: 91.9% → 96.4%

Time: 8.6s

Alternatives: 12

Speedup: 0.6×

• 28.5% 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: 91.9% 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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - t \cdot \frac{z}{a \cdot y}\right)\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* y (/ (- x (* t (/ z y))) a))
     (if (<= t_1 1e+308) (/ t_1 a) (* y (- (/ x a) (* t (/ z (* a y)))))))))

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)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 1e+308) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (t * (z / (a * y))));
	}
	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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 1e+308) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (t * (z / (a * y))));
	}
	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 <= -math.inf:
		tmp = y * ((x - (t * (z / y))) / a)
	elif t_1 <= 1e+308:
		tmp = t_1 / a
	else:
		tmp = y * ((x / a) - (t * (z / (a * y))))
	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))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	elseif (t_1 <= 1e+308)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(t * Float64(z / Float64(a * y)))));
	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 <= -Inf)
		tmp = y * ((x - (t * (z / y))) / a);
	elseif (t_1 <= 1e+308)
		tmp = t_1 / a;
	else
		tmp = y * ((x / a) - (t * (z / (a * y))));
	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, (-Infinity)], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(t * N[(z / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. associate-/l* 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0 81.6%

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

      1. times-frac 88.8%

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

      2. associate-*l/ 89.0%

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

      3. associate-/l* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*r/ 89.0%

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

      6. div-sub 92.7%

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

      7. associate-*r/ 85.6%

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

      8. *-commutative 85.6%

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

      9. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e308

   1. Initial program 99.6%

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

   if 1e308 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+308}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - t \cdot \frac{z}{a \cdot y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{+79}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 (<= a 1.95e+79)
   (/ (fma x y (* z (- t))) a)
   (- (* (/ x (sqrt a)) (/ y (sqrt 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 (a <= 1.95e+79) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = ((x / sqrt(a)) * (y / sqrt(a))) - (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 (a <= 1.95e+79)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(Float64(Float64(x / sqrt(a)) * Float64(y / sqrt(a))) - Float64(t * Float64(z / 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_] := If[LessEqual[a, 1.95e+79], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(x / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(y / N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.9499999999999999e79

   1. Initial program 94.7%

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

      1. div-sub 91.8%

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

      2. *-commutative 91.8%

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

      3. div-sub 94.7%

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

      4. *-commutative 94.7%

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

      5. fmm-def 95.2%

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

      6. distribute-rgt-neg-out 95.2%

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

   3. Simplified 95.2%

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

   if 1.9499999999999999e79 < a

   1. Initial program 79.1%

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

      1. div-sub 79.1%

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

      2. *-un-lft-identity 79.1%

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

      3. add-sqr-sqrt 78.9%

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

      4. times-frac 78.9%

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

      5. fmm-def 78.9%

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

      6. associate-/l* 87.1%

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

   4. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -z \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. fmm-undef 87.1%

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

      2. associate-*l/ 87.1%

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

      3. *-lft-identity 87.1%

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

      4. associate-/l* 91.2%

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

      5. associate-*l/ 95.4%

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

      6. associate-*r/ 85.2%

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

      7. *-commutative 85.2%

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

      8. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{+79}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \frac{\frac{y}{a}}{t} - \frac{z}{a}\right)\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* y (/ (- x (* t (/ z y))) a))
     (if (<= t_1 2e+220) (/ t_1 a) (* t (- (* x (/ (/ y 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 2e+220) {
		tmp = t_1 / a;
	} else {
		tmp = t * ((x * ((y / a) / 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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else if (t_1 <= 2e+220) {
		tmp = t_1 / a;
	} else {
		tmp = t * ((x * ((y / a) / 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 <= -math.inf:
		tmp = y * ((x - (t * (z / y))) / a)
	elif t_1 <= 2e+220:
		tmp = t_1 / a
	else:
		tmp = t * ((x * ((y / a) / 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 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(x - Float64(t * Float64(z / y))) / a));
	elseif (t_1 <= 2e+220)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(x * Float64(Float64(y / a) / t)) - 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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((x - (t * (z / y))) / a);
	elseif (t_1 <= 2e+220)
		tmp = t_1 / a;
	else
		tmp = t * ((x * ((y / a) / 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, (-Infinity)], N[(y * N[(N[(x - N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+220], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(x * N[(N[(y / a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. associate-/l* 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in x around 0 81.6%

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

      1. times-frac 88.8%

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

      2. associate-*l/ 89.0%

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

      3. associate-/l* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*r/ 89.0%

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

      6. div-sub 92.7%

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

      7. associate-*r/ 85.6%

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

      8. *-commutative 85.6%

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

      9. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2e220

   1. Initial program 99.6%

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

   if 2e220 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. associate-/l* 85.5%

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

      5. associate-/r* 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \frac{\frac{y}{a}}{t} - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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 (* z (/ (- t) a))))
   (if (<= (* x y) -1e+29)
     (* y (/ x a))
     (if (<= (* x y) 5e-208)
       t_1
       (if (<= (* x y) 0.001)
         (* x (/ y a))
         (if (<= (* x y) 2e+47) t_1 (/ y (/ a x))))))))

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 = z * (-t / a);
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * (y / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	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 = z * (-t / a)
    if ((x * y) <= (-1d+29)) then
        tmp = y * (x / a)
    else if ((x * y) <= 5d-208) then
        tmp = t_1
    else if ((x * y) <= 0.001d0) then
        tmp = x * (y / a)
    else if ((x * y) <= 2d+47) then
        tmp = t_1
    else
        tmp = y / (a / x)
    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 = z * (-t / a);
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * (y / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = z * (-t / a)
	tmp = 0
	if (x * y) <= -1e+29:
		tmp = y * (x / a)
	elif (x * y) <= 5e-208:
		tmp = t_1
	elif (x * y) <= 0.001:
		tmp = x * (y / a)
	elif (x * y) <= 2e+47:
		tmp = t_1
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-t) / a))
	tmp = 0.0
	if (Float64(x * y) <= -1e+29)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e-208)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.001)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / x));
	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 = z * (-t / a);
	tmp = 0.0;
	if ((x * y) <= -1e+29)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e-208)
		tmp = t_1;
	elseif ((x * y) <= 0.001)
		tmp = x * (y / a);
	elseif ((x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = y / (a / x);
	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[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+29], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.001], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+47], t$95$1, N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999914e28

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 96.4%

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

      1. +-commutative 96.4%

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

      2. mul-1-neg 96.4%

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

      3. unsub-neg 96.4%

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

      4. associate-/l* 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in x around inf 86.6%

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

   if -9.99999999999999914e28 < (*.f64 x y) < 4.99999999999999963e-208 or 1e-3 < (*.f64 x y) < 2.0000000000000001e47

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r/ 73.7%

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

      4. distribute-rgt-neg-in 73.7%

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

      5. distribute-frac-neg 73.7%

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

   5. Simplified 73.7%

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

   if 4.99999999999999963e-208 < (*.f64 x y) < 1e-3

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

   if 2.0000000000000001e47 < (*.f64 x y)

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x around inf 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.4%

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

   8. Applied egg-rr 78.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-t\right)}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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 (/ (* z (- t)) a)))
   (if (<= (* x y) -1e+29)
     (* y (/ x a))
     (if (<= (* x y) 5e-208)
       t_1
       (if (<= (* x y) 0.001)
         (* x (/ y a))
         (if (<= (* x y) 2e+47) t_1 (/ y (/ a x))))))))

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 = (z * -t) / a;
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * (y / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	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 = (z * -t) / a
    if ((x * y) <= (-1d+29)) then
        tmp = y * (x / a)
    else if ((x * y) <= 5d-208) then
        tmp = t_1
    else if ((x * y) <= 0.001d0) then
        tmp = x * (y / a)
    else if ((x * y) <= 2d+47) then
        tmp = t_1
    else
        tmp = y / (a / x)
    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 = (z * -t) / a;
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * (y / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * -t) / a
	tmp = 0
	if (x * y) <= -1e+29:
		tmp = y * (x / a)
	elif (x * y) <= 5e-208:
		tmp = t_1
	elif (x * y) <= 0.001:
		tmp = x * (y / a)
	elif (x * y) <= 2e+47:
		tmp = t_1
	else:
		tmp = y / (a / x)
	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(z * Float64(-t)) / a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+29)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e-208)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.001)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / x));
	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 = (z * -t) / a;
	tmp = 0.0;
	if ((x * y) <= -1e+29)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e-208)
		tmp = t_1;
	elseif ((x * y) <= 0.001)
		tmp = x * (y / a);
	elseif ((x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = y / (a / x);
	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[(z * (-t)), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+29], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.001], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+47], t$95$1, N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999914e28

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 96.4%

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

      1. +-commutative 96.4%

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

      2. mul-1-neg 96.4%

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

      3. unsub-neg 96.4%

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

      4. associate-/l* 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in x around inf 86.6%

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

   if -9.99999999999999914e28 < (*.f64 x y) < 4.99999999999999963e-208 or 1e-3 < (*.f64 x y) < 2.0000000000000001e47

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. associate-*r* 79.6%

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

      2. mul-1-neg 79.6%

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

   5. Simplified 79.6%

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

   if 4.99999999999999963e-208 < (*.f64 x y) < 1e-3

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

   if 2.0000000000000001e47 < (*.f64 x y)

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. associate-/l* 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in x around inf 78.5%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.4%

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

   8. Applied egg-rr 78.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+299}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

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 (- INFINITY)) (not (<= t_1 1e+299)))
     (* 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 <= -((double) INFINITY)) || !(t_1 <= 1e+299)) {
		tmp = y * ((x - (t * (z / y))) / a);
	} else {
		tmp = t_1 / 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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+299)) {
		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 <= -math.inf) or not (t_1 <= 1e+299):
		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 <= Float64(-Inf)) || !(t_1 <= 1e+299))
		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 <= -Inf) || ~((t_1 <= 1e+299)))
		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, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+299]], $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)) < -inf.0 or 1.0000000000000001e299 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.8%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in x around 0 78.0%

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

      1. times-frac 82.6%

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

      2. associate-*l/ 82.9%

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

      3. associate-/l* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r/ 82.9%

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

      6. div-sub 87.7%

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

      7. associate-*r/ 81.4%

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

      8. *-commutative 81.4%

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

      9. associate-/l* 87.7%

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

   8. Simplified 87.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e299

   1. Initial program 99.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+299}\right):\\ \;\;\;\;y \cdot \frac{x - t \cdot \frac{z}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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-53)
   (* y (/ x a))
   (if (<= (* x y) 5e-208) (* 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-53) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		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-53)) then
        tmp = y * (x / a)
    else if ((x * y) <= 5d-208) 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-53) {
		tmp = y * (x / a);
	} else if ((x * y) <= 5e-208) {
		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-53:
		tmp = y * (x / a)
	elif (x * y) <= 5e-208:
		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-53)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 5e-208)
		tmp = Float64(t * Float64(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-53)
		tmp = y * (x / a);
	elseif ((x * y) <= 5e-208)
		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-53], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], 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) < -2.00000000000000006e-53

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 94.2%

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

      1. +-commutative 94.2%

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

      2. mul-1-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. associate-/l* 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in x around inf 79.5%

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

   if -2.00000000000000006e-53 < (*.f64 x y) < 4.99999999999999963e-208

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 84.3%

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

      3. distribute-rgt-neg-in 84.3%

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

      4. distribute-neg-frac2 84.3%

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

   5. Simplified 84.3%

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

   if 4.99999999999999963e-208 < (*.f64 x y)

   1. Initial program 89.2%

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

   3. Taylor expanded in x around inf 67.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.7% accurate, 0.6× speedup

Math

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

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(t * Float64(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 59.9%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-/l* 94.7%

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

      3. distribute-rgt-neg-in 94.7%

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

      4. distribute-neg-frac2 94.7%

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

   5. Simplified 94.7%

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

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

   1. Initial program 94.5%

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

4. Final simplification 94.5%

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

Alternative 9: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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+237) (/ x (/ a y)) (/ (* 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+237) {
		tmp = x / (a / y);
	} 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+237)) then
        tmp = x / (a / y)
    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+237) {
		tmp = x / (a / y);
	} 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+237:
		tmp = x / (a / y)
	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+237)
		tmp = Float64(x / Float64(a / y));
	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+237)
		tmp = x / (a / y);
	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+237], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999988e237

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 95.6%

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

      1. +-commutative 95.6%

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

      2. mul-1-neg 95.6%

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

      3. unsub-neg 95.6%

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

      4. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/r/ 91.9%

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

   8. Applied egg-rr 91.9%

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

   if -1.99999999999999988e237 < (*.f64 x y)

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 52.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% 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 91.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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/ 52.1%

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

5. Simplified 52.1%

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

6. Final simplification 52.1%

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

Alternative 11: 51.5% 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 91.9%

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

3. Taylor expanded in y around inf 82.1%

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

   1. +-commutative 82.1%

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

   2. mul-1-neg 82.1%

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

   3. unsub-neg 82.1%

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

   4. associate-/l* 78.8%

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

5. Simplified 78.8%

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

6. Taylor expanded in x around inf 54.9%

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

7. Final simplification 54.9%

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

Alternative 12: 51.5% accurate, 1.8× speedup

Math

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

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 (/ a x)))

C

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

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 / (a / x)
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 / (a / x);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 91.9%

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

3. Taylor expanded in y around inf 82.1%

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

   1. +-commutative 82.1%

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

   2. mul-1-neg 82.1%

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

   3. unsub-neg 82.1%

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

   4. associate-/l* 78.8%

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

5. Simplified 78.8%

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

6. Taylor expanded in x around inf 54.9%

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

   1. clear-num 54.8%

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

   2. un-div-inv 54.9%

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

8. Applied egg-rr 54.9%

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

9. Final simplification 54.9%

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

Developer target: 91.5% 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 2024095 
(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))