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

Percentage Accurate: 91.6% → 93.6%

Time: 10.7s

Alternatives: 9

Speedup: 0.7×

• 27.7% 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: 91.6% 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: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 10^{+283}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} - t \cdot \frac{z}{y \cdot a}\right)\\ \end{array} \end{array} \]

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 1e+283) (/ t_1 a) (* y (- (/ x a) (* t (/ z (* 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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 1e+283) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (t * (z / (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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= 1d+283) then
        tmp = t_1 / a
    else
        tmp = y * ((x / a) - (t * (z / (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 t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= 1e+283) {
		tmp = t_1 / a;
	} else {
		tmp = y * ((x / a) - (t * (z / (y * 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 <= 1e+283:
		tmp = t_1 / a
	else:
		tmp = y * ((x / a) - (t * (z / (y * 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 <= 1e+283)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(y * Float64(Float64(x / a) - Float64(t * Float64(z / Float64(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)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= 1e+283)
		tmp = t_1 / a;
	else
		tmp = y * ((x / a) - (t * (z / (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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+283], N[(t$95$1 / a), $MachinePrecision], N[(y * N[(N[(x / a), $MachinePrecision] - N[(t * N[(z / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 9.99999999999999955e282

   1. Initial program 97.7%

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

   if 9.99999999999999955e282 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 69.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 96.1

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

   8. Applied rewrites 96.1%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{a} - t \cdot \frac{z}{y \cdot a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

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) a)))
   (if (<= (* x y) -5e-86)
     t_1
     (if (<= (* x y) 2e-31)
       (/ (* z (- t)) a)
       (if (<= (* x y) 5e+43)
         t_1
         (if (<= (* x y) 5e+111) (* t (/ z (- a))) (* x (* y (/ 1.0 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) / a;
	double tmp;
	if ((x * y) <= -5e-86) {
		tmp = t_1;
	} else if ((x * y) <= 2e-31) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+43) {
		tmp = t_1;
	} else if ((x * y) <= 5e+111) {
		tmp = t * (z / -a);
	} else {
		tmp = x * (y * (1.0 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / a
    if ((x * y) <= (-5d-86)) then
        tmp = t_1
    else if ((x * y) <= 2d-31) then
        tmp = (z * -t) / a
    else if ((x * y) <= 5d+43) then
        tmp = t_1
    else if ((x * y) <= 5d+111) then
        tmp = t * (z / -a)
    else
        tmp = x * (y * (1.0d0 / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -5e-86) {
		tmp = t_1;
	} else if ((x * y) <= 2e-31) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+43) {
		tmp = t_1;
	} else if ((x * y) <= 5e+111) {
		tmp = t * (z / -a);
	} else {
		tmp = x * (y * (1.0 / 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) / a
	tmp = 0
	if (x * y) <= -5e-86:
		tmp = t_1
	elif (x * y) <= 2e-31:
		tmp = (z * -t) / a
	elif (x * y) <= 5e+43:
		tmp = t_1
	elif (x * y) <= 5e+111:
		tmp = t * (z / -a)
	else:
		tmp = x * (y * (1.0 / 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) / a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-86)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-31)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	elseif (Float64(x * y) <= 5e+43)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+111)
		tmp = Float64(t * Float64(z / Float64(-a)));
	else
		tmp = Float64(x * Float64(y * Float64(1.0 / 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) / a;
	tmp = 0.0;
	if ((x * y) <= -5e-86)
		tmp = t_1;
	elseif ((x * y) <= 2e-31)
		tmp = (z * -t) / a;
	elseif ((x * y) <= 5e+43)
		tmp = t_1;
	elseif ((x * y) <= 5e+111)
		tmp = t * (z / -a);
	else
		tmp = x * (y * (1.0 / 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] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-86], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-31], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+43], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+111], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.9999999999999999e-86 or 2e-31 < (*.f64 x y) < 5.0000000000000004e43

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -4.9999999999999999e-86 < (*.f64 x y) < 2e-31

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if 5.0000000000000004e43 < (*.f64 x y) < 4.9999999999999997e111

   1. Initial program 85.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 32.3

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

   5. Applied rewrites 32.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 75.8

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

   8. Applied rewrites 75.8%

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

   10. Applied rewrites 70.5%

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

   if 4.9999999999999997e111 < (*.f64 x y)

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 19.4

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

   8. Applied rewrites 19.4%

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

   9. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 82.3

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

   11. Applied rewrites 82.3%

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

   13. Applied rewrites 82.3%

       \[\leadsto x \cdot \left(\frac{1}{a} \cdot \color{blue}{y}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (* x y) a)))
   (if (<= (* x y) -5e-86)
     t_1
     (if (<= (* x y) 2e-31)
       (/ (* z (- t)) a)
       (if (<= (* x y) 5e+43)
         t_1
         (if (<= (* x y) 5e+111) (* 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 t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -5e-86) {
		tmp = t_1;
	} else if ((x * y) <= 2e-31) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+43) {
		tmp = t_1;
	} else if ((x * y) <= 5e+111) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / a
    if ((x * y) <= (-5d-86)) then
        tmp = t_1
    else if ((x * y) <= 2d-31) then
        tmp = (z * -t) / a
    else if ((x * y) <= 5d+43) then
        tmp = t_1
    else if ((x * y) <= 5d+111) 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 t_1 = (x * y) / a;
	double tmp;
	if ((x * y) <= -5e-86) {
		tmp = t_1;
	} else if ((x * y) <= 2e-31) {
		tmp = (z * -t) / a;
	} else if ((x * y) <= 5e+43) {
		tmp = t_1;
	} else if ((x * y) <= 5e+111) {
		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):
	t_1 = (x * y) / a
	tmp = 0
	if (x * y) <= -5e-86:
		tmp = t_1
	elif (x * y) <= 2e-31:
		tmp = (z * -t) / a
	elif (x * y) <= 5e+43:
		tmp = t_1
	elif (x * y) <= 5e+111:
		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)
	t_1 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-86)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-31)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	elseif (Float64(x * y) <= 5e+43)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+111)
		tmp = Float64(t * Float64(z / Float64(-a)));
	else
		tmp = Float64(x * Float64(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)
	t_1 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -5e-86)
		tmp = t_1;
	elseif ((x * y) <= 2e-31)
		tmp = (z * -t) / a;
	elseif ((x * y) <= 5e+43)
		tmp = t_1;
	elseif ((x * y) <= 5e+111)
		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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-86], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-31], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+43], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+111], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.9999999999999999e-86 or 2e-31 < (*.f64 x y) < 5.0000000000000004e43

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -4.9999999999999999e-86 < (*.f64 x y) < 2e-31

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if 5.0000000000000004e43 < (*.f64 x y) < 4.9999999999999997e111

   1. Initial program 85.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 32.3

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

   5. Applied rewrites 32.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 75.8

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

   8. Applied rewrites 75.8%

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

   10. Applied rewrites 70.5%

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

   if 4.9999999999999997e111 < (*.f64 x y)

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 19.4

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

   8. Applied rewrites 19.4%

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

   9. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 82.3

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

   11. Applied rewrites 82.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, t \cdot \frac{z}{-a}\right)\\ \end{array} \end{array} \]

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 5e+262) (/ t_1 a) (fma (/ y a) x (* 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 <= 5e+262) {
		tmp = t_1 / a;
	} else {
		tmp = fma((y / a), x, (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 <= 5e+262)
		tmp = Float64(t_1 / a);
	else
		tmp = fma(Float64(y / a), x, Float64(t * Float64(z / Float64(-a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+262], N[(t$95$1 / a), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x + N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000008e262

   1. Initial program 97.6%

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

   if 5.00000000000000008e262 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 74.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 85.6

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

   4. Applied rewrites 85.6%

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

      1. lift-neg.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 96.7

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

   6. Applied rewrites 96.7%

      \[\leadsto \mathsf{fma}\left(\frac{y}{a}, x, \color{blue}{\left(-t\right) \cdot \frac{z}{a}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, t \cdot \frac{z}{-a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq 10^{+268}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- (* x y) (* z t)) a) 1e+268) (/ (* x y) a) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - (z * t)) / a) <= 1e+268) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((((x * y) - (z * t)) / a) <= 1d+268) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((x * y) - (z * t)) / a) <= 1e+268) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (((x * y) - (z * t)) / a) <= 1e+268:
		tmp = (x * y) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) - Float64(z * t)) / a) <= 1e+268)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((((x * y) - (z * t)) / a) <= 1e+268)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], 1e+268], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 9.9999999999999997e267

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if 9.9999999999999997e267 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 57.6

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

   8. Applied rewrites 57.6%

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

   9. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 49.9

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

   11. Applied rewrites 49.9%

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

   13. Applied rewrites 52.1%

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

Alternative 6: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -1e-103)
   (* t (/ z (- a)))
   (if (<= (* z t) 5e+101) (/ (* x y) a) (* z (/ t (- a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e-103) {
		tmp = t * (z / -a);
	} else if ((z * t) <= 5e+101) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (t / -a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-1d-103)) then
        tmp = t * (z / -a)
    else if ((z * t) <= 5d+101) then
        tmp = (x * y) / a
    else
        tmp = z * (t / -a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -1e-103) {
		tmp = t * (z / -a);
	} else if ((z * t) <= 5e+101) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (t / -a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -1e-103:
		tmp = t * (z / -a)
	elif (z * t) <= 5e+101:
		tmp = (x * y) / a
	else:
		tmp = z * (t / -a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -1e-103)
		tmp = Float64(t * Float64(z / Float64(-a)));
	elseif (Float64(z * t) <= 5e+101)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(z * Float64(t / Float64(-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) <= -1e-103)
		tmp = t * (z / -a);
	elseif ((z * t) <= 5e+101)
		tmp = (x * y) / a;
	else
		tmp = z * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e-103], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+101], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.99999999999999958e-104

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 27.8

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

   5. Applied rewrites 27.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 73.9

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

   8. Applied rewrites 73.9%

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

   10. Applied rewrites 68.0%

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

   if -9.99999999999999958e-104 < (*.f64 z t) < 4.99999999999999989e101

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 76.0

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

   5. Applied rewrites 76.0%

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

   if 4.99999999999999989e101 < (*.f64 z t)

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 20.5

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

   5. Applied rewrites 20.5%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 84.4

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

   8. Applied rewrites 84.4%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{t}{-a}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* z (/ t (- a)))))
   (if (<= (* z t) -1e-103) t_1 (if (<= (* z t) 5e+101) (/ (* x y) 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 = z * (t / -a);
	double tmp;
	if ((z * t) <= -1e-103) {
		tmp = t_1;
	} else if ((z * t) <= 5e+101) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	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 ((z * t) <= (-1d-103)) then
        tmp = t_1
    else if ((z * t) <= 5d+101) then
        tmp = (x * y) / a
    else
        tmp = t_1
    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 ((z * t) <= -1e-103) {
		tmp = t_1;
	} else if ((z * t) <= 5e+101) {
		tmp = (x * y) / 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 = z * (t / -a)
	tmp = 0
	if (z * t) <= -1e-103:
		tmp = t_1
	elif (z * t) <= 5e+101:
		tmp = (x * y) / 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(z * Float64(t / Float64(-a)))
	tmp = 0.0
	if (Float64(z * t) <= -1e-103)
		tmp = t_1;
	elseif (Float64(z * t) <= 5e+101)
		tmp = Float64(Float64(x * y) / 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 = z * (t / -a);
	tmp = 0.0;
	if ((z * t) <= -1e-103)
		tmp = t_1;
	elseif ((z * t) <= 5e+101)
		tmp = (x * y) / 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[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e-103], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5e+101], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999958e-104 or 4.99999999999999989e101 < (*.f64 z t)

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 25.1

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

   5. Applied rewrites 25.1%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 77.7

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

   8. Applied rewrites 77.7%

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

   if -9.99999999999999958e-104 < (*.f64 z t) < 4.99999999999999989e101

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 76.0

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

   5. Applied rewrites 76.0%

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

Alternative 8: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* x y) 4e+303) (/ (- (* x y) (* z t)) a) (* x (* y (/ 1.0 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) <= 4e+303) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y * (1.0 / 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) <= 4d+303) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * (y * (1.0d0 / 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) <= 4e+303) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y * (1.0 / 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) <= 4e+303:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (y * (1.0 / 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) <= 4e+303)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(y * Float64(1.0 / 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) <= 4e+303)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (y * (1.0 / 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], 4e+303], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 4e303

   1. Initial program 96.3%

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

   if 4e303 < (*.f64 x y)

   1. Initial program 57.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 57.7

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 10.3

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

   8. Applied rewrites 10.3%

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

   9. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 99.7

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

   11. Applied rewrites 99.7%

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

   13. Applied rewrites 99.9%

       \[\leadsto x \cdot \left(\frac{1}{a} \cdot \color{blue}{y}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.7% accurate, 1.5× 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 94.7%

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

3. Taylor expanded in x around inf

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

   1. lower-*.f64 52.2

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

5. Applied rewrites 52.2%

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

6. Taylor expanded in x around 0

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

   1. associate-*l/ N/A

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

   2. associate-*l* N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. distribute-neg-frac2 N/A

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

   7. mul-1-neg N/A

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

   8. lower-/.f64 N/A

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

   9. mul-1-neg N/A

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

   10. lower-neg.f64 52.3

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

8. Applied rewrites 52.3%

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

9. Taylor expanded in x around inf

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

    1. associate-/l* N/A

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

    2. lower-*.f64 N/A

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

    3. lower-/.f64 51.5

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

11. Applied rewrites 51.5%

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

Developer Target 1: 90.8% accurate, 0.5× 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 2024238 
(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))