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

Percentage Accurate: 91.3% → 90.5%

Time: 11.1s

Alternatives: 12

Speedup: 1.0×

• 27.9% 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: 91.3% 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: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -1.4e-231)
   (/ (fma x y (* z (- t))) a)
   (- (/ (* x y) a) (/ t (/ a z)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -1.4e-231) {
		tmp = fma(x, y, (z * -t)) / a;
	} else {
		tmp = ((x * y) / a) - (t / (a / z));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.4e-231)
		tmp = Float64(fma(x, y, Float64(z * Float64(-t))) / a);
	else
		tmp = Float64(Float64(Float64(x * y) / a) - Float64(t / Float64(a / z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -1.4e-231], N[(N[(x * y + N[(z * (-t)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e-231

   1. Initial program 93.8%

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

      1. fma-neg 94.7%

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

      2. distribute-rgt-neg-out 94.7%

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

   3. Simplified 94.7%

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

   if -1.3999999999999999e-231 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 92.4%

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

      1. clear-num 92.0%

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

      2. associate-/r/ 92.4%

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

   5. Applied egg-rr 92.4%

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

      1. associate-*l/ 92.4%

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

      2. *-un-lft-identity 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 94.3%

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

      5. clear-num 94.3%

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

      6. associate-*l/ 94.6%

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

      7. *-un-lft-identity 94.6%

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

   7. Applied egg-rr 94.6%

      \[\leadsto -1 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} + \frac{x \cdot y}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a}\\ t_2 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* t (/ (- z) a))) (t_2 (/ (* x y) a)))
   (if (<= (* x y) -1e+109)
     (/ y (/ a x))
     (if (<= (* x y) -5e+38)
       t_1
       (if (<= (* x y) -4e-84)
         t_2
         (if (<= (* x y) 5e-53)
           t_1
           (if (<= (* x y) 1e-22)
             t_2
             (if (<= (* x y) 2e+31) t_1 (/ x (/ a y))))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / a);
	double t_2 = (x * y) / a;
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = y / (a / x);
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = t * (-z / a)
    t_2 = (x * y) / a
    if ((x * y) <= (-1d+109)) then
        tmp = y / (a / x)
    else if ((x * y) <= (-5d+38)) then
        tmp = t_1
    else if ((x * y) <= (-4d-84)) then
        tmp = t_2
    else if ((x * y) <= 5d-53) then
        tmp = t_1
    else if ((x * y) <= 1d-22) then
        tmp = t_2
    else if ((x * y) <= 2d+31) then
        tmp = t_1
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = t * (-z / a);
	double t_2 = (x * y) / a;
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = y / (a / x);
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (-z / a)
	t_2 = (x * y) / a
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = y / (a / x)
	elif (x * y) <= -5e+38:
		tmp = t_1
	elif (x * y) <= -4e-84:
		tmp = t_2
	elif (x * y) <= 5e-53:
		tmp = t_1
	elif (x * y) <= 1e-22:
		tmp = t_2
	elif (x * y) <= 2e+31:
		tmp = t_1
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / a))
	t_2 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= -5e+38)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-53)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-22)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+31)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / a);
	t_2 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = y / (a / x);
	elseif ((x * y) <= -5e+38)
		tmp = t_1;
	elseif ((x * y) <= -4e-84)
		tmp = t_2;
	elseif ((x * y) <= 5e-53)
		tmp = t_1;
	elseif ((x * y) <= 1e-22)
		tmp = t_2;
	elseif ((x * y) <= 2e+31)
		tmp = t_1;
	else
		tmp = x / (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.
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[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], t$95$1, N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999982e108

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 85.3%

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

      1. associate-*r/ 89.2%

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

   5. Simplified 89.2%

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

      1. associate-*r/ 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-/l* 87.5%

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

   7. Applied egg-rr 87.5%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38 or -4.0000000000000001e-84 < (*.f64 x y) < 5e-53 or 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*l/ 78.2%

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

      4. distribute-rgt-neg-in 78.2%

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

   5. Simplified 78.2%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84 or 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 72.4%

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

   if 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. associate-*r/ 83.0%

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

   5. Simplified 83.0%

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

      1. associate-*r/ 81.1%

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

      2. associate-/l* 83.1%

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

   7. Applied egg-rr 83.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a}\\ t_2 := \frac{x \cdot y}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* t (/ (- z) a))) (t_2 (/ (* x y) a)))
   (if (<= (* x y) -1e+109)
     (/ y (/ a x))
     (if (<= (* x y) -5e+38)
       t_1
       (if (<= (* x y) -4e-84)
         t_2
         (if (<= (* x y) 5e-53)
           t_1
           (if (<= (* x y) 1e-22)
             t_2
             (if (<= (* x y) 2e+31) (/ (* z (- t)) a) (/ x (/ a y))))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / a);
	double t_2 = (x * y) / a;
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = y / (a / x);
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = (z * -t) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = t * (-z / a)
    t_2 = (x * y) / a
    if ((x * y) <= (-1d+109)) then
        tmp = y / (a / x)
    else if ((x * y) <= (-5d+38)) then
        tmp = t_1
    else if ((x * y) <= (-4d-84)) then
        tmp = t_2
    else if ((x * y) <= 5d-53) then
        tmp = t_1
    else if ((x * y) <= 1d-22) then
        tmp = t_2
    else if ((x * y) <= 2d+31) then
        tmp = (z * -t) / a
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 = t * (-z / a);
	double t_2 = (x * y) / a;
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = y / (a / x);
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = (z * -t) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (-z / a)
	t_2 = (x * y) / a
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = y / (a / x)
	elif (x * y) <= -5e+38:
		tmp = t_1
	elif (x * y) <= -4e-84:
		tmp = t_2
	elif (x * y) <= 5e-53:
		tmp = t_1
	elif (x * y) <= 1e-22:
		tmp = t_2
	elif (x * y) <= 2e+31:
		tmp = (z * -t) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / a))
	t_2 = Float64(Float64(x * y) / a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= -5e+38)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-53)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-22)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / a);
	t_2 = (x * y) / a;
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = y / (a / x);
	elseif ((x * y) <= -5e+38)
		tmp = t_1;
	elseif ((x * y) <= -4e-84)
		tmp = t_2;
	elseif ((x * y) <= 5e-53)
		tmp = t_1;
	elseif ((x * y) <= 1e-22)
		tmp = t_2;
	elseif ((x * y) <= 2e+31)
		tmp = (z * -t) / a;
	else
		tmp = x / (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.
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[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.99999999999999982e108

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 85.3%

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

      1. associate-*r/ 89.2%

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

   5. Simplified 89.2%

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

      1. associate-*r/ 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-/l* 87.5%

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

   7. Applied egg-rr 87.5%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38 or -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*l/ 78.7%

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

      4. distribute-rgt-neg-in 78.7%

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

   5. Simplified 78.7%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84 or 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 72.4%

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

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

   5. Simplified 82.5%

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

   if 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. associate-*r/ 83.0%

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

   5. Simplified 83.0%

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

      1. associate-*r/ 81.1%

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

      2. associate-/l* 83.1%

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

   7. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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-118)
     (/ (* x y) a)
     (if (<= (* x y) 5e-53)
       t_1
       (if (<= (* x y) 2.0)
         (/ y (/ a x))
         (if (<= (* x y) 2e+31) t_1 (/ x (/ a y))))))))

C

assert(x < y && y < z && z < t && t < a);
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-118) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 2.0) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+31) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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-118)) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-53) then
        tmp = t_1
    else if ((x * y) <= 2.0d0) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d+31) then
        tmp = t_1
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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-118) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-53) {
		tmp = t_1;
	} else if ((x * y) <= 2.0) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e+31) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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-118:
		tmp = (x * y) / a
	elif (x * y) <= 5e-53:
		tmp = t_1
	elif (x * y) <= 2.0:
		tmp = y / (a / x)
	elif (x * y) <= 2e+31:
		tmp = t_1
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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-118)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-53)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.0)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e+31)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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-118)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-53)
		tmp = t_1;
	elseif ((x * y) <= 2.0)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e+31)
		tmp = t_1;
	else
		tmp = x / (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.
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-118], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.0], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], t$95$1, N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999985e-119

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 72.4%

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

   if -9.99999999999999985e-119 < (*.f64 x y) < 5e-53 or 2 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 92.6%

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

   4. Taylor expanded in t around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. associate-*l/ 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

   6. Simplified 83.2%

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

   if 5e-53 < (*.f64 x y) < 2

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 38.6%

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

   5. Simplified 38.6%

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

      1. associate-*r/ 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-/l* 66.0%

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

   7. Applied egg-rr 66.0%

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

   if 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. associate-*r/ 83.0%

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

   5. Simplified 83.0%

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

      1. associate-*r/ 81.1%

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

      2. associate-/l* 83.1%

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

   7. Applied egg-rr 83.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+173}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 4e+173) (/ (- (* x y) (* z t)) a) (- (* x (/ y a)) (* z (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 4e+173) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x * (y / a)) - (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (a <= 4d+173) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = (x * (y / a)) - (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 (a <= 4e+173) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x * (y / a)) - (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 4e+173:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (x * (y / a)) - (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4e+173)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 (a <= 4e+173)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (x * (y / a)) - (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.
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, 4e+173], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.0000000000000001e173

   1. Initial program 95.5%

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

   if 4.0000000000000001e173 < a

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

      4. associate-*r/ 76.8%

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

      5. associate-/l* 86.5%

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

      6. associate-/r/ 84.5%

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

   5. Applied egg-rr 84.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+173}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 2.2e+172)
   (/ (- (* x y) (* z t)) a)
   (- (/ x (/ a y)) (/ z (/ a t)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 2.2e+172) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (a <= 2.2d+172) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = (x / (a / y)) - (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 (a <= 2.2e+172) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (x / (a / y)) - (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.2e+172:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (x / (a / y)) - (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.2e+172)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 (a <= 2.2e+172)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (x / (a / y)) - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 2.2e+172], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.2000000000000001e172

   1. Initial program 95.5%

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

   if 2.2000000000000001e172 < a

   1. Initial program 76.9%

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

      1. div-sub 76.9%

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

      2. associate-/l* 76.9%

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

      3. associate-/l* 84.8%

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

   4. Applied egg-rr 84.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -6.2e-232)
   (/ (- (* x y) (* z t)) a)
   (- (/ (* x y) a) (/ t (/ a z)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -6.2e-232) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = ((x * y) / a) - (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-6.2d-232)) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = ((x * y) / a) - (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -6.2e-232) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = ((x * y) / a) - (t / (a / z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.2e-232:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = ((x * y) / a) - (t / (a / z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.2e-232)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(Float64(x * y) / a) - Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -6.2e-232)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = ((x * y) / a) - (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[x, -6.2e-232], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999998e-232

   1. Initial program 93.8%

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

   if -6.1999999999999998e-232 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 92.4%

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

      1. clear-num 92.0%

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

      2. associate-/r/ 92.4%

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

   5. Applied egg-rr 92.4%

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

      1. associate-*l/ 92.4%

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

      2. *-un-lft-identity 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*l/ 94.3%

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

      5. clear-num 94.3%

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

      6. associate-*l/ 94.6%

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

      7. *-un-lft-identity 94.6%

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

   7. Applied egg-rr 94.6%

      \[\leadsto -1 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} + \frac{x \cdot y}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -4.6e-203) (* x (/ y a)) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -4.6e-203) {
		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.
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 <= (-4.6d-203)) 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;
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 <= -4.6e-203) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e-203:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e-203)
		tmp = Float64(x * Float64(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])){:}
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 <= -4.6e-203)
		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.
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[z, -4.6e-203], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.59999999999999983e-203

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 43.8%

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

      1. associate-*r/ 46.9%

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

   5. Simplified 46.9%

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

   if -4.59999999999999983e-203 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. associate-*l/ 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -6e-56) (/ y (/ a x)) (* x (/ y a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -6e-56) {
		tmp = y / (a / x);
	} 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.
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 <= (-6d-56)) then
        tmp = y / (a / x)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -6e-56) {
		tmp = y / (a / x);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -6e-56:
		tmp = y / (a / x)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6e-56)
		tmp = Float64(y / Float64(a / x));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -6e-56)
		tmp = y / (a / x);
	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.
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[x, -6e-56], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999979e-56

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 65.5%

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

      1. associate-*r/ 63.1%

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

   5. Simplified 63.1%

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

      1. associate-*r/ 65.5%

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

      2. *-commutative 65.5%

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

      3. associate-/l* 66.4%

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

   7. Applied egg-rr 66.4%

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

   if -5.99999999999999979e-56 < x

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 47.6%

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

      1. associate-*r/ 47.6%

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

   5. Simplified 47.6%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -4.2e-94) (* x (/ y a)) (/ (* x y) a)))

C

assert(x < y && y < z && z < t && t < a);
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 <= -4.2e-94) {
		tmp = x * (y / 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.
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 <= (-4.2d-94)) then
        tmp = x * (y / a)
    else
        tmp = (x * y) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -4.2e-94) {
		tmp = x * (y / a);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e-94:
		tmp = x * (y / a)
	else:
		tmp = (x * y) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e-94)
		tmp = Float64(x * Float64(y / 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])){:}
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 <= -4.2e-94)
		tmp = x * (y / 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.
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[z, -4.2e-94], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-94

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf 35.9%

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

      1. associate-*r/ 38.7%

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

   5. Simplified 38.7%

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

   if -4.2000000000000002e-94 < z

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 59.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

assert x < y && y < z && z < t && t < a;
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) - (z * t)) / a;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

3. Final simplification 93.4%

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

Alternative 12: 51.8% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 93.4%

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

3. Taylor expanded in x around inf 53.0%

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

   1. associate-*r/ 52.3%

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

5. Simplified 52.3%

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

6. Final simplification 52.3%

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

Developer target: 91.9% 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 2024034 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (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))