Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 98.0% → 97.7%

Time: 13.6s

Alternatives: 17

Speedup: 0.5×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ t_2 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+251}:\\ \;\;\;\;c + \left(t\_2 - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot \left(y + 0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)) (t_2 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= t_2 5e+251)
     (+ c (- t_2 t_1))
     (+ c (- (* x (+ y (* 0.0625 (* t (/ z x))))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if (t_2 <= 5e+251) {
		tmp = c + (t_2 - t_1);
	} else {
		tmp = c + ((x * (y + (0.0625 * (t * (z / x))))) - t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) / 4.0d0
    t_2 = (x * y) + ((z * t) / 16.0d0)
    if (t_2 <= 5d+251) then
        tmp = c + (t_2 - t_1)
    else
        tmp = c + ((x * (y + (0.0625d0 * (t * (z / x))))) - t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if (t_2 <= 5e+251) {
		tmp = c + (t_2 - t_1);
	} else {
		tmp = c + ((x * (y + (0.0625 * (t * (z / x))))) - t_1);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	t_2 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if t_2 <= 5e+251:
		tmp = c + (t_2 - t_1)
	else:
		tmp = c + ((x * (y + (0.0625 * (t * (z / x))))) - t_1)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (t_2 <= 5e+251)
		tmp = Float64(c + Float64(t_2 - t_1));
	else
		tmp = Float64(c + Float64(Float64(x * Float64(y + Float64(0.0625 * Float64(t * Float64(z / x))))) - t_1));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	t_2 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if (t_2 <= 5e+251)
		tmp = c + (t_2 - t_1);
	else
		tmp = c + ((x * (y + (0.0625 * (t * (z / x))))) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 5e+251], N[(c + N[(t$95$2 - t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * N[(y + N[(0.0625 * N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < 5.0000000000000005e251

   1. Initial program 99.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   if 5.0000000000000005e251 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64)))

   1. Initial program 85.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y + 0.0625 \cdot \frac{t \cdot z}{x}\right)} - \frac{a \cdot b}{4}\right) + c \]
   4. Step-by-step derivation

      1. associate-/l* 97.0%

         \[\leadsto \left(x \cdot \left(y + 0.0625 \cdot \color{blue}{\left(t \cdot \frac{z}{x}\right)}\right) - \frac{a \cdot b}{4}\right) + c \]

   5. Simplified 97.0%

      \[\leadsto \left(\color{blue}{x \cdot \left(y + 0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right)} - \frac{a \cdot b}{4}\right) + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + \frac{z \cdot t}{16} \leq 5 \cdot 10^{+251}:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot \left(y + 0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right) - \frac{a \cdot b}{4}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (+ (fma x y (fma z (/ t 16.0) (/ (* a b) -4.0))) c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma(z, (t / 16.0), ((a * b) / -4.0))) + c;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(fma(x, y, fma(z, Float64(t / 16.0), Float64(Float64(a * b) / -4.0))) + c)
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y + N[(z * N[(t / 16.0), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate--l+ 97.6%

      \[\leadsto \color{blue}{\left(x \cdot y + \left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)\right)} + c \]

   2. fma-define 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)} + c \]

   3. associate-/l* 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \frac{t}{16}} - \frac{a \cdot b}{4}\right) + c \]

   4. fma-neg 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(z, \frac{t}{16}, -\frac{a \cdot b}{4}\right)}\right) + c \]

   5. distribute-neg-frac2 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \color{blue}{\frac{a \cdot b}{-4}}\right)\right) + c \]

   6. metadata-eval 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{\color{blue}{-4}}\right)\right) + c \]

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c} \]
4. Add Preprocessing

5. Final simplification 98.4%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c \]
6. Add Preprocessing

Alternative 3: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (fma x y (* z (/ t 16.0))) (* a (/ b 4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (fma(x, y, (z * (t / 16.0))) - (a * (b / 4.0)));
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(fma(x, y, Float64(z * Float64(t / 16.0))) - Float64(a * Float64(b / 4.0))))
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(x * y + N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.6%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 97.6%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. *-commutative 97.6%

      \[\leadsto \left(x \cdot y + \frac{\color{blue}{t \cdot z}}{16}\right) - \left(\frac{a \cdot b}{4} - c\right) \]

   3. associate-+l- 97.6%

      \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{t \cdot z}{16}\right) - \frac{a \cdot b}{4}\right) + c} \]

   4. fma-define 98.4%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, y, \frac{t \cdot z}{16}\right)} - \frac{a \cdot b}{4}\right) + c \]

   5. *-commutative 98.4%

      \[\leadsto \left(\mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot t}}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   6. associate-/l* 98.4%

      \[\leadsto \left(\mathsf{fma}\left(x, y, \color{blue}{z \cdot \frac{t}{16}}\right) - \frac{a \cdot b}{4}\right) + c \]

   7. associate-/l* 98.4%

      \[\leadsto \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - \color{blue}{a \cdot \frac{b}{4}}\right) + c \]

3. Simplified 98.4%

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) + c} \]
4. Add Preprocessing

5. Final simplification 98.4%

   \[\leadsto c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) \]
6. Add Preprocessing

Alternative 4: 42.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{+20}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-316}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-154}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.12 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= (* x y) -2.1e+182)
     (* x y)
     (if (<= (* x y) -9.5e+20)
       c
       (if (<= (* x y) 5e-316)
         t_1
         (if (<= (* x y) 6.6e-154)
           c
           (if (<= (* x y) 1.12e+169) t_1 (* x y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -2.1e+182) {
		tmp = x * y;
	} else if ((x * y) <= -9.5e+20) {
		tmp = c;
	} else if ((x * y) <= 5e-316) {
		tmp = t_1;
	} else if ((x * y) <= 6.6e-154) {
		tmp = c;
	} else if ((x * y) <= 1.12e+169) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    if ((x * y) <= (-2.1d+182)) then
        tmp = x * y
    else if ((x * y) <= (-9.5d+20)) then
        tmp = c
    else if ((x * y) <= 5d-316) then
        tmp = t_1
    else if ((x * y) <= 6.6d-154) then
        tmp = c
    else if ((x * y) <= 1.12d+169) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -2.1e+182) {
		tmp = x * y;
	} else if ((x * y) <= -9.5e+20) {
		tmp = c;
	} else if ((x * y) <= 5e-316) {
		tmp = t_1;
	} else if ((x * y) <= 6.6e-154) {
		tmp = c;
	} else if ((x * y) <= 1.12e+169) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if (x * y) <= -2.1e+182:
		tmp = x * y
	elif (x * y) <= -9.5e+20:
		tmp = c
	elif (x * y) <= 5e-316:
		tmp = t_1
	elif (x * y) <= 6.6e-154:
		tmp = c
	elif (x * y) <= 1.12e+169:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+182)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -9.5e+20)
		tmp = c;
	elseif (Float64(x * y) <= 5e-316)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.6e-154)
		tmp = c;
	elseif (Float64(x * y) <= 1.12e+169)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	tmp = 0.0;
	if ((x * y) <= -2.1e+182)
		tmp = x * y;
	elseif ((x * y) <= -9.5e+20)
		tmp = c;
	elseif ((x * y) <= 5e-316)
		tmp = t_1;
	elseif ((x * y) <= 6.6e-154)
		tmp = c;
	elseif ((x * y) <= 1.12e+169)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+182], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -9.5e+20], c, If[LessEqual[N[(x * y), $MachinePrecision], 5e-316], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.6e-154], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.12e+169], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0999999999999999e182 or 1.11999999999999996e169 < (*.f64 x y)

   1. Initial program 90.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.8%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in x around inf 80.3%

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

   if -2.0999999999999999e182 < (*.f64 x y) < -9.5e20 or 5.000000017e-316 < (*.f64 x y) < 6.60000000000000055e-154

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 43.3%

      \[\leadsto \color{blue}{c} \]

   if -9.5e20 < (*.f64 x y) < 5.000000017e-316 or 6.60000000000000055e-154 < (*.f64 x y) < 1.11999999999999996e169

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 66.6%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 37.3%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 37.3%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

      3. *-commutative 37.3%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} \]

   6. Simplified 37.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{+20}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-316}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-154}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.12 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))))
   (if (<= (* x y) -2e+182)
     (- (* x y) (* (* a b) 0.25))
     (if (<= (* x y) 3e-272)
       t_1
       (if (<= (* x y) 5e-55)
         (* z (+ (* t 0.0625) (/ c z)))
         (if (<= (* x y) 1e+97) t_1 (* y (+ x (* 0.0625 (/ (* z t) y))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -2e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 3e-272) {
		tmp = t_1;
	} else if ((x * y) <= 5e-55) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 1e+97) {
		tmp = t_1;
	} else {
		tmp = y * (x + (0.0625 * ((z * t) / y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    if ((x * y) <= (-2d+182)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((x * y) <= 3d-272) then
        tmp = t_1
    else if ((x * y) <= 5d-55) then
        tmp = z * ((t * 0.0625d0) + (c / z))
    else if ((x * y) <= 1d+97) then
        tmp = t_1
    else
        tmp = y * (x + (0.0625d0 * ((z * t) / y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -2e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 3e-272) {
		tmp = t_1;
	} else if ((x * y) <= 5e-55) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 1e+97) {
		tmp = t_1;
	} else {
		tmp = y * (x + (0.0625 * ((z * t) / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	tmp = 0
	if (x * y) <= -2e+182:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (x * y) <= 3e-272:
		tmp = t_1
	elif (x * y) <= 5e-55:
		tmp = z * ((t * 0.0625) + (c / z))
	elif (x * y) <= 1e+97:
		tmp = t_1
	else:
		tmp = y * (x + (0.0625 * ((z * t) / y)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+182)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(x * y) <= 3e-272)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-55)
		tmp = Float64(z * Float64(Float64(t * 0.0625) + Float64(c / z)));
	elseif (Float64(x * y) <= 1e+97)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x + Float64(0.0625 * Float64(Float64(z * t) / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((x * y) <= -2e+182)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((x * y) <= 3e-272)
		tmp = t_1;
	elseif ((x * y) <= 5e-55)
		tmp = z * ((t * 0.0625) + (c / z));
	elseif ((x * y) <= 1e+97)
		tmp = t_1;
	else
		tmp = y * (x + (0.0625 * ((z * t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+182], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e-272], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-55], N[(z * N[(N[(t * 0.0625), $MachinePrecision] + N[(c / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+97], t$95$1, N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.0000000000000001e182

   1. Initial program 89.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.1%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 93.1%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.0000000000000001e182 < (*.f64 x y) < 3.0000000000000003e-272 or 5.0000000000000002e-55 < (*.f64 x y) < 1.0000000000000001e97

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 67.3%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 67.3%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]

   if 3.0000000000000003e-272 < (*.f64 x y) < 5.0000000000000002e-55

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in t around inf 74.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   5. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(z \cdot t\right)} \cdot 0.0625 + c \]

      3. associate-*r* 74.4%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 74.4%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   6. Simplified 74.4%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   7. Taylor expanded in z around inf 69.9%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t + \frac{c}{z}\right)} \]

   if 1.0000000000000001e97 < (*.f64 x y)

   1. Initial program 94.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   4. Taylor expanded in c around 0 75.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]

   5. Taylor expanded in y around inf 75.9%

      \[\leadsto \color{blue}{y \cdot \left(x + 0.0625 \cdot \frac{t \cdot z}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-272}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+97}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))))
   (if (<= (* x y) -1.05e+57)
     (+ c (* x y))
     (if (<= (* x y) 2.9e-272)
       t_1
       (if (<= (* x y) 5.6e-51)
         (* z (+ (* t 0.0625) (/ c z)))
         (if (<= (* x y) 8.8e+101) t_1 (+ (* x y) (* 0.0625 (* z t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1.05e+57) {
		tmp = c + (x * y);
	} else if ((x * y) <= 2.9e-272) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-51) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 8.8e+101) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    if ((x * y) <= (-1.05d+57)) then
        tmp = c + (x * y)
    else if ((x * y) <= 2.9d-272) then
        tmp = t_1
    else if ((x * y) <= 5.6d-51) then
        tmp = z * ((t * 0.0625d0) + (c / z))
    else if ((x * y) <= 8.8d+101) then
        tmp = t_1
    else
        tmp = (x * y) + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1.05e+57) {
		tmp = c + (x * y);
	} else if ((x * y) <= 2.9e-272) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-51) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 8.8e+101) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	tmp = 0
	if (x * y) <= -1.05e+57:
		tmp = c + (x * y)
	elif (x * y) <= 2.9e-272:
		tmp = t_1
	elif (x * y) <= 5.6e-51:
		tmp = z * ((t * 0.0625) + (c / z))
	elif (x * y) <= 8.8e+101:
		tmp = t_1
	else:
		tmp = (x * y) + (0.0625 * (z * t))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -1.05e+57)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 2.9e-272)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.6e-51)
		tmp = Float64(z * Float64(Float64(t * 0.0625) + Float64(c / z)));
	elseif (Float64(x * y) <= 8.8e+101)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((x * y) <= -1.05e+57)
		tmp = c + (x * y);
	elseif ((x * y) <= 2.9e-272)
		tmp = t_1;
	elseif ((x * y) <= 5.6e-51)
		tmp = z * ((t * 0.0625) + (c / z));
	elseif ((x * y) <= 8.8e+101)
		tmp = t_1;
	else
		tmp = (x * y) + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.05e+57], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.9e-272], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.6e-51], N[(z * N[(N[(t * 0.0625), $MachinePrecision] + N[(c / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.8e+101], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.04999999999999995e57

   1. Initial program 93.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in x around inf 79.6%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -1.04999999999999995e57 < (*.f64 x y) < 2.89999999999999995e-272 or 5.6e-51 < (*.f64 x y) < 8.8000000000000003e101

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 68.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 68.3%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 68.3%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 68.3%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]

   if 2.89999999999999995e-272 < (*.f64 x y) < 5.6e-51

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in t around inf 74.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   5. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(z \cdot t\right)} \cdot 0.0625 + c \]

      3. associate-*r* 74.4%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 74.4%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   6. Simplified 74.4%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   7. Taylor expanded in z around inf 69.9%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t + \frac{c}{z}\right)} \]

   if 8.8000000000000003e101 < (*.f64 x y)

   1. Initial program 94.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   4. Taylor expanded in c around 0 75.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.9 \cdot 10^{-272}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+101}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 2.45 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))))
   (if (<= (* x y) -1.8e+182)
     (- (* x y) (* (* a b) 0.25))
     (if (<= (* x y) 2.45e-272)
       t_1
       (if (<= (* x y) 4.8e-52)
         (* z (+ (* t 0.0625) (/ c z)))
         (if (<= (* x y) 8.5e+101) t_1 (+ (* x y) (* 0.0625 (* z t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1.8e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 2.45e-272) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e-52) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 8.5e+101) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    if ((x * y) <= (-1.8d+182)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((x * y) <= 2.45d-272) then
        tmp = t_1
    else if ((x * y) <= 4.8d-52) then
        tmp = z * ((t * 0.0625d0) + (c / z))
    else if ((x * y) <= 8.5d+101) then
        tmp = t_1
    else
        tmp = (x * y) + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1.8e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 2.45e-272) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e-52) {
		tmp = z * ((t * 0.0625) + (c / z));
	} else if ((x * y) <= 8.5e+101) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	tmp = 0
	if (x * y) <= -1.8e+182:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (x * y) <= 2.45e-272:
		tmp = t_1
	elif (x * y) <= 4.8e-52:
		tmp = z * ((t * 0.0625) + (c / z))
	elif (x * y) <= 8.5e+101:
		tmp = t_1
	else:
		tmp = (x * y) + (0.0625 * (z * t))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+182)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(x * y) <= 2.45e-272)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.8e-52)
		tmp = Float64(z * Float64(Float64(t * 0.0625) + Float64(c / z)));
	elseif (Float64(x * y) <= 8.5e+101)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((x * y) <= -1.8e+182)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((x * y) <= 2.45e-272)
		tmp = t_1;
	elseif ((x * y) <= 4.8e-52)
		tmp = z * ((t * 0.0625) + (c / z));
	elseif ((x * y) <= 8.5e+101)
		tmp = t_1;
	else
		tmp = (x * y) + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+182], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.45e-272], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.8e-52], N[(z * N[(N[(t * 0.0625), $MachinePrecision] + N[(c / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.5e+101], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.8e182

   1. Initial program 89.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.1%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 93.1%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.8e182 < (*.f64 x y) < 2.4499999999999999e-272 or 4.8000000000000003e-52 < (*.f64 x y) < 8.5000000000000001e101

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 67.3%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 67.3%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 67.3%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]

   if 2.4499999999999999e-272 < (*.f64 x y) < 4.8000000000000003e-52

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in t around inf 74.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   5. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. *-commutative 74.4%

         \[\leadsto \color{blue}{\left(z \cdot t\right)} \cdot 0.0625 + c \]

      3. associate-*r* 74.4%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 74.4%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   6. Simplified 74.4%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   7. Taylor expanded in z around inf 69.9%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t + \frac{c}{z}\right)} \]

   if 8.5000000000000001e101 < (*.f64 x y)

   1. Initial program 94.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   4. Taylor expanded in c around 0 75.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 2.45 \cdot 10^{-272}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{c}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+101}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY)
     (+ c t_1)
     (+ c (* y (+ x (* 0.0625 (/ (* z t) y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(c + Float64(y * Float64(x + Float64(0.0625 * Float64(Float64(z * t) / y)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(c + N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 33.3%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   4. Taylor expanded in y around inf 66.7%

      \[\leadsto c + \color{blue}{y \cdot \left(x + 0.0625 \cdot \frac{t \cdot z}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_3 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-70}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* z (* t 0.0625))))
        (t_3 (+ c (* b (* a -0.25)))))
   (if (<= z -4.7e+122)
     t_2
     (if (<= z -1.52e-74)
       t_1
       (if (<= z 5.5e-306)
         t_3
         (if (<= z 1.5e-238) t_1 (if (<= z 9.5e-70) t_3 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (z <= -4.7e+122) {
		tmp = t_2;
	} else if (z <= -1.52e-74) {
		tmp = t_1;
	} else if (z <= 5.5e-306) {
		tmp = t_3;
	} else if (z <= 1.5e-238) {
		tmp = t_1;
	} else if (z <= 9.5e-70) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (z * (t * 0.0625d0))
    t_3 = c + (b * (a * (-0.25d0)))
    if (z <= (-4.7d+122)) then
        tmp = t_2
    else if (z <= (-1.52d-74)) then
        tmp = t_1
    else if (z <= 5.5d-306) then
        tmp = t_3
    else if (z <= 1.5d-238) then
        tmp = t_1
    else if (z <= 9.5d-70) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (z <= -4.7e+122) {
		tmp = t_2;
	} else if (z <= -1.52e-74) {
		tmp = t_1;
	} else if (z <= 5.5e-306) {
		tmp = t_3;
	} else if (z <= 1.5e-238) {
		tmp = t_1;
	} else if (z <= 9.5e-70) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (z * (t * 0.0625))
	t_3 = c + (b * (a * -0.25))
	tmp = 0
	if z <= -4.7e+122:
		tmp = t_2
	elif z <= -1.52e-74:
		tmp = t_1
	elif z <= 5.5e-306:
		tmp = t_3
	elif z <= 1.5e-238:
		tmp = t_1
	elif z <= 9.5e-70:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_3 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (z <= -4.7e+122)
		tmp = t_2;
	elseif (z <= -1.52e-74)
		tmp = t_1;
	elseif (z <= 5.5e-306)
		tmp = t_3;
	elseif (z <= 1.5e-238)
		tmp = t_1;
	elseif (z <= 9.5e-70)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (z * (t * 0.0625));
	t_3 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (z <= -4.7e+122)
		tmp = t_2;
	elseif (z <= -1.52e-74)
		tmp = t_1;
	elseif (z <= 5.5e-306)
		tmp = t_3;
	elseif (z <= 1.5e-238)
		tmp = t_1;
	elseif (z <= 9.5e-70)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+122], t$95$2, If[LessEqual[z, -1.52e-74], t$95$1, If[LessEqual[z, 5.5e-306], t$95$3, If[LessEqual[z, 1.5e-238], t$95$1, If[LessEqual[z, 9.5e-70], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.70000000000000023e122 or 9.4999999999999994e-70 < z

   1. Initial program 95.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   5. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

      2. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(z \cdot t\right)} \cdot 0.0625 + c \]

      3. associate-*r* 63.4%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 63.4%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   6. Simplified 63.4%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   if -4.70000000000000023e122 < z < -1.51999999999999997e-74 or 5.49999999999999992e-306 < z < 1.5e-238

   1. Initial program 98.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 98.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -1.51999999999999997e-74 < z < 5.49999999999999992e-306 or 1.5e-238 < z < 9.4999999999999994e-70

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 65.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 65.2%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 65.2%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 65.2%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 65.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+122}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-74}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-306}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-238}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-70}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := t\_2 - t\_1\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+94}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+239}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))) (t_3 (- t_2 t_1)))
   (if (<= (* a b) -1e+154)
     t_3
     (if (<= (* a b) 2e+94)
       (+ c (+ (* x y) t_2))
       (if (<= (* a b) 4e+239) (- (+ c (* x y)) t_1) t_3)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double t_3 = t_2 - t_1;
	double tmp;
	if ((a * b) <= -1e+154) {
		tmp = t_3;
	} else if ((a * b) <= 2e+94) {
		tmp = c + ((x * y) + t_2);
	} else if ((a * b) <= 4e+239) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    t_3 = t_2 - t_1
    if ((a * b) <= (-1d+154)) then
        tmp = t_3
    else if ((a * b) <= 2d+94) then
        tmp = c + ((x * y) + t_2)
    else if ((a * b) <= 4d+239) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double t_3 = t_2 - t_1;
	double tmp;
	if ((a * b) <= -1e+154) {
		tmp = t_3;
	} else if ((a * b) <= 2e+94) {
		tmp = c + ((x * y) + t_2);
	} else if ((a * b) <= 4e+239) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	t_3 = t_2 - t_1
	tmp = 0
	if (a * b) <= -1e+154:
		tmp = t_3
	elif (a * b) <= 2e+94:
		tmp = c + ((x * y) + t_2)
	elif (a * b) <= 4e+239:
		tmp = (c + (x * y)) - t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(t_2 - t_1)
	tmp = 0.0
	if (Float64(a * b) <= -1e+154)
		tmp = t_3;
	elseif (Float64(a * b) <= 2e+94)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	elseif (Float64(a * b) <= 4e+239)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	t_3 = t_2 - t_1;
	tmp = 0.0;
	if ((a * b) <= -1e+154)
		tmp = t_3;
	elseif ((a * b) <= 2e+94)
		tmp = c + ((x * y) + t_2);
	elseif ((a * b) <= 4e+239)
		tmp = (c + (x * y)) - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - t$95$1), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+154], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 2e+94], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e+239], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000004e154 or 3.99999999999999996e239 < (*.f64 a b)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 92.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000004e154 < (*.f64 a b) < 2e94

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.2%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 2e94 < (*.f64 a b) < 3.99999999999999996e239

   1. Initial program 94.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+154}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+94}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+239}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (<= (* x y) -2e+14)
     (- (+ c (* x y)) t_1)
     (if (<= (* x y) 2e+151)
       (- (+ c (* 0.0625 (* z t))) t_1)
       (+ c (* y (+ x (* 0.0625 (/ (* z t) y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -2e+14) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 2e+151) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if ((x * y) <= (-2d+14)) then
        tmp = (c + (x * y)) - t_1
    else if ((x * y) <= 2d+151) then
        tmp = (c + (0.0625d0 * (z * t))) - t_1
    else
        tmp = c + (y * (x + (0.0625d0 * ((z * t) / y))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -2e+14) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 2e+151) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if (x * y) <= -2e+14:
		tmp = (c + (x * y)) - t_1
	elif (x * y) <= 2e+151:
		tmp = (c + (0.0625 * (z * t))) - t_1
	else:
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(x * y) <= -2e+14)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(x * y) <= 2e+151)
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - t_1);
	else
		tmp = Float64(c + Float64(y * Float64(x + Float64(0.0625 * Float64(Float64(z * t) / y)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if ((x * y) <= -2e+14)
		tmp = (c + (x * y)) - t_1;
	elseif ((x * y) <= 2e+151)
		tmp = (c + (0.0625 * (z * t))) - t_1;
	else
		tmp = c + (y * (x + (0.0625 * ((z * t) / y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+14], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+151], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(c + N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e14

   1. Initial program 94.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.8%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2e14 < (*.f64 x y) < 2.00000000000000003e151

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if 2.00000000000000003e151 < (*.f64 x y)

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 87.5%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   4. Taylor expanded in y around inf 90.2%

      \[\leadsto c + \color{blue}{y \cdot \left(x + 0.0625 \cdot \frac{t \cdot z}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+154} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;t\_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* a b) -1e+154) (not (<= (* a b) 5e+114)))
     (- t_1 (* (* a b) 0.25))
     (+ c (+ (* x y) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+154) || !((a * b) <= 5e+114)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((a * b) <= (-1d+154)) .or. (.not. ((a * b) <= 5d+114))) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((a * b) <= -1e+154) || !((a * b) <= 5e+114)) {
		tmp = t_1 - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((a * b) <= -1e+154) or not ((a * b) <= 5e+114):
		tmp = t_1 - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -1e+154) || !(Float64(a * b) <= 5e+114))
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((a * b) <= -1e+154) || ~(((a * b) <= 5e+114)))
		tmp = t_1 - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+154], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+114]], $MachinePrecision]], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.00000000000000004e154 or 5.0000000000000001e114 < (*.f64 a b)

   1. Initial program 96.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 86.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000004e154 < (*.f64 a b) < 5.0000000000000001e114

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 89.8%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+154} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+151}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1e+151)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 5e+114)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* b (* a -0.25))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+151) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+114) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-1d+151)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 5d+114) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+151) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+114) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -1e+151:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 5e+114:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -1e+151)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 5e+114)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -1e+151)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 5e+114)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+151], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+114], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000002e151

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.6%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 79.3%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000002e151 < (*.f64 a b) < 5.0000000000000001e114

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.2%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]

   if 5.0000000000000001e114 < (*.f64 a b)

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 78.5%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 78.5%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 78.5%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 78.5%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+151}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+57} \lor \neg \left(x \cdot y \leq 4.6 \cdot 10^{+82}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.4e+57) (not (<= (* x y) 4.6e+82)))
   (+ c (* x y))
   (+ c (* b (* a -0.25)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.4e+57) || !((x * y) <= 4.6e+82)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.4d+57)) .or. (.not. ((x * y) <= 4.6d+82))) then
        tmp = c + (x * y)
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.4e+57) || !((x * y) <= 4.6e+82)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.4e+57) or not ((x * y) <= 4.6e+82):
		tmp = c + (x * y)
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.4e+57) || !(Float64(x * y) <= 4.6e+82))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.4e+57) || ~(((x * y) <= 4.6e+82)))
		tmp = c + (x * y);
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.4e+57], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.6e+82]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.4e57 or 4.59999999999999976e82 < (*.f64 x y)

   1. Initial program 94.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 86.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in x around inf 71.9%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -1.4e57 < (*.f64 x y) < 4.59999999999999976e82

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 63.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 63.0%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

      2. *-commutative 63.0%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} + c \]

      3. *-commutative 63.0%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} + c \]

   5. Simplified 63.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+57} \lor \neg \left(x \cdot y \leq 4.6 \cdot 10^{+82}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+182} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.8e+182) (not (<= (* x y) 7.5e+96))) (* x y) c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.8e+182) || !((x * y) <= 7.5e+96)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.8d+182)) .or. (.not. ((x * y) <= 7.5d+96))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.8e+182) || !((x * y) <= 7.5e+96)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.8e+182) or not ((x * y) <= 7.5e+96):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.8e+182) || !(Float64(x * y) <= 7.5e+96))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.8e+182) || ~(((x * y) <= 7.5e+96)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.8e+182], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+96]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.8e182 or 7.4999999999999996e96 < (*.f64 x y)

   1. Initial program 92.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 79.9%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in x around inf 66.9%

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

   if -1.8e182 < (*.f64 x y) < 7.4999999999999996e96

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 30.7%

      \[\leadsto \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+182} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+127} \lor \neg \left(a \leq 1.26 \cdot 10^{+44}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.7e+127) (not (<= a 1.26e+44)))
   (* b (* a -0.25))
   (+ c (* x y))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.7e+127) || !(a <= 1.26e+44)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.7d+127)) .or. (.not. (a <= 1.26d+44))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.7e+127) || !(a <= 1.26e+44)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.7e+127) or not (a <= 1.26e+44):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.7e+127) || !(a <= 1.26e+44))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.7e+127) || ~((a <= 1.26e+44)))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.7e+127], N[Not[LessEqual[a, 1.26e+44]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999989e127 or 1.25999999999999996e44 < a

   1. Initial program 98.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in a around inf 52.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 52.2%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 52.2%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

      3. *-commutative 52.2%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot -0.25\right)} \]

   6. Simplified 52.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]

   if -1.69999999999999989e127 < a < 1.25999999999999996e44

   1. Initial program 97.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 93.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{x \cdot y}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} + c \]

   4. Taylor expanded in x around inf 60.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+127} \lor \neg \left(a \leq 1.26 \cdot 10^{+44}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 97.6%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in c around inf 23.6%

   \[\leadsto \color{blue}{c} \]

4. Final simplification 23.6%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024075 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))