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

Percentage Accurate: 97.6% → 98.9%

Time: 11.9s

Alternatives: 13

Speedup: 1.0×

• 33.8% 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: 97.6% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

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 98.0%

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

   1. associate--l+ 98.0%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

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

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

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 98.0%

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

   1. associate-+l- 98.0%

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

   2. *-commutative 98.0%

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

   3. associate-+l- 98.0%

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

   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 3: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-178}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+132}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+239}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* (* a b) -0.25))))
   (if (<= (* a b) -4e+63)
     t_1
     (if (<= (* a b) 5e-178)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* a b) 2e+132)
         (+ c (* x y))
         (if (<= (* a b) 1e+239) (+ c (* a (* b -0.25))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) * -0.25);
	double tmp;
	if ((a * b) <= -4e+63) {
		tmp = t_1;
	} else if ((a * b) <= 5e-178) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 2e+132) {
		tmp = c + (x * y);
	} else if ((a * b) <= 1e+239) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((a * b) * (-0.25d0))
    if ((a * b) <= (-4d+63)) then
        tmp = t_1
    else if ((a * b) <= 5d-178) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((a * b) <= 2d+132) then
        tmp = c + (x * y)
    else if ((a * b) <= 1d+239) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((a * b) * -0.25);
	double tmp;
	if ((a * b) <= -4e+63) {
		tmp = t_1;
	} else if ((a * b) <= 5e-178) {
		tmp = c + (0.0625 * (z * t));
	} else if ((a * b) <= 2e+132) {
		tmp = c + (x * y);
	} else if ((a * b) <= 1e+239) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((a * b) * -0.25)
	tmp = 0
	if (a * b) <= -4e+63:
		tmp = t_1
	elif (a * b) <= 5e-178:
		tmp = c + (0.0625 * (z * t))
	elif (a * b) <= 2e+132:
		tmp = c + (x * y)
	elif (a * b) <= 1e+239:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(a * b) * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= -4e+63)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e-178)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(a * b) <= 2e+132)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 1e+239)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((a * b) * -0.25);
	tmp = 0.0;
	if ((a * b) <= -4e+63)
		tmp = t_1;
	elseif ((a * b) <= 5e-178)
		tmp = c + (0.0625 * (z * t));
	elseif ((a * b) <= 2e+132)
		tmp = c + (x * y);
	elseif ((a * b) <= 1e+239)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+63], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e-178], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+132], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+239], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.00000000000000023e63 or 9.99999999999999991e238 < (*.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 z around 0 89.7%

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

   4. Taylor expanded in b around inf 89.9%

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

   5. Taylor expanded in c around 0 90.0%

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

   6. Taylor expanded in b around 0 89.8%

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

   if -4.00000000000000023e63 < (*.f64 a b) < 4.99999999999999976e-178

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 74.4%

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

   if 4.99999999999999976e-178 < (*.f64 a b) < 1.99999999999999998e132

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 66.5%

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

   if 1.99999999999999998e132 < (*.f64 a b) < 9.99999999999999991e238

   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 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*r* 64.9%

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

   5. Simplified 64.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-178}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+132}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+239}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-141}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot y + t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -4e+63)
     (+ (* x y) (* (* a b) -0.25))
     (if (<= (* a b) 1e-141)
       (+ c t_1)
       (if (<= (* a b) 5e+141)
         (+ (* x y) t_1)
         (* b (- (/ (* x y) b) (* a 0.25))))))))

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) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 1e-141) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+141) {
		tmp = (x * y) + t_1;
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-4d+63)) then
        tmp = (x * y) + ((a * b) * (-0.25d0))
    else if ((a * b) <= 1d-141) then
        tmp = c + t_1
    else if ((a * b) <= 5d+141) then
        tmp = (x * y) + t_1
    else
        tmp = b * (((x * y) / b) - (a * 0.25d0))
    end if
    code = tmp
end function

Java

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) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 1e-141) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+141) {
		tmp = (x * y) + t_1;
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -4e+63:
		tmp = (x * y) + ((a * b) * -0.25)
	elif (a * b) <= 1e-141:
		tmp = c + t_1
	elif (a * b) <= 5e+141:
		tmp = (x * y) + t_1
	else:
		tmp = b * (((x * y) / b) - (a * 0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -4e+63)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 1e-141)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 5e+141)
		tmp = Float64(Float64(x * y) + t_1);
	else
		tmp = Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -4e+63)
		tmp = (x * y) + ((a * b) * -0.25);
	elseif ((a * b) <= 1e-141)
		tmp = c + t_1;
	elseif ((a * b) <= 5e+141)
		tmp = (x * y) + t_1;
	else
		tmp = b * (((x * y) / b) - (a * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+63], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-141], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+141], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.00000000000000023e63

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 90.7%

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

   4. Taylor expanded in b around inf 88.7%

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

   5. Taylor expanded in c around 0 88.8%

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

   6. Taylor expanded in b around 0 90.9%

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

   if -4.00000000000000023e63 < (*.f64 a b) < 1e-141

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 74.5%

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

   if 1e-141 < (*.f64 a b) < 5.00000000000000025e141

   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 88.6%

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

   4. Taylor expanded in c around 0 72.5%

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

   if 5.00000000000000025e141 < (*.f64 a b)

   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 z around 0 87.3%

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

   4. Taylor expanded in b around inf 89.9%

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

   5. Taylor expanded in c around 0 80.2%

      \[\leadsto \color{blue}{b \cdot \left(\frac{x \cdot y}{b} - 0.25 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-141}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-141}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -4e+63)
     (+ (* x y) (* (* a b) -0.25))
     (if (<= (* a b) 1e-141)
       (+ c t_1)
       (if (<= (* a b) 8e+132) (+ (* x y) t_1) (+ c (* a (* b -0.25))))))))

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) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 1e-141) {
		tmp = c + t_1;
	} else if ((a * b) <= 8e+132) {
		tmp = (x * y) + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-4d+63)) then
        tmp = (x * y) + ((a * b) * (-0.25d0))
    else if ((a * b) <= 1d-141) then
        tmp = c + t_1
    else if ((a * b) <= 8d+132) then
        tmp = (x * y) + t_1
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

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) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 1e-141) {
		tmp = c + t_1;
	} else if ((a * b) <= 8e+132) {
		tmp = (x * y) + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -4e+63:
		tmp = (x * y) + ((a * b) * -0.25)
	elif (a * b) <= 1e-141:
		tmp = c + t_1
	elif (a * b) <= 8e+132:
		tmp = (x * y) + t_1
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -4e+63)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 1e-141)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 8e+132)
		tmp = Float64(Float64(x * y) + t_1);
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -4e+63)
		tmp = (x * y) + ((a * b) * -0.25);
	elseif ((a * b) <= 1e-141)
		tmp = c + t_1;
	elseif ((a * b) <= 8e+132)
		tmp = (x * y) + t_1;
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+63], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-141], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8e+132], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.00000000000000023e63

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 90.7%

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

   4. Taylor expanded in b around inf 88.7%

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

   5. Taylor expanded in c around 0 88.8%

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

   6. Taylor expanded in b around 0 90.9%

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

   if -4.00000000000000023e63 < (*.f64 a b) < 1e-141

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 74.5%

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

   if 1e-141 < (*.f64 a b) < 7.99999999999999993e132

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 88.2%

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

   4. Taylor expanded in c around 0 73.4%

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

   if 7.99999999999999993e132 < (*.f64 a b)

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*r* 76.9%

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

   5. Simplified 76.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-141}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-196}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* 0.0625 (* z t)))))
   (if (<= z -1.36e+38)
     t_2
     (if (<= z -1.8e-128)
       t_1
       (if (<= z 3.25e-196)
         (+ c (* a (* b -0.25)))
         (if (<= z 3.7e-53) t_1 t_2))))))

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 + (0.0625 * (z * t));
	double tmp;
	if (z <= -1.36e+38) {
		tmp = t_2;
	} else if (z <= -1.8e-128) {
		tmp = t_1;
	} else if (z <= 3.25e-196) {
		tmp = c + (a * (b * -0.25));
	} else if (z <= 3.7e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (0.0625d0 * (z * t))
    if (z <= (-1.36d+38)) then
        tmp = t_2
    else if (z <= (-1.8d-128)) then
        tmp = t_1
    else if (z <= 3.25d-196) then
        tmp = c + (a * (b * (-0.25d0)))
    else if (z <= 3.7d-53) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 + (0.0625 * (z * t));
	double tmp;
	if (z <= -1.36e+38) {
		tmp = t_2;
	} else if (z <= -1.8e-128) {
		tmp = t_1;
	} else if (z <= 3.25e-196) {
		tmp = c + (a * (b * -0.25));
	} else if (z <= 3.7e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (0.0625 * (z * t))
	tmp = 0
	if z <= -1.36e+38:
		tmp = t_2
	elif z <= -1.8e-128:
		tmp = t_1
	elif z <= 3.25e-196:
		tmp = c + (a * (b * -0.25))
	elif z <= 3.7e-53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (z <= -1.36e+38)
		tmp = t_2;
	elseif (z <= -1.8e-128)
		tmp = t_1;
	elseif (z <= 3.25e-196)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (z <= 3.7e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (0.0625 * (z * t));
	tmp = 0.0;
	if (z <= -1.36e+38)
		tmp = t_2;
	elseif (z <= -1.8e-128)
		tmp = t_1;
	elseif (z <= 3.25e-196)
		tmp = c + (a * (b * -0.25));
	elseif (z <= 3.7e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.36e+38], t$95$2, If[LessEqual[z, -1.8e-128], t$95$1, If[LessEqual[z, 3.25e-196], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36000000000000002e38 or 3.69999999999999982e-53 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   if -1.36000000000000002e38 < z < -1.80000000000000012e-128 or 3.2500000000000002e-196 < z < 3.69999999999999982e-53

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -1.80000000000000012e-128 < z < 3.2500000000000002e-196

   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 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r* 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+38}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-196}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+141}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+44)
   (+ c (- (* x y) (* (* a b) 0.25)))
   (if (<= (* a b) 5e+141)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* b (- (/ (* x y) b) (* a 0.25)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+44) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else if ((a * b) <= 5e+141) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (b * (((x * y) / b) - (a * 0.25)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a * b) <= (-2d+44)) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else if ((a * b) <= 5d+141) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (b * (((x * y) / b) - (a * 0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+44) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else if ((a * b) <= 5e+141) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (b * (((x * y) / b) - (a * 0.25)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+44:
		tmp = c + ((x * y) - ((a * b) * 0.25))
	elif (a * b) <= 5e+141:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (b * (((x * y) / b) - (a * 0.25)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+44)
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	elseif (Float64(a * b) <= 5e+141)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+44)
		tmp = c + ((x * y) - ((a * b) * 0.25));
	elseif ((a * b) <= 5e+141)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (b * (((x * y) / b) - (a * 0.25)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+44], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+141], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000002e44

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 89.2%

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

   if -2.0000000000000002e44 < (*.f64 a b) < 5.00000000000000025e141

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 94.6%

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

   if 5.00000000000000025e141 < (*.f64 a b)

   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 z around 0 87.3%

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

   4. Taylor expanded in b around inf 89.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+141}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+44} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+44) (not (<= (* a b) 5e+141)))
   (+ c (- (* x y) (* (* a b) 0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+44) || !((a * b) <= 5e+141)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (((a * b) <= (-2d+44)) .or. (.not. ((a * b) <= 5d+141))) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+44) || !((a * b) <= 5e+141)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e+44) or not ((a * b) <= 5e+141):
		tmp = c + ((x * y) - ((a * b) * 0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e+44) || !(Float64(a * b) <= 5e+141))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e+44) || ~(((a * b) <= 5e+141)))
		tmp = c + ((x * y) - ((a * b) * 0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+44], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+141]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.0000000000000002e44 or 5.00000000000000025e141 < (*.f64 a b)

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 88.3%

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

   if -2.0000000000000002e44 < (*.f64 a b) < 5.00000000000000025e141

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 94.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+44} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+173}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -4e+63)
   (+ (* x y) (* (* a b) -0.25))
   (if (<= (* a b) 2e+173)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* b (- (/ (* x y) b) (* a 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 2e+173) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a * b) <= (-4d+63)) then
        tmp = (x * y) + ((a * b) * (-0.25d0))
    else if ((a * b) <= 2d+173) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = b * (((x * y) / b) - (a * 0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -4e+63) {
		tmp = (x * y) + ((a * b) * -0.25);
	} else if ((a * b) <= 2e+173) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -4e+63:
		tmp = (x * y) + ((a * b) * -0.25)
	elif (a * b) <= 2e+173:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = b * (((x * y) / b) - (a * 0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -4e+63)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 2e+173)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -4e+63)
		tmp = (x * y) + ((a * b) * -0.25);
	elseif ((a * b) <= 2e+173)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = b * (((x * y) / b) - (a * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+63], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+173], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.00000000000000023e63

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 90.7%

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

   4. Taylor expanded in b around inf 88.7%

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

   5. Taylor expanded in c around 0 88.8%

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

   6. Taylor expanded in b around 0 90.9%

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

   if -4.00000000000000023e63 < (*.f64 a b) < 2e173

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 92.8%

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

   if 2e173 < (*.f64 a b)

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 88.1%

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

   4. Taylor expanded in b around inf 91.1%

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

   5. Taylor expanded in c around 0 85.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+173}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+38} \lor \neg \left(z \leq 7.2 \cdot 10^{-53}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.4e+38) (not (<= z 7.2e-53)))
   (+ c (* 0.0625 (* z t)))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+38) || !(z <= 7.2e-53)) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((z <= (-1.4d+38)) .or. (.not. (z <= 7.2d-53))) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.4e+38) || !(z <= 7.2e-53)) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.4e+38) or not (z <= 7.2e-53):
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.4e+38) || !(z <= 7.2e-53))
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.4e+38) || ~((z <= 7.2e-53)))
		tmp = c + (0.0625 * (z * t));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.4e+38], N[Not[LessEqual[z, 7.2e-53]], $MachinePrecision]], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e38 or 7.1999999999999998e-53 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 62.5%

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

   if -1.4e38 < z < 7.1999999999999998e-53

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 66.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+38} \lor \neg \left(z \leq 7.2 \cdot 10^{-53}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = c + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 98.0%

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

Alternative 12: 47.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ c + x \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (+ c (* x y)))

C

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

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 = c + (x * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

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 x around inf 51.2%

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

4. Final simplification 51.2%

   \[\leadsto c + x \cdot y \]
5. Add Preprocessing

Alternative 13: 21.6% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 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 = c
end function

Java

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

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

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 x around inf 51.2%

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

4. Taylor expanded in x around 0 24.1%

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

5. Final simplification 24.1%

   \[\leadsto c \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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))