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

Percentage Accurate: 97.8% → 98.3%

Time: 15.3s

Alternatives: 12

Speedup: 1.0×

• 32.9% 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: 97.8% 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: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. associate-+l- 99.3%

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

   2. *-commutative 99.3%

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

   3. associate-+l- 99.3%

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

   4. fma-define 99.3%

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

   5. *-commutative 99.3%

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

   6. associate-/l* 99.3%

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

   7. associate-/l* 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-281}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* a (* b -0.25))))
   (if (<= y -4.8e-17)
     (* x y)
     (if (<= y -1.8e-101)
       t_1
       (if (<= y -4.2e-245)
         t_2
         (if (<= y 1.65e-281)
           c
           (if (<= y 2.65e-229) t_2 (if (<= y 1.32e+108) t_1 (* x y)))))))))

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 t_2 = a * (b * -0.25);
	double tmp;
	if (y <= -4.8e-17) {
		tmp = x * y;
	} else if (y <= -1.8e-101) {
		tmp = t_1;
	} else if (y <= -4.2e-245) {
		tmp = t_2;
	} else if (y <= 1.65e-281) {
		tmp = c;
	} else if (y <= 2.65e-229) {
		tmp = t_2;
	} else if (y <= 1.32e+108) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = a * (b * (-0.25d0))
    if (y <= (-4.8d-17)) then
        tmp = x * y
    else if (y <= (-1.8d-101)) then
        tmp = t_1
    else if (y <= (-4.2d-245)) then
        tmp = t_2
    else if (y <= 1.65d-281) then
        tmp = c
    else if (y <= 2.65d-229) then
        tmp = t_2
    else if (y <= 1.32d+108) then
        tmp = t_1
    else
        tmp = 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 t_1 = 0.0625 * (z * t);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (y <= -4.8e-17) {
		tmp = x * y;
	} else if (y <= -1.8e-101) {
		tmp = t_1;
	} else if (y <= -4.2e-245) {
		tmp = t_2;
	} else if (y <= 1.65e-281) {
		tmp = c;
	} else if (y <= 2.65e-229) {
		tmp = t_2;
	} else if (y <= 1.32e+108) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = a * (b * -0.25)
	tmp = 0
	if y <= -4.8e-17:
		tmp = x * y
	elif y <= -1.8e-101:
		tmp = t_1
	elif y <= -4.2e-245:
		tmp = t_2
	elif y <= 1.65e-281:
		tmp = c
	elif y <= 2.65e-229:
		tmp = t_2
	elif y <= 1.32e+108:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (y <= -4.8e-17)
		tmp = Float64(x * y);
	elseif (y <= -1.8e-101)
		tmp = t_1;
	elseif (y <= -4.2e-245)
		tmp = t_2;
	elseif (y <= 1.65e-281)
		tmp = c;
	elseif (y <= 2.65e-229)
		tmp = t_2;
	elseif (y <= 1.32e+108)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = a * (b * -0.25);
	tmp = 0.0;
	if (y <= -4.8e-17)
		tmp = x * y;
	elseif (y <= -1.8e-101)
		tmp = t_1;
	elseif (y <= -4.2e-245)
		tmp = t_2;
	elseif (y <= 1.65e-281)
		tmp = c;
	elseif (y <= 2.65e-229)
		tmp = t_2;
	elseif (y <= 1.32e+108)
		tmp = t_1;
	else
		tmp = x * y;
	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]}, Block[{t$95$2 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-17], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.8e-101], t$95$1, If[LessEqual[y, -4.2e-245], t$95$2, If[LessEqual[y, 1.65e-281], c, If[LessEqual[y, 2.65e-229], t$95$2, If[LessEqual[y, 1.32e+108], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.79999999999999973e-17 or 1.32000000000000013e108 < y

   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 y around inf 99.1%

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

   4. Taylor expanded in t around 0 77.1%

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

   5. Taylor expanded in c around 0 64.6%

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

   6. Taylor expanded in x around inf 45.6%

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

   if -4.79999999999999973e-17 < y < -1.8e-101 or 2.64999999999999999e-229 < y < 1.32000000000000013e108

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 86.3%

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

   4. Taylor expanded in t around inf 66.8%

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

   5. Taylor expanded in t around inf 35.4%

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

   if -1.8e-101 < y < -4.2000000000000002e-245 or 1.65e-281 < y < 2.64999999999999999e-229

   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 70.4%

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

   4. Taylor expanded in c around 0 48.5%

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

   5. Taylor expanded in a around inf 48.4%

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

   6. Taylor expanded in a around inf 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*r* 42.4%

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

      3. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -4.2000000000000002e-245 < y < 1.65e-281

   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 38.4%

      \[\leadsto \color{blue}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-245}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-281}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+108}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-285}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-114}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= t -5.2e-139)
     t_1
     (if (<= t 7.2e-285)
       c
       (if (<= t 7.5e-170)
         (* x y)
         (if (<= t 2.3e-114) c (if (<= t 3.2e+55) (* x y) t_1)))))))

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 (t <= -5.2e-139) {
		tmp = t_1;
	} else if (t <= 7.2e-285) {
		tmp = c;
	} else if (t <= 7.5e-170) {
		tmp = x * y;
	} else if (t <= 2.3e-114) {
		tmp = c;
	} else if (t <= 3.2e+55) {
		tmp = x * y;
	} 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 = 0.0625d0 * (z * t)
    if (t <= (-5.2d-139)) then
        tmp = t_1
    else if (t <= 7.2d-285) then
        tmp = c
    else if (t <= 7.5d-170) then
        tmp = x * y
    else if (t <= 2.3d-114) then
        tmp = c
    else if (t <= 3.2d+55) then
        tmp = x * y
    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 = 0.0625 * (z * t);
	double tmp;
	if (t <= -5.2e-139) {
		tmp = t_1;
	} else if (t <= 7.2e-285) {
		tmp = c;
	} else if (t <= 7.5e-170) {
		tmp = x * y;
	} else if (t <= 2.3e-114) {
		tmp = c;
	} else if (t <= 3.2e+55) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if t <= -5.2e-139:
		tmp = t_1
	elif t <= 7.2e-285:
		tmp = c
	elif t <= 7.5e-170:
		tmp = x * y
	elif t <= 2.3e-114:
		tmp = c
	elif t <= 3.2e+55:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (t <= -5.2e-139)
		tmp = t_1;
	elseif (t <= 7.2e-285)
		tmp = c;
	elseif (t <= 7.5e-170)
		tmp = Float64(x * y);
	elseif (t <= 2.3e-114)
		tmp = c;
	elseif (t <= 3.2e+55)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	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 (t <= -5.2e-139)
		tmp = t_1;
	elseif (t <= 7.2e-285)
		tmp = c;
	elseif (t <= 7.5e-170)
		tmp = x * y;
	elseif (t <= 2.3e-114)
		tmp = c;
	elseif (t <= 3.2e+55)
		tmp = x * y;
	else
		tmp = t_1;
	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[t, -5.2e-139], t$95$1, If[LessEqual[t, 7.2e-285], c, If[LessEqual[t, 7.5e-170], N[(x * y), $MachinePrecision], If[LessEqual[t, 2.3e-114], c, If[LessEqual[t, 3.2e+55], N[(x * y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999996e-139 or 3.2000000000000003e55 < t

   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 y around inf 86.2%

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

   4. Taylor expanded in t around inf 65.7%

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

   5. Taylor expanded in t around inf 49.1%

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

   if -5.1999999999999996e-139 < t < 7.20000000000000008e-285 or 7.4999999999999998e-170 < t < 2.2999999999999999e-114

   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 41.4%

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

   if 7.20000000000000008e-285 < t < 7.4999999999999998e-170 or 2.2999999999999999e-114 < t < 3.2000000000000003e55

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 88.8%

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

   4. Taylor expanded in t around 0 84.3%

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

   5. Taylor expanded in c around 0 62.3%

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

   6. Taylor expanded in x around inf 38.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-139}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-285}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-114}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-235}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t)))))
   (if (<= y -1.08e-16)
     (* x y)
     (if (<= y -3e-100)
       t_1
       (if (<= y 4.9e-235)
         (+ c (* b (* a -0.25)))
         (if (<= y 6.6e+106) t_1 (+ c (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double tmp;
	if (y <= -1.08e-16) {
		tmp = x * y;
	} else if (y <= -3e-100) {
		tmp = t_1;
	} else if (y <= 4.9e-235) {
		tmp = c + (b * (a * -0.25));
	} else if (y <= 6.6e+106) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = c + (0.0625d0 * (z * t))
    if (y <= (-1.08d-16)) then
        tmp = x * y
    else if (y <= (-3d-100)) then
        tmp = t_1
    else if (y <= 4.9d-235) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (y <= 6.6d+106) then
        tmp = t_1
    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 t_1 = c + (0.0625 * (z * t));
	double tmp;
	if (y <= -1.08e-16) {
		tmp = x * y;
	} else if (y <= -3e-100) {
		tmp = t_1;
	} else if (y <= 4.9e-235) {
		tmp = c + (b * (a * -0.25));
	} else if (y <= 6.6e+106) {
		tmp = t_1;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	tmp = 0
	if y <= -1.08e-16:
		tmp = x * y
	elif y <= -3e-100:
		tmp = t_1
	elif y <= 4.9e-235:
		tmp = c + (b * (a * -0.25))
	elif y <= 6.6e+106:
		tmp = t_1
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (y <= -1.08e-16)
		tmp = Float64(x * y);
	elseif (y <= -3e-100)
		tmp = t_1;
	elseif (y <= 4.9e-235)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (y <= 6.6e+106)
		tmp = t_1;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (z * t));
	tmp = 0.0;
	if (y <= -1.08e-16)
		tmp = x * y;
	elseif (y <= -3e-100)
		tmp = t_1;
	elseif (y <= 4.9e-235)
		tmp = c + (b * (a * -0.25));
	elseif (y <= 6.6e+106)
		tmp = t_1;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e-16], N[(x * y), $MachinePrecision], If[LessEqual[y, -3e-100], t$95$1, If[LessEqual[y, 4.9e-235], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+106], t$95$1, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.08e-16

   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 y around inf 99.9%

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

   4. Taylor expanded in t around 0 74.5%

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

   5. Taylor expanded in c around 0 61.4%

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

   6. Taylor expanded in x around inf 40.2%

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

   if -1.08e-16 < y < -3.0000000000000001e-100 or 4.89999999999999965e-235 < y < 6.60000000000000015e106

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 86.7%

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

   4. Taylor expanded in t around inf 66.5%

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

   if -3.0000000000000001e-100 < y < 4.89999999999999965e-235

   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 61.1%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   if 6.60000000000000015e106 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 97.8%

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

   4. Taylor expanded in x around inf 65.4%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-100}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-235}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+106}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* 0.0625 (* z t))))
   (if (<= t -2e-8)
     t_2
     (if (<= t 3.8e-206)
       t_1
       (if (<= t 1.15e-185) (* a (* b -0.25)) (if (<= t 9e+58) 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 = 0.0625 * (z * t);
	double tmp;
	if (t <= -2e-8) {
		tmp = t_2;
	} else if (t <= 3.8e-206) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = a * (b * -0.25);
	} else if (t <= 9e+58) {
		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 = 0.0625d0 * (z * t)
    if (t <= (-2d-8)) then
        tmp = t_2
    else if (t <= 3.8d-206) then
        tmp = t_1
    else if (t <= 1.15d-185) then
        tmp = a * (b * (-0.25d0))
    else if (t <= 9d+58) 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 = 0.0625 * (z * t);
	double tmp;
	if (t <= -2e-8) {
		tmp = t_2;
	} else if (t <= 3.8e-206) {
		tmp = t_1;
	} else if (t <= 1.15e-185) {
		tmp = a * (b * -0.25);
	} else if (t <= 9e+58) {
		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 = 0.0625 * (z * t)
	tmp = 0
	if t <= -2e-8:
		tmp = t_2
	elif t <= 3.8e-206:
		tmp = t_1
	elif t <= 1.15e-185:
		tmp = a * (b * -0.25)
	elif t <= 9e+58:
		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(0.0625 * Float64(z * t))
	tmp = 0.0
	if (t <= -2e-8)
		tmp = t_2;
	elseif (t <= 3.8e-206)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (t <= 9e+58)
		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 = 0.0625 * (z * t);
	tmp = 0.0;
	if (t <= -2e-8)
		tmp = t_2;
	elseif (t <= 3.8e-206)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = a * (b * -0.25);
	elseif (t <= 9e+58)
		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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-8], t$95$2, If[LessEqual[t, 3.8e-206], t$95$1, If[LessEqual[t, 1.15e-185], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e-8 or 8.9999999999999996e58 < t

   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 y around inf 85.2%

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

   4. Taylor expanded in t around inf 70.9%

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

   5. Taylor expanded in t around inf 56.9%

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

   if -2e-8 < t < 3.80000000000000003e-206 or 1.15e-185 < t < 8.9999999999999996e58

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 91.0%

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

   4. Taylor expanded in x around inf 65.8%

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

   if 3.80000000000000003e-206 < t < 1.15e-185

   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 89.9%

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

   4. Taylor expanded in c around 0 78.9%

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

   5. Taylor expanded in a around inf 68.6%

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

   6. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*r* 45.8%

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

      3. *-commutative 45.8%

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

   8. Simplified 45.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-8}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+58}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y - t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (<= (* a b) -4e+197)
     (- (* x y) t_1)
     (if (<= (* a b) 1e+134)
       (+ c (+ (* x y) (* 0.0625 (* z t))))
       (- (+ c (* x y)) t_1)))))

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 ((a * b) <= -4e+197) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 1e+134) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - 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 = (a * b) * 0.25d0
    if ((a * b) <= (-4d+197)) then
        tmp = (x * y) - t_1
    else if ((a * b) <= 1d+134) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (c + (x * y)) - 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 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -4e+197) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 1e+134) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -4e+197:
		tmp = (x * y) - t_1
	elif (a * b) <= 1e+134:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -4e+197)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -4e+197)
		tmp = (x * y) - t_1;
	elseif ((a * b) <= 1e+134)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+197], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.9999999999999998e197

   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 86.6%

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

   4. Taylor expanded in c around 0 86.6%

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

   if -3.9999999999999998e197 < (*.f64 a b) < 9.99999999999999921e133

   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

   3. Taylor expanded in a around 0 92.3%

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

   if 9.99999999999999921e133 < (*.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 92.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot y}{a} - b \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -4e+197)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 1e+134)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* a (- (/ (* x y) a) (* b 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+197) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 1e+134) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = a * (((x * y) / 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) :: tmp
    if ((a * b) <= (-4d+197)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 1d+134) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = a * (((x * y) / 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 tmp;
	if ((a * b) <= -4e+197) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 1e+134) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = a * (((x * y) / a) - (b * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -4e+197:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 1e+134:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = a * (((x * y) / a) - (b * 0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -4e+197)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(a * Float64(Float64(Float64(x * y) / a) - Float64(b * 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+197)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 1e+134)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = a * (((x * y) / a) - (b * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+197], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision] - N[(b * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.9999999999999998e197

   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 86.6%

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

   4. Taylor expanded in c around 0 86.6%

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

   if -3.9999999999999998e197 < (*.f64 a b) < 9.99999999999999921e133

   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

   3. Taylor expanded in a around 0 92.3%

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

   if 9.99999999999999921e133 < (*.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 92.0%

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

   4. Taylor expanded in c around 0 89.1%

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

   5. Taylor expanded in a around inf 91.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+197}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot y}{a} - b \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := x \cdot y + t\_1\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-235}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (+ (* x y) t_1)))
   (if (<= y -7.5e-101)
     t_2
     (if (<= y 6e-235)
       (+ c (* b (* a -0.25)))
       (if (<= y 3.7e+101) (+ c t_1) t_2)))))

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 t_2 = (x * y) + t_1;
	double tmp;
	if (y <= -7.5e-101) {
		tmp = t_2;
	} else if (y <= 6e-235) {
		tmp = c + (b * (a * -0.25));
	} else if (y <= 3.7e+101) {
		tmp = c + 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 = 0.0625d0 * (z * t)
    t_2 = (x * y) + t_1
    if (y <= (-7.5d-101)) then
        tmp = t_2
    else if (y <= 6d-235) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (y <= 3.7d+101) then
        tmp = c + 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 = 0.0625 * (z * t);
	double t_2 = (x * y) + t_1;
	double tmp;
	if (y <= -7.5e-101) {
		tmp = t_2;
	} else if (y <= 6e-235) {
		tmp = c + (b * (a * -0.25));
	} else if (y <= 3.7e+101) {
		tmp = c + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (x * y) + t_1
	tmp = 0
	if y <= -7.5e-101:
		tmp = t_2
	elif y <= 6e-235:
		tmp = c + (b * (a * -0.25))
	elif y <= 3.7e+101:
		tmp = c + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(x * y) + t_1)
	tmp = 0.0
	if (y <= -7.5e-101)
		tmp = t_2;
	elseif (y <= 6e-235)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (y <= 3.7e+101)
		tmp = Float64(c + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (x * y) + t_1;
	tmp = 0.0;
	if (y <= -7.5e-101)
		tmp = t_2;
	elseif (y <= 6e-235)
		tmp = c + (b * (a * -0.25));
	elseif (y <= 3.7e+101)
		tmp = c + 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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[y, -7.5e-101], t$95$2, If[LessEqual[y, 6e-235], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+101], N[(c + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000001e-101 or 3.6999999999999997e101 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 81.5%

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

   4. Taylor expanded in c around 0 66.7%

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

   if -7.5000000000000001e-101 < y < 5.9999999999999997e-235

   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 61.1%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   if 5.9999999999999997e-235 < y < 3.6999999999999997e101

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 84.4%

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

   4. Taylor expanded in t around inf 64.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-101}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-235}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+129} \lor \neg \left(z \leq 4 \cdot 10^{-48}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.4e+129) (not (<= z 4e-48)))
   (+ 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 <= -2.4e+129) || !(z <= 4e-48)) {
		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 <= (-2.4d+129)) .or. (.not. (z <= 4d-48))) 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 <= -2.4e+129) || !(z <= 4e-48)) {
		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 <= -2.4e+129) or not (z <= 4e-48):
		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 <= -2.4e+129) || !(z <= 4e-48))
		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 <= -2.4e+129) || ~((z <= 4e-48)))
		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, -2.4e+129], N[Not[LessEqual[z, 4e-48]], $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 < -2.3999999999999999e129 or 3.9999999999999999e-48 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 84.0%

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

   4. Taylor expanded in t around inf 68.0%

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

   if -2.3999999999999999e129 < z < 3.9999999999999999e-48

   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 y around inf 91.6%

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

   4. Taylor expanded in x around inf 65.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+129} \lor \neg \left(z \leq 4 \cdot 10^{-48}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.8% 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 99.3%

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

3. Final simplification 99.3%

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

Alternative 11: 35.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-44} \lor \neg \left(y \leq 1.85 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -4.6e-44) (not (<= y 1.85e+101))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -4.6e-44) || !(y <= 1.85e+101)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	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 ((y <= (-4.6d-44)) .or. (.not. (y <= 1.85d+101))) then
        tmp = x * y
    else
        tmp = c
    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 ((y <= -4.6e-44) || !(y <= 1.85e+101)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -4.6e-44) or not (y <= 1.85e+101):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -4.6e-44) || !(y <= 1.85e+101))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -4.6e-44) || ~((y <= 1.85e+101)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -4.6e-44], N[Not[LessEqual[y, 1.85e+101]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999996e-44 or 1.8499999999999999e101 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 98.5%

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

   4. Taylor expanded in t around 0 74.0%

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

   5. Taylor expanded in c around 0 60.8%

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

   6. Taylor expanded in x around inf 42.2%

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

   if -4.59999999999999996e-44 < y < 1.8499999999999999e101

   1. Initial program 99.3%

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

   3. Taylor expanded in c around inf 33.1%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-44} \lor \neg \left(y \leq 1.85 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.5% 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 99.3%

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

3. Taylor expanded in c around inf 23.8%

   \[\leadsto \color{blue}{c} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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))