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

Percentage Accurate: 97.8% → 97.7%

Time: 13.5s

Alternatives: 13

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: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{1}{\frac{\frac{4}{b}}{a}}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ 1.0 (/ (/ 4.0 b) a))) 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)) - (1.0 / ((4.0 / b) / a))) + 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)) - (1.0d0 / ((4.0d0 / b) / a))) + 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)) - (1.0 / ((4.0 / b) / a))) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - (1.0 / ((4.0 / b) / a))) + 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(1.0 / Float64(Float64(4.0 / b) / a))) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - (1.0 / ((4.0 / b) / a))) + 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[(1.0 / N[(N[(4.0 / b), $MachinePrecision] / a), $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. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right) + c\\ t_2 := -0.25 \cdot \left(a \cdot b\right) + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right) + c\\ \mathbf{elif}\;x \cdot y \leq 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* 0.0625 (* t z)) c)) (t_2 (+ (* -0.25 (* a b)) (* x y))))
   (if (<= (* x y) -2e+75)
     t_2
     (if (<= (* x y) 4e-200)
       t_1
       (if (<= (* x y) 2e-133)
         (+ (* a (* b -0.25)) c)
         (if (<= (* x y) 1e+209) 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 * (t * z)) + c;
	double t_2 = (-0.25 * (a * b)) + (x * y);
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_2;
	} else if ((x * y) <= 4e-200) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = (a * (b * -0.25)) + c;
	} else if ((x * y) <= 1e+209) {
		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 = (0.0625d0 * (t * z)) + c
    t_2 = ((-0.25d0) * (a * b)) + (x * y)
    if ((x * y) <= (-2d+75)) then
        tmp = t_2
    else if ((x * y) <= 4d-200) then
        tmp = t_1
    else if ((x * y) <= 2d-133) then
        tmp = (a * (b * (-0.25d0))) + c
    else if ((x * y) <= 1d+209) 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 = (0.0625 * (t * z)) + c;
	double t_2 = (-0.25 * (a * b)) + (x * y);
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_2;
	} else if ((x * y) <= 4e-200) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = (a * (b * -0.25)) + c;
	} else if ((x * y) <= 1e+209) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.0625 * (t * z)) + c
	t_2 = (-0.25 * (a * b)) + (x * y)
	tmp = 0
	if (x * y) <= -2e+75:
		tmp = t_2
	elif (x * y) <= 4e-200:
		tmp = t_1
	elif (x * y) <= 2e-133:
		tmp = (a * (b * -0.25)) + c
	elif (x * y) <= 1e+209:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.0625 * Float64(t * z)) + c)
	t_2 = Float64(Float64(-0.25 * Float64(a * b)) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+75)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-200)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-133)
		tmp = Float64(Float64(a * Float64(b * -0.25)) + c);
	elseif (Float64(x * y) <= 1e+209)
		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 = (0.0625 * (t * z)) + c;
	t_2 = (-0.25 * (a * b)) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2e+75)
		tmp = t_2;
	elseif ((x * y) <= 4e-200)
		tmp = t_1;
	elseif ((x * y) <= 2e-133)
		tmp = (a * (b * -0.25)) + c;
	elseif ((x * y) <= 1e+209)
		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[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+75], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-200], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-133], N[(N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+209], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 1.0000000000000001e209 < (*.f64 x y)

   1. Initial program 98.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1.99999999999999985e75 < (*.f64 x y) < 3.9999999999999999e-200 or 2.0000000000000001e-133 < (*.f64 x y) < 1.0000000000000001e209

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.9999999999999999e-200 < (*.f64 x y) < 2.0000000000000001e-133

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right) + c\\ t_2 := x \cdot y + c\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-133}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right) + c\\ \mathbf{elif}\;x \cdot y \leq 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* 0.0625 (* t z)) c)) (t_2 (+ (* x y) c)))
   (if (<= (* x y) -2e+75)
     t_2
     (if (<= (* x y) 4e-200)
       t_1
       (if (<= (* x y) 2e-133)
         (+ (* a (* b -0.25)) c)
         (if (<= (* x y) 1e+227) 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 * (t * z)) + c;
	double t_2 = (x * y) + c;
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_2;
	} else if ((x * y) <= 4e-200) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = (a * (b * -0.25)) + c;
	} else if ((x * y) <= 1e+227) {
		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 = (0.0625d0 * (t * z)) + c
    t_2 = (x * y) + c
    if ((x * y) <= (-2d+75)) then
        tmp = t_2
    else if ((x * y) <= 4d-200) then
        tmp = t_1
    else if ((x * y) <= 2d-133) then
        tmp = (a * (b * (-0.25d0))) + c
    else if ((x * y) <= 1d+227) 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 = (0.0625 * (t * z)) + c;
	double t_2 = (x * y) + c;
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_2;
	} else if ((x * y) <= 4e-200) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = (a * (b * -0.25)) + c;
	} else if ((x * y) <= 1e+227) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.0625 * (t * z)) + c
	t_2 = (x * y) + c
	tmp = 0
	if (x * y) <= -2e+75:
		tmp = t_2
	elif (x * y) <= 4e-200:
		tmp = t_1
	elif (x * y) <= 2e-133:
		tmp = (a * (b * -0.25)) + c
	elif (x * y) <= 1e+227:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.0625 * Float64(t * z)) + c)
	t_2 = Float64(Float64(x * y) + c)
	tmp = 0.0
	if (Float64(x * y) <= -2e+75)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-200)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-133)
		tmp = Float64(Float64(a * Float64(b * -0.25)) + c);
	elseif (Float64(x * y) <= 1e+227)
		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 = (0.0625 * (t * z)) + c;
	t_2 = (x * y) + c;
	tmp = 0.0;
	if ((x * y) <= -2e+75)
		tmp = t_2;
	elseif ((x * y) <= 4e-200)
		tmp = t_1;
	elseif ((x * y) <= 2e-133)
		tmp = (a * (b * -0.25)) + c;
	elseif ((x * y) <= 1e+227)
		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[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+75], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-200], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-133], N[(N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+227], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 1.0000000000000001e227 < (*.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.99999999999999985e75 < (*.f64 x y) < 3.9999999999999999e-200 or 2.0000000000000001e-133 < (*.f64 x y) < 1.0000000000000001e227

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.9999999999999999e-200 < (*.f64 x y) < 2.0000000000000001e-133

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 42.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-133}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= (* x y) -2e+75)
     (* x y)
     (if (<= (* x y) -1e-266)
       t_1
       (if (<= (* x y) 2e-133) c (if (<= (* x y) 1e+227) 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 * (t * z);
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = x * y;
	} else if ((x * y) <= -1e-266) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = c;
	} else if ((x * y) <= 1e+227) {
		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) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if ((x * y) <= (-2d+75)) then
        tmp = x * y
    else if ((x * y) <= (-1d-266)) then
        tmp = t_1
    else if ((x * y) <= 2d-133) then
        tmp = c
    else if ((x * y) <= 1d+227) 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 * (t * z);
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = x * y;
	} else if ((x * y) <= -1e-266) {
		tmp = t_1;
	} else if ((x * y) <= 2e-133) {
		tmp = c;
	} else if ((x * y) <= 1e+227) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if (x * y) <= -2e+75:
		tmp = x * y
	elif (x * y) <= -1e-266:
		tmp = t_1
	elif (x * y) <= 2e-133:
		tmp = c
	elif (x * y) <= 1e+227:
		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(t * z))
	tmp = 0.0
	if (Float64(x * y) <= -2e+75)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1e-266)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-133)
		tmp = c;
	elseif (Float64(x * y) <= 1e+227)
		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 * (t * z);
	tmp = 0.0;
	if ((x * y) <= -2e+75)
		tmp = x * y;
	elseif ((x * y) <= -1e-266)
		tmp = t_1;
	elseif ((x * y) <= 2e-133)
		tmp = c;
	elseif ((x * y) <= 1e+227)
		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[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+75], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-266], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-133], c, If[LessEqual[N[(x * y), $MachinePrecision], 1e+227], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 1.0000000000000001e227 < (*.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.99999999999999985e75 < (*.f64 x y) < -9.9999999999999998e-267 or 2.0000000000000001e-133 < (*.f64 x y) < 1.0000000000000001e227

   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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.9999999999999998e-267 < (*.f64 x y) < 2.0000000000000001e-133

   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 c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) c)) (t_2 (* 0.0625 (* t z))))
   (if (<= t -2.2e-8)
     t_2
     (if (<= t 3.8e-206)
       t_1
       (if (<= t 1.15e-185) (* a (* b -0.25)) (if (<= t 1.85e+59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + c;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (t <= -2.2e-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 <= 1.85e+59) {
		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 = (x * y) + c
    t_2 = 0.0625d0 * (t * z)
    if (t <= (-2.2d-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 <= 1.85d+59) 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 = (x * y) + c;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (t <= -2.2e-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 <= 1.85e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + c
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if t <= -2.2e-8:
		tmp = t_2
	elif t <= 3.8e-206:
		tmp = t_1
	elif t <= 1.15e-185:
		tmp = a * (b * -0.25)
	elif t <= 1.85e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + c)
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (t <= -2.2e-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 <= 1.85e+59)
		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 = (x * y) + c;
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if (t <= -2.2e-8)
		tmp = t_2;
	elseif (t <= 3.8e-206)
		tmp = t_1;
	elseif (t <= 1.15e-185)
		tmp = a * (b * -0.25);
	elseif (t <= 1.85e+59)
		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[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-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, 1.85e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999998e-8 or 1.84999999999999999e59 < 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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.1999999999999998e-8 < t < 3.80000000000000003e-206 or 1.15e-185 < t < 1.84999999999999999e59

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   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 a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 87.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -4e+197)
   (+ (* -0.25 (* a b)) (* x y))
   (if (<= (* a b) 1e+134)
     (+ (+ (* 0.0625 (* t z)) (* x y)) c)
     (- (+ c (* y x)) (/ a (/ 4.0 b))))))

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 = (-0.25 * (a * b)) + (x * y);
	} else if ((a * b) <= 1e+134) {
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	} else {
		tmp = (c + (y * x)) - (a / (4.0 / b));
	}
	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 = ((-0.25d0) * (a * b)) + (x * y)
    else if ((a * b) <= 1d+134) then
        tmp = ((0.0625d0 * (t * z)) + (x * y)) + c
    else
        tmp = (c + (y * x)) - (a / (4.0d0 / b))
    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 = (-0.25 * (a * b)) + (x * y);
	} else if ((a * b) <= 1e+134) {
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	} else {
		tmp = (c + (y * x)) - (a / (4.0 / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -4e+197:
		tmp = (-0.25 * (a * b)) + (x * y)
	elif (a * b) <= 1e+134:
		tmp = ((0.0625 * (t * z)) + (x * y)) + c
	else:
		tmp = (c + (y * x)) - (a / (4.0 / b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -4e+197)
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + Float64(x * y));
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)) + c);
	else
		tmp = Float64(Float64(c + Float64(y * x)) - Float64(a / Float64(4.0 / b)));
	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 = (-0.25 * (a * b)) + (x * y);
	elseif ((a * b) <= 1e+134)
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	else
		tmp = (c + (y * x)) - (a / (4.0 / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+197], N[(N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(c + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(a / N[(4.0 / b), $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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 87.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -4e+197)
   (+ (* -0.25 (* a b)) (* x y))
   (if (<= (* a b) 1e+134)
     (+ (+ (* 0.0625 (* t z)) (* x y)) c)
     (+ (- (* x y) (/ (* a b) 4.0)) c))))

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 = (-0.25 * (a * b)) + (x * y);
	} else if ((a * b) <= 1e+134) {
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	} else {
		tmp = ((x * y) - ((a * b) / 4.0)) + 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 ((a * b) <= (-4d+197)) then
        tmp = ((-0.25d0) * (a * b)) + (x * y)
    else if ((a * b) <= 1d+134) then
        tmp = ((0.0625d0 * (t * z)) + (x * y)) + c
    else
        tmp = ((x * y) - ((a * b) / 4.0d0)) + 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 ((a * b) <= -4e+197) {
		tmp = (-0.25 * (a * b)) + (x * y);
	} else if ((a * b) <= 1e+134) {
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	} else {
		tmp = ((x * y) - ((a * b) / 4.0)) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -4e+197:
		tmp = (-0.25 * (a * b)) + (x * y)
	elif (a * b) <= 1e+134:
		tmp = ((0.0625 * (t * z)) + (x * y)) + c
	else:
		tmp = ((x * y) - ((a * b) / 4.0)) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -4e+197)
		tmp = Float64(Float64(-0.25 * Float64(a * b)) + Float64(x * y));
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)) + c);
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(a * b) / 4.0)) + c);
	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 = (-0.25 * (a * b)) + (x * y);
	elseif ((a * b) <= 1e+134)
		tmp = ((0.0625 * (t * z)) + (x * y)) + c;
	else
		tmp = ((x * y) - ((a * b) / 4.0)) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+197], N[(N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 86.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = t_1 + (x * y);
	tmp = 0.0;
	if (y <= -7.5e-101)
		tmp = t_2;
	elseif (y <= 6e-235)
		tmp = (a * (b * -0.25)) + c;
	elseif (y <= 3.7e+101)
		tmp = t_1 + c;
	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[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-101], t$95$2, If[LessEqual[y, 6e-235], N[(N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[y, 3.7e+101], N[(t$95$1 + c), $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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in c around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+227}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) c)))
   (if (<= (* x y) -2e+75)
     t_1
     (if (<= (* x y) 1e+227) (+ (* 0.0625 (* t z)) c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + c;
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_1;
	} else if ((x * y) <= 1e+227) {
		tmp = (0.0625 * (t * z)) + c;
	} 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) + c
    if ((x * y) <= (-2d+75)) then
        tmp = t_1
    else if ((x * y) <= 1d+227) then
        tmp = (0.0625d0 * (t * z)) + c
    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) + c;
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = t_1;
	} else if ((x * y) <= 1e+227) {
		tmp = (0.0625 * (t * z)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + c
	tmp = 0
	if (x * y) <= -2e+75:
		tmp = t_1
	elif (x * y) <= 1e+227:
		tmp = (0.0625 * (t * z)) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + c)
	tmp = 0.0
	if (Float64(x * y) <= -2e+75)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+227)
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + c;
	tmp = 0.0;
	if ((x * y) <= -2e+75)
		tmp = t_1;
	elseif ((x * y) <= 1e+227)
		tmp = (0.0625 * (t * z)) + c;
	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] + c), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+75], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+227], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 1.0000000000000001e227 < (*.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.99999999999999985e75 < (*.f64 x y) < 1.0000000000000001e227

   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 z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 42.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2.1e+65) (* x y) (if (<= (* x y) 2.15e+70) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -2.1e+65) {
		tmp = x * y;
	} else if ((x * y) <= 2.15e+70) {
		tmp = c;
	} 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) :: tmp
    if ((x * y) <= (-2.1d+65)) then
        tmp = x * y
    else if ((x * y) <= 2.15d+70) then
        tmp = c
    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 tmp;
	if ((x * y) <= -2.1e+65) {
		tmp = x * y;
	} else if ((x * y) <= 2.15e+70) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -2.1e+65:
		tmp = x * y
	elif (x * y) <= 2.15e+70:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+65)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.15e+70)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -2.1e+65)
		tmp = x * y;
	elseif ((x * y) <= 2.15e+70)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+65], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+70], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.09999999999999991e65 or 2.15e70 < (*.f64 x y)

   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 x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.09999999999999991e65 < (*.f64 x y) < 2.15e70

   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 c around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 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]

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. Add Preprocessing

Alternative 13: 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 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. 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))