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

Percentage Accurate: 97.8% → 98.9%

Time: 9.9s

Alternatives: 14

Speedup: 1.0×

• 32.2% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate--l+ 98.4%

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

   2. fma-define 98.8%

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

   3. associate-/l* 99.2%

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

   4. fmm-def 99.6%

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

   5. distribute-neg-frac2 99.6%

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

   6. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate-+l- 98.4%

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

   2. +-commutative 98.4%

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

   3. *-commutative 98.4%

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

   4. +-commutative 98.4%

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

   5. associate-+l- 98.4%

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

   6. fma-define 98.8%

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

   7. *-commutative 98.8%

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

   8. associate-/l* 99.2%

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

   9. associate-/l* 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-198}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* x (+ y (* 0.0625 (/ (* z t) x))))))
   (if (<= (* x y) -2e+176)
     t_2
     (if (<= (* x y) -2e-98)
       t_1
       (if (<= (* x y) 2e-198)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 2e+44) 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 + (a * (b * -0.25));
	double t_2 = x * (y + (0.0625 * ((z * t) / x)));
	double tmp;
	if ((x * y) <= -2e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2e-98) {
		tmp = t_1;
	} else if ((x * y) <= 2e-198) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e+44) {
		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 + (a * (b * (-0.25d0)))
    t_2 = x * (y + (0.0625d0 * ((z * t) / x)))
    if ((x * y) <= (-2d+176)) then
        tmp = t_2
    else if ((x * y) <= (-2d-98)) then
        tmp = t_1
    else if ((x * y) <= 2d-198) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2d+44) 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 + (a * (b * -0.25));
	double t_2 = x * (y + (0.0625 * ((z * t) / x)));
	double tmp;
	if ((x * y) <= -2e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2e-98) {
		tmp = t_1;
	} else if ((x * y) <= 2e-198) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = x * (y + (0.0625 * ((z * t) / x)))
	tmp = 0
	if (x * y) <= -2e+176:
		tmp = t_2
	elif (x * y) <= -2e-98:
		tmp = t_1
	elif (x * y) <= 2e-198:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(x * Float64(y + Float64(0.0625 * Float64(Float64(z * t) / x))))
	tmp = 0.0
	if (Float64(x * y) <= -2e+176)
		tmp = t_2;
	elseif (Float64(x * y) <= -2e-98)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-198)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2e+44)
		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 + (a * (b * -0.25));
	t_2 = x * (y + (0.0625 * ((z * t) / x)));
	tmp = 0.0;
	if ((x * y) <= -2e+176)
		tmp = t_2;
	elseif ((x * y) <= -2e-98)
		tmp = t_1;
	elseif ((x * y) <= 2e-198)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2e+44)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+176], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2e-98], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-198], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e176 or 2.0000000000000002e44 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 96.7%

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

   4. Taylor expanded in a around 0 83.6%

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

   5. Taylor expanded in c around 0 80.2%

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

   if -2e176 < (*.f64 x y) < -1.99999999999999988e-98 or 1.9999999999999998e-198 < (*.f64 x y) < 2.0000000000000002e44

   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 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r* 68.5%

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

   5. Simplified 68.5%

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

   if -1.99999999999999988e-98 < (*.f64 x y) < 1.9999999999999998e-198

   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 76.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-98}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-198}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.0625 \cdot \frac{z \cdot t}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot y + t\_2\\ \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -1.85 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.46 \cdot 10^{-198}:\\ \;\;\;\;c + t\_2\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ (* x y) t_2)))
   (if (<= (* x y) -1.9e+150)
     t_3
     (if (<= (* x y) -1.85e-103)
       t_1
       (if (<= (* x y) 1.46e-198)
         (+ c t_2)
         (if (<= (* x y) 6.8e+47) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.9e+150) {
		tmp = t_3;
	} else if ((x * y) <= -1.85e-103) {
		tmp = t_1;
	} else if ((x * y) <= 1.46e-198) {
		tmp = c + t_2;
	} else if ((x * y) <= 6.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (z * t)
    t_3 = (x * y) + t_2
    if ((x * y) <= (-1.9d+150)) then
        tmp = t_3
    else if ((x * y) <= (-1.85d-103)) then
        tmp = t_1
    else if ((x * y) <= 1.46d-198) then
        tmp = c + t_2
    else if ((x * y) <= 6.8d+47) then
        tmp = t_1
    else
        tmp = t_3
    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 + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.9e+150) {
		tmp = t_3;
	} else if ((x * y) <= -1.85e-103) {
		tmp = t_1;
	} else if ((x * y) <= 1.46e-198) {
		tmp = c + t_2;
	} else if ((x * y) <= 6.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (z * t)
	t_3 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -1.9e+150:
		tmp = t_3
	elif (x * y) <= -1.85e-103:
		tmp = t_1
	elif (x * y) <= 1.46e-198:
		tmp = c + t_2
	elif (x * y) <= 6.8e+47:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -1.9e+150)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.85e-103)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.46e-198)
		tmp = Float64(c + t_2);
	elseif (Float64(x * y) <= 6.8e+47)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = 0.0625 * (z * t);
	t_3 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -1.9e+150)
		tmp = t_3;
	elseif ((x * y) <= -1.85e-103)
		tmp = t_1;
	elseif ((x * y) <= 1.46e-198)
		tmp = c + t_2;
	elseif ((x * y) <= 6.8e+47)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.9e+150], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e-103], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.46e-198], N[(c + t$95$2), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.8e+47], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.89999999999999995e150 or 6.7999999999999996e47 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 96.7%

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

   4. Taylor expanded in a around 0 83.6%

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

   5. Taylor expanded in c around 0 80.2%

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

   6. Taylor expanded in x around 0 79.1%

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

   if -1.89999999999999995e150 < (*.f64 x y) < -1.85e-103 or 1.46e-198 < (*.f64 x y) < 6.7999999999999996e47

   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 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*r* 68.5%

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

   5. Simplified 68.5%

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

   if -1.85e-103 < (*.f64 x y) < 1.46e-198

   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 76.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.85 \cdot 10^{-103}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.46 \cdot 10^{-198}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -6.1 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{-198}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -6.1e+178)
     t_2
     (if (<= (* x y) -7e-104)
       t_1
       (if (<= (* x y) 1.5e-198)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 2.2e+39) 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 + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -6.1e+178) {
		tmp = t_2;
	} else if ((x * y) <= -7e-104) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-198) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.2e+39) {
		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 + (a * (b * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-6.1d+178)) then
        tmp = t_2
    else if ((x * y) <= (-7d-104)) then
        tmp = t_1
    else if ((x * y) <= 1.5d-198) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 2.2d+39) 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 + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -6.1e+178) {
		tmp = t_2;
	} else if ((x * y) <= -7e-104) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-198) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 2.2e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -6.1e+178:
		tmp = t_2
	elif (x * y) <= -7e-104:
		tmp = t_1
	elif (x * y) <= 1.5e-198:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 2.2e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -6.1e+178)
		tmp = t_2;
	elseif (Float64(x * y) <= -7e-104)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.5e-198)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 2.2e+39)
		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 + (a * (b * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -6.1e+178)
		tmp = t_2;
	elseif ((x * y) <= -7e-104)
		tmp = t_1;
	elseif ((x * y) <= 1.5e-198)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 2.2e+39)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.1e+178], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -7e-104], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.5e-198], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.1000000000000001e178 or 2.2000000000000001e39 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 74.5%

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

   if -6.1000000000000001e178 < (*.f64 x y) < -7.00000000000000057e-104 or 1.5000000000000001e-198 < (*.f64 x y) < 2.2000000000000001e39

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.1%

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

   5. Simplified 67.1%

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

   if -7.00000000000000057e-104 < (*.f64 x y) < 1.5000000000000001e-198

   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 76.1%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.1 \cdot 10^{+178}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{-104}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{-198}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+39}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+222} \lor \neg \left(a \leq -2.9 \cdot 10^{+153}\right) \land \left(a \leq -7.5 \cdot 10^{+133} \lor \neg \left(a \leq 1.1 \cdot 10^{-15}\right)\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.1e+222)
         (and (not (<= a -2.9e+153))
              (or (<= a -7.5e+133) (not (<= a 1.1e-15)))))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.1e+222) || (!(a <= -2.9e+153) && ((a <= -7.5e+133) || !(a <= 1.1e-15)))) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.1d+222)) .or. (.not. (a <= (-2.9d+153))) .and. (a <= (-7.5d+133)) .or. (.not. (a <= 1.1d-15))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.1e+222) || (!(a <= -2.9e+153) && ((a <= -7.5e+133) || !(a <= 1.1e-15)))) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.1e+222) or (not (a <= -2.9e+153) and ((a <= -7.5e+133) or not (a <= 1.1e-15))):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.1e+222) || (!(a <= -2.9e+153) && ((a <= -7.5e+133) || !(a <= 1.1e-15))))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.1e+222) || (~((a <= -2.9e+153)) && ((a <= -7.5e+133) || ~((a <= 1.1e-15)))))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.1e+222], And[N[Not[LessEqual[a, -2.9e+153]], $MachinePrecision], Or[LessEqual[a, -7.5e+133], N[Not[LessEqual[a, 1.1e-15]], $MachinePrecision]]]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1000000000000001e222 or -2.90000000000000002e153 < a < -7.49999999999999992e133 or 1.09999999999999993e-15 < a

   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 a around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 71.1%

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

   5. Simplified 71.1%

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

   if -1.1000000000000001e222 < a < -2.90000000000000002e153 or -7.49999999999999992e133 < a < 1.09999999999999993e-15

   1. Initial program 98.2%

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

   3. Taylor expanded in a around 0 82.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+222} \lor \neg \left(a \leq -2.9 \cdot 10^{+153}\right) \land \left(a \leq -7.5 \cdot 10^{+133} \lor \neg \left(a \leq 1.1 \cdot 10^{-15}\right)\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147}:\\ \;\;\;\;c + \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{-84}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(t\_2 - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+147)
     (+ c (- (* x y) t_1))
     (if (<= (* a b) 1e-84) (+ c (+ (* x y) t_2)) (+ c (- t_2 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+147) {
		tmp = c + ((x * y) - t_1);
	} else if ((a * b) <= 1e-84) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = c + (t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+147)) then
        tmp = c + ((x * y) - t_1)
    else if ((a * b) <= 1d-84) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = c + (t_2 - 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+147) {
		tmp = c + ((x * y) - t_1);
	} else if ((a * b) <= 1e-84) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = c + (t_2 - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+147:
		tmp = c + ((x * y) - t_1)
	elif (a * b) <= 1e-84:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = c + (t_2 - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+147)
		tmp = Float64(c + Float64(Float64(x * y) - t_1));
	elseif (Float64(a * b) <= 1e-84)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(c + Float64(t_2 - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+147)
		tmp = c + ((x * y) - t_1);
	elseif ((a * b) <= 1e-84)
		tmp = c + ((x * y) + t_2);
	else
		tmp = c + (t_2 - 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]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+147], N[(c + N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-84], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(c + N[(t$95$2 - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000002e147

   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 z around 0 97.3%

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

   if -5.0000000000000002e147 < (*.f64 a b) < 1e-84

   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 a around 0 95.9%

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

   if 1e-84 < (*.f64 a b)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.5%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147}:\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{-84}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147} \lor \neg \left(a \cdot b \leq 6 \cdot 10^{+102}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+147) (not (<= (* a b) 6e+102)))
   (+ c (- (* x y) (* (* a b) 0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+147) || !((a * b) <= 6e+102)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+147)) .or. (.not. ((a * b) <= 6d+102))) then
        tmp = c + ((x * y) - ((a * b) * 0.25d0))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+147) || !((a * b) <= 6e+102)) {
		tmp = c + ((x * y) - ((a * b) * 0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+147) or not ((a * b) <= 6e+102):
		tmp = c + ((x * y) - ((a * b) * 0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+147) || !(Float64(a * b) <= 6e+102))
		tmp = Float64(c + Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+147) || ~(((a * b) <= 6e+102)))
		tmp = c + ((x * y) - ((a * b) * 0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+147], N[Not[LessEqual[N[(a * b), $MachinePrecision], 6e+102]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000002e147 or 5.9999999999999996e102 < (*.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 96.2%

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

   if -5.0000000000000002e147 < (*.f64 a b) < 5.9999999999999996e102

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 92.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+147} \lor \neg \left(a \cdot b \leq 6 \cdot 10^{+102}\right):\\ \;\;\;\;c + \left(x \cdot y - \left(a \cdot b\right) \cdot 0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.8e+176) (not (<= (* x y) 1.35e+39)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.8e+176) || !((x * y) <= 1.35e+39)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-2.8d+176)) .or. (.not. ((x * y) <= 1.35d+39))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.8e+176) || !((x * y) <= 1.35e+39)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.8e+176) or not ((x * y) <= 1.35e+39):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.8e+176) || !(Float64(x * y) <= 1.35e+39))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2.8e+176) || ~(((x * y) <= 1.35e+39)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e+176], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+39]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8000000000000002e176 or 1.35000000000000002e39 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 74.5%

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

   if -2.8000000000000002e176 < (*.f64 x y) < 1.35000000000000002e39

   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 60.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 4.15 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.8e+176) (not (<= (* x y) 4.15e+43)))
   (* x y)
   (* t (* z 0.0625))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.8e+176) || !((x * y) <= 4.15e+43)) {
		tmp = x * y;
	} else {
		tmp = t * (z * 0.0625);
	}
	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) <= (-2.8d+176)) .or. (.not. ((x * y) <= 4.15d+43))) then
        tmp = x * y
    else
        tmp = t * (z * 0.0625d0)
    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) <= -2.8e+176) || !((x * y) <= 4.15e+43)) {
		tmp = x * y;
	} else {
		tmp = t * (z * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.8e+176) or not ((x * y) <= 4.15e+43):
		tmp = x * y
	else:
		tmp = t * (z * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.8e+176) || !(Float64(x * y) <= 4.15e+43))
		tmp = Float64(x * y);
	else
		tmp = Float64(t * Float64(z * 0.0625));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2.8e+176) || ~(((x * y) <= 4.15e+43)))
		tmp = x * y;
	else
		tmp = t * (z * 0.0625);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e+176], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.15e+43]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8000000000000002e176 or 4.14999999999999979e43 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 96.7%

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

   4. Taylor expanded in a around 0 83.6%

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

   5. Taylor expanded in x around inf 69.6%

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

   if -2.8000000000000002e176 < (*.f64 x y) < 4.14999999999999979e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.4%

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

   4. Taylor expanded in a around 0 51.4%

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

   5. Taylor expanded in t around inf 35.2%

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

      1. associate-*r* 35.2%

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

      2. *-commutative 35.2%

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

      3. associate-*r* 35.2%

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

   7. Simplified 35.2%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 4.15 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 9 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.8e+176) (not (<= (* x y) 9e+46))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.8e+176) || !((x * y) <= 9e+46)) {
		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 (((x * y) <= (-2.8d+176)) .or. (.not. ((x * y) <= 9d+46))) 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 (((x * y) <= -2.8e+176) || !((x * y) <= 9e+46)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.8e+176) or not ((x * y) <= 9e+46):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.8e+176) || !(Float64(x * y) <= 9e+46))
		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 (((x * y) <= -2.8e+176) || ~(((x * y) <= 9e+46)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e+176], N[Not[LessEqual[N[(x * y), $MachinePrecision], 9e+46]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8000000000000002e176 or 9.00000000000000019e46 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 96.6%

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

   4. Taylor expanded in a around 0 83.5%

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

   5. Taylor expanded in x around inf 70.4%

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

   if -2.8000000000000002e176 < (*.f64 x y) < 9.00000000000000019e46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 32.4%

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

   4. Taylor expanded in x around 0 27.6%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 9 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 13: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+147} \lor \neg \left(z \leq 1.95 \cdot 10^{-90}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.8e+147) (not (<= z 1.95e-90)))
   (* t (* z 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.8e+147) || !(z <= 1.95e-90)) {
		tmp = t * (z * 0.0625);
	} 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 <= (-2.8d+147)) .or. (.not. (z <= 1.95d-90))) then
        tmp = t * (z * 0.0625d0)
    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 <= -2.8e+147) || !(z <= 1.95e-90)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.8e+147) or not (z <= 1.95e-90):
		tmp = t * (z * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.8e+147) || !(z <= 1.95e-90))
		tmp = Float64(t * Float64(z * 0.0625));
	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 <= -2.8e+147) || ~((z <= 1.95e-90)))
		tmp = t * (z * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.8e+147], N[Not[LessEqual[z, 1.95e-90]], $MachinePrecision]], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e147 or 1.95000000000000002e-90 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 82.7%

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

   4. Taylor expanded in a around 0 56.0%

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

   5. Taylor expanded in t around inf 41.5%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

      3. associate-*r* 41.5%

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

   7. Simplified 41.5%

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

   if -2.8000000000000001e147 < z < 1.95000000000000002e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.9%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+147} \lor \neg \left(z \leq 1.95 \cdot 10^{-90}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 98.4%

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

3. Taylor expanded in x around inf 46.8%

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

4. Taylor expanded in x around 0 20.0%

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

5. Final simplification 20.0%

   \[\leadsto c \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(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))