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

Percentage Accurate: 97.6% → 98.9%

Time: 11.5s

Alternatives: 14

Speedup: 1.0×

• 32.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate--l+ 98.0%

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

   2. fma-define 99.2%

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

   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. fma-neg 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. Add Preprocessing

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l- 98.0%

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

   2. *-commutative 98.0%

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

   3. associate-+l- 98.0%

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

   4. fma-define 98.4%

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

   5. *-commutative 98.4%

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

   6. associate-/l* 98.4%

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

   7. associate-/l* 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 44.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-223}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-85}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+51}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -1.18e+83)
     (* x y)
     (if (<= (* x y) -3.9e+34)
       t_1
       (if (<= (* x y) -8.2e-268)
         c
         (if (<= (* x y) 1.32e-306)
           t_1
           (if (<= (* x y) 3.5e-223)
             c
             (if (<= (* x y) 6.6e-98)
               t_1
               (if (<= (* x y) 1e-85)
                 c
                 (if (<= (* x y) 6.6e-79)
                   t_1
                   (if (<= (* x y) 4.3e-75)
                     (* a (* b -0.25))
                     (if (<= (* x y) 2.15e+51)
                       c
                       (if (<= (* x y) 2.2e+112) t_1 (* x y))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -1.18e+83) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e+34) {
		tmp = t_1;
	} else if ((x * y) <= -8.2e-268) {
		tmp = c;
	} else if ((x * y) <= 1.32e-306) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-223) {
		tmp = c;
	} else if ((x * y) <= 6.6e-98) {
		tmp = t_1;
	} else if ((x * y) <= 1e-85) {
		tmp = c;
	} else if ((x * y) <= 6.6e-79) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-75) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 2.15e+51) {
		tmp = c;
	} else if ((x * y) <= 2.2e+112) {
		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 = z * (t * 0.0625d0)
    if ((x * y) <= (-1.18d+83)) then
        tmp = x * y
    else if ((x * y) <= (-3.9d+34)) then
        tmp = t_1
    else if ((x * y) <= (-8.2d-268)) then
        tmp = c
    else if ((x * y) <= 1.32d-306) then
        tmp = t_1
    else if ((x * y) <= 3.5d-223) then
        tmp = c
    else if ((x * y) <= 6.6d-98) then
        tmp = t_1
    else if ((x * y) <= 1d-85) then
        tmp = c
    else if ((x * y) <= 6.6d-79) then
        tmp = t_1
    else if ((x * y) <= 4.3d-75) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 2.15d+51) then
        tmp = c
    else if ((x * y) <= 2.2d+112) 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 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -1.18e+83) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e+34) {
		tmp = t_1;
	} else if ((x * y) <= -8.2e-268) {
		tmp = c;
	} else if ((x * y) <= 1.32e-306) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-223) {
		tmp = c;
	} else if ((x * y) <= 6.6e-98) {
		tmp = t_1;
	} else if ((x * y) <= 1e-85) {
		tmp = c;
	} else if ((x * y) <= 6.6e-79) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-75) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 2.15e+51) {
		tmp = c;
	} else if ((x * y) <= 2.2e+112) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -1.18e+83:
		tmp = x * y
	elif (x * y) <= -3.9e+34:
		tmp = t_1
	elif (x * y) <= -8.2e-268:
		tmp = c
	elif (x * y) <= 1.32e-306:
		tmp = t_1
	elif (x * y) <= 3.5e-223:
		tmp = c
	elif (x * y) <= 6.6e-98:
		tmp = t_1
	elif (x * y) <= 1e-85:
		tmp = c
	elif (x * y) <= 6.6e-79:
		tmp = t_1
	elif (x * y) <= 4.3e-75:
		tmp = a * (b * -0.25)
	elif (x * y) <= 2.15e+51:
		tmp = c
	elif (x * y) <= 2.2e+112:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -1.18e+83)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.9e+34)
		tmp = t_1;
	elseif (Float64(x * y) <= -8.2e-268)
		tmp = c;
	elseif (Float64(x * y) <= 1.32e-306)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e-223)
		tmp = c;
	elseif (Float64(x * y) <= 6.6e-98)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-85)
		tmp = c;
	elseif (Float64(x * y) <= 6.6e-79)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.3e-75)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 2.15e+51)
		tmp = c;
	elseif (Float64(x * y) <= 2.2e+112)
		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 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -1.18e+83)
		tmp = x * y;
	elseif ((x * y) <= -3.9e+34)
		tmp = t_1;
	elseif ((x * y) <= -8.2e-268)
		tmp = c;
	elseif ((x * y) <= 1.32e-306)
		tmp = t_1;
	elseif ((x * y) <= 3.5e-223)
		tmp = c;
	elseif ((x * y) <= 6.6e-98)
		tmp = t_1;
	elseif ((x * y) <= 1e-85)
		tmp = c;
	elseif ((x * y) <= 6.6e-79)
		tmp = t_1;
	elseif ((x * y) <= 4.3e-75)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 2.15e+51)
		tmp = c;
	elseif ((x * y) <= 2.2e+112)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.18e+83], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.9e+34], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -8.2e-268], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.32e-306], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-223], c, If[LessEqual[N[(x * y), $MachinePrecision], 6.6e-98], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-85], c, If[LessEqual[N[(x * y), $MachinePrecision], 6.6e-79], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.3e-75], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+51], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.2e+112], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.1799999999999999e83 or 2.1999999999999999e112 < (*.f64 x y)

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 95.9%

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

   4. Taylor expanded in a around 0 91.9%

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

   5. Taylor expanded in y around inf 71.0%

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

   if -1.1799999999999999e83 < (*.f64 x y) < -3.90000000000000019e34 or -8.1999999999999998e-268 < (*.f64 x y) < 1.32e-306 or 3.50000000000000009e-223 < (*.f64 x y) < 6.6000000000000002e-98 or 9.9999999999999998e-86 < (*.f64 x y) < 6.5999999999999996e-79 or 2.1499999999999999e51 < (*.f64 x y) < 2.1999999999999999e112

   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 85.3%

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

   4. Taylor expanded in t around inf 52.3%

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

   if -3.90000000000000019e34 < (*.f64 x y) < -8.1999999999999998e-268 or 1.32e-306 < (*.f64 x y) < 3.50000000000000009e-223 or 6.6000000000000002e-98 < (*.f64 x y) < 9.9999999999999998e-86 or 4.2999999999999999e-75 < (*.f64 x y) < 2.1499999999999999e51

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 50.2%

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

   if 6.5999999999999996e-79 < (*.f64 x y) < 4.2999999999999999e-75

   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 0 100.0%

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

   4. Taylor expanded in a around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l* 75.3%

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

   6. Simplified 75.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.32 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-223}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-98}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-85}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+51}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.56 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.8 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \frac{c}{z}\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+50}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8.1 \cdot 10^{+117}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -1.8e+83)
     (* x y)
     (if (<= (* x y) -8.8e+36)
       t_1
       (if (<= (* x y) -1.56e-24)
         (* x y)
         (if (<= (* x y) -8.8e-132)
           (* z (/ c z))
           (if (<= (* x y) 2.75e+50)
             c
             (if (<= (* x y) 8e+116)
               t_1
               (if (<= (* x y) 8.1e+117) c (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -1.8e+83) {
		tmp = x * y;
	} else if ((x * y) <= -8.8e+36) {
		tmp = t_1;
	} else if ((x * y) <= -1.56e-24) {
		tmp = x * y;
	} else if ((x * y) <= -8.8e-132) {
		tmp = z * (c / z);
	} else if ((x * y) <= 2.75e+50) {
		tmp = c;
	} else if ((x * y) <= 8e+116) {
		tmp = t_1;
	} else if ((x * y) <= 8.1e+117) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    if ((x * y) <= (-1.8d+83)) then
        tmp = x * y
    else if ((x * y) <= (-8.8d+36)) then
        tmp = t_1
    else if ((x * y) <= (-1.56d-24)) then
        tmp = x * y
    else if ((x * y) <= (-8.8d-132)) then
        tmp = z * (c / z)
    else if ((x * y) <= 2.75d+50) then
        tmp = c
    else if ((x * y) <= 8d+116) then
        tmp = t_1
    else if ((x * y) <= 8.1d+117) 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 t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -1.8e+83) {
		tmp = x * y;
	} else if ((x * y) <= -8.8e+36) {
		tmp = t_1;
	} else if ((x * y) <= -1.56e-24) {
		tmp = x * y;
	} else if ((x * y) <= -8.8e-132) {
		tmp = z * (c / z);
	} else if ((x * y) <= 2.75e+50) {
		tmp = c;
	} else if ((x * y) <= 8e+116) {
		tmp = t_1;
	} else if ((x * y) <= 8.1e+117) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -1.8e+83:
		tmp = x * y
	elif (x * y) <= -8.8e+36:
		tmp = t_1
	elif (x * y) <= -1.56e-24:
		tmp = x * y
	elif (x * y) <= -8.8e-132:
		tmp = z * (c / z)
	elif (x * y) <= 2.75e+50:
		tmp = c
	elif (x * y) <= 8e+116:
		tmp = t_1
	elif (x * y) <= 8.1e+117:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+83)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -8.8e+36)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.56e-24)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -8.8e-132)
		tmp = Float64(z * Float64(c / z));
	elseif (Float64(x * y) <= 2.75e+50)
		tmp = c;
	elseif (Float64(x * y) <= 8e+116)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.1e+117)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -1.8e+83)
		tmp = x * y;
	elseif ((x * y) <= -8.8e+36)
		tmp = t_1;
	elseif ((x * y) <= -1.56e-24)
		tmp = x * y;
	elseif ((x * y) <= -8.8e-132)
		tmp = z * (c / z);
	elseif ((x * y) <= 2.75e+50)
		tmp = c;
	elseif ((x * y) <= 8e+116)
		tmp = t_1;
	elseif ((x * y) <= 8.1e+117)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+83], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.8e+36], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.56e-24], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.8e-132], N[(z * N[(c / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.75e+50], c, If[LessEqual[N[(x * y), $MachinePrecision], 8e+116], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.1e+117], c, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.7999999999999999e83 or -8.80000000000000002e36 < (*.f64 x y) < -1.56e-24 or 8.0999999999999996e117 < (*.f64 x y)

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf 96.2%

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

   4. Taylor expanded in a around 0 90.7%

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

   5. Taylor expanded in y around inf 70.7%

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

   if -1.7999999999999999e83 < (*.f64 x y) < -8.80000000000000002e36 or 2.7499999999999999e50 < (*.f64 x y) < 8.00000000000000012e116

   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 79.9%

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

   4. Taylor expanded in t around inf 59.5%

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

   if -1.56e-24 < (*.f64 x y) < -8.79999999999999963e-132

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 94.7%

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

   4. Taylor expanded in c around inf 36.2%

      \[\leadsto z \cdot \color{blue}{\frac{c}{z}} \]

   if -8.79999999999999963e-132 < (*.f64 x y) < 2.7499999999999999e50 or 8.00000000000000012e116 < (*.f64 x y) < 8.0999999999999996e117

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 42.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.8 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1.56 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.8 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \frac{c}{z}\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+50}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 8.1 \cdot 10^{+117}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-205}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625)))
        (t_2 (+ c (* x y)))
        (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -1e+77)
     t_2
     (if (<= (* x y) -5e+38)
       t_1
       (if (<= (* x y) -2e+34)
         (* x y)
         (if (<= (* x y) 4e-205)
           t_3
           (if (<= (* x y) 1e-84) t_1 (if (<= (* x y) 5e+48) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * (t * 0.0625);
	double t_2 = c + (x * y);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -1e+77) {
		tmp = t_2;
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -2e+34) {
		tmp = x * y;
	} else if ((x * y) <= 4e-205) {
		tmp = t_3;
	} else if ((x * y) <= 1e-84) {
		tmp = t_1;
	} else if ((x * y) <= 5e+48) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    t_2 = c + (x * y)
    t_3 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-1d+77)) then
        tmp = t_2
    else if ((x * y) <= (-5d+38)) then
        tmp = t_1
    else if ((x * y) <= (-2d+34)) then
        tmp = x * y
    else if ((x * y) <= 4d-205) then
        tmp = t_3
    else if ((x * y) <= 1d-84) then
        tmp = t_1
    else if ((x * y) <= 5d+48) then
        tmp = t_3
    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 = z * (t * 0.0625);
	double t_2 = c + (x * y);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -1e+77) {
		tmp = t_2;
	} else if ((x * y) <= -5e+38) {
		tmp = t_1;
	} else if ((x * y) <= -2e+34) {
		tmp = x * y;
	} else if ((x * y) <= 4e-205) {
		tmp = t_3;
	} else if ((x * y) <= 1e-84) {
		tmp = t_1;
	} else if ((x * y) <= 5e+48) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	t_2 = c + (x * y)
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -1e+77:
		tmp = t_2
	elif (x * y) <= -5e+38:
		tmp = t_1
	elif (x * y) <= -2e+34:
		tmp = x * y
	elif (x * y) <= 4e-205:
		tmp = t_3
	elif (x * y) <= 1e-84:
		tmp = t_1
	elif (x * y) <= 5e+48:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+77)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e+38)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e+34)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 4e-205)
		tmp = t_3;
	elseif (Float64(x * y) <= 1e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+48)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	t_2 = c + (x * y);
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -1e+77)
		tmp = t_2;
	elseif ((x * y) <= -5e+38)
		tmp = t_1;
	elseif ((x * y) <= -2e+34)
		tmp = x * y;
	elseif ((x * y) <= 4e-205)
		tmp = t_3;
	elseif ((x * y) <= 1e-84)
		tmp = t_1;
	elseif ((x * y) <= 5e+48)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+77], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e+34], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-205], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+48], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999983e76 or 4.99999999999999973e48 < (*.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 73.9%

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

   if -9.99999999999999983e76 < (*.f64 x y) < -4.9999999999999997e38 or 4e-205 < (*.f64 x y) < 1e-84

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 87.0%

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

   4. Taylor expanded in t around inf 65.5%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -1.99999999999999989e34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in a around 0 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1.99999999999999989e34 < (*.f64 x y) < 4e-205 or 1e-84 < (*.f64 x y) < 4.99999999999999973e48

   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 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*r* 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+77}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-205}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-84}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+48}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -4e+25)
   (+ (* x y) (* 0.0625 (* z t)))
   (if (<= (* x y) -2e-29)
     (+ c (* a (* b -0.25)))
     (if (<= (* x y) 5e+49)
       (+ c (* t (* z 0.0625)))
       (* y (+ x (* 0.0625 (/ (* z t) y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4e+25) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((x * y) <= -2e-29) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 5e+49) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = y * (x + (0.0625 * ((z * t) / 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) <= (-4d+25)) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else if ((x * y) <= (-2d-29)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 5d+49) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = y * (x + (0.0625d0 * ((z * t) / 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) <= -4e+25) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else if ((x * y) <= -2e-29) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 5e+49) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = y * (x + (0.0625 * ((z * t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -4e+25:
		tmp = (x * y) + (0.0625 * (z * t))
	elif (x * y) <= -2e-29:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 5e+49:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = y * (x + (0.0625 * ((z * t) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4e+25)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= -2e-29)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 5e+49)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(y * Float64(x + Float64(0.0625 * Float64(Float64(z * t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -4e+25)
		tmp = (x * y) + (0.0625 * (z * t));
	elseif ((x * y) <= -2e-29)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 5e+49)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = y * (x + (0.0625 * ((z * t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+25], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-29], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+49], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(0.0625 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.00000000000000036e25

   1. Initial program 98.1%

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

   3. Taylor expanded in y around inf 98.1%

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

   4. Taylor expanded in a around 0 85.1%

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

   5. Taylor expanded in c around 0 77.4%

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

   6. Taylor expanded in y around 0 77.4%

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

   if -4.00000000000000036e25 < (*.f64 x y) < -1.99999999999999989e-29

   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 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*r* 76.4%

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

   5. Simplified 76.4%

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

   if -1.99999999999999989e-29 < (*.f64 x y) < 5.0000000000000004e49

   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 76.4%

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

      1. associate-*r* 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-*r* 76.4%

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

   5. Simplified 76.4%

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

   if 5.0000000000000004e49 < (*.f64 x y)

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 94.2%

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

   4. Taylor expanded in a around 0 92.8%

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

   5. Taylor expanded in c around 0 85.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 0.0625 \cdot \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.24 \cdot 10^{+33} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+49} \lor \neg \left(x \cdot y \leq 2.46 \cdot 10^{+241}\right) \land x \cdot y \leq 9.2 \cdot 10^{+246}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.24e+33)
         (not
          (or (<= (* x y) 7.5e+49)
              (and (not (<= (* x y) 2.46e+241)) (<= (* x y) 9.2e+246)))))
   (* 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) <= -1.24e+33) || !(((x * y) <= 7.5e+49) || (!((x * y) <= 2.46e+241) && ((x * y) <= 9.2e+246)))) {
		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) <= (-1.24d+33)) .or. (.not. ((x * y) <= 7.5d+49) .or. (.not. ((x * y) <= 2.46d+241)) .and. ((x * y) <= 9.2d+246))) 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) <= -1.24e+33) || !(((x * y) <= 7.5e+49) || (!((x * y) <= 2.46e+241) && ((x * y) <= 9.2e+246)))) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.24e+33) or not (((x * y) <= 7.5e+49) or (not ((x * y) <= 2.46e+241) and ((x * y) <= 9.2e+246))):
		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) <= -1.24e+33) || !((Float64(x * y) <= 7.5e+49) || (!(Float64(x * y) <= 2.46e+241) && (Float64(x * y) <= 9.2e+246))))
		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) <= -1.24e+33) || ~((((x * y) <= 7.5e+49) || (~(((x * y) <= 2.46e+241)) && ((x * y) <= 9.2e+246)))))
		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], -1.24e+33], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], 7.5e+49], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.46e+241]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 9.2e+246]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.23999999999999997e33 or 7.4999999999999995e49 < (*.f64 x y) < 2.46000000000000003e241 or 9.20000000000000055e246 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 95.7%

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

   4. Taylor expanded in a around 0 89.1%

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

   5. Taylor expanded in y around inf 64.0%

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

   if -1.23999999999999997e33 < (*.f64 x y) < 7.4999999999999995e49 or 2.46000000000000003e241 < (*.f64 x y) < 9.20000000000000055e246

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 41.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.24 \cdot 10^{+33} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+49} \lor \neg \left(x \cdot y \leq 2.46 \cdot 10^{+241}\right) \land x \cdot y \leq 9.2 \cdot 10^{+246}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* 0.0625 (* z t)))))
   (if (<= (* x y) -4e+25)
     t_1
     (if (<= (* x y) -2e-29)
       (+ c (* a (* b -0.25)))
       (if (<= (* x y) 5e+49) (+ c (* t (* z 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -4e+25) {
		tmp = t_1;
	} else if ((x * y) <= -2e-29) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 5e+49) {
		tmp = c + (t * (z * 0.0625));
	} 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) + (0.0625d0 * (z * t))
    if ((x * y) <= (-4d+25)) then
        tmp = t_1
    else if ((x * y) <= (-2d-29)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 5d+49) then
        tmp = c + (t * (z * 0.0625d0))
    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) + (0.0625 * (z * t));
	double tmp;
	if ((x * y) <= -4e+25) {
		tmp = t_1;
	} else if ((x * y) <= -2e-29) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 5e+49) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + (0.0625 * (z * t))
	tmp = 0
	if (x * y) <= -4e+25:
		tmp = t_1
	elif (x * y) <= -2e-29:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 5e+49:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -4e+25)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-29)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 5e+49)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + (0.0625 * (z * t));
	tmp = 0.0;
	if ((x * y) <= -4e+25)
		tmp = t_1;
	elseif ((x * y) <= -2e-29)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 5e+49)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+25], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-29], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+49], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.00000000000000036e25 or 5.0000000000000004e49 < (*.f64 x y)

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 95.9%

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

   4. Taylor expanded in a around 0 89.5%

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

   5. Taylor expanded in c around 0 82.0%

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

   6. Taylor expanded in y around 0 82.0%

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

   if -4.00000000000000036e25 < (*.f64 x y) < -1.99999999999999989e-29

   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 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*r* 76.4%

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

   5. Simplified 76.4%

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

   if -1.99999999999999989e-29 < (*.f64 x y) < 5.0000000000000004e49

   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 76.4%

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

      1. associate-*r* 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-*r* 76.4%

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

   5. Simplified 76.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-29}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+83} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+49}\right):\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t\_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -2e+83) (not (<= (* x y) 2e+49)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -2e+83) || !((x * y) <= 2e+49)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((x * y) <= (-2d+83)) .or. (.not. ((x * y) <= 2d+49))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -2e+83) || !((x * y) <= 2e+49)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -2e+83) or not ((x * y) <= 2e+49):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(x * y) <= -2e+83) || !(Float64(x * y) <= 2e+49))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((x * y) <= -2e+83) || ~(((x * y) <= 2e+49)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+83], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+49]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000006e83 or 1.99999999999999989e49 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 90.1%

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

   if -2.00000000000000006e83 < (*.f64 x y) < 1.99999999999999989e49

   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 94.6%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+83} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+49}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* a b) (- INFINITY))
     t_1
     (if (<= (* a b) 4e+114) (+ c (+ (* x y) (* 0.0625 (* z t)))) (+ c t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((a * b) <= 4e+114) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((a * b) <= 4e+114) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (a * b) <= -math.inf:
		tmp = t_1
	elif (a * b) <= 4e+114:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(a * b) <= 4e+114)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if ((a * b) <= -Inf)
		tmp = t_1;
	elseif ((a * b) <= 4e+114)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4e+114], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -inf.0

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 91.7%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

   6. Simplified 100.0%

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

   if -inf.0 < (*.f64 a b) < 4e114

   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 0 91.0%

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

   if 4e114 < (*.f64 a b)

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r* 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -\infty:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+162} \lor \neg \left(z \leq -6 \cdot 10^{+30}\right) \land z \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.5e+162) (and (not (<= z -6e+30)) (<= z -5.5e+30)))
   (* z (* t 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 <= -5.5e+162) || (!(z <= -6e+30) && (z <= -5.5e+30))) {
		tmp = z * (t * 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 <= (-5.5d+162)) .or. (.not. (z <= (-6d+30))) .and. (z <= (-5.5d+30))) then
        tmp = z * (t * 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 <= -5.5e+162) || (!(z <= -6e+30) && (z <= -5.5e+30))) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5.5e+162) or (not (z <= -6e+30) and (z <= -5.5e+30)):
		tmp = z * (t * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.5e+162) || (!(z <= -6e+30) && (z <= -5.5e+30)))
		tmp = Float64(z * Float64(t * 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 <= -5.5e+162) || (~((z <= -6e+30)) && (z <= -5.5e+30)))
		tmp = z * (t * 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, -5.5e+162], And[N[Not[LessEqual[z, -6e+30]], $MachinePrecision], LessEqual[z, -5.5e+30]]], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999966e162 or -5.99999999999999956e30 < z < -5.50000000000000025e30

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 97.1%

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

   4. Taylor expanded in t around inf 71.9%

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

   if -5.49999999999999966e162 < z < -5.99999999999999956e30 or -5.50000000000000025e30 < z

   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 60.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+162} \lor \neg \left(z \leq -6 \cdot 10^{+30}\right) \land z \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-35} \lor \neg \left(y \leq 2.4 \cdot 10^{+23}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.55e-35) (not (<= y 2.4e+23)))
   (+ c (* x y))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.55e-35) || !(y <= 2.4e+23)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (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 ((y <= (-1.55d-35)) .or. (.not. (y <= 2.4d+23))) then
        tmp = c + (x * y)
    else
        tmp = c + (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 ((y <= -1.55e-35) || !(y <= 2.4e+23)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.55e-35) or not (y <= 2.4e+23):
		tmp = c + (x * y)
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.55e-35) || !(y <= 2.4e+23))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + 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 ((y <= -1.55e-35) || ~((y <= 2.4e+23)))
		tmp = c + (x * y);
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.55e-35], N[Not[LessEqual[y, 2.4e+23]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000006e-35 or 2.4e23 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 69.5%

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

   if -1.55000000000000006e-35 < y < 2.4e23

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r* 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-35} \lor \neg \left(y \leq 2.4 \cdot 10^{+23}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 14: 22.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in c around inf 26.6%

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

Reproduce

herbie shell --seed 2024105 
(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))