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

Percentage Accurate: 97.7% → 98.9%

Time: 10.6s

Alternatives: 14

Speedup: 1.0×

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% 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 98.4%

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

   3. associate-/l* 98.4%

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

   4. fmm-def 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 98.4% 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 98.4%

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

   7. *-commutative 98.4%

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

   8. associate-/l* 98.4%

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

   9. associate-/l* 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: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x + \frac{c}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* x y) -1e+49)
     (* y (+ x (/ c y)))
     (if (<= (* x y) 1e-89)
       t_1
       (if (<= (* x y) 5e+36)
         t_2
         (if (<= (* x y) 5e+98)
           t_1
           (if (<= (* x y) 5e+125) t_2 (+ c (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = y * (x + (c / y));
	} else if ((x * y) <= 1e-89) {
		tmp = t_1;
	} else if ((x * y) <= 5e+36) {
		tmp = t_2;
	} else if ((x * y) <= 5e+98) {
		tmp = t_1;
	} else if ((x * y) <= 5e+125) {
		tmp = t_2;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + (b * (a * (-0.25d0)))
    if ((x * y) <= (-1d+49)) then
        tmp = y * (x + (c / y))
    else if ((x * y) <= 1d-89) then
        tmp = t_1
    else if ((x * y) <= 5d+36) then
        tmp = t_2
    else if ((x * y) <= 5d+98) then
        tmp = t_1
    else if ((x * y) <= 5d+125) then
        tmp = t_2
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = y * (x + (c / y));
	} else if ((x * y) <= 1e-89) {
		tmp = t_1;
	} else if ((x * y) <= 5e+36) {
		tmp = t_2;
	} else if ((x * y) <= 5e+98) {
		tmp = t_1;
	} else if ((x * y) <= 5e+125) {
		tmp = t_2;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (x * y) <= -1e+49:
		tmp = y * (x + (c / y))
	elif (x * y) <= 1e-89:
		tmp = t_1
	elif (x * y) <= 5e+36:
		tmp = t_2
	elif (x * y) <= 5e+98:
		tmp = t_1
	elif (x * y) <= 5e+125:
		tmp = t_2
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+49)
		tmp = Float64(y * Float64(x + Float64(c / y)));
	elseif (Float64(x * y) <= 1e-89)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+36)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e+98)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+125)
		tmp = t_2;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((x * y) <= -1e+49)
		tmp = y * (x + (c / y));
	elseif ((x * y) <= 1e-89)
		tmp = t_1;
	elseif ((x * y) <= 5e+36)
		tmp = t_2;
	elseif ((x * y) <= 5e+98)
		tmp = t_1;
	elseif ((x * y) <= 5e+125)
		tmp = t_2;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+49], N[(y * N[(x + N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-89], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+36], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e+98], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+125], t$95$2, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999946e48

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 74.3%

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

   4. Taylor expanded in y around inf 74.3%

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

   if -9.99999999999999946e48 < (*.f64 x y) < 1.00000000000000004e-89 or 4.99999999999999977e36 < (*.f64 x y) < 4.9999999999999998e98

   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 70.8%

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

      1. associate-*r* 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-*r* 70.8%

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

   5. Simplified 70.8%

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

   if 1.00000000000000004e-89 < (*.f64 x y) < 4.99999999999999977e36 or 4.9999999999999998e98 < (*.f64 x y) < 4.99999999999999962e125

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-*r* 74.6%

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

   5. Simplified 74.6%

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

   if 4.99999999999999962e125 < (*.f64 x y)

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 86.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x + \frac{c}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-89}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+36}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+98}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+125}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-283}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= y -2.4e-69)
     (* x y)
     (if (<= y -4.5e-254)
       t_1
       (if (<= y 2.95e-283)
         c
         (if (<= y 1.38e-226)
           t_1
           (if (<= y 1.65e-87) c (if (<= y 3.9e+111) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (y <= -2.4e-69) {
		tmp = x * y;
	} else if (y <= -4.5e-254) {
		tmp = t_1;
	} else if (y <= 2.95e-283) {
		tmp = c;
	} else if (y <= 1.38e-226) {
		tmp = t_1;
	} else if (y <= 1.65e-87) {
		tmp = c;
	} else if (y <= 3.9e+111) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (y <= (-2.4d-69)) then
        tmp = x * y
    else if (y <= (-4.5d-254)) then
        tmp = t_1
    else if (y <= 2.95d-283) then
        tmp = c
    else if (y <= 1.38d-226) then
        tmp = t_1
    else if (y <= 1.65d-87) then
        tmp = c
    else if (y <= 3.9d+111) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (y <= -2.4e-69) {
		tmp = x * y;
	} else if (y <= -4.5e-254) {
		tmp = t_1;
	} else if (y <= 2.95e-283) {
		tmp = c;
	} else if (y <= 1.38e-226) {
		tmp = t_1;
	} else if (y <= 1.65e-87) {
		tmp = c;
	} else if (y <= 3.9e+111) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if y <= -2.4e-69:
		tmp = x * y
	elif y <= -4.5e-254:
		tmp = t_1
	elif y <= 2.95e-283:
		tmp = c
	elif y <= 1.38e-226:
		tmp = t_1
	elif y <= 1.65e-87:
		tmp = c
	elif y <= 3.9e+111:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (y <= -2.4e-69)
		tmp = Float64(x * y);
	elseif (y <= -4.5e-254)
		tmp = t_1;
	elseif (y <= 2.95e-283)
		tmp = c;
	elseif (y <= 1.38e-226)
		tmp = t_1;
	elseif (y <= 1.65e-87)
		tmp = c;
	elseif (y <= 3.9e+111)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (y <= -2.4e-69)
		tmp = x * y;
	elseif (y <= -4.5e-254)
		tmp = t_1;
	elseif (y <= 2.95e-283)
		tmp = c;
	elseif (y <= 1.38e-226)
		tmp = t_1;
	elseif (y <= 1.65e-87)
		tmp = c;
	elseif (y <= 3.9e+111)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-69], N[(x * y), $MachinePrecision], If[LessEqual[y, -4.5e-254], t$95$1, If[LessEqual[y, 2.95e-283], c, If[LessEqual[y, 1.38e-226], t$95$1, If[LessEqual[y, 1.65e-87], c, If[LessEqual[y, 3.9e+111], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e-69 or 3.89999999999999979e111 < y

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 66.9%

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

   4. Taylor expanded in y around inf 66.8%

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

   5. Taylor expanded in x around inf 52.2%

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

   if -2.4000000000000001e-69 < y < -4.5e-254 or 2.94999999999999992e-283 < y < 1.37999999999999998e-226 or 1.65e-87 < y < 3.89999999999999979e111

   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 72.3%

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

   4. Taylor expanded in c around 0 50.7%

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

   5. Taylor expanded in t around inf 36.5%

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

   if -4.5e-254 < y < 2.94999999999999992e-283 or 1.37999999999999998e-226 < y < 1.65e-87

   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 43.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-254}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-283}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-226}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-87}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+111}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;t \leq -18.5:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 0.0175:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= t -18.5)
     (+ c (* t (* z 0.0625)))
     (if (<= t 8e-218)
       t_1
       (if (<= t 1.95e-113)
         t_2
         (if (<= t 0.0175)
           t_1
           (if (<= t 6.7e+109) t_2 (+ (* x y) (* 0.0625 (* z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -18.5) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 8e-218) {
		tmp = t_1;
	} else if (t <= 1.95e-113) {
		tmp = t_2;
	} else if (t <= 0.0175) {
		tmp = t_1;
	} else if (t <= 6.7e+109) {
		tmp = t_2;
	} else {
		tmp = (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    if (t <= (-18.5d0)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (t <= 8d-218) then
        tmp = t_1
    else if (t <= 1.95d-113) then
        tmp = t_2
    else if (t <= 0.0175d0) then
        tmp = t_1
    else if (t <= 6.7d+109) then
        tmp = t_2
    else
        tmp = (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 t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if (t <= -18.5) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 8e-218) {
		tmp = t_1;
	} else if (t <= 1.95e-113) {
		tmp = t_2;
	} else if (t <= 0.0175) {
		tmp = t_1;
	} else if (t <= 6.7e+109) {
		tmp = t_2;
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if t <= -18.5:
		tmp = c + (t * (z * 0.0625))
	elif t <= 8e-218:
		tmp = t_1
	elif t <= 1.95e-113:
		tmp = t_2
	elif t <= 0.0175:
		tmp = t_1
	elif t <= 6.7e+109:
		tmp = t_2
	else:
		tmp = (x * y) + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (t <= -18.5)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (t <= 8e-218)
		tmp = t_1;
	elseif (t <= 1.95e-113)
		tmp = t_2;
	elseif (t <= 0.0175)
		tmp = t_1;
	elseif (t <= 6.7e+109)
		tmp = t_2;
	else
		tmp = 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)
	t_1 = c + (x * y);
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (t <= -18.5)
		tmp = c + (t * (z * 0.0625));
	elseif (t <= 8e-218)
		tmp = t_1;
	elseif (t <= 1.95e-113)
		tmp = t_2;
	elseif (t <= 0.0175)
		tmp = t_1;
	elseif (t <= 6.7e+109)
		tmp = t_2;
	else
		tmp = (x * y) + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -18.5], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-218], t$95$1, If[LessEqual[t, 1.95e-113], t$95$2, If[LessEqual[t, 0.0175], t$95$1, If[LessEqual[t, 6.7e+109], t$95$2, N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -18.5

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 64.9%

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

      1. associate-*r* 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r* 64.9%

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

   5. Simplified 64.9%

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

   if -18.5 < t < 8.0000000000000003e-218 or 1.9499999999999999e-113 < t < 0.017500000000000002

   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 64.4%

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

   if 8.0000000000000003e-218 < t < 1.9499999999999999e-113 or 0.017500000000000002 < t < 6.70000000000000036e109

   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 53.7%

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

      1. *-commutative 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 53.7%

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

   5. Simplified 53.7%

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

   if 6.70000000000000036e109 < t

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 84.0%

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

   4. Taylor expanded in c around 0 76.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -18.5:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-113}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 0.0175:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+109}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -11800:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -11800.0)
   (+ c (* t (* z 0.0625)))
   (if (<= t 3.25e-218)
     (+ c (* x y))
     (if (<= t 7.5e-90)
       (+ c (* b (* a -0.25)))
       (if (<= t 5.2e+55)
         (- (* x y) (* (* a b) 0.25))
         (+ (* 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 (t <= -11800.0) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 3.25e-218) {
		tmp = c + (x * y);
	} else if (t <= 7.5e-90) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 5.2e+55) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = (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 (t <= (-11800.0d0)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (t <= 3.25d-218) then
        tmp = c + (x * y)
    else if (t <= 7.5d-90) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (t <= 5.2d+55) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = (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 (t <= -11800.0) {
		tmp = c + (t * (z * 0.0625));
	} else if (t <= 3.25e-218) {
		tmp = c + (x * y);
	} else if (t <= 7.5e-90) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 5.2e+55) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = (x * y) + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -11800.0:
		tmp = c + (t * (z * 0.0625))
	elif t <= 3.25e-218:
		tmp = c + (x * y)
	elif t <= 7.5e-90:
		tmp = c + (b * (a * -0.25))
	elif t <= 5.2e+55:
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = (x * y) + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -11800.0)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (t <= 3.25e-218)
		tmp = Float64(c + Float64(x * y));
	elseif (t <= 7.5e-90)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (t <= 5.2e+55)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = 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 (t <= -11800.0)
		tmp = c + (t * (z * 0.0625));
	elseif (t <= 3.25e-218)
		tmp = c + (x * y);
	elseif (t <= 7.5e-90)
		tmp = c + (b * (a * -0.25));
	elseif (t <= 5.2e+55)
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = (x * y) + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -11800.0], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e-218], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-90], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+55], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -11800

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. associate-*r* 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r* 65.9%

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

   5. Simplified 65.9%

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

   if -11800 < t < 3.24999999999999991e-218

   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 65.0%

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

   if 3.24999999999999991e-218 < t < 7.4999999999999999e-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 a around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r* 64.9%

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

   5. Simplified 64.9%

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

   if 7.4999999999999999e-90 < t < 5.2e55

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.4%

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

   4. Taylor expanded in c around 0 63.4%

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

   if 5.2e55 < t

   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 a around 0 85.6%

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

   4. Taylor expanded in c around 0 75.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -11800:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+210}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+210)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 2e+166)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* b (- (/ (* x y) b) (* a 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+210) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2d+210)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+166) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = b * (((x * y) / b) - (a * 0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+210) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+210:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 2e+166:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = b * (((x * y) / b) - (a * 0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+210)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+166)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+210)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+166)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = b * (((x * y) / b) - (a * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+210], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+166], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.99999999999999985e210

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.9%

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

   4. Taylor expanded in c around 0 96.9%

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

   if -1.99999999999999985e210 < (*.f64 a b) < 1.99999999999999988e166

   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 92.7%

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

   if 1.99999999999999988e166 < (*.f64 a b)

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 94.7%

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

   4. Taylor expanded in t around 0 89.5%

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

   5. Taylor expanded in c around 0 89.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+210}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+156}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1e+156)
   (- (+ c (* x y)) (* (* a b) 0.25))
   (if (<= (* a b) 2e+166)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* b (- (/ (* x y) b) (* a 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+156) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-1d+156)) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+166) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = b * (((x * y) / b) - (a * 0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -1e+156) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = b * (((x * y) / b) - (a * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -1e+156:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	elif (a * b) <= 2e+166:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = b * (((x * y) / b) - (a * 0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -1e+156)
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+166)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -1e+156)
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+166)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = b * (((x * y) / b) - (a * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+156], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+166], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.9999999999999998e155

   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 0 97.5%

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

   if -9.9999999999999998e155 < (*.f64 a b) < 1.99999999999999988e166

   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 93.0%

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

   if 1.99999999999999988e166 < (*.f64 a b)

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 94.7%

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

   4. Taylor expanded in t around 0 89.5%

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

   5. Taylor expanded in c around 0 89.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+156}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+156}:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (- (/ (* x y) b) (* a 0.25)))))
   (if (<= (* a b) -1e+156)
     (+ c t_1)
     (if (<= (* a b) 2e+166) (+ c (+ (* x y) (* 0.0625 (* z t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (((x * y) / b) - (a * 0.25));
	double tmp;
	if ((a * b) <= -1e+156) {
		tmp = c + t_1;
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} 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 = b * (((x * y) / b) - (a * 0.25d0))
    if ((a * b) <= (-1d+156)) then
        tmp = c + t_1
    else if ((a * b) <= 2d+166) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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 = b * (((x * y) / b) - (a * 0.25));
	double tmp;
	if ((a * b) <= -1e+156) {
		tmp = c + t_1;
	} else if ((a * b) <= 2e+166) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (((x * y) / b) - (a * 0.25))
	tmp = 0
	if (a * b) <= -1e+156:
		tmp = c + t_1
	elif (a * b) <= 2e+166:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(Float64(Float64(x * y) / b) - Float64(a * 0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -1e+156)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 2e+166)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (((x * y) / b) - (a * 0.25));
	tmp = 0.0;
	if ((a * b) <= -1e+156)
		tmp = c + t_1;
	elseif ((a * b) <= 2e+166)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+156], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+166], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.9999999999999998e155

   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 b around inf 100.0%

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

   4. Taylor expanded in t around 0 97.6%

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

   if -9.9999999999999998e155 < (*.f64 a b) < 1.99999999999999988e166

   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 93.0%

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

   if 1.99999999999999988e166 < (*.f64 a b)

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 94.7%

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

   4. Taylor expanded in t around 0 89.5%

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

   5. Taylor expanded in c around 0 89.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+156}:\\ \;\;\;\;c + b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+166}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{x \cdot y}{b} - a \cdot 0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;y \cdot \left(x + \frac{c}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+125}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -0.1)
   (* y (+ x (/ c y)))
   (if (<= (* x y) 5e+125) (+ c (* b (* a -0.25))) (+ c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -0.1) {
		tmp = y * (x + (c / y));
	} else if ((x * y) <= 5e+125) {
		tmp = c + (b * (a * -0.25));
	} 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 ((x * y) <= (-0.1d0)) then
        tmp = y * (x + (c / y))
    else if ((x * y) <= 5d+125) then
        tmp = c + (b * (a * (-0.25d0)))
    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 ((x * y) <= -0.1) {
		tmp = y * (x + (c / y));
	} else if ((x * y) <= 5e+125) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -0.1:
		tmp = y * (x + (c / y))
	elif (x * y) <= 5e+125:
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -0.1)
		tmp = Float64(y * Float64(x + Float64(c / y)));
	elseif (Float64(x * y) <= 5e+125)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	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 ((x * y) <= -0.1)
		tmp = y * (x + (c / y));
	elseif ((x * y) <= 5e+125)
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -0.1], N[(y * N[(x + N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+125], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.10000000000000001

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 72.2%

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

   4. Taylor expanded in y around inf 72.2%

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

   if -0.10000000000000001 < (*.f64 x y) < 4.99999999999999962e125

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*r* 61.8%

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

   5. Simplified 61.8%

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

   if 4.99999999999999962e125 < (*.f64 x y)

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 86.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.1:\\ \;\;\;\;y \cdot \left(x + \frac{c}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+125}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% 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 12: 52.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-28} \lor \neg \left(b \leq 2.75 \cdot 10^{+191}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1e-28) (not (<= b 2.75e+191)))
   (* b (* a -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1e-28) || !(b <= 2.75e+191)) {
		tmp = b * (a * -0.25);
	} 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 ((b <= (-1d-28)) .or. (.not. (b <= 2.75d+191))) then
        tmp = b * (a * (-0.25d0))
    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 ((b <= -1e-28) || !(b <= 2.75e+191)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1e-28) or not (b <= 2.75e+191):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1e-28) || !(b <= 2.75e+191))
		tmp = Float64(b * Float64(a * -0.25));
	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 ((b <= -1e-28) || ~((b <= 2.75e+191)))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1e-28], N[Not[LessEqual[b, 2.75e+191]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.99999999999999971e-29 or 2.7500000000000001e191 < b

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 78.8%

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

   4. Taylor expanded in c around 0 58.0%

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

   5. Taylor expanded in x around 0 43.5%

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

      1. associate-*r* 43.5%

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

      2. *-commutative 43.5%

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

   7. Simplified 43.5%

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

   if -9.99999999999999971e-29 < b < 2.7500000000000001e191

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 59.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-28} \lor \neg \left(b \leq 2.75 \cdot 10^{+191}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-78} \lor \neg \left(y \leq 8.2 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.4e-78) (not (<= y 8.2e+96))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.4e-78) || !(y <= 8.2e+96)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y <= (-1.4d-78)) .or. (.not. (y <= 8.2d+96))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.4e-78) || !(y <= 8.2e+96)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.4e-78) or not (y <= 8.2e+96):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.4e-78) || !(y <= 8.2e+96))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -1.4e-78) || ~((y <= 8.2e+96)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.4e-78], N[Not[LessEqual[y, 8.2e+96]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000012e-78 or 8.19999999999999996e96 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 65.3%

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

   4. Taylor expanded in y around inf 65.3%

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

   5. Taylor expanded in x around inf 51.2%

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

   if -1.40000000000000012e-78 < y < 8.19999999999999996e96

   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 30.8%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-78} \lor \neg \left(y \leq 8.2 \cdot 10^{+96}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.2% 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 c around inf 21.9%

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

4. Final simplification 21.9%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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))