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

Percentage Accurate: 97.8% → 98.9%

Time: 11.9s

Alternatives: 16

Speedup: 0.5×

• 32.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% 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 96.9%

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

   1. associate--l+ 96.9%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 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. Add Preprocessing

Alternative 2: 98.3% 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 96.9%

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

   1. associate-+l- 96.9%

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

   2. *-commutative 96.9%

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

   3. associate-+l- 96.9%

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

   4. fma-define 97.6%

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

   5. *-commutative 97.6%

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

   6. associate-/l* 97.6%

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

   7. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 44.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -3.65 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -860000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 280000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{+202}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* z (* t 0.0625))))
   (if (<= (* x y) -3.65e+140)
     (* x y)
     (if (<= (* x y) -3.9e+39)
       t_1
       (if (<= (* x y) -860000000.0)
         t_2
         (if (<= (* x y) -8.2e-64)
           c
           (if (<= (* x y) 280000000000.0)
             t_1
             (if (<= (* x y) 1.1e+202) t_2 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -3.65e+140) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e+39) {
		tmp = t_1;
	} else if ((x * y) <= -860000000.0) {
		tmp = t_2;
	} else if ((x * y) <= -8.2e-64) {
		tmp = c;
	} else if ((x * y) <= 280000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e+202) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    t_2 = z * (t * 0.0625d0)
    if ((x * y) <= (-3.65d+140)) then
        tmp = x * y
    else if ((x * y) <= (-3.9d+39)) then
        tmp = t_1
    else if ((x * y) <= (-860000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= (-8.2d-64)) then
        tmp = c
    else if ((x * y) <= 280000000000.0d0) then
        tmp = t_1
    else if ((x * y) <= 1.1d+202) then
        tmp = t_2
    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 = b * (a * -0.25);
	double t_2 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -3.65e+140) {
		tmp = x * y;
	} else if ((x * y) <= -3.9e+39) {
		tmp = t_1;
	} else if ((x * y) <= -860000000.0) {
		tmp = t_2;
	} else if ((x * y) <= -8.2e-64) {
		tmp = c;
	} else if ((x * y) <= 280000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e+202) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -3.65e+140:
		tmp = x * y
	elif (x * y) <= -3.9e+39:
		tmp = t_1
	elif (x * y) <= -860000000.0:
		tmp = t_2
	elif (x * y) <= -8.2e-64:
		tmp = c
	elif (x * y) <= 280000000000.0:
		tmp = t_1
	elif (x * y) <= 1.1e+202:
		tmp = t_2
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -3.65e+140)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.9e+39)
		tmp = t_1;
	elseif (Float64(x * y) <= -860000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= -8.2e-64)
		tmp = c;
	elseif (Float64(x * y) <= 280000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.1e+202)
		tmp = t_2;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	t_2 = z * (t * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -3.65e+140)
		tmp = x * y;
	elseif ((x * y) <= -3.9e+39)
		tmp = t_1;
	elseif ((x * y) <= -860000000.0)
		tmp = t_2;
	elseif ((x * y) <= -8.2e-64)
		tmp = c;
	elseif ((x * y) <= 280000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 1.1e+202)
		tmp = t_2;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.65e+140], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.9e+39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -860000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -8.2e-64], c, If[LessEqual[N[(x * y), $MachinePrecision], 280000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.1e+202], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.6500000000000002e140 or 1.09999999999999989e202 < (*.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 75.7%

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

   4. Taylor expanded in x around inf 70.2%

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

   if -3.6500000000000002e140 < (*.f64 x y) < -3.9000000000000001e39 or -8.2000000000000001e-64 < (*.f64 x y) < 2.8e11

   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 78.9%

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

   4. Taylor expanded in a around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. *-commutative 45.6%

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

      3. associate-*r* 45.6%

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

   6. Simplified 45.6%

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

   if -3.9000000000000001e39 < (*.f64 x y) < -8.6e8 or 2.8e11 < (*.f64 x y) < 1.09999999999999989e202

   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 80.3%

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

   4. Taylor expanded in t around inf 50.6%

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

   if -8.6e8 < (*.f64 x y) < -8.2000000000000001e-64

   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 52.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.65 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -860000000:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-64}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 280000000000:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t\_2 - t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-126} \lor \neg \left(a \cdot b \leq 10^{-23}\right) \land a \cdot b \leq 5 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -1e+137)
     (- t_2 t_1)
     (if (or (<= (* a b) 5e-126)
             (and (not (<= (* a b) 1e-23)) (<= (* a b) 5e+46)))
       (+ c (+ (* x y) t_2))
       (- (+ c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+137) {
		tmp = t_2 - t_1;
	} else if (((a * b) <= 5e-126) || (!((a * b) <= 1e-23) && ((a * b) <= 5e+46))) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-1d+137)) then
        tmp = t_2 - t_1
    else if (((a * b) <= 5d-126) .or. (.not. ((a * b) <= 1d-23)) .and. ((a * b) <= 5d+46)) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + (x * y)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+137) {
		tmp = t_2 - t_1;
	} else if (((a * b) <= 5e-126) || (!((a * b) <= 1e-23) && ((a * b) <= 5e+46))) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -1e+137:
		tmp = t_2 - t_1
	elif ((a * b) <= 5e-126) or (not ((a * b) <= 1e-23) and ((a * b) <= 5e+46)):
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e+137)
		tmp = Float64(t_2 - t_1);
	elseif ((Float64(a * b) <= 5e-126) || (!(Float64(a * b) <= 1e-23) && (Float64(a * b) <= 5e+46)))
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -1e+137)
		tmp = t_2 - t_1;
	elseif (((a * b) <= 5e-126) || (~(((a * b) <= 1e-23)) && ((a * b) <= 5e+46)))
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+137], N[(t$95$2 - t$95$1), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 5e-126], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e-23]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 5e+46]]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1e137

   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 x around 0 94.3%

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

   4. Taylor expanded in c around 0 89.0%

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

   if -1e137 < (*.f64 a b) < 5.00000000000000006e-126 or 9.9999999999999996e-24 < (*.f64 a b) < 5.0000000000000002e46

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0 91.7%

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

   if 5.00000000000000006e-126 < (*.f64 a b) < 9.9999999999999996e-24 or 5.0000000000000002e46 < (*.f64 a b)

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 88.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-126} \lor \neg \left(a \cdot b \leq 10^{-23}\right) \land a \cdot b \leq 5 \cdot 10^{+46}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10000000000:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+187}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* x y) -2e+132)
     t_1
     (if (<= (* x y) 10000000000.0)
       (+ c (* b (* a -0.25)))
       (if (<= (* x y) 1e+187)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 5e+290) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -2e+132) {
		tmp = t_1;
	} else if ((x * y) <= 10000000000.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 1e+187) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5e+290) {
		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 = (x * y) - ((a * b) * 0.25d0)
    if ((x * y) <= (-2d+132)) then
        tmp = t_1
    else if ((x * y) <= 10000000000.0d0) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((x * y) <= 1d+187) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 5d+290) 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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((x * y) <= -2e+132) {
		tmp = t_1;
	} else if ((x * y) <= 10000000000.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 1e+187) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5e+290) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (x * y) <= -2e+132:
		tmp = t_1
	elif (x * y) <= 10000000000.0:
		tmp = c + (b * (a * -0.25))
	elif (x * y) <= 1e+187:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 5e+290:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(x * y) <= -2e+132)
		tmp = t_1;
	elseif (Float64(x * y) <= 10000000000.0)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(x * y) <= 1e+187)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 5e+290)
		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 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((x * y) <= -2e+132)
		tmp = t_1;
	elseif ((x * y) <= 10000000000.0)
		tmp = c + (b * (a * -0.25));
	elseif ((x * y) <= 1e+187)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 5e+290)
		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[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+132], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 10000000000.0], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+187], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+290], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999998e132 or 9.99999999999999907e186 < (*.f64 x y) < 4.9999999999999998e290

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 84.0%

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

   4. Taylor expanded in c around 0 80.1%

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

   if -1.99999999999999998e132 < (*.f64 x y) < 1e10

   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 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if 1e10 < (*.f64 x y) < 9.99999999999999907e186

   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 81.2%

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

   4. Taylor expanded in x around 0 74.0%

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

   if 4.9999999999999998e290 < (*.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in z around inf 74.9%

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

   4. Taylor expanded in x around inf 90.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 10000000000:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+187}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+290}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (- (* 0.0625 (* z t)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (0.0625 * (z * t)) - ((a * b) * 0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (0.0625 * (z * t)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (0.0625 * (z * t)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(0.0625 * Float64(z * t)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (0.0625 * (z * t)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 62.5%

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

   4. Taylor expanded in c around 0 62.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-40}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+49} \lor \neg \left(b \leq 5 \cdot 10^{+98}\right) \land b \leq 1.4 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))))
   (if (<= b -1.25e+54)
     t_2
     (if (<= b 1.55e-209)
       t_1
       (if (<= b 5.1e-40)
         (+ c (* 0.0625 (* z t)))
         (if (or (<= b 2.4e+49) (and (not (<= b 5e+98)) (<= b 1.4e+158)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e+54) {
		tmp = t_2;
	} else if (b <= 1.55e-209) {
		tmp = t_1;
	} else if (b <= 5.1e-40) {
		tmp = c + (0.0625 * (z * t));
	} else if ((b <= 2.4e+49) || (!(b <= 5e+98) && (b <= 1.4e+158))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = b * (a * (-0.25d0))
    if (b <= (-1.25d+54)) then
        tmp = t_2
    else if (b <= 1.55d-209) then
        tmp = t_1
    else if (b <= 5.1d-40) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((b <= 2.4d+49) .or. (.not. (b <= 5d+98)) .and. (b <= 1.4d+158)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e+54) {
		tmp = t_2;
	} else if (b <= 1.55e-209) {
		tmp = t_1;
	} else if (b <= 5.1e-40) {
		tmp = c + (0.0625 * (z * t));
	} else if ((b <= 2.4e+49) || (!(b <= 5e+98) && (b <= 1.4e+158))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = b * (a * -0.25)
	tmp = 0
	if b <= -1.25e+54:
		tmp = t_2
	elif b <= 1.55e-209:
		tmp = t_1
	elif b <= 5.1e-40:
		tmp = c + (0.0625 * (z * t))
	elif (b <= 2.4e+49) or (not (b <= 5e+98) and (b <= 1.4e+158)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -1.25e+54)
		tmp = t_2;
	elseif (b <= 1.55e-209)
		tmp = t_1;
	elseif (b <= 5.1e-40)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif ((b <= 2.4e+49) || (!(b <= 5e+98) && (b <= 1.4e+158)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -1.25e+54)
		tmp = t_2;
	elseif (b <= 1.55e-209)
		tmp = t_1;
	elseif (b <= 5.1e-40)
		tmp = c + (0.0625 * (z * t));
	elseif ((b <= 2.4e+49) || (~((b <= 5e+98)) && (b <= 1.4e+158)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+54], t$95$2, If[LessEqual[b, 1.55e-209], t$95$1, If[LessEqual[b, 5.1e-40], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.4e+49], And[N[Not[LessEqual[b, 5e+98]], $MachinePrecision], LessEqual[b, 1.4e+158]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000001e54 or 2.4e49 < b < 4.9999999999999998e98 or 1.40000000000000001e158 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 75.0%

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

   4. Taylor expanded in a around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-*r* 63.3%

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

   6. Simplified 63.3%

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

   if -1.25000000000000001e54 < b < 1.55e-209 or 5.10000000000000037e-40 < b < 2.4e49 or 4.9999999999999998e98 < b < 1.40000000000000001e158

   1. Initial program 97.5%

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

   3. Taylor expanded in a around 0 83.2%

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

   4. Taylor expanded in t around 0 63.8%

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

   if 1.55e-209 < b < 5.10000000000000037e-40

   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 86.2%

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

   4. Taylor expanded in x around 0 72.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-209}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-40}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+49} \lor \neg \left(b \leq 5 \cdot 10^{+98}\right) \land b \leq 1.4 \cdot 10^{+158}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10000000000:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+202}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -2e+145)
     t_1
     (if (<= (* x y) 10000000000.0)
       (+ c (* b (* a -0.25)))
       (if (<= (* x y) 2e+202) (+ c (* 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 = c + (x * y);
	double tmp;
	if ((x * y) <= -2e+145) {
		tmp = t_1;
	} else if ((x * y) <= 10000000000.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 2e+202) {
		tmp = c + (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 = c + (x * y)
    if ((x * y) <= (-2d+145)) then
        tmp = t_1
    else if ((x * y) <= 10000000000.0d0) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((x * y) <= 2d+202) then
        tmp = c + (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 = c + (x * y);
	double tmp;
	if ((x * y) <= -2e+145) {
		tmp = t_1;
	} else if ((x * y) <= 10000000000.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 2e+202) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -2e+145:
		tmp = t_1
	elif (x * y) <= 10000000000.0:
		tmp = c + (b * (a * -0.25))
	elif (x * y) <= 2e+202:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+145)
		tmp = t_1;
	elseif (Float64(x * y) <= 10000000000.0)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(x * y) <= 2e+202)
		tmp = Float64(c + 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 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2e+145)
		tmp = t_1;
	elseif ((x * y) <= 10000000000.0)
		tmp = c + (b * (a * -0.25));
	elseif ((x * y) <= 2e+202)
		tmp = c + (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[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+145], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 10000000000.0], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+202], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e145 or 1.9999999999999998e202 < (*.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in a around 0 77.4%

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

   4. Taylor expanded in t around 0 73.1%

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

   if -2e145 < (*.f64 x y) < 1e10

   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 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   if 1e10 < (*.f64 x y) < 1.9999999999999998e202

   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 77.5%

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

   4. Taylor expanded in x around 0 70.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+145}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 10000000000:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+202}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+54} \lor \neg \left(b \leq 3.6 \cdot 10^{+50}\right) \land \left(b \leq 2.7 \cdot 10^{+99} \lor \neg \left(b \leq 4.5 \cdot 10^{+158}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.5e+54)
         (and (not (<= b 3.6e+50)) (or (<= b 2.7e+99) (not (<= b 4.5e+158)))))
   (* 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 <= -1.5e+54) || (!(b <= 3.6e+50) && ((b <= 2.7e+99) || !(b <= 4.5e+158)))) {
		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 <= (-1.5d+54)) .or. (.not. (b <= 3.6d+50)) .and. (b <= 2.7d+99) .or. (.not. (b <= 4.5d+158))) 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 <= -1.5e+54) || (!(b <= 3.6e+50) && ((b <= 2.7e+99) || !(b <= 4.5e+158)))) {
		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 <= -1.5e+54) or (not (b <= 3.6e+50) and ((b <= 2.7e+99) or not (b <= 4.5e+158))):
		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 <= -1.5e+54) || (!(b <= 3.6e+50) && ((b <= 2.7e+99) || !(b <= 4.5e+158))))
		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 <= -1.5e+54) || (~((b <= 3.6e+50)) && ((b <= 2.7e+99) || ~((b <= 4.5e+158)))))
		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, -1.5e+54], And[N[Not[LessEqual[b, 3.6e+50]], $MachinePrecision], Or[LessEqual[b, 2.7e+99], N[Not[LessEqual[b, 4.5e+158]], $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 < -1.4999999999999999e54 or 3.59999999999999986e50 < b < 2.69999999999999989e99 or 4.50000000000000046e158 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 75.0%

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

   4. Taylor expanded in a around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-*r* 63.3%

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

   6. Simplified 63.3%

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

   if -1.4999999999999999e54 < b < 3.59999999999999986e50 or 2.69999999999999989e99 < b < 4.50000000000000046e158

   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 a around 0 83.9%

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

   4. Taylor expanded in t around 0 57.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+54} \lor \neg \left(b \leq 3.6 \cdot 10^{+50}\right) \land \left(b \leq 2.7 \cdot 10^{+99} \lor \neg \left(b \leq 4.5 \cdot 10^{+158}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+158) (not (<= (* a b) 5e+93)))
   (+ c (* b (* a -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+158) || !((a * b) <= 5e+93)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+158)) .or. (.not. ((a * b) <= 5d+93))) then
        tmp = c + (b * (a * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+158) || !((a * b) <= 5e+93)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+158) or not ((a * b) <= 5e+93):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+158) || !(Float64(a * b) <= 5e+93))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+158) || ~(((a * b) <= 5e+93)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+158], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+93]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.9999999999999996e158 or 5.0000000000000001e93 < (*.f64 a b)

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 82.9%

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

      1. associate-*r* 82.9%

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

      2. *-commutative 82.9%

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

      3. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -4.9999999999999996e158 < (*.f64 a b) < 5.0000000000000001e93

   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 a around 0 86.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t\_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+93}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -1e+137)
     (- t_1 (* (* a b) 0.25))
     (if (<= (* a b) 5e+93) (+ c (+ (* x y) t_1)) (+ c (* b (* a -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 ((a * b) <= -1e+137) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+93) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = c + (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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-1d+137)) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else if ((a * b) <= 5d+93) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = c + (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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -1e+137) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+93) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -1e+137:
		tmp = t_1 - ((a * b) * 0.25)
	elif (a * b) <= 5e+93:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = c + (b * (a * -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(a * b) <= -1e+137)
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 5e+93)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(c + Float64(b * Float64(a * -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 ((a * b) <= -1e+137)
		tmp = t_1 - ((a * b) * 0.25);
	elseif ((a * b) <= 5e+93)
		tmp = c + ((x * y) + t_1);
	else
		tmp = c + (b * (a * -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[LessEqual[N[(a * b), $MachinePrecision], -1e+137], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+93], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1e137

   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 x around 0 94.3%

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

   4. Taylor expanded in c around 0 89.0%

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

   if -1e137 < (*.f64 a b) < 5.0000000000000001e93

   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 a around 0 87.6%

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

   if 5.0000000000000001e93 < (*.f64 a b)

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 82.5%

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

      1. associate-*r* 82.5%

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

      2. *-commutative 82.5%

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

      3. *-commutative 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+93}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2e+145) (not (<= (* x y) 2e+133)))
   (+ (* x y) (* 0.0625 (* z t)))
   (+ c (* b (* a -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2e+145) || !((x * y) <= 2e+133)) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else {
		tmp = c + (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 (((x * y) <= (-2d+145)) .or. (.not. ((x * y) <= 2d+133))) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    else
        tmp = c + (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 (((x * y) <= -2e+145) || !((x * y) <= 2e+133)) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2e+145) or not ((x * y) <= 2e+133):
		tmp = (x * y) + (0.0625 * (z * t))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+145) || !(Float64(x * y) <= 2e+133))
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(c + Float64(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 (((x * y) <= -2e+145) || ~(((x * y) <= 2e+133)))
		tmp = (x * y) + (0.0625 * (z * t));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+145], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+133]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e145 or 2e133 < (*.f64 x y)

   1. Initial program 89.9%

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

   3. Taylor expanded in a around 0 76.7%

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

   4. Taylor expanded in c around 0 74.2%

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

   if -2e145 < (*.f64 x y) < 2e133

   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 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+179}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;\left(c + t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= x -2.1e+179)
     (- (+ c (* x y)) t_1)
     (if (<= x 1.6e-77) (- (+ c t_2) t_1) (+ c (+ (* x y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (x <= -2.1e+179) {
		tmp = (c + (x * y)) - t_1;
	} else if (x <= 1.6e-77) {
		tmp = (c + t_2) - t_1;
	} else {
		tmp = c + ((x * y) + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if (x <= (-2.1d+179)) then
        tmp = (c + (x * y)) - t_1
    else if (x <= 1.6d-77) then
        tmp = (c + t_2) - t_1
    else
        tmp = c + ((x * y) + 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 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (x <= -2.1e+179) {
		tmp = (c + (x * y)) - t_1;
	} else if (x <= 1.6e-77) {
		tmp = (c + t_2) - t_1;
	} else {
		tmp = c + ((x * y) + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if x <= -2.1e+179:
		tmp = (c + (x * y)) - t_1
	elif x <= 1.6e-77:
		tmp = (c + t_2) - t_1
	else:
		tmp = c + ((x * y) + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (x <= -2.1e+179)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (x <= 1.6e-77)
		tmp = Float64(Float64(c + t_2) - t_1);
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if (x <= -2.1e+179)
		tmp = (c + (x * y)) - t_1;
	elseif (x <= 1.6e-77)
		tmp = (c + t_2) - t_1;
	else
		tmp = c + ((x * y) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+179], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.6e-77], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e179

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 88.0%

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

   if -2.0999999999999999e179 < x < 1.6e-77

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 90.6%

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

   if 1.6e-77 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 71.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+179}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+142} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+202}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -7.5e+142) (not (<= (* x y) 1.1e+202)))
   (* 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 (((x * y) <= -7.5e+142) || !((x * y) <= 1.1e+202)) {
		tmp = x * y;
	} else {
		tmp = 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 (((x * y) <= (-7.5d+142)) .or. (.not. ((x * y) <= 1.1d+202))) then
        tmp = x * y
    else
        tmp = 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 (((x * y) <= -7.5e+142) || !((x * y) <= 1.1e+202)) {
		tmp = x * y;
	} else {
		tmp = b * (a * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -7.5e+142) or not ((x * y) <= 1.1e+202):
		tmp = x * y
	else:
		tmp = b * (a * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -7.5e+142) || !(Float64(x * y) <= 1.1e+202))
		tmp = Float64(x * y);
	else
		tmp = Float64(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 (((x * y) <= -7.5e+142) || ~(((x * y) <= 1.1e+202)))
		tmp = x * y;
	else
		tmp = b * (a * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -7.5e+142], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.1e+202]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -7.5000000000000002e142 or 1.09999999999999989e202 < (*.f64 x y)

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 75.7%

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

   4. Taylor expanded in x around inf 70.2%

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

   if -7.5000000000000002e142 < (*.f64 x y) < 1.09999999999999989e202

   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 78.8%

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

   4. Taylor expanded in a around inf 40.6%

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

      1. *-commutative 40.6%

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

      2. *-commutative 40.6%

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

      3. associate-*r* 40.6%

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

   6. Simplified 40.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+142} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+202}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+135} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+97}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.2e+135) (not (<= (* x y) 1.35e+97))) (* 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) <= -3.2e+135) || !((x * y) <= 1.35e+97)) {
		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) <= (-3.2d+135)) .or. (.not. ((x * y) <= 1.35d+97))) 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) <= -3.2e+135) || !((x * y) <= 1.35e+97)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.2e+135) or not ((x * y) <= 1.35e+97):
		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) <= -3.2e+135) || !(Float64(x * y) <= 1.35e+97))
		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) <= -3.2e+135) || ~(((x * y) <= 1.35e+97)))
		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], -3.2e+135], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+97]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.19999999999999975e135 or 1.34999999999999997e97 < (*.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 78.1%

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

   4. Taylor expanded in x around inf 61.4%

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

   if -3.19999999999999975e135 < (*.f64 x y) < 1.34999999999999997e97

   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 30.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+135} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+97}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 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 c around inf 22.6%

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

Reproduce

herbie shell --seed 2024084 
(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))