Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.9% → 98.0%

Time: 11.7s

Alternatives: 16

Speedup: 0.4×

• 40.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(a * b)) + Float64(c * i))
end

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(c, i, fma(a, b, fma(x, y, Float64(z * t))))
end

Wolfram

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

Derivation

1. Initial program 94.1%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
2. Step-by-step derivation

   1. +-commutative 94.1%

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

   2. fma-define 95.7%

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

   3. +-commutative 95.7%

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

   4. fma-define 96.9%

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

   5. fma-define 98.0%

      \[\leadsto \mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)}\right)\right) \]

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 2: 66.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+30}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot i \leq -2.15 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* x y) (* a b)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.9e+30)
     t_3
     (if (<= (* c i) -2.15e-91)
       t_1
       (if (<= (* c i) -1e-319)
         t_2
         (if (<= (* c i) 8e-238)
           t_1
           (if (<= (* c i) 7.2e-162)
             t_2
             (if (<= (* c i) 1.6e+112) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.9e+30) {
		tmp = t_3;
	} else if ((c * i) <= -2.15e-91) {
		tmp = t_1;
	} else if ((c * i) <= -1e-319) {
		tmp = t_2;
	} else if ((c * i) <= 8e-238) {
		tmp = t_1;
	} else if ((c * i) <= 7.2e-162) {
		tmp = t_2;
	} else if ((c * i) <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (a * b)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-1.9d+30)) then
        tmp = t_3
    else if ((c * i) <= (-2.15d-91)) then
        tmp = t_1
    else if ((c * i) <= (-1d-319)) then
        tmp = t_2
    else if ((c * i) <= 8d-238) then
        tmp = t_1
    else if ((c * i) <= 7.2d-162) then
        tmp = t_2
    else if ((c * i) <= 1.6d+112) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.9e+30) {
		tmp = t_3;
	} else if ((c * i) <= -2.15e-91) {
		tmp = t_1;
	} else if ((c * i) <= -1e-319) {
		tmp = t_2;
	} else if ((c * i) <= 8e-238) {
		tmp = t_1;
	} else if ((c * i) <= 7.2e-162) {
		tmp = t_2;
	} else if ((c * i) <= 1.6e+112) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (a * b)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.9e+30:
		tmp = t_3
	elif (c * i) <= -2.15e-91:
		tmp = t_1
	elif (c * i) <= -1e-319:
		tmp = t_2
	elif (c * i) <= 8e-238:
		tmp = t_1
	elif (c * i) <= 7.2e-162:
		tmp = t_2
	elif (c * i) <= 1.6e+112:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.9e+30)
		tmp = t_3;
	elseif (Float64(c * i) <= -2.15e-91)
		tmp = t_1;
	elseif (Float64(c * i) <= -1e-319)
		tmp = t_2;
	elseif (Float64(c * i) <= 8e-238)
		tmp = t_1;
	elseif (Float64(c * i) <= 7.2e-162)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.6e+112)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (a * b);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.9e+30)
		tmp = t_3;
	elseif ((c * i) <= -2.15e-91)
		tmp = t_1;
	elseif ((c * i) <= -1e-319)
		tmp = t_2;
	elseif ((c * i) <= 8e-238)
		tmp = t_1;
	elseif ((c * i) <= 7.2e-162)
		tmp = t_2;
	elseif ((c * i) <= 1.6e+112)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.9e+30], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -2.15e-91], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1e-319], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 8e-238], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 7.2e-162], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.6e+112], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.9000000000000001e30 or 1.59999999999999993e112 < (*.f64 c i)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in t around 0 73.6%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -1.9000000000000001e30 < (*.f64 c i) < -2.15e-91 or -9.99989e-320 < (*.f64 c i) < 7.9999999999999999e-238 or 7.1999999999999996e-162 < (*.f64 c i) < 1.59999999999999993e112

   1. Initial program 94.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 89.0%

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

   4. Taylor expanded in x around 0 70.9%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -2.15e-91 < (*.f64 c i) < -9.99989e-320 or 7.9999999999999999e-238 < (*.f64 c i) < 7.1999999999999996e-162

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 100.0%

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

   4. Taylor expanded in t around 0 81.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+30}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.15 \cdot 10^{-91}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{-238}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{-162}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* a b) -5e+72)
     (+ (* a b) (* z t))
     (if (<= (* a b) -5e-106)
       t_1
       (if (<= (* a b) -5e-308)
         t_2
         (if (<= (* a b) 5e-253)
           t_1
           (if (<= (* a b) 1e-23) t_2 (+ (* a b) (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -5e+72) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= -5e-106) {
		tmp = t_1;
	} else if ((a * b) <= -5e-308) {
		tmp = t_2;
	} else if ((a * b) <= 5e-253) {
		tmp = t_1;
	} else if ((a * b) <= 1e-23) {
		tmp = t_2;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (c * i)
    t_2 = (x * y) + (z * t)
    if ((a * b) <= (-5d+72)) then
        tmp = (a * b) + (z * t)
    else if ((a * b) <= (-5d-106)) then
        tmp = t_1
    else if ((a * b) <= (-5d-308)) then
        tmp = t_2
    else if ((a * b) <= 5d-253) then
        tmp = t_1
    else if ((a * b) <= 1d-23) then
        tmp = t_2
    else
        tmp = (a * b) + (c * i)
    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 i) {
	double t_1 = (x * y) + (c * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -5e+72) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= -5e-106) {
		tmp = t_1;
	} else if ((a * b) <= -5e-308) {
		tmp = t_2;
	} else if ((a * b) <= 5e-253) {
		tmp = t_1;
	} else if ((a * b) <= 1e-23) {
		tmp = t_2;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -5e+72:
		tmp = (a * b) + (z * t)
	elif (a * b) <= -5e-106:
		tmp = t_1
	elif (a * b) <= -5e-308:
		tmp = t_2
	elif (a * b) <= 5e-253:
		tmp = t_1
	elif (a * b) <= 1e-23:
		tmp = t_2
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+72)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(a * b) <= -5e-106)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e-308)
		tmp = t_2;
	elseif (Float64(a * b) <= 5e-253)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e-23)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+72)
		tmp = (a * b) + (z * t);
	elseif ((a * b) <= -5e-106)
		tmp = t_1;
	elseif ((a * b) <= -5e-308)
		tmp = t_2;
	elseif ((a * b) <= 5e-253)
		tmp = t_1;
	elseif ((a * b) <= 1e-23)
		tmp = t_2;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+72], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-106], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e-308], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5e-253], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e-23], t$95$2, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.99999999999999992e72

   1. Initial program 88.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 81.7%

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

   4. Taylor expanded in x around 0 79.6%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -4.99999999999999992e72 < (*.f64 a b) < -4.99999999999999983e-106 or -4.99999999999999955e-308 < (*.f64 a b) < 4.99999999999999971e-253

   1. Initial program 94.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.8%

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

   4. Taylor expanded in a around 0 76.9%

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

   if -4.99999999999999983e-106 < (*.f64 a b) < -4.99999999999999955e-308 or 4.99999999999999971e-253 < (*.f64 a b) < 9.9999999999999996e-24

   1. Initial program 93.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 81.0%

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

   4. Taylor expanded in a around 0 74.9%

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

   if 9.9999999999999996e-24 < (*.f64 a b)

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 90.0%

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

   4. Taylor expanded in t around 0 74.0%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-106}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-308}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{-23}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-220}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-160}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.12 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.2e+30)
   (* c i)
   (if (<= (* c i) -2.3e-220)
     (* z t)
     (if (<= (* c i) 1.15e-160)
       (* a b)
       (if (<= (* c i) 1.12e+27)
         (* z t)
         (if (<= (* c i) 4.6e+111) (* a b) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.2e+30) {
		tmp = c * i;
	} else if ((c * i) <= -2.3e-220) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e-160) {
		tmp = a * b;
	} else if ((c * i) <= 1.12e+27) {
		tmp = z * t;
	} else if ((c * i) <= 4.6e+111) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.2d+30)) then
        tmp = c * i
    else if ((c * i) <= (-2.3d-220)) then
        tmp = z * t
    else if ((c * i) <= 1.15d-160) then
        tmp = a * b
    else if ((c * i) <= 1.12d+27) then
        tmp = z * t
    else if ((c * i) <= 4.6d+111) then
        tmp = a * b
    else
        tmp = c * i
    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 i) {
	double tmp;
	if ((c * i) <= -3.2e+30) {
		tmp = c * i;
	} else if ((c * i) <= -2.3e-220) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e-160) {
		tmp = a * b;
	} else if ((c * i) <= 1.12e+27) {
		tmp = z * t;
	} else if ((c * i) <= 4.6e+111) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.2e+30:
		tmp = c * i
	elif (c * i) <= -2.3e-220:
		tmp = z * t
	elif (c * i) <= 1.15e-160:
		tmp = a * b
	elif (c * i) <= 1.12e+27:
		tmp = z * t
	elif (c * i) <= 4.6e+111:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.2e+30)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.3e-220)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.15e-160)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1.12e+27)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 4.6e+111)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.2e+30)
		tmp = c * i;
	elseif ((c * i) <= -2.3e-220)
		tmp = z * t;
	elseif ((c * i) <= 1.15e-160)
		tmp = a * b;
	elseif ((c * i) <= 1.12e+27)
		tmp = z * t;
	elseif ((c * i) <= 4.6e+111)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.2e+30], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.3e-220], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.15e-160], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.12e+27], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.6e+111], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.19999999999999973e30 or 4.60000000000000004e111 < (*.f64 c i)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 61.7%

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

   if -3.19999999999999973e30 < (*.f64 c i) < -2.29999999999999981e-220 or 1.14999999999999992e-160 < (*.f64 c i) < 1.12e27

   1. Initial program 96.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.6%

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

   4. Taylor expanded in z around inf 52.5%

      \[\leadsto \color{blue}{t \cdot z} \]

   if -2.29999999999999981e-220 < (*.f64 c i) < 1.14999999999999992e-160 or 1.12e27 < (*.f64 c i) < 4.60000000000000004e111

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.4%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-220}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-160}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.12 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \left(c \cdot \frac{i}{a} + \left(t \cdot \frac{z}{a} + x \cdot \frac{y}{a}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))))
   (if (<= t_1 1e+307)
     (+ (* c i) t_1)
     (* a (+ b (+ (* c (/ i a)) (+ (* t (/ z a)) (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= 1e+307) {
		tmp = (c * i) + t_1;
	} else {
		tmp = a * (b + ((c * (i / a)) + ((t * (z / a)) + (x * (y / a)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + ((x * y) + (z * t))
    if (t_1 <= 1d+307) then
        tmp = (c * i) + t_1
    else
        tmp = a * (b + ((c * (i / a)) + ((t * (z / a)) + (x * (y / a)))))
    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 i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= 1e+307) {
		tmp = (c * i) + t_1;
	} else {
		tmp = a * (b + ((c * (i / a)) + ((t * (z / a)) + (x * (y / a)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + ((x * y) + (z * t))
	tmp = 0
	if t_1 <= 1e+307:
		tmp = (c * i) + t_1
	else:
		tmp = a * (b + ((c * (i / a)) + ((t * (z / a)) + (x * (y / a)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (t_1 <= 1e+307)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(a * Float64(b + Float64(Float64(c * Float64(i / a)) + Float64(Float64(t * Float64(z / a)) + Float64(x * Float64(y / a))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + ((x * y) + (z * t));
	tmp = 0.0;
	if (t_1 <= 1e+307)
		tmp = (c * i) + t_1;
	else
		tmp = a * (b + ((c * (i / a)) + ((t * (z / a)) + (x * (y / a)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+307], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a * N[(b + N[(N[(c * N[(i / a), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < 9.99999999999999986e306

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   if 9.99999999999999986e306 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 71.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 71.4%

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

      1. associate-/l* 73.8%

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

      2. associate-/l* 78.6%

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

      3. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b + \left(x \cdot y + z \cdot t\right) \leq 10^{+307}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + \left(x \cdot y + z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \left(c \cdot \frac{i}{a} + \left(t \cdot \frac{z}{a} + x \cdot \frac{y}{a}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2.45 \cdot 10^{+175}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -2.45e+175)
     (+ (* a b) (* c i))
     (if (<= (* c i) -3.4e-91)
       t_1
       (if (<= (* c i) -1e-319)
         (+ (* x y) (* a b))
         (if (<= (* c i) 9.2e+110) (+ (* a b) (* z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -2.45e+175) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -3.4e-91) {
		tmp = t_1;
	} else if ((c * i) <= -1e-319) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 9.2e+110) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((c * i) <= (-2.45d+175)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-3.4d-91)) then
        tmp = t_1
    else if ((c * i) <= (-1d-319)) then
        tmp = (x * y) + (a * b)
    else if ((c * i) <= 9.2d+110) then
        tmp = (a * b) + (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 i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -2.45e+175) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -3.4e-91) {
		tmp = t_1;
	} else if ((c * i) <= -1e-319) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 9.2e+110) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -2.45e+175:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -3.4e-91:
		tmp = t_1
	elif (c * i) <= -1e-319:
		tmp = (x * y) + (a * b)
	elif (c * i) <= 9.2e+110:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -2.45e+175)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -3.4e-91)
		tmp = t_1;
	elseif (Float64(c * i) <= -1e-319)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(c * i) <= 9.2e+110)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2.45e+175)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -3.4e-91)
		tmp = t_1;
	elseif ((c * i) <= -1e-319)
		tmp = (x * y) + (a * b);
	elseif ((c * i) <= 9.2e+110)
		tmp = (a * b) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.45e+175], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.4e-91], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1e-319], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.2e+110], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.45e175

   1. Initial program 92.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.1%

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

   4. Taylor expanded in t around 0 90.5%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -2.45e175 < (*.f64 c i) < -3.40000000000000027e-91 or 9.2000000000000001e110 < (*.f64 c i)

   1. Initial program 93.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.1%

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

   4. Taylor expanded in a around 0 68.1%

      \[\leadsto \color{blue}{c \cdot i + t \cdot z} \]

   if -3.40000000000000027e-91 < (*.f64 c i) < -9.99989e-320

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 100.0%

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

   4. Taylor expanded in t around 0 78.5%

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

   if -9.99989e-320 < (*.f64 c i) < 9.2000000000000001e110

   1. Initial program 93.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 90.5%

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

   4. Taylor expanded in x around 0 68.3%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.45 \cdot 10^{+175}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.6 \cdot 10^{+170}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.75 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.6e+170)
   (+ (* a b) (* c i))
   (if (<= (* c i) -5.2e-91)
     (+ (* c i) (* z t))
     (if (<= (* c i) -1e-319)
       (+ (* x y) (* a b))
       (if (<= (* c i) 3.75e+108) (+ (* a b) (* z t)) (+ (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.6e+170) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -5.2e-91) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -1e-319) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 3.75e+108) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-6.6d+170)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-5.2d-91)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= (-1d-319)) then
        tmp = (x * y) + (a * b)
    else if ((c * i) <= 3.75d+108) then
        tmp = (a * b) + (z * t)
    else
        tmp = (x * y) + (c * i)
    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 i) {
	double tmp;
	if ((c * i) <= -6.6e+170) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -5.2e-91) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -1e-319) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 3.75e+108) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6.6e+170:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -5.2e-91:
		tmp = (c * i) + (z * t)
	elif (c * i) <= -1e-319:
		tmp = (x * y) + (a * b)
	elif (c * i) <= 3.75e+108:
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6.6e+170)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -5.2e-91)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= -1e-319)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(c * i) <= 3.75e+108)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -6.6e+170)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -5.2e-91)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= -1e-319)
		tmp = (x * y) + (a * b);
	elseif ((c * i) <= 3.75e+108)
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -6.6e+170], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5.2e-91], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1e-319], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.75e+108], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -6.60000000000000047e170

   1. Initial program 92.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.1%

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

   4. Taylor expanded in t around 0 90.5%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -6.60000000000000047e170 < (*.f64 c i) < -5.20000000000000028e-91

   1. Initial program 94.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.0%

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

   4. Taylor expanded in a around 0 65.7%

      \[\leadsto \color{blue}{c \cdot i + t \cdot z} \]

   if -5.20000000000000028e-91 < (*.f64 c i) < -9.99989e-320

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 100.0%

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

   4. Taylor expanded in t around 0 78.5%

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

   if -9.99989e-320 < (*.f64 c i) < 3.75000000000000019e108

   1. Initial program 93.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 90.3%

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

   4. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if 3.75000000000000019e108 < (*.f64 c i)

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.8%

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

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \color{blue}{c \cdot i + x \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.6 \cdot 10^{+170}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-319}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.75 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.1% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Java

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

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 26.7%

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

   4. Taylor expanded in z around inf 53.8%

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

4. Final simplification 97.3%

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

Alternative 9: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+108}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -4e+176)
     (+ (* a b) (* c i))
     (if (or (<= (* c i) -2.0) (not (<= (* c i) 5e+108)))
       (+ (* c i) t_1)
       (+ (* a b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -4e+176) {
		tmp = (a * b) + (c * i);
	} else if (((c * i) <= -2.0) || !((c * i) <= 5e+108)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-4d+176)) then
        tmp = (a * b) + (c * i)
    else if (((c * i) <= (-2.0d0)) .or. (.not. ((c * i) <= 5d+108))) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + 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 i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -4e+176) {
		tmp = (a * b) + (c * i);
	} else if (((c * i) <= -2.0) || !((c * i) <= 5e+108)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -4e+176:
		tmp = (a * b) + (c * i)
	elif ((c * i) <= -2.0) or not ((c * i) <= 5e+108):
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -4e+176)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif ((Float64(c * i) <= -2.0) || !(Float64(c * i) <= 5e+108))
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -4e+176)
		tmp = (a * b) + (c * i);
	elseif (((c * i) <= -2.0) || ~(((c * i) <= 5e+108)))
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -4e+176], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.0], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5e+108]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4e176

   1. Initial program 92.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.1%

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

   4. Taylor expanded in t around 0 90.5%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -4e176 < (*.f64 c i) < -2 or 4.99999999999999991e108 < (*.f64 c i)

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 86.0%

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

   if -2 < (*.f64 c i) < 4.99999999999999991e108

   1. Initial program 95.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 92.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+108}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+147}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c + \frac{x \cdot y}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+147)
   (+ (* a b) (* c i))
   (if (<= (* c i) 5e+110)
     (+ (* a b) (+ (* x y) (* z t)))
     (* i (+ c (/ (* x y) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+147) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 5e+110) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = i * (c + ((x * y) / i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1d+147)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 5d+110) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = i * (c + ((x * y) / i))
    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 i) {
	double tmp;
	if ((c * i) <= -1e+147) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 5e+110) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = i * (c + ((x * y) / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+147:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 5e+110:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = i * (c + ((x * y) / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+147)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 5e+110)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(i * Float64(c + Float64(Float64(x * y) / i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1e+147)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 5e+110)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = i * (c + ((x * y) / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1e+147], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+110], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(c + N[(N[(x * y), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.9999999999999998e146

   1. Initial program 90.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.2%

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

   4. Taylor expanded in t around 0 88.8%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -9.9999999999999998e146 < (*.f64 c i) < 4.99999999999999978e110

   1. Initial program 95.8%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 88.6%

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

   if 4.99999999999999978e110 < (*.f64 c i)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.1%

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

   4. Taylor expanded in a around 0 77.8%

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

   5. Taylor expanded in i around inf 79.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+147}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c + \frac{x \cdot y}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+54}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -2e+54)
     (+ (* c i) (+ (* a b) (* z t)))
     (if (<= (* c i) 5e+108) (+ (* a b) t_1) (+ (* c i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2e+54) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 5e+108) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-2d+54)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((c * i) <= 5d+108) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + 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 i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2e+54) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 5e+108) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -2e+54:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (c * i) <= 5e+108:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -2e+54)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(c * i) <= 5e+108)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2e+54)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((c * i) <= 5e+108)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2e+54], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+108], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.0000000000000002e54

   1. Initial program 92.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.9%

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

   if -2.0000000000000002e54 < (*.f64 c i) < 4.99999999999999991e108

   1. Initial program 95.4%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 91.0%

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

   if 4.99999999999999991e108 < (*.f64 c i)

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 86.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+54}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+34}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -5e+34)
     (+ (* c i) (+ (* x y) (* a b)))
     (if (<= (* c i) 5e+108) (+ (* a b) t_1) (+ (* c i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -5e+34) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((c * i) <= 5e+108) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-5d+34)) then
        tmp = (c * i) + ((x * y) + (a * b))
    else if ((c * i) <= 5d+108) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + 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 i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -5e+34) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((c * i) <= 5e+108) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -5e+34:
		tmp = (c * i) + ((x * y) + (a * b))
	elif (c * i) <= 5e+108:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -5e+34)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	elseif (Float64(c * i) <= 5e+108)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -5e+34)
		tmp = (c * i) + ((x * y) + (a * b));
	elseif ((c * i) <= 5e+108)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5e+34], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+108], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4.9999999999999998e34

   1. Initial program 91.5%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.7%

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

   if -4.9999999999999998e34 < (*.f64 c i) < 4.99999999999999991e108

   1. Initial program 95.9%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 92.1%

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

   if 4.99999999999999991e108 < (*.f64 c i)

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 86.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+34}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+34} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.9e+34) (not (<= (* c i) 3.8e+110)))
   (+ (* a b) (* c i))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.9e+34) || !((c * i) <= 3.8e+110)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-2.9d+34)) .or. (.not. ((c * i) <= 3.8d+110))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (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 i) {
	double tmp;
	if (((c * i) <= -2.9e+34) || !((c * i) <= 3.8e+110)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.9e+34) or not ((c * i) <= 3.8e+110):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.9e+34) || !(Float64(c * i) <= 3.8e+110))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -2.9e+34) || ~(((c * i) <= 3.8e+110)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.9e+34], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.8e+110]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.9000000000000001e34 or 3.79999999999999989e110 < (*.f64 c i)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in t around 0 73.6%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -2.9000000000000001e34 < (*.f64 c i) < 3.79999999999999989e110

   1. Initial program 96.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 92.2%

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

   4. Taylor expanded in x around 0 67.6%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+34} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{-57} \lor \neg \left(c \cdot i \leq 5.6 \cdot 10^{+110}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5e-57) (not (<= (* c i) 5.6e+110))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5e-57) || !((c * i) <= 5.6e+110)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-5d-57)) .or. (.not. ((c * i) <= 5.6d+110))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5e-57) || !((c * i) <= 5.6e+110)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -5e-57) or not ((c * i) <= 5.6e+110):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -5e-57) || !(Float64(c * i) <= 5.6e+110))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -5e-57) || ~(((c * i) <= 5.6e+110)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -5e-57], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.6e+110]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5.0000000000000002e-57 or 5.59999999999999973e110 < (*.f64 c i)

   1. Initial program 92.3%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.1%

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

   if -5.0000000000000002e-57 < (*.f64 c i) < 5.59999999999999973e110

   1. Initial program 95.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.1%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{-57} \lor \neg \left(c \cdot i \leq 5.6 \cdot 10^{+110}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+64} \lor \neg \left(t \leq 1.2 \cdot 10^{+197}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -2.2e+64) (not (<= t 1.2e+197))) (* z t) (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -2.2e+64) || !(t <= 1.2e+197)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-2.2d+64)) .or. (.not. (t <= 1.2d+197))) then
        tmp = z * t
    else
        tmp = (a * b) + (c * i)
    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 i) {
	double tmp;
	if ((t <= -2.2e+64) || !(t <= 1.2e+197)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -2.2e+64) or not (t <= 1.2e+197):
		tmp = z * t
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -2.2e+64) || !(t <= 1.2e+197))
		tmp = Float64(z * t);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -2.2e+64) || ~((t <= 1.2e+197)))
		tmp = z * t;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -2.2e+64], N[Not[LessEqual[t, 1.2e+197]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000002e64 or 1.1999999999999999e197 < t

   1. Initial program 88.2%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.6%

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

   4. Taylor expanded in z around inf 58.6%

      \[\leadsto \color{blue}{t \cdot z} \]

   if -2.20000000000000002e64 < t < 1.1999999999999999e197

   1. Initial program 96.6%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.3%

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

   4. Taylor expanded in t around 0 58.8%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+64} \lor \neg \left(t \leq 1.2 \cdot 10^{+197}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(a * b)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
2. Add Preprocessing

3. Taylor expanded in a around inf 26.7%

   \[\leadsto \color{blue}{a \cdot b} \]

4. Final simplification 26.7%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))