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

Percentage Accurate: 95.8% → 98.0%

Time: 7.3s

Alternatives: 13

Speedup: 1.0×

• 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: 95.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l+ 98.0%

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

   2. associate-+l+ 98.0%

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

   3. fma-def 98.0%

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

   4. fma-def 98.4%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. fma-def 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-def 98.4%

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

   5. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{+165}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.28 \cdot 10^{+67} \lor \neg \left(a \cdot b \leq -1.15 \cdot 10^{+21} \lor \neg \left(a \cdot b \leq -4.6 \cdot 10^{-109}\right) \land \left(a \cdot b \leq 1.3 \cdot 10^{-77} \lor \neg \left(a \cdot b \leq 1.7 \cdot 10^{+29}\right) \land a \cdot b \leq 2.8 \cdot 10^{+210}\right)\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.3e+165)
   (+ (* a b) (* x y))
   (if (or (<= (* a b) -1.28e+67)
           (not
            (or (<= (* a b) -1.15e+21)
                (and (not (<= (* a b) -4.6e-109))
                     (or (<= (* a b) 1.3e-77)
                         (and (not (<= (* a b) 1.7e+29))
                              (<= (* a b) 2.8e+210)))))))
     (+ (* a b) (* z t))
     (+ (* c i) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.3e+165) {
		tmp = (a * b) + (x * y);
	} else if (((a * b) <= -1.28e+67) || !(((a * b) <= -1.15e+21) || (!((a * b) <= -4.6e-109) && (((a * b) <= 1.3e-77) || (!((a * b) <= 1.7e+29) && ((a * b) <= 2.8e+210)))))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (c * i) + (x * y);
	}
	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 ((a * b) <= (-2.3d+165)) then
        tmp = (a * b) + (x * y)
    else if (((a * b) <= (-1.28d+67)) .or. (.not. ((a * b) <= (-1.15d+21)) .or. (.not. ((a * b) <= (-4.6d-109))) .and. ((a * b) <= 1.3d-77) .or. (.not. ((a * b) <= 1.7d+29)) .and. ((a * b) <= 2.8d+210))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (c * i) + (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 i) {
	double tmp;
	if ((a * b) <= -2.3e+165) {
		tmp = (a * b) + (x * y);
	} else if (((a * b) <= -1.28e+67) || !(((a * b) <= -1.15e+21) || (!((a * b) <= -4.6e-109) && (((a * b) <= 1.3e-77) || (!((a * b) <= 1.7e+29) && ((a * b) <= 2.8e+210)))))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -2.3e+165:
		tmp = (a * b) + (x * y)
	elif ((a * b) <= -1.28e+67) or not (((a * b) <= -1.15e+21) or (not ((a * b) <= -4.6e-109) and (((a * b) <= 1.3e-77) or (not ((a * b) <= 1.7e+29) and ((a * b) <= 2.8e+210))))):
		tmp = (a * b) + (z * t)
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -2.3e+165)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif ((Float64(a * b) <= -1.28e+67) || !((Float64(a * b) <= -1.15e+21) || (!(Float64(a * b) <= -4.6e-109) && ((Float64(a * b) <= 1.3e-77) || (!(Float64(a * b) <= 1.7e+29) && (Float64(a * b) <= 2.8e+210))))))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(c * i) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -2.3e+165)
		tmp = (a * b) + (x * y);
	elseif (((a * b) <= -1.28e+67) || ~((((a * b) <= -1.15e+21) || (~(((a * b) <= -4.6e-109)) && (((a * b) <= 1.3e-77) || (~(((a * b) <= 1.7e+29)) && ((a * b) <= 2.8e+210)))))))
		tmp = (a * b) + (z * t);
	else
		tmp = (c * i) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.3e+165], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.28e+67], N[Not[Or[LessEqual[N[(a * b), $MachinePrecision], -1.15e+21], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], -4.6e-109]], $MachinePrecision], Or[LessEqual[N[(a * b), $MachinePrecision], 1.3e-77], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.7e+29]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 2.8e+210]]]]]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.30000000000000016e165

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 97.2%

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

   3. Taylor expanded in c around 0 93.0%

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

   if -2.30000000000000016e165 < (*.f64 a b) < -1.28e67 or -1.15e21 < (*.f64 a b) < -4.6000000000000003e-109 or 1.3000000000000001e-77 < (*.f64 a b) < 1.69999999999999991e29 or 2.8000000000000002e210 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in x around 0 87.3%

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

   3. Taylor expanded in c around 0 71.4%

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

   if -1.28e67 < (*.f64 a b) < -1.15e21 or -4.6000000000000003e-109 < (*.f64 a b) < 1.3000000000000001e-77 or 1.69999999999999991e29 < (*.f64 a b) < 2.8000000000000002e210

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.7%

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

   3. Taylor expanded in a around 0 76.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{+165}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.28 \cdot 10^{+67} \lor \neg \left(a \cdot b \leq -1.15 \cdot 10^{+21} \lor \neg \left(a \cdot b \leq -4.6 \cdot 10^{-109}\right) \land \left(a \cdot b \leq 1.3 \cdot 10^{-77} \lor \neg \left(a \cdot b \leq 1.7 \cdot 10^{+29}\right) \land a \cdot b \leq 2.8 \cdot 10^{+210}\right)\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 4: 42.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-290}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.72 \cdot 10^{-212}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.3 \cdot 10^{-106}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+213}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.25e+115)
   (* a b)
   (if (<= (* a b) -2.3e-116)
     (* z t)
     (if (<= (* a b) -2e-316)
       (* c i)
       (if (<= (* a b) 2.3e-290)
         (* x y)
         (if (<= (* a b) 1.72e-212)
           (* c i)
           (if (<= (* a b) 8.3e-106)
             (* x y)
             (if (<= (* a b) 4e+213) (* z t) (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.25e+115) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-116) {
		tmp = z * t;
	} else if ((a * b) <= -2e-316) {
		tmp = c * i;
	} else if ((a * b) <= 2.3e-290) {
		tmp = x * y;
	} else if ((a * b) <= 1.72e-212) {
		tmp = c * i;
	} else if ((a * b) <= 8.3e-106) {
		tmp = x * y;
	} else if ((a * b) <= 4e+213) {
		tmp = z * t;
	} 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 ((a * b) <= (-1.25d+115)) then
        tmp = a * b
    else if ((a * b) <= (-2.3d-116)) then
        tmp = z * t
    else if ((a * b) <= (-2d-316)) then
        tmp = c * i
    else if ((a * b) <= 2.3d-290) then
        tmp = x * y
    else if ((a * b) <= 1.72d-212) then
        tmp = c * i
    else if ((a * b) <= 8.3d-106) then
        tmp = x * y
    else if ((a * b) <= 4d+213) then
        tmp = z * t
    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 ((a * b) <= -1.25e+115) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-116) {
		tmp = z * t;
	} else if ((a * b) <= -2e-316) {
		tmp = c * i;
	} else if ((a * b) <= 2.3e-290) {
		tmp = x * y;
	} else if ((a * b) <= 1.72e-212) {
		tmp = c * i;
	} else if ((a * b) <= 8.3e-106) {
		tmp = x * y;
	} else if ((a * b) <= 4e+213) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.25e+115:
		tmp = a * b
	elif (a * b) <= -2.3e-116:
		tmp = z * t
	elif (a * b) <= -2e-316:
		tmp = c * i
	elif (a * b) <= 2.3e-290:
		tmp = x * y
	elif (a * b) <= 1.72e-212:
		tmp = c * i
	elif (a * b) <= 8.3e-106:
		tmp = x * y
	elif (a * b) <= 4e+213:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.25e+115)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.3e-116)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -2e-316)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 2.3e-290)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.72e-212)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 8.3e-106)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 4e+213)
		tmp = Float64(z * t);
	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 ((a * b) <= -1.25e+115)
		tmp = a * b;
	elseif ((a * b) <= -2.3e-116)
		tmp = z * t;
	elseif ((a * b) <= -2e-316)
		tmp = c * i;
	elseif ((a * b) <= 2.3e-290)
		tmp = x * y;
	elseif ((a * b) <= 1.72e-212)
		tmp = c * i;
	elseif ((a * b) <= 8.3e-106)
		tmp = x * y;
	elseif ((a * b) <= 4e+213)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.25e+115], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.3e-116], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2e-316], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.3e-290], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.72e-212], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.3e-106], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e+213], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.25000000000000002e115 or 3.99999999999999994e213 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in a around inf 73.5%

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

   if -1.25000000000000002e115 < (*.f64 a b) < -2.30000000000000002e-116 or 8.30000000000000047e-106 < (*.f64 a b) < 3.99999999999999994e213

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 40.5%

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

   if -2.30000000000000002e-116 < (*.f64 a b) < -2.000000017e-316 or 2.3000000000000001e-290 < (*.f64 a b) < 1.7200000000000001e-212

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 56.1%

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

   if -2.000000017e-316 < (*.f64 a b) < 2.3000000000000001e-290 or 1.7200000000000001e-212 < (*.f64 a b) < 8.30000000000000047e-106

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-290}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.72 \cdot 10^{-212}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.3 \cdot 10^{-106}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+213}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.06 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.05 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -1.06e+185)
     (* c i)
     (if (<= (* c i) 3.05e-146)
       t_1
       (if (<= (* c i) 6.6e-94)
         (* x y)
         (if (<= (* c i) 2.8e+219) t_1 (* c i)))))))

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 tmp;
	if ((c * i) <= -1.06e+185) {
		tmp = c * i;
	} else if ((c * i) <= 3.05e-146) {
		tmp = t_1;
	} else if ((c * i) <= 6.6e-94) {
		tmp = x * y;
	} else if ((c * i) <= 2.8e+219) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-1.06d+185)) then
        tmp = c * i
    else if ((c * i) <= 3.05d-146) then
        tmp = t_1
    else if ((c * i) <= 6.6d-94) then
        tmp = x * y
    else if ((c * i) <= 2.8d+219) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.06e+185) {
		tmp = c * i;
	} else if ((c * i) <= 3.05e-146) {
		tmp = t_1;
	} else if ((c * i) <= 6.6e-94) {
		tmp = x * y;
	} else if ((c * i) <= 2.8e+219) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -1.06e+185:
		tmp = c * i
	elif (c * i) <= 3.05e-146:
		tmp = t_1
	elif (c * i) <= 6.6e-94:
		tmp = x * y
	elif (c * i) <= 2.8e+219:
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.06e+185)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3.05e-146)
		tmp = t_1;
	elseif (Float64(c * i) <= 6.6e-94)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2.8e+219)
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.06e+185)
		tmp = c * i;
	elseif ((c * i) <= 3.05e-146)
		tmp = t_1;
	elseif ((c * i) <= 6.6e-94)
		tmp = x * y;
	elseif ((c * i) <= 2.8e+219)
		tmp = t_1;
	else
		tmp = c * i;
	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]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.06e+185], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.05e-146], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 6.6e-94], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.8e+219], t$95$1, N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.06000000000000004e185 or 2.80000000000000015e219 < (*.f64 c i)

   1. Initial program 95.1%

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

   2. Taylor expanded in c around inf 76.3%

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

   if -1.06000000000000004e185 < (*.f64 c i) < 3.0499999999999998e-146 or 6.6000000000000003e-94 < (*.f64 c i) < 2.80000000000000015e219

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 72.0%

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

   3. Taylor expanded in c around 0 58.4%

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

   if 3.0499999999999998e-146 < (*.f64 c i) < 6.6000000000000003e-94

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.06 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.05 \cdot 10^{-146}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 6: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + a \cdot b\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \leq -0.55:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* a b))) (t_2 (+ (* a b) (* z t))))
   (if (<= x -1.4e+47)
     (+ (* a b) (* x y))
     (if (<= x -0.55)
       t_1
       (if (<= x -5e-62)
         t_2
         (if (<= x -3.05e-239)
           t_1
           (if (<= x -2.9e-300) t_2 (if (<= x 1.1e-18) t_1 (* x y)))))))))

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);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if (x <= -1.4e+47) {
		tmp = (a * b) + (x * y);
	} else if (x <= -0.55) {
		tmp = t_1;
	} else if (x <= -5e-62) {
		tmp = t_2;
	} else if (x <= -3.05e-239) {
		tmp = t_1;
	} else if (x <= -2.9e-300) {
		tmp = t_2;
	} else if (x <= 1.1e-18) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	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 = (c * i) + (a * b)
    t_2 = (a * b) + (z * t)
    if (x <= (-1.4d+47)) then
        tmp = (a * b) + (x * y)
    else if (x <= (-0.55d0)) then
        tmp = t_1
    else if (x <= (-5d-62)) then
        tmp = t_2
    else if (x <= (-3.05d-239)) then
        tmp = t_1
    else if (x <= (-2.9d-300)) then
        tmp = t_2
    else if (x <= 1.1d-18) 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 i) {
	double t_1 = (c * i) + (a * b);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if (x <= -1.4e+47) {
		tmp = (a * b) + (x * y);
	} else if (x <= -0.55) {
		tmp = t_1;
	} else if (x <= -5e-62) {
		tmp = t_2;
	} else if (x <= -3.05e-239) {
		tmp = t_1;
	} else if (x <= -2.9e-300) {
		tmp = t_2;
	} else if (x <= 1.1e-18) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (a * b)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if x <= -1.4e+47:
		tmp = (a * b) + (x * y)
	elif x <= -0.55:
		tmp = t_1
	elif x <= -5e-62:
		tmp = t_2
	elif x <= -3.05e-239:
		tmp = t_1
	elif x <= -2.9e-300:
		tmp = t_2
	elif x <= 1.1e-18:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(a * b))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (x <= -1.4e+47)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (x <= -0.55)
		tmp = t_1;
	elseif (x <= -5e-62)
		tmp = t_2;
	elseif (x <= -3.05e-239)
		tmp = t_1;
	elseif (x <= -2.9e-300)
		tmp = t_2;
	elseif (x <= 1.1e-18)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (a * b);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if (x <= -1.4e+47)
		tmp = (a * b) + (x * y);
	elseif (x <= -0.55)
		tmp = t_1;
	elseif (x <= -5e-62)
		tmp = t_2;
	elseif (x <= -3.05e-239)
		tmp = t_1;
	elseif (x <= -2.9e-300)
		tmp = t_2;
	elseif (x <= 1.1e-18)
		tmp = t_1;
	else
		tmp = x * y;
	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[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+47], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -0.55], t$95$1, If[LessEqual[x, -5e-62], t$95$2, If[LessEqual[x, -3.05e-239], t$95$1, If[LessEqual[x, -2.9e-300], t$95$2, If[LessEqual[x, 1.1e-18], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.39999999999999994e47

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 82.9%

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

   3. Taylor expanded in c around 0 68.7%

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

   if -1.39999999999999994e47 < x < -0.55000000000000004 or -5.0000000000000002e-62 < x < -3.05e-239 or -2.89999999999999992e-300 < x < 1.0999999999999999e-18

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in t around 0 65.0%

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

   if -0.55000000000000004 < x < -5.0000000000000002e-62 or -3.05e-239 < x < -2.89999999999999992e-300

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.6%

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

   3. Taylor expanded in c around 0 70.4%

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

   if 1.0999999999999999e-18 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 48.2%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \leq -0.55:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-239}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-300}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 42.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.3 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-76}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.8e+115)
   (* a b)
   (if (<= (* a b) -4.3e-116)
     (* z t)
     (if (<= (* a b) 1.25e-76)
       (* c i)
       (if (<= (* a b) 4.1e+213) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.8e+115) {
		tmp = a * b;
	} else if ((a * b) <= -4.3e-116) {
		tmp = z * t;
	} else if ((a * b) <= 1.25e-76) {
		tmp = c * i;
	} else if ((a * b) <= 4.1e+213) {
		tmp = z * t;
	} 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 ((a * b) <= (-1.8d+115)) then
        tmp = a * b
    else if ((a * b) <= (-4.3d-116)) then
        tmp = z * t
    else if ((a * b) <= 1.25d-76) then
        tmp = c * i
    else if ((a * b) <= 4.1d+213) then
        tmp = z * t
    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 ((a * b) <= -1.8e+115) {
		tmp = a * b;
	} else if ((a * b) <= -4.3e-116) {
		tmp = z * t;
	} else if ((a * b) <= 1.25e-76) {
		tmp = c * i;
	} else if ((a * b) <= 4.1e+213) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.8e+115:
		tmp = a * b
	elif (a * b) <= -4.3e-116:
		tmp = z * t
	elif (a * b) <= 1.25e-76:
		tmp = c * i
	elif (a * b) <= 4.1e+213:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.8e+115)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -4.3e-116)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.25e-76)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 4.1e+213)
		tmp = Float64(z * t);
	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 ((a * b) <= -1.8e+115)
		tmp = a * b;
	elseif ((a * b) <= -4.3e-116)
		tmp = z * t;
	elseif ((a * b) <= 1.25e-76)
		tmp = c * i;
	elseif ((a * b) <= 4.1e+213)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.8e+115], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.3e-116], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.25e-76], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.1e+213], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.8e115 or 4.0999999999999997e213 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in a around inf 73.5%

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

   if -1.8e115 < (*.f64 a b) < -4.2999999999999997e-116 or 1.2499999999999999e-76 < (*.f64 a b) < 4.0999999999999997e213

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 41.5%

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

   if -4.2999999999999997e-116 < (*.f64 a b) < 1.2499999999999999e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 40.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.3 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-76}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+154} \lor \neg \left(x \leq 1.1 \cdot 10^{-18}\right):\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.1e+154) (not (<= x 1.1e-18)))
   (+ (* c i) (* x y))
   (+ (* 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 ((x <= -3.1e+154) || !(x <= 1.1e-18)) {
		tmp = (c * i) + (x * y);
	} else {
		tmp = (c * i) + ((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 ((x <= (-3.1d+154)) .or. (.not. (x <= 1.1d-18))) then
        tmp = (c * i) + (x * y)
    else
        tmp = (c * i) + ((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 ((x <= -3.1e+154) || !(x <= 1.1e-18)) {
		tmp = (c * i) + (x * y);
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.1e+154) or not (x <= 1.1e-18):
		tmp = (c * i) + (x * y)
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.1e+154) || !(x <= 1.1e-18))
		tmp = Float64(Float64(c * i) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + 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 ((x <= -3.1e+154) || ~((x <= 1.1e-18)))
		tmp = (c * i) + (x * y);
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.1e+154], N[Not[LessEqual[x, 1.1e-18]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1000000000000001e154 or 1.0999999999999999e-18 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 77.4%

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

   3. Taylor expanded in a around 0 63.0%

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

   if -3.1000000000000001e154 < x < 1.0999999999999999e-18

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 84.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+154} \lor \neg \left(x \leq 1.1 \cdot 10^{-18}\right):\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 9: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-147} \lor \neg \left(t \leq 2.45 \cdot 10^{+135}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -6.6e-147) (not (<= t 2.45e+135)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -6.6e-147) || !(t <= 2.45e+135)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	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 <= (-6.6d-147)) .or. (.not. (t <= 2.45d+135))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (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 i) {
	double tmp;
	if ((t <= -6.6e-147) || !(t <= 2.45e+135)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -6.6e-147) or not (t <= 2.45e+135):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -6.6e-147) || !(t <= 2.45e+135))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -6.6e-147) || ~((t <= 2.45e+135)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -6.6e-147], N[Not[LessEqual[t, 2.45e+135]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999975e-147 or 2.4500000000000001e135 < t

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 80.3%

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

   if -6.59999999999999975e-147 < t < 2.4500000000000001e135

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 90.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-147} \lor \neg \left(t \leq 2.45 \cdot 10^{+135}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 10: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (c * i) + ((a * b) + ((z * t) + (x * y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 11: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-117} \lor \neg \left(y \leq 4.7 \cdot 10^{+55}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.08e-117) (not (<= y 4.7e+55)))
   (+ (* a b) (* x y))
   (+ (* 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 ((y <= -1.08e-117) || !(y <= 4.7e+55)) {
		tmp = (a * b) + (x * y);
	} 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 ((y <= (-1.08d-117)) .or. (.not. (y <= 4.7d+55))) then
        tmp = (a * b) + (x * y)
    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 ((y <= -1.08e-117) || !(y <= 4.7e+55)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.08e-117) or not (y <= 4.7e+55):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.08e-117) || !(y <= 4.7e+55))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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 ((y <= -1.08e-117) || ~((y <= 4.7e+55)))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.08e-117], N[Not[LessEqual[y, 4.7e+55]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.07999999999999998e-117 or 4.7000000000000001e55 < y

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 83.1%

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

   3. Taylor expanded in c around 0 58.1%

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

   if -1.07999999999999998e-117 < y < 4.7000000000000001e55

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 88.6%

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

   3. Taylor expanded in c around 0 61.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-117} \lor \neg \left(y \leq 4.7 \cdot 10^{+55}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 12: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+235}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.8e+66) (* a b) (if (<= (* a b) 5.4e+235) (* 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 ((a * b) <= -5.8e+66) {
		tmp = a * b;
	} else if ((a * b) <= 5.4e+235) {
		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 ((a * b) <= (-5.8d+66)) then
        tmp = a * b
    else if ((a * b) <= 5.4d+235) 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 ((a * b) <= -5.8e+66) {
		tmp = a * b;
	} else if ((a * b) <= 5.4e+235) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5.8e+66:
		tmp = a * b
	elif (a * b) <= 5.4e+235:
		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(a * b) <= -5.8e+66)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 5.4e+235)
		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 ((a * b) <= -5.8e+66)
		tmp = a * b;
	elseif ((a * b) <= 5.4e+235)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5.8e+66], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.4e+235], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.79999999999999972e66 or 5.3999999999999995e235 < (*.f64 a b)

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf 66.9%

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

   if -5.79999999999999972e66 < (*.f64 a b) < 5.3999999999999995e235

   1. Initial program 99.4%

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

   2. Taylor expanded in c around inf 34.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+235}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 28.3% 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 98.0%

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

2. Taylor expanded in a around inf 24.1%

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

3. Final simplification 24.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023257 
(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)))