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

Percentage Accurate: 95.7% → 98.0%

Time: 13.7s

Alternatives: 14

Speedup: 0.4×

• 42.3% 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: 95.7% 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 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 98.0%

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

   3. +-commutative 98.0%

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

   4. fma-define 98.8%

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

   5. fma-define 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l+ 96.9%

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

   2. fma-define 97.6%

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

3. Simplified 97.6%

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

Alternative 3: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1.07 \cdot 10^{-215}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* a b) -7.8e+61)
     t_2
     (if (<= (* a b) -1.07e-215)
       (+ (* c i) (* x y))
       (if (<= (* a b) 3.5e-307)
         t_1
         (if (<= (* a b) 1.4e-60)
           (+ (* c i) (* z t))
           (if (<= (* a b) 3.4e+78) t_1 t_2)))))))

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 t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -7.8e+61) {
		tmp = t_2;
	} else if ((a * b) <= -1.07e-215) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 3.5e-307) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e-60) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 3.4e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((a * b) <= (-7.8d+61)) then
        tmp = t_2
    else if ((a * b) <= (-1.07d-215)) then
        tmp = (c * i) + (x * y)
    else if ((a * b) <= 3.5d-307) then
        tmp = t_1
    else if ((a * b) <= 1.4d-60) then
        tmp = (c * i) + (z * t)
    else if ((a * b) <= 3.4d+78) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -7.8e+61) {
		tmp = t_2;
	} else if ((a * b) <= -1.07e-215) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 3.5e-307) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e-60) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 3.4e+78) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -7.8e+61:
		tmp = t_2
	elif (a * b) <= -1.07e-215:
		tmp = (c * i) + (x * y)
	elif (a * b) <= 3.5e-307:
		tmp = t_1
	elif (a * b) <= 1.4e-60:
		tmp = (c * i) + (z * t)
	elif (a * b) <= 3.4e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -7.8e+61)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.07e-215)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(a * b) <= 3.5e-307)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.4e-60)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(a * b) <= 3.4e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -7.8e+61)
		tmp = t_2;
	elseif ((a * b) <= -1.07e-215)
		tmp = (c * i) + (x * y);
	elseif ((a * b) <= 3.5e-307)
		tmp = t_1;
	elseif ((a * b) <= 1.4e-60)
		tmp = (c * i) + (z * t);
	elseif ((a * b) <= 3.4e+78)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -7.8e+61], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.07e-215], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.5e-307], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.4e-60], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.4e+78], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -7.79999999999999975e61 or 3.40000000000000007e78 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 84.8%

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

   4. Taylor expanded in t around 0 72.6%

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

   if -7.79999999999999975e61 < (*.f64 a b) < -1.07000000000000003e-215

   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 a around 0 94.9%

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

   4. Taylor expanded in t around 0 72.3%

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

   if -1.07000000000000003e-215 < (*.f64 a b) < 3.5000000000000002e-307 or 1.4000000000000001e-60 < (*.f64 a b) < 3.40000000000000007e78

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0 86.5%

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

   4. Taylor expanded in c around 0 79.0%

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

   if 3.5000000000000002e-307 < (*.f64 a b) < 1.4000000000000001e-60

   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 x around 0 92.0%

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

   4. Taylor expanded in a around 0 89.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+61}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1.07 \cdot 10^{-215}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{+78}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{-45}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1e+64)
   (+ (* a b) (* c i))
   (if (<= (* a b) -5e-215)
     (+ (* c i) (* x y))
     (if (<= (* a b) 0.0)
       (+ (* x y) (* z t))
       (if (<= (* a b) 1e-45)
         (+ (* c i) (* z t))
         (* a (+ b (/ (* x y) a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 0.0) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e-45) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = a * (b + ((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) :: tmp
    if ((a * b) <= (-1d+64)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-5d-215)) then
        tmp = (c * i) + (x * y)
    else if ((a * b) <= 0.0d0) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 1d-45) then
        tmp = (c * i) + (z * t)
    else
        tmp = a * (b + ((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 tmp;
	if ((a * b) <= -1e+64) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -5e-215) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 0.0) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e-45) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = a * (b + ((x * y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1e+64:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -5e-215:
		tmp = (c * i) + (x * y)
	elif (a * b) <= 0.0:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 1e-45:
		tmp = (c * i) + (z * t)
	else:
		tmp = a * (b + ((x * y) / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1e+64)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -5e-215)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 1e-45)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(a * Float64(b + Float64(Float64(x * y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1e+64)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -5e-215)
		tmp = (c * i) + (x * y);
	elseif ((a * b) <= 0.0)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 1e-45)
		tmp = (c * i) + (z * t);
	else
		tmp = a * (b + ((x * y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+64], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-215], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-45], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(b + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -1.00000000000000002e64

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 86.5%

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

   4. Taylor expanded in t around 0 72.4%

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

   if -1.00000000000000002e64 < (*.f64 a b) < -4.99999999999999956e-215

   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 a around 0 94.9%

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

   4. Taylor expanded in t around 0 72.3%

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

   if -4.99999999999999956e-215 < (*.f64 a b) < 0.0

   1. Initial program 93.2%

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

   3. Taylor expanded in a around 0 93.2%

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

   4. Taylor expanded in c around 0 82.2%

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

   if 0.0 < (*.f64 a b) < 9.99999999999999984e-46

   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 x around 0 90.3%

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

   4. Taylor expanded in a around 0 87.9%

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

   if 9.99999999999999984e-46 < (*.f64 a b)

   1. Initial program 97.1%

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

   3. Taylor expanded in c around 0 90.1%

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

   4. Taylor expanded in a around inf 86.3%

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

   5. Taylor expanded in t around 0 75.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-215}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{-45}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.12 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.12e+138)
     (* x y)
     (if (<= (* x y) 8.5e-182)
       t_1
       (if (<= (* x y) 3.1e-52)
         (* z t)
         (if (<= (* x y) 5.8e+100) 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 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.12e+138) {
		tmp = x * y;
	} else if ((x * y) <= 8.5e-182) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e-52) {
		tmp = z * t;
	} else if ((x * y) <= 5.8e+100) {
		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) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-1.12d+138)) then
        tmp = x * y
    else if ((x * y) <= 8.5d-182) then
        tmp = t_1
    else if ((x * y) <= 3.1d-52) then
        tmp = z * t
    else if ((x * y) <= 5.8d+100) 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 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.12e+138) {
		tmp = x * y;
	} else if ((x * y) <= 8.5e-182) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e-52) {
		tmp = z * t;
	} else if ((x * y) <= 5.8e+100) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.12e+138:
		tmp = x * y
	elif (x * y) <= 8.5e-182:
		tmp = t_1
	elif (x * y) <= 3.1e-52:
		tmp = z * t
	elif (x * y) <= 5.8e+100:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.12e+138)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 8.5e-182)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.1e-52)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 5.8e+100)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.12e+138)
		tmp = x * y;
	elseif ((x * y) <= 8.5e-182)
		tmp = t_1;
	elseif ((x * y) <= 3.1e-52)
		tmp = z * t;
	elseif ((x * y) <= 5.8e+100)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.12e+138], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.5e-182], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e-52], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.8e+100], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.12e138 or 5.8000000000000001e100 < (*.f64 x y)

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0 80.6%

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

   4. Taylor expanded in x around inf 62.5%

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

   if -1.12e138 < (*.f64 x y) < 8.5000000000000001e-182 or 3.0999999999999999e-52 < (*.f64 x y) < 5.8000000000000001e100

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 91.5%

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

   4. Taylor expanded in t around 0 64.9%

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

   if 8.5000000000000001e-182 < (*.f64 x y) < 3.0999999999999999e-52

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 59.5%

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

   4. Taylor expanded in t around inf 60.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.12 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+100}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.4× speedup

Math

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

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 (* a (+ b (+ (/ (* z t) 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 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (b + (((z * t) / a) + ((x * y) / a)));
	}
	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 = a * (b + (((z * t) / a) + ((x * y) / a)));
	}
	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 = a * (b + (((z * t) / a) + ((x * y) / a)))
	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(a * Float64(b + Float64(Float64(Float64(z * t) / a) + Float64(Float64(x * y) / a))));
	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 = a * (b + (((z * t) / 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[(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[(a * N[(b + N[(N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 c around 0 37.5%

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

   4. Taylor expanded in a around inf 62.5%

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

4. Final simplification 98.8%

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

Alternative 7: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-300}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* a b) -3.7e+61)
     t_1
     (if (<= (* a b) -5e-300)
       (+ (* c i) (* x y))
       (if (<= (* a b) 3.8e+64) (+ (* c i) (* 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -3.7e+61) {
		tmp = t_1;
	} else if ((a * b) <= -5e-300) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 3.8e+64) {
		tmp = (c * i) + (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 = (a * b) + (c * i)
    if ((a * b) <= (-3.7d+61)) then
        tmp = t_1
    else if ((a * b) <= (-5d-300)) then
        tmp = (c * i) + (x * y)
    else if ((a * b) <= 3.8d+64) then
        tmp = (c * i) + (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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -3.7e+61) {
		tmp = t_1;
	} else if ((a * b) <= -5e-300) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 3.8e+64) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -3.7e+61:
		tmp = t_1
	elif (a * b) <= -5e-300:
		tmp = (c * i) + (x * y)
	elif (a * b) <= 3.8e+64:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -3.7e+61)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e-300)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(a * b) <= 3.8e+64)
		tmp = Float64(Float64(c * i) + 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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -3.7e+61)
		tmp = t_1;
	elseif ((a * b) <= -5e-300)
		tmp = (c * i) + (x * y);
	elseif ((a * b) <= 3.8e+64)
		tmp = (c * i) + (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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.7e+61], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e-300], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+64], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.70000000000000003e61 or 3.8000000000000001e64 < (*.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. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

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

   4. Taylor expanded in t around 0 72.2%

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

   if -3.70000000000000003e61 < (*.f64 a b) < -4.99999999999999996e-300

   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 a around 0 95.5%

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

   4. Taylor expanded in t around 0 72.6%

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

   if -4.99999999999999996e-300 < (*.f64 a b) < 3.8000000000000001e64

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 77.4%

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

   4. Taylor expanded in a around 0 71.4%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.7 \cdot 10^{+61}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-300}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+113} \lor \neg \left(c \cdot i \leq 5.5 \cdot 10^{+34}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.55e+113) (not (<= (* c i) 5.5e+34)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* a b) (+ (* x y) (* 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) <= -1.55e+113) || !((c * i) <= 5.5e+34)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (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) <= (-1.55d+113)) .or. (.not. ((c * i) <= 5.5d+34))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + ((x * y) + (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) <= -1.55e+113) || !((c * i) <= 5.5e+34)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.55e+113) or not ((c * i) <= 5.5e+34):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.55e+113) || !(Float64(c * i) <= 5.5e+34))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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) <= -1.55e+113) || ~(((c * i) <= 5.5e+34)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.55e+113], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.5e+34]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.54999999999999996e113 or 5.4999999999999996e34 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 88.5%

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

   if -1.54999999999999996e113 < (*.f64 c i) < 5.4999999999999996e34

   1. Initial program 98.2%

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

   3. Taylor expanded in c around 0 95.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+113} \lor \neg \left(c \cdot i \leq 5.5 \cdot 10^{+34}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+113} \lor \neg \left(c \cdot i \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* c i) -1.55e+113) (not (<= (* c i) 8e+53)))
     (+ (* 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) <= -1.55e+113) || !((c * i) <= 8e+53)) {
		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) <= (-1.55d+113)) .or. (.not. ((c * i) <= 8d+53))) 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) <= -1.55e+113) || !((c * i) <= 8e+53)) {
		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) <= -1.55e+113) or not ((c * i) <= 8e+53):
		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) <= -1.55e+113) || !(Float64(c * i) <= 8e+53))
		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) <= -1.55e+113) || ~(((c * i) <= 8e+53)))
		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[Or[LessEqual[N[(c * i), $MachinePrecision], -1.55e+113], N[Not[LessEqual[N[(c * i), $MachinePrecision], 8e+53]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.54999999999999996e113 or 7.9999999999999999e53 < (*.f64 c i)

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 85.5%

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

   if -1.54999999999999996e113 < (*.f64 c i) < 7.9999999999999999e53

   1. Initial program 98.2%

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

   3. Taylor expanded in c around 0 95.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+113} \lor \neg \left(c \cdot i \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.95 \cdot 10^{+114} \lor \neg \left(c \cdot i \leq 1.26 \cdot 10^{+54}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.95e+114) (not (<= (* c i) 1.26e+54)))
   (+ (* c i) (* z t))
   (+ (* a b) (+ (* x y) (* 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) <= -3.95e+114) || !((c * i) <= 1.26e+54)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (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) <= (-3.95d+114)) .or. (.not. ((c * i) <= 1.26d+54))) then
        tmp = (c * i) + (z * t)
    else
        tmp = (a * b) + ((x * y) + (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) <= -3.95e+114) || !((c * i) <= 1.26e+54)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.95e+114) or not ((c * i) <= 1.26e+54):
		tmp = (c * i) + (z * t)
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.95e+114) || !(Float64(c * i) <= 1.26e+54))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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) <= -3.95e+114) || ~(((c * i) <= 1.26e+54)))
		tmp = (c * i) + (z * t);
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.95e+114], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.26e+54]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.9500000000000001e114 or 1.25999999999999995e54 < (*.f64 c i)

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in a around 0 78.2%

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

   if -3.9500000000000001e114 < (*.f64 c i) < 1.25999999999999995e54

   1. Initial program 98.2%

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

   3. Taylor expanded in c around 0 95.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.95 \cdot 10^{+114} \lor \neg \left(c \cdot i \leq 1.26 \cdot 10^{+54}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-254}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.6e+109)
   (* a b)
   (if (<= (* a b) -3e-254)
     (* c i)
     (if (<= (* a b) 2.5e+69) (* 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) <= -2.6e+109) {
		tmp = a * b;
	} else if ((a * b) <= -3e-254) {
		tmp = c * i;
	} else if ((a * b) <= 2.5e+69) {
		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) <= (-2.6d+109)) then
        tmp = a * b
    else if ((a * b) <= (-3d-254)) then
        tmp = c * i
    else if ((a * b) <= 2.5d+69) 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) <= -2.6e+109) {
		tmp = a * b;
	} else if ((a * b) <= -3e-254) {
		tmp = c * i;
	} else if ((a * b) <= 2.5e+69) {
		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) <= -2.6e+109:
		tmp = a * b
	elif (a * b) <= -3e-254:
		tmp = c * i
	elif (a * b) <= 2.5e+69:
		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) <= -2.6e+109)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -3e-254)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 2.5e+69)
		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) <= -2.6e+109)
		tmp = a * b;
	elseif ((a * b) <= -3e-254)
		tmp = c * i;
	elseif ((a * b) <= 2.5e+69)
		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], -2.6e+109], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3e-254], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+69], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.5999999999999998e109 or 2.50000000000000018e69 < (*.f64 a b)

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf 62.5%

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

   if -2.5999999999999998e109 < (*.f64 a b) < -3.00000000000000012e-254

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 41.7%

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

   if -3.00000000000000012e-254 < (*.f64 a b) < 2.50000000000000018e69

   1. Initial program 96.9%

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

   3. Taylor expanded in a around 0 91.1%

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

   4. Taylor expanded in t around inf 47.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3 \cdot 10^{-254}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.4 \cdot 10^{+68} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+69}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.4e+68) (not (<= (* a b) 1.5e+69)))
   (+ (* a b) (* c i))
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.4e+68) || !((a * b) <= 1.5e+69)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (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 (((a * b) <= (-1.4d+68)) .or. (.not. ((a * b) <= 1.5d+69))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (c * i) + (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 (((a * b) <= -1.4e+68) || !((a * b) <= 1.5e+69)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.4e+68) or not ((a * b) <= 1.5e+69):
		tmp = (a * b) + (c * i)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.4e+68) || !(Float64(a * b) <= 1.5e+69))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -1.4e+68) || ~(((a * b) <= 1.5e+69)))
		tmp = (a * b) + (c * i);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.4e+68], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.5e+69]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.4e68 or 1.49999999999999992e69 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 84.0%

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

   4. Taylor expanded in t around 0 72.9%

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

   if -1.4e68 < (*.f64 a b) < 1.49999999999999992e69

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 71.7%

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

   4. Taylor expanded in a around 0 66.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.4 \cdot 10^{+68} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+69}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+112} \lor \neg \left(c \cdot i \leq 1.02 \cdot 10^{+49}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.9e+112) (not (<= (* c i) 1.02e+49))) (* 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) <= -1.9e+112) || !((c * i) <= 1.02e+49)) {
		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) <= (-1.9d+112)) .or. (.not. ((c * i) <= 1.02d+49))) 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) <= -1.9e+112) || !((c * i) <= 1.02e+49)) {
		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) <= -1.9e+112) or not ((c * i) <= 1.02e+49):
		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) <= -1.9e+112) || !(Float64(c * i) <= 1.02e+49))
		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) <= -1.9e+112) || ~(((c * i) <= 1.02e+49)))
		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], -1.9e+112], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.02e+49]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.90000000000000004e112 or 1.02e49 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in c around inf 60.2%

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

   if -1.90000000000000004e112 < (*.f64 c i) < 1.02e49

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 36.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+112} \lor \neg \left(c \cdot i \leq 1.02 \cdot 10^{+49}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.7% 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 96.9%

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

3. Taylor expanded in a around inf 28.3%

   \[\leadsto \color{blue}{a \cdot b} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))