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

Percentage Accurate: 96.1% → 97.3%

Time: 9.4s

Alternatives: 13

Speedup: 0.4×

• 40.1% 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: 96.1% 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: 97.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $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 a around inf 50.2%

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

4. Final simplification 96.1%

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

Alternative 2: 98.2% 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 92.2%

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

   1. +-commutative 92.2%

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

   2. fma-define 93.3%

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

   3. associate-+l+ 93.3%

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

   4. fma-define 94.1%

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

   5. fma-define 96.1%

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

3. Simplified 96.1%

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

Alternative 3: 98.3% 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 92.2%

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

   1. +-commutative 92.2%

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

   2. fma-define 93.3%

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

   3. +-commutative 93.3%

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

   4. fma-define 94.9%

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

   5. fma-define 95.3%

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

3. Simplified 95.3%

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

Alternative 4: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.5 \cdot 10^{+193}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.4 \cdot 10^{-48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-315}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.1 \cdot 10^{-289}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9 \cdot 10^{-179}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-61}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.5e+193)
   (* c i)
   (if (<= (* c i) -1.4e-48)
     (* x y)
     (if (<= (* c i) -5e-315)
       (* a b)
       (if (<= (* c i) 1.1e-289)
         (* x y)
         (if (<= (* c i) 9e-179)
           (* z t)
           (if (<= (* c i) 2.1e-155)
             (* x y)
             (if (<= (* c i) 6.2e-61)
               (* a b)
               (if (<= (* c i) 5e+90) (* x y) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.5e+193) {
		tmp = c * i;
	} else if ((c * i) <= -1.4e-48) {
		tmp = x * y;
	} else if ((c * i) <= -5e-315) {
		tmp = a * b;
	} else if ((c * i) <= 1.1e-289) {
		tmp = x * y;
	} else if ((c * i) <= 9e-179) {
		tmp = z * t;
	} else if ((c * i) <= 2.1e-155) {
		tmp = x * y;
	} else if ((c * i) <= 6.2e-61) {
		tmp = a * b;
	} else if ((c * i) <= 5e+90) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.5d+193)) then
        tmp = c * i
    else if ((c * i) <= (-1.4d-48)) then
        tmp = x * y
    else if ((c * i) <= (-5d-315)) then
        tmp = a * b
    else if ((c * i) <= 1.1d-289) then
        tmp = x * y
    else if ((c * i) <= 9d-179) then
        tmp = z * t
    else if ((c * i) <= 2.1d-155) then
        tmp = x * y
    else if ((c * i) <= 6.2d-61) then
        tmp = a * b
    else if ((c * i) <= 5d+90) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.5e+193) {
		tmp = c * i;
	} else if ((c * i) <= -1.4e-48) {
		tmp = x * y;
	} else if ((c * i) <= -5e-315) {
		tmp = a * b;
	} else if ((c * i) <= 1.1e-289) {
		tmp = x * y;
	} else if ((c * i) <= 9e-179) {
		tmp = z * t;
	} else if ((c * i) <= 2.1e-155) {
		tmp = x * y;
	} else if ((c * i) <= 6.2e-61) {
		tmp = a * b;
	} else if ((c * i) <= 5e+90) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.5e+193:
		tmp = c * i
	elif (c * i) <= -1.4e-48:
		tmp = x * y
	elif (c * i) <= -5e-315:
		tmp = a * b
	elif (c * i) <= 1.1e-289:
		tmp = x * y
	elif (c * i) <= 9e-179:
		tmp = z * t
	elif (c * i) <= 2.1e-155:
		tmp = x * y
	elif (c * i) <= 6.2e-61:
		tmp = a * b
	elif (c * i) <= 5e+90:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.5e+193)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.4e-48)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -5e-315)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1.1e-289)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 9e-179)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.1e-155)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 6.2e-61)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 5e+90)
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.5e+193)
		tmp = c * i;
	elseif ((c * i) <= -1.4e-48)
		tmp = x * y;
	elseif ((c * i) <= -5e-315)
		tmp = a * b;
	elseif ((c * i) <= 1.1e-289)
		tmp = x * y;
	elseif ((c * i) <= 9e-179)
		tmp = z * t;
	elseif ((c * i) <= 2.1e-155)
		tmp = x * y;
	elseif ((c * i) <= 6.2e-61)
		tmp = a * b;
	elseif ((c * i) <= 5e+90)
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.5e+193], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.4e-48], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5e-315], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.1e-289], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9e-179], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.1e-155], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-61], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+90], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.5e193 or 5.0000000000000004e90 < (*.f64 c i)

   1. Initial program 89.2%

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

   3. Taylor expanded in c around inf 75.0%

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

   if -1.5e193 < (*.f64 c i) < -1.40000000000000002e-48 or -5.0000000023e-315 < (*.f64 c i) < 1.1e-289 or 8.99999999999999984e-179 < (*.f64 c i) < 2.1000000000000002e-155 or 6.1999999999999999e-61 < (*.f64 c i) < 5.0000000000000004e90

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 71.1%

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

   4. Taylor expanded in x around inf 47.5%

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

   if -1.40000000000000002e-48 < (*.f64 c i) < -5.0000000023e-315 or 2.1000000000000002e-155 < (*.f64 c i) < 6.1999999999999999e-61

   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 z around 0 69.9%

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

   4. Taylor expanded in a around inf 48.8%

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

   if 1.1e-289 < (*.f64 c i) < 8.99999999999999984e-179

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 54.9%

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

   4. Taylor expanded in z around inf 54.9%

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

   5. Taylor expanded in t around inf 54.9%

      \[\leadsto z \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+184}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot i \leq -3.2 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -8.5e+184)
     t_3
     (if (<= (* c i) -3.2e-58)
       t_1
       (if (<= (* c i) 1.15e-180)
         t_2
         (if (<= (* c i) 9.5e-56)
           t_1
           (if (<= (* c i) 1.75e+19)
             t_2
             (if (<= (* c i) 6.5e+94) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+184) {
		tmp = t_3;
	} else if ((c * i) <= -3.2e-58) {
		tmp = t_1;
	} else if ((c * i) <= 1.15e-180) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-56) {
		tmp = t_1;
	} else if ((c * i) <= 1.75e+19) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (a * b) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-8.5d+184)) then
        tmp = t_3
    else if ((c * i) <= (-3.2d-58)) then
        tmp = t_1
    else if ((c * i) <= 1.15d-180) then
        tmp = t_2
    else if ((c * i) <= 9.5d-56) then
        tmp = t_1
    else if ((c * i) <= 1.75d+19) then
        tmp = t_2
    else if ((c * i) <= 6.5d+94) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+184) {
		tmp = t_3;
	} else if ((c * i) <= -3.2e-58) {
		tmp = t_1;
	} else if ((c * i) <= 1.15e-180) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-56) {
		tmp = t_1;
	} else if ((c * i) <= 1.75e+19) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -8.5e+184:
		tmp = t_3
	elif (c * i) <= -3.2e-58:
		tmp = t_1
	elif (c * i) <= 1.15e-180:
		tmp = t_2
	elif (c * i) <= 9.5e-56:
		tmp = t_1
	elif (c * i) <= 1.75e+19:
		tmp = t_2
	elif (c * i) <= 6.5e+94:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -8.5e+184)
		tmp = t_3;
	elseif (Float64(c * i) <= -3.2e-58)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.15e-180)
		tmp = t_2;
	elseif (Float64(c * i) <= 9.5e-56)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.75e+19)
		tmp = t_2;
	elseif (Float64(c * i) <= 6.5e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (a * b) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -8.5e+184)
		tmp = t_3;
	elseif ((c * i) <= -3.2e-58)
		tmp = t_1;
	elseif ((c * i) <= 1.15e-180)
		tmp = t_2;
	elseif ((c * i) <= 9.5e-56)
		tmp = t_1;
	elseif ((c * i) <= 1.75e+19)
		tmp = t_2;
	elseif ((c * i) <= 6.5e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.5e+184], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -3.2e-58], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.15e-180], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 9.5e-56], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.75e+19], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6.5e+94], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.50000000000000043e184 or 6.49999999999999976e94 < (*.f64 c i)

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf 87.4%

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

   if -8.50000000000000043e184 < (*.f64 c i) < -3.2000000000000001e-58 or 1.14999999999999998e-180 < (*.f64 c i) < 9.4999999999999991e-56 or 1.75e19 < (*.f64 c i) < 6.49999999999999976e94

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 81.7%

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

   4. Taylor expanded in c around 0 71.2%

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

   if -3.2000000000000001e-58 < (*.f64 c i) < 1.14999999999999998e-180 or 9.4999999999999991e-56 < (*.f64 c i) < 1.75e19

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 70.9%

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

   4. Taylor expanded in c around 0 69.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+184}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-180}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{+19}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+149}\right) \land \left(x \cdot y \leq 5.3 \cdot 10^{+265} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+281}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.7e+177)
         (and (not (<= (* x y) 1.25e+149))
              (or (<= (* x y) 5.3e+265) (not (<= (* x y) 1.9e+281)))))
   (* x y)
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.7e+177) || (!((x * y) <= 1.25e+149) && (((x * y) <= 5.3e+265) || !((x * y) <= 1.9e+281)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2.7d+177)) .or. (.not. ((x * y) <= 1.25d+149)) .and. ((x * y) <= 5.3d+265) .or. (.not. ((x * y) <= 1.9d+281))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.7e+177) || (!((x * y) <= 1.25e+149) && (((x * y) <= 5.3e+265) || !((x * y) <= 1.9e+281)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.7e+177) or (not ((x * y) <= 1.25e+149) and (((x * y) <= 5.3e+265) or not ((x * y) <= 1.9e+281))):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.7e+177) || (!(Float64(x * y) <= 1.25e+149) && ((Float64(x * y) <= 5.3e+265) || !(Float64(x * y) <= 1.9e+281))))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2.7e+177) || (~(((x * y) <= 1.25e+149)) && (((x * y) <= 5.3e+265) || ~(((x * y) <= 1.9e+281)))))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.7e+177], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.25e+149]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 5.3e+265], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.9e+281]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.69999999999999991e177 or 1.24999999999999998e149 < (*.f64 x y) < 5.30000000000000033e265 or 1.90000000000000006e281 < (*.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in x around inf 74.1%

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

   if -2.69999999999999991e177 < (*.f64 x y) < 1.24999999999999998e149 or 5.30000000000000033e265 < (*.f64 x y) < 1.90000000000000006e281

   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 a around inf 67.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+149}\right) \land \left(x \cdot y \leq 5.3 \cdot 10^{+265} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+281}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+24} \lor \neg \left(c \cdot i \leq 17500000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.9e+134)
     t_1
     (if (<= (* c i) -8.8e+77)
       (* x y)
       (if (or (<= (* c i) -1.3e+24) (not (<= (* c i) 17500000000.0)))
         t_1
         (+ (* a b) (* z t)))))))

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 ((c * i) <= -1.9e+134) {
		tmp = t_1;
	} else if ((c * i) <= -8.8e+77) {
		tmp = x * y;
	} else if (((c * i) <= -1.3e+24) || !((c * i) <= 17500000000.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((c * i) <= (-1.9d+134)) then
        tmp = t_1
    else if ((c * i) <= (-8.8d+77)) then
        tmp = x * y
    else if (((c * i) <= (-1.3d+24)) .or. (.not. ((c * i) <= 17500000000.0d0))) then
        tmp = t_1
    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 t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.9e+134) {
		tmp = t_1;
	} else if ((c * i) <= -8.8e+77) {
		tmp = x * y;
	} else if (((c * i) <= -1.3e+24) || !((c * i) <= 17500000000.0)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.9e+134:
		tmp = t_1
	elif (c * i) <= -8.8e+77:
		tmp = x * y
	elif ((c * i) <= -1.3e+24) or not ((c * i) <= 17500000000.0):
		tmp = t_1
	else:
		tmp = (a * b) + (z * t)
	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(c * i) <= -1.9e+134)
		tmp = t_1;
	elseif (Float64(c * i) <= -8.8e+77)
		tmp = Float64(x * y);
	elseif ((Float64(c * i) <= -1.3e+24) || !(Float64(c * i) <= 17500000000.0))
		tmp = t_1;
	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)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.9e+134)
		tmp = t_1;
	elseif ((c * i) <= -8.8e+77)
		tmp = x * y;
	elseif (((c * i) <= -1.3e+24) || ~(((c * i) <= 17500000000.0)))
		tmp = t_1;
	else
		tmp = (a * b) + (z * t);
	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[(c * i), $MachinePrecision], -1.9e+134], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -8.8e+77], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.3e+24], N[Not[LessEqual[N[(c * i), $MachinePrecision], 17500000000.0]], $MachinePrecision]], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.89999999999999999e134 or -8.8000000000000002e77 < (*.f64 c i) < -1.2999999999999999e24 or 1.75e10 < (*.f64 c i)

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 75.7%

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

   if -1.89999999999999999e134 < (*.f64 c i) < -8.8000000000000002e77

   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 z around 0 88.9%

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

   4. Taylor expanded in x around inf 78.1%

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

   if -1.2999999999999999e24 < (*.f64 c i) < 1.75e10

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 69.3%

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

   4. Taylor expanded in c around 0 66.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+24} \lor \neg \left(c \cdot i \leq 17500000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9 \cdot 10^{+184}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.06 \cdot 10^{-60}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -9e+184)
   (* c i)
   (if (<= (* c i) -4e-49)
     (* x y)
     (if (<= (* c i) 1.06e-60)
       (* a b)
       (if (<= (* c i) 4.5e+92) (* x y) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9e+184) {
		tmp = c * i;
	} else if ((c * i) <= -4e-49) {
		tmp = x * y;
	} else if ((c * i) <= 1.06e-60) {
		tmp = a * b;
	} else if ((c * i) <= 4.5e+92) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-9d+184)) then
        tmp = c * i
    else if ((c * i) <= (-4d-49)) then
        tmp = x * y
    else if ((c * i) <= 1.06d-60) then
        tmp = a * b
    else if ((c * i) <= 4.5d+92) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9e+184) {
		tmp = c * i;
	} else if ((c * i) <= -4e-49) {
		tmp = x * y;
	} else if ((c * i) <= 1.06e-60) {
		tmp = a * b;
	} else if ((c * i) <= 4.5e+92) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -9e+184:
		tmp = c * i
	elif (c * i) <= -4e-49:
		tmp = x * y
	elif (c * i) <= 1.06e-60:
		tmp = a * b
	elif (c * i) <= 4.5e+92:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -9e+184)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -4e-49)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1.06e-60)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.5e+92)
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -9e+184)
		tmp = c * i;
	elseif ((c * i) <= -4e-49)
		tmp = x * y;
	elseif ((c * i) <= 1.06e-60)
		tmp = a * b;
	elseif ((c * i) <= 4.5e+92)
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -9e+184], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4e-49], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.06e-60], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.5e+92], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.00000000000000072e184 or 4.4999999999999999e92 < (*.f64 c i)

   1. Initial program 89.2%

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

   3. Taylor expanded in c around inf 75.0%

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

   if -9.00000000000000072e184 < (*.f64 c i) < -3.99999999999999975e-49 or 1.06e-60 < (*.f64 c i) < 4.4999999999999999e92

   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 z around 0 71.8%

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

   4. Taylor expanded in x around inf 46.7%

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

   if -3.99999999999999975e-49 < (*.f64 c i) < 1.06e-60

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 65.3%

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

   4. Taylor expanded in a around inf 38.0%

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

Alternative 9: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+99} \lor \neg \left(z \cdot t \leq 10^{+105}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -4e+99) (not (<= (* z t) 1e+105)))
   (+ (* 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 (((z * t) <= -4e+99) || !((z * t) <= 1e+105)) {
		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 (((z * t) <= (-4d+99)) .or. (.not. ((z * t) <= 1d+105))) 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 (((z * t) <= -4e+99) || !((z * t) <= 1e+105)) {
		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 ((z * t) <= -4e+99) or not ((z * t) <= 1e+105):
		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 ((Float64(z * t) <= -4e+99) || !(Float64(z * t) <= 1e+105))
		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 (((z * t) <= -4e+99) || ~(((z * t) <= 1e+105)))
		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[N[(z * t), $MachinePrecision], -4e+99], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+105]], $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 (*.f64 z t) < -3.9999999999999999e99 or 9.9999999999999994e104 < (*.f64 z t)

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0 84.8%

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

   if -3.9999999999999999e99 < (*.f64 z t) < 9.9999999999999994e104

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 91.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+99} \lor \neg \left(z \cdot t \leq 10^{+105}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -8.2e+176) (not (<= (* x y) 4.2e+121)))
   (+ (* x y) (* c i))
   (+ (* 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 * y) <= -8.2e+176) || !((x * y) <= 4.2e+121)) {
		tmp = (x * y) + (c * i);
	} 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 * y) <= (-8.2d+176)) .or. (.not. ((x * y) <= 4.2d+121))) then
        tmp = (x * y) + (c * i)
    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 * y) <= -8.2e+176) || !((x * y) <= 4.2e+121)) {
		tmp = (x * y) + (c * i);
	} 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 * y) <= -8.2e+176) or not ((x * y) <= 4.2e+121):
		tmp = (x * y) + (c * i)
	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 ((Float64(x * y) <= -8.2e+176) || !(Float64(x * y) <= 4.2e+121))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	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 * y) <= -8.2e+176) || ~(((x * y) <= 4.2e+121)))
		tmp = (x * y) + (c * i);
	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[N[(x * y), $MachinePrecision], -8.2e+176], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.2e+121]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $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 (*.f64 x y) < -8.1999999999999998e176 or 4.2000000000000003e121 < (*.f64 x y)

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -8.1999999999999998e176 < (*.f64 x y) < 4.2000000000000003e121

   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 x around 0 89.3%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+176} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+121}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;y \leq -8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-84}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+60}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= y -8e-77)
     t_1
     (if (<= y 7e-84)
       (+ (* a b) (* c i))
       (if (<= y 9.8e+60) (+ (* a b) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if (y <= -8e-77) {
		tmp = t_1;
	} else if (y <= 7e-84) {
		tmp = (a * b) + (c * i);
	} else if (y <= 9.8e+60) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (c * i)
    if (y <= (-8d-77)) then
        tmp = t_1
    else if (y <= 7d-84) then
        tmp = (a * b) + (c * i)
    else if (y <= 9.8d+60) then
        tmp = (a * b) + (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if (y <= -8e-77) {
		tmp = t_1;
	} else if (y <= 7e-84) {
		tmp = (a * b) + (c * i);
	} else if (y <= 9.8e+60) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if y <= -8e-77:
		tmp = t_1
	elif y <= 7e-84:
		tmp = (a * b) + (c * i)
	elif y <= 9.8e+60:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (y <= -8e-77)
		tmp = t_1;
	elseif (y <= 7e-84)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (y <= 9.8e+60)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if (y <= -8e-77)
		tmp = t_1;
	elseif (y <= 7e-84)
		tmp = (a * b) + (c * i);
	elseif (y <= 9.8e+60)
		tmp = (a * b) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e-77], t$95$1, If[LessEqual[y, 7e-84], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+60], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999994e-77 or 9.8000000000000005e60 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 65.2%

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

   if -7.9999999999999994e-77 < y < 7.0000000000000002e-84

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 70.1%

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

   if 7.0000000000000002e-84 < y < 9.8000000000000005e60

   1. Initial program 88.9%

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

   3. Taylor expanded in x around 0 70.7%

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

   4. Taylor expanded in c around 0 56.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-84}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+60}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.25 \cdot 10^{+113} \lor \neg \left(a \cdot b \leq 4.9 \cdot 10^{+163}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.25e+113) (not (<= (* a b) 4.9e+163))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -2.25e+113) || !((a * b) <= 4.9e+163)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-2.25d+113)) .or. (.not. ((a * b) <= 4.9d+163))) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -2.25e+113) || !((a * b) <= 4.9e+163)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -2.25e+113) or not ((a * b) <= 4.9e+163):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -2.25e+113) || !(Float64(a * b) <= 4.9e+163))
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -2.25e+113) || ~(((a * b) <= 4.9e+163)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2.25e+113], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.9e+163]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.25e113 or 4.9e163 < (*.f64 a b)

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 83.7%

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

   4. Taylor expanded in a around inf 72.9%

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

   if -2.25e113 < (*.f64 a b) < 4.9e163

   1. Initial program 96.2%

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

   3. Taylor expanded in c around inf 41.3%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.25 \cdot 10^{+113} \lor \neg \left(a \cdot b \leq 4.9 \cdot 10^{+163}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.9% 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 92.2%

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

3. Taylor expanded in z around 0 76.5%

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

4. Taylor expanded in a around inf 26.3%

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

Reproduce

herbie shell --seed 2024103 
(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)))