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

Percentage Accurate: 96.1% → 98.2%

Time: 13.3s

Alternatives: 12

Speedup: 0.4×

• 41.0% 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: 98.2% accurate, 0.4× speedup

Math

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

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 (* c (+ i (* a (/ b c)))))))

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 = c * (i + (a * (b / c)));
	}
	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 = c * (i + (a * (b / c)));
	}
	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 = c * (i + (a * (b / c)))
	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(c * Float64(i + Float64(a * Float64(b / c))));
	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 = c * (i + (a * (b / c)));
	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[(c * N[(i + N[(a * N[(b / c), $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 x around 0 36.4%

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

   4. Taylor expanded in t around 0 27.7%

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

   5. Taylor expanded in c around inf 45.9%

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

      1. associate-/l* 55.0%

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

   7. Simplified 55.0%

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

4. Final simplification 98.1%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. +-commutative 95.7%

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

   2. fma-define 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-define 98.0%

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

   5. fma-define 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 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 95.7%

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

   1. +-commutative 95.7%

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

   2. fma-define 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-define 97.3%

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

   5. fma-define 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 4: 60.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.86 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.86e+248)
     (* x y)
     (if (<= (* x y) -2.8e+176)
       t_1
       (if (<= (* x y) -8.2e+51)
         (* x y)
         (if (<= (* x y) -2.9e-56)
           t_1
           (if (<= (* x y) -6.4e-72)
             (* z t)
             (if (<= (* x y) 2.25e+104) 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) <= -1.86e+248) {
		tmp = x * y;
	} else if ((x * y) <= -2.8e+176) {
		tmp = t_1;
	} else if ((x * y) <= -8.2e+51) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-56) {
		tmp = t_1;
	} else if ((x * y) <= -6.4e-72) {
		tmp = z * t;
	} else if ((x * y) <= 2.25e+104) {
		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) <= (-1.86d+248)) then
        tmp = x * y
    else if ((x * y) <= (-2.8d+176)) then
        tmp = t_1
    else if ((x * y) <= (-8.2d+51)) then
        tmp = x * y
    else if ((x * y) <= (-2.9d-56)) then
        tmp = t_1
    else if ((x * y) <= (-6.4d-72)) then
        tmp = z * t
    else if ((x * y) <= 2.25d+104) 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) <= -1.86e+248) {
		tmp = x * y;
	} else if ((x * y) <= -2.8e+176) {
		tmp = t_1;
	} else if ((x * y) <= -8.2e+51) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-56) {
		tmp = t_1;
	} else if ((x * y) <= -6.4e-72) {
		tmp = z * t;
	} else if ((x * y) <= 2.25e+104) {
		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) <= -1.86e+248:
		tmp = x * y
	elif (x * y) <= -2.8e+176:
		tmp = t_1
	elif (x * y) <= -8.2e+51:
		tmp = x * y
	elif (x * y) <= -2.9e-56:
		tmp = t_1
	elif (x * y) <= -6.4e-72:
		tmp = z * t
	elif (x * y) <= 2.25e+104:
		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) <= -1.86e+248)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.8e+176)
		tmp = t_1;
	elseif (Float64(x * y) <= -8.2e+51)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.9e-56)
		tmp = t_1;
	elseif (Float64(x * y) <= -6.4e-72)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.25e+104)
		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) <= -1.86e+248)
		tmp = x * y;
	elseif ((x * y) <= -2.8e+176)
		tmp = t_1;
	elseif ((x * y) <= -8.2e+51)
		tmp = x * y;
	elseif ((x * y) <= -2.9e-56)
		tmp = t_1;
	elseif ((x * y) <= -6.4e-72)
		tmp = z * t;
	elseif ((x * y) <= 2.25e+104)
		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], -1.86e+248], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.8e+176], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+51], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.9e-56], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -6.4e-72], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.25e+104], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.85999999999999988e248 or -2.8000000000000002e176 < (*.f64 x y) < -8.20000000000000021e51 or 2.2499999999999999e104 < (*.f64 x y)

   1. Initial program 89.5%

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

   3. Taylor expanded in x around inf 72.1%

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

   if -1.85999999999999988e248 < (*.f64 x y) < -2.8000000000000002e176 or -8.20000000000000021e51 < (*.f64 x y) < -2.89999999999999991e-56 or -6.39999999999999998e-72 < (*.f64 x y) < 2.2499999999999999e104

   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 93.0%

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

   4. Taylor expanded in t around 0 64.9%

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

   if -2.89999999999999991e-56 < (*.f64 x y) < -6.39999999999999998e-72

   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 inf 86.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.86 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+104}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -0.38:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.12 \cdot 10^{-104}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{-232}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.8e+48)
   (* c i)
   (if (<= (* c i) -0.38)
     (* x y)
     (if (<= (* c i) -2.12e-104)
       (* z t)
       (if (<= (* c i) 1.5e-232)
         (* a b)
         (if (<= (* c i) 2.9e+143) (* z t) (* 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) <= -4.8e+48) {
		tmp = c * i;
	} else if ((c * i) <= -0.38) {
		tmp = x * y;
	} else if ((c * i) <= -2.12e-104) {
		tmp = z * t;
	} else if ((c * i) <= 1.5e-232) {
		tmp = a * b;
	} else if ((c * i) <= 2.9e+143) {
		tmp = z * t;
	} 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) <= (-4.8d+48)) then
        tmp = c * i
    else if ((c * i) <= (-0.38d0)) then
        tmp = x * y
    else if ((c * i) <= (-2.12d-104)) then
        tmp = z * t
    else if ((c * i) <= 1.5d-232) then
        tmp = a * b
    else if ((c * i) <= 2.9d+143) then
        tmp = z * t
    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) <= -4.8e+48) {
		tmp = c * i;
	} else if ((c * i) <= -0.38) {
		tmp = x * y;
	} else if ((c * i) <= -2.12e-104) {
		tmp = z * t;
	} else if ((c * i) <= 1.5e-232) {
		tmp = a * b;
	} else if ((c * i) <= 2.9e+143) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.8e+48:
		tmp = c * i
	elif (c * i) <= -0.38:
		tmp = x * y
	elif (c * i) <= -2.12e-104:
		tmp = z * t
	elif (c * i) <= 1.5e-232:
		tmp = a * b
	elif (c * i) <= 2.9e+143:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.8e+48)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -0.38)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -2.12e-104)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.5e-232)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.9e+143)
		tmp = Float64(z * t);
	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) <= -4.8e+48)
		tmp = c * i;
	elseif ((c * i) <= -0.38)
		tmp = x * y;
	elseif ((c * i) <= -2.12e-104)
		tmp = z * t;
	elseif ((c * i) <= 1.5e-232)
		tmp = a * b;
	elseif ((c * i) <= 2.9e+143)
		tmp = z * t;
	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], -4.8e+48], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -0.38], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.12e-104], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.5e-232], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.9e+143], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.8000000000000002e48 or 2.8999999999999998e143 < (*.f64 c i)

   1. Initial program 92.8%

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

   3. Taylor expanded in c around inf 69.0%

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

   if -4.8000000000000002e48 < (*.f64 c i) < -0.38

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 55.4%

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

   if -0.38 < (*.f64 c i) < -2.1200000000000001e-104 or 1.49999999999999995e-232 < (*.f64 c i) < 2.8999999999999998e143

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 46.0%

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

   if -2.1200000000000001e-104 < (*.f64 c i) < 1.49999999999999995e-232

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 42.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -0.38:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.12 \cdot 10^{-104}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{-232}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -7e+50)
     t_2
     (if (<= (* x y) -2.9e-56)
       t_1
       (if (<= (* x y) -6.4e-72) (* z t) (if (<= (* x y) 8.6e+99) 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 = (a * b) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7e+50) {
		tmp = t_2;
	} else if ((x * y) <= -2.9e-56) {
		tmp = t_1;
	} else if ((x * y) <= -6.4e-72) {
		tmp = z * t;
	} else if ((x * y) <= 8.6e+99) {
		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 = (a * b) + (c * i)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-7d+50)) then
        tmp = t_2
    else if ((x * y) <= (-2.9d-56)) then
        tmp = t_1
    else if ((x * y) <= (-6.4d-72)) then
        tmp = z * t
    else if ((x * y) <= 8.6d+99) 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 = (a * b) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7e+50) {
		tmp = t_2;
	} else if ((x * y) <= -2.9e-56) {
		tmp = t_1;
	} else if ((x * y) <= -6.4e-72) {
		tmp = z * t;
	} else if ((x * y) <= 8.6e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -7e+50:
		tmp = t_2
	elif (x * y) <= -2.9e-56:
		tmp = t_1
	elif (x * y) <= -6.4e-72:
		tmp = z * t
	elif (x * y) <= 8.6e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -7e+50)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.9e-56)
		tmp = t_1;
	elseif (Float64(x * y) <= -6.4e-72)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 8.6e+99)
		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 = (a * b) + (c * i);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -7e+50)
		tmp = t_2;
	elseif ((x * y) <= -2.9e-56)
		tmp = t_1;
	elseif ((x * y) <= -6.4e-72)
		tmp = z * t;
	elseif ((x * y) <= 8.6e+99)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7e+50], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.9e-56], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -6.4e-72], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.6e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.00000000000000012e50 or 8.6000000000000003e99 < (*.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 91.5%

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

   4. Taylor expanded in x around inf 81.0%

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

   5. Taylor expanded in c around 0 76.9%

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

   if -7.00000000000000012e50 < (*.f64 x y) < -2.89999999999999991e-56 or -6.39999999999999998e-72 < (*.f64 x y) < 8.6000000000000003e99

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in t around 0 64.3%

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

   if -2.89999999999999991e-56 < (*.f64 x y) < -6.39999999999999998e-72

   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 inf 86.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{+99}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -4.9 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5.9 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -4.9e+116)
     t_2
     (if (<= (* x y) 5.9e-211)
       t_1
       (if (<= (* x y) 6.4e-63)
         (+ (* a b) (* c i))
         (if (<= (* x y) 6.5e+99) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -4.9e+116) {
		tmp = t_2;
	} else if ((x * y) <= 5.9e-211) {
		tmp = t_1;
	} else if ((x * y) <= 6.4e-63) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.5e+99) {
		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 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-4.9d+116)) then
        tmp = t_2
    else if ((x * y) <= 5.9d-211) then
        tmp = t_1
    else if ((x * y) <= 6.4d-63) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 6.5d+99) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -4.9e+116) {
		tmp = t_2;
	} else if ((x * y) <= 5.9e-211) {
		tmp = t_1;
	} else if ((x * y) <= 6.4e-63) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.5e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -4.9e+116:
		tmp = t_2
	elif (x * y) <= 5.9e-211:
		tmp = t_1
	elif (x * y) <= 6.4e-63:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 6.5e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -4.9e+116)
		tmp = t_2;
	elseif (Float64(x * y) <= 5.9e-211)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.4e-63)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 6.5e+99)
		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 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -4.9e+116)
		tmp = t_2;
	elseif ((x * y) <= 5.9e-211)
		tmp = t_1;
	elseif ((x * y) <= 6.4e-63)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 6.5e+99)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.9e+116], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5.9e-211], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.4e-63], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.5e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.8999999999999998e116 or 6.5000000000000004e99 < (*.f64 x y)

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 91.6%

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

   4. Taylor expanded in x around inf 85.0%

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

   5. Taylor expanded in c around 0 81.5%

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

   if -4.8999999999999998e116 < (*.f64 x y) < 5.9000000000000002e-211 or 6.39999999999999978e-63 < (*.f64 x y) < 6.5000000000000004e99

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 90.0%

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

   4. Taylor expanded in a around 0 71.4%

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

   if 5.9000000000000002e-211 < (*.f64 x y) < 6.39999999999999978e-63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.0%

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

   4. Taylor expanded in t around 0 76.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.9 \cdot 10^{+116}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.9 \cdot 10^{-211}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-104}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-229}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+145}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.1e+39)
   (* c i)
   (if (<= (* c i) -2.4e-104)
     (* z t)
     (if (<= (* c i) 9.2e-229)
       (* a b)
       (if (<= (* c i) 2.5e+145) (* z t) (* 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) <= -2.1e+39) {
		tmp = c * i;
	} else if ((c * i) <= -2.4e-104) {
		tmp = z * t;
	} else if ((c * i) <= 9.2e-229) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+145) {
		tmp = z * t;
	} 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) <= (-2.1d+39)) then
        tmp = c * i
    else if ((c * i) <= (-2.4d-104)) then
        tmp = z * t
    else if ((c * i) <= 9.2d-229) then
        tmp = a * b
    else if ((c * i) <= 2.5d+145) then
        tmp = z * t
    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) <= -2.1e+39) {
		tmp = c * i;
	} else if ((c * i) <= -2.4e-104) {
		tmp = z * t;
	} else if ((c * i) <= 9.2e-229) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+145) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.1e+39:
		tmp = c * i
	elif (c * i) <= -2.4e-104:
		tmp = z * t
	elif (c * i) <= 9.2e-229:
		tmp = a * b
	elif (c * i) <= 2.5e+145:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.1e+39)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.4e-104)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 9.2e-229)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.5e+145)
		tmp = Float64(z * t);
	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) <= -2.1e+39)
		tmp = c * i;
	elseif ((c * i) <= -2.4e-104)
		tmp = z * t;
	elseif ((c * i) <= 9.2e-229)
		tmp = a * b;
	elseif ((c * i) <= 2.5e+145)
		tmp = z * t;
	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], -2.1e+39], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.4e-104], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.2e-229], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.5e+145], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.0999999999999999e39 or 2.49999999999999983e145 < (*.f64 c i)

   1. Initial program 92.9%

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

   3. Taylor expanded in c around inf 68.1%

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

   if -2.0999999999999999e39 < (*.f64 c i) < -2.4000000000000001e-104 or 9.19999999999999983e-229 < (*.f64 c i) < 2.49999999999999983e145

   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 z around inf 42.8%

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

   if -2.4000000000000001e-104 < (*.f64 c i) < 9.19999999999999983e-229

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 42.7%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+39}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-104}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-229}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+145}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+40} \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+143}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5e+40) (not (<= (* c i) 5e+143)))
   (+ (* x y) (* c i))
   (+ (* 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) <= -5e+40) || !((c * i) <= 5e+143)) {
		tmp = (x * y) + (c * i);
	} 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) <= (-5d+40)) .or. (.not. ((c * i) <= 5d+143))) then
        tmp = (x * y) + (c * i)
    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) <= -5e+40) || !((c * i) <= 5e+143)) {
		tmp = (x * y) + (c * i);
	} 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) <= -5e+40) or not ((c * i) <= 5e+143):
		tmp = (x * y) + (c * i)
	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) <= -5e+40) || !(Float64(c * i) <= 5e+143))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	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) <= -5e+40) || ~(((c * i) <= 5e+143)))
		tmp = (x * y) + (c * i);
	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], -5e+40], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5e+143]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $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) < -5.00000000000000003e40 or 5.00000000000000012e143 < (*.f64 c i)

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 90.0%

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

   4. Taylor expanded in x around inf 87.3%

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

   5. Taylor expanded in a around 0 82.3%

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

   if -5.00000000000000003e40 < (*.f64 c i) < 5.00000000000000012e143

   1. Initial program 97.4%

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

   3. Taylor expanded in c around 0 94.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+40} \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+143}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -5000000000000 \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+143}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* c i) -5000000000000.0) (not (<= (* c i) 5e+143)))
     (+ (* 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) <= -5000000000000.0) || !((c * i) <= 5e+143)) {
		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) <= (-5000000000000.0d0)) .or. (.not. ((c * i) <= 5d+143))) 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) <= -5000000000000.0) || !((c * i) <= 5e+143)) {
		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) <= -5000000000000.0) or not ((c * i) <= 5e+143):
		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) <= -5000000000000.0) || !(Float64(c * i) <= 5e+143))
		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) <= -5000000000000.0) || ~(((c * i) <= 5e+143)))
		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], -5000000000000.0], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5e+143]], $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) < -5e12 or 5.00000000000000012e143 < (*.f64 c i)

   1. Initial program 92.3%

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

   3. Taylor expanded in a around 0 88.5%

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

   if -5e12 < (*.f64 c i) < 5.00000000000000012e143

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 95.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5000000000000 \lor \neg \left(c \cdot i \leq 5 \cdot 10^{+143}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+16} \lor \neg \left(c \cdot i \leq 2.9 \cdot 10^{+143}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.8e+16) (not (<= (* c i) 2.9e+143))) (* 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) <= -3.8e+16) || !((c * i) <= 2.9e+143)) {
		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) <= (-3.8d+16)) .or. (.not. ((c * i) <= 2.9d+143))) 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) <= -3.8e+16) || !((c * i) <= 2.9e+143)) {
		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) <= -3.8e+16) or not ((c * i) <= 2.9e+143):
		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) <= -3.8e+16) || !(Float64(c * i) <= 2.9e+143))
		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) <= -3.8e+16) || ~(((c * i) <= 2.9e+143)))
		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], -3.8e+16], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.9e+143]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8e16 or 2.8999999999999998e143 < (*.f64 c i)

   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 c around inf 65.5%

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

   if -3.8e16 < (*.f64 c i) < 2.8999999999999998e143

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 34.3%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+16} \lor \neg \left(c \cdot i \leq 2.9 \cdot 10^{+143}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 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 25.4%

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

4. Final simplification 25.4%

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

Reproduce

herbie shell --seed 2024053 
(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)))