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

Percentage Accurate: 95.9% → 97.6%

Time: 10.4s

Alternatives: 12

Speedup: 0.4×

• 41.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(b + N[(N[(c * i), $MachinePrecision] / a), $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 z around inf 17.6%

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

      1. associate-/l* 29.4%

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

   5. Simplified 29.4%

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

   6. Taylor expanded in a around inf 53.0%

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

   7. Taylor expanded in a around inf 58.9%

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

4. Final simplification 97.3%

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

Alternative 2: 98.1% 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 93.4%

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

   1. +-commutative 93.4%

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

   2. fma-define 94.5%

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

   3. associate-+l+ 94.5%

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

   4. fma-define 96.1%

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

   5. fma-define 96.5%

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

3. Simplified 96.5%

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

Alternative 3: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+215}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -6.8 \cdot 10^{+31} \lor \neg \left(c \cdot i \leq 2.7 \cdot 10^{+72}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -5.5e+215)
     (+ (* a b) (* c i))
     (if (or (<= (* c i) -6.8e+31) (not (<= (* c i) 2.7e+72)))
       (+ (* 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) <= -5.5e+215) {
		tmp = (a * b) + (c * i);
	} else if (((c * i) <= -6.8e+31) || !((c * i) <= 2.7e+72)) {
		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) <= (-5.5d+215)) then
        tmp = (a * b) + (c * i)
    else if (((c * i) <= (-6.8d+31)) .or. (.not. ((c * i) <= 2.7d+72))) 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) <= -5.5e+215) {
		tmp = (a * b) + (c * i);
	} else if (((c * i) <= -6.8e+31) || !((c * i) <= 2.7e+72)) {
		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) <= -5.5e+215:
		tmp = (a * b) + (c * i)
	elif ((c * i) <= -6.8e+31) or not ((c * i) <= 2.7e+72):
		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) <= -5.5e+215)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif ((Float64(c * i) <= -6.8e+31) || !(Float64(c * i) <= 2.7e+72))
		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) <= -5.5e+215)
		tmp = (a * b) + (c * i);
	elseif (((c * i) <= -6.8e+31) || ~(((c * i) <= 2.7e+72)))
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5.5e+215], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], -6.8e+31], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.7e+72]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.5e215

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in a around inf 93.9%

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

   if -5.5e215 < (*.f64 c i) < -6.7999999999999996e31 or 2.7000000000000001e72 < (*.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 a around 0 89.5%

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

   if -6.7999999999999996e31 < (*.f64 c i) < 2.7000000000000001e72

   1. Initial program 96.0%

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

   3. Taylor expanded in c around 0 95.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+215}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -6.8 \cdot 10^{+31} \lor \neg \left(c \cdot i \leq 2.7 \cdot 10^{+72}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.15 \cdot 10^{+99}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.12 \cdot 10^{+18}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.3 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.15e+99)
   (* c i)
   (if (<= (* c i) -1.12e+18)
     (* x y)
     (if (<= (* c i) 5.2e+72)
       (* a b)
       (if (<= (* c i) 2.3e+140) (* 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) <= -4.15e+99) {
		tmp = c * i;
	} else if ((c * i) <= -1.12e+18) {
		tmp = x * y;
	} else if ((c * i) <= 5.2e+72) {
		tmp = a * b;
	} else if ((c * i) <= 2.3e+140) {
		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) <= (-4.15d+99)) then
        tmp = c * i
    else if ((c * i) <= (-1.12d+18)) then
        tmp = x * y
    else if ((c * i) <= 5.2d+72) then
        tmp = a * b
    else if ((c * i) <= 2.3d+140) 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) <= -4.15e+99) {
		tmp = c * i;
	} else if ((c * i) <= -1.12e+18) {
		tmp = x * y;
	} else if ((c * i) <= 5.2e+72) {
		tmp = a * b;
	} else if ((c * i) <= 2.3e+140) {
		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) <= -4.15e+99:
		tmp = c * i
	elif (c * i) <= -1.12e+18:
		tmp = x * y
	elif (c * i) <= 5.2e+72:
		tmp = a * b
	elif (c * i) <= 2.3e+140:
		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) <= -4.15e+99)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.12e+18)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 5.2e+72)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.3e+140)
		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) <= -4.15e+99)
		tmp = c * i;
	elseif ((c * i) <= -1.12e+18)
		tmp = x * y;
	elseif ((c * i) <= 5.2e+72)
		tmp = a * b;
	elseif ((c * i) <= 2.3e+140)
		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], -4.15e+99], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.12e+18], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.2e+72], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.3e+140], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4.15e99 or 2.2999999999999999e140 < (*.f64 c i)

   1. Initial program 87.2%

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

   3. Taylor expanded in c around inf 68.7%

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

   if -4.15e99 < (*.f64 c i) < -1.12e18 or 5.19999999999999963e72 < (*.f64 c i) < 2.2999999999999999e140

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.6%

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

   if -1.12e18 < (*.f64 c i) < 5.19999999999999963e72

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 43.4%

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

Alternative 5: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-83}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+103}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.7e+154)
   (* x y)
   (if (<= (* x y) 6.6e-83)
     (+ (* a b) (* c i))
     (if (<= (* x y) 4.4e+103) (+ (* c i) (* z t)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.7e+154) {
		tmp = x * y;
	} else if ((x * y) <= 6.6e-83) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.4e+103) {
		tmp = (c * i) + (z * t);
	} 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) :: tmp
    if ((x * y) <= (-1.7d+154)) then
        tmp = x * y
    else if ((x * y) <= 6.6d-83) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 4.4d+103) then
        tmp = (c * i) + (z * t)
    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 tmp;
	if ((x * y) <= -1.7e+154) {
		tmp = x * y;
	} else if ((x * y) <= 6.6e-83) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.4e+103) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.7e+154:
		tmp = x * y
	elif (x * y) <= 6.6e-83:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 4.4e+103:
		tmp = (c * i) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.7e+154)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 6.6e-83)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 4.4e+103)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.7e+154)
		tmp = x * y;
	elseif ((x * y) <= 6.6e-83)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 4.4e+103)
		tmp = (c * i) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.7e+154], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.6e-83], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.4e+103], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.69999999999999987e154 or 4.39999999999999985e103 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -1.69999999999999987e154 < (*.f64 x y) < 6.5999999999999999e-83

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in a around inf 69.1%

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

   if 6.5999999999999999e-83 < (*.f64 x y) < 4.39999999999999985e103

   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 z around inf 85.0%

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

      1. associate-/l* 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in z around inf 67.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-83}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+103}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+198}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.6 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.05e+198)
   (+ (* a b) (* c i))
   (if (<= (* c i) 8.6e+125)
     (+ (* a b) (+ (* x y) (* 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 ((c * i) <= -1.05e+198) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 8.6e+125) {
		tmp = (a * b) + ((x * y) + (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 ((c * i) <= (-1.05d+198)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 8.6d+125) then
        tmp = (a * b) + ((x * y) + (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 ((c * i) <= -1.05e+198) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 8.6e+125) {
		tmp = (a * b) + ((x * y) + (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 (c * i) <= -1.05e+198:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 8.6e+125:
		tmp = (a * b) + ((x * y) + (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(c * i) <= -1.05e+198)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 8.6e+125)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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 ((c * i) <= -1.05e+198)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 8.6e+125)
		tmp = (a * b) + ((x * y) + (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[LessEqual[N[(c * i), $MachinePrecision], -1.05e+198], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.6e+125], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $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 3 regimes

2. if (*.f64 c i) < -1.05000000000000006e198

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf 73.4%

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

      1. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in a around inf 91.6%

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

   if -1.05000000000000006e198 < (*.f64 c i) < 8.60000000000000071e125

   1. Initial program 96.3%

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

   3. Taylor expanded in c around 0 90.4%

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

   if 8.60000000000000071e125 < (*.f64 c i)

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 84.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+198}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.6 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.4 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{c \cdot i}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.4e+195)
   (+ (* a b) (* c i))
   (if (<= (* c i) 2.9e+141)
     (+ (* a b) (+ (* x y) (* z t)))
     (* a (+ b (/ (* c i) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.4e+195) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 2.9e+141) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = a * (b + ((c * i) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-4.4d+195)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 2.9d+141) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = a * (b + ((c * i) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.4e+195) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 2.9e+141) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = a * (b + ((c * i) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.4e+195:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 2.9e+141:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = a * (b + ((c * i) / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.4e+195)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 2.9e+141)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(a * Float64(b + Float64(Float64(c * i) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4.4e+195)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 2.9e+141)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = a * (b + ((c * i) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.4e+195], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.9e+141], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b + N[(N[(c * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4.4e195

   1. Initial program 83.8%

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

   3. Taylor expanded in z around inf 73.4%

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

      1. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in a around inf 91.6%

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

   if -4.4e195 < (*.f64 c i) < 2.90000000000000007e141

   1. Initial program 96.3%

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

   3. Taylor expanded in c around 0 90.5%

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

   if 2.90000000000000007e141 < (*.f64 c i)

   1. Initial program 85.7%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in a around inf 81.0%

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

   7. Taylor expanded in a around inf 81.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.4 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.9 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{c \cdot i}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{+181}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{c \cdot i}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2e-129)
   (+ (* a b) (* c i))
   (if (<= (* a b) 1e+181) (+ (* x y) (* z t)) (* a (+ b (/ (* c i) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2e-129) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 1e+181) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = a * (b + ((c * i) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-2d-129)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= 1d+181) then
        tmp = (x * y) + (z * t)
    else
        tmp = a * (b + ((c * i) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2e-129) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 1e+181) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = a * (b + ((c * i) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -2e-129:
		tmp = (a * b) + (c * i)
	elif (a * b) <= 1e+181:
		tmp = (x * y) + (z * t)
	else:
		tmp = a * (b + ((c * i) / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -2e-129)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= 1e+181)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(a * Float64(b + Float64(Float64(c * i) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -2e-129)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= 1e+181)
		tmp = (x * y) + (z * t);
	else
		tmp = a * (b + ((c * i) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e-129], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+181], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(b + N[(N[(c * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e-129

   1. Initial program 92.0%

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

   3. Taylor expanded in z around inf 77.0%

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

      1. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in a around inf 70.0%

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

   if -1.9999999999999999e-129 < (*.f64 a b) < 9.9999999999999992e180

   1. Initial program 94.6%

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

   3. Taylor expanded in c around 0 77.7%

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

   4. Taylor expanded in a around 0 70.5%

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

   if 9.9999999999999992e180 < (*.f64 a b)

   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 77.7%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in a around inf 81.8%

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

   7. Taylor expanded in a around inf 81.8%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{+181}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b + \frac{c \cdot i}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.15 \cdot 10^{-129} \lor \neg \left(a \cdot b \leq 10^{+181}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.15e-129) (not (<= (* a b) 1e+181)))
   (+ (* a b) (* c i))
   (+ (* 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 (((a * b) <= -2.15e-129) || !((a * b) <= 1e+181)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (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 (((a * b) <= (-2.15d-129)) .or. (.not. ((a * b) <= 1d+181))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (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 (((a * b) <= -2.15e-129) || !((a * b) <= 1e+181)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -2.15e-129) or not ((a * b) <= 1e+181):
		tmp = (a * b) + (c * i)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -2.15e-129) || !(Float64(a * b) <= 1e+181))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = 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 (((a * b) <= -2.15e-129) || ~(((a * b) <= 1e+181)))
		tmp = (a * b) + (c * i);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2.15e-129], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+181]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.1499999999999999e-129 or 9.9999999999999992e180 < (*.f64 a b)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in a around inf 73.6%

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

   if -2.1499999999999999e-129 < (*.f64 a b) < 9.9999999999999992e180

   1. Initial program 94.6%

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

   3. Taylor expanded in c around 0 77.7%

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

   4. Taylor expanded in a around 0 70.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.15 \cdot 10^{-129} \lor \neg \left(a \cdot b \leq 10^{+181}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 9.5 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4e+152) (not (<= (* x y) 9.5e+103)))
   (* 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) <= -4e+152) || !((x * y) <= 9.5e+103)) {
		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) <= (-4d+152)) .or. (.not. ((x * y) <= 9.5d+103))) 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) <= -4e+152) || !((x * y) <= 9.5e+103)) {
		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) <= -4e+152) or not ((x * y) <= 9.5e+103):
		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) <= -4e+152) || !(Float64(x * y) <= 9.5e+103))
		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) <= -4e+152) || ~(((x * y) <= 9.5e+103)))
		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], -4e+152], N[Not[LessEqual[N[(x * y), $MachinePrecision], 9.5e+103]], $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) < -4.0000000000000002e152 or 9.49999999999999922e103 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -4.0000000000000002e152 < (*.f64 x y) < 9.49999999999999922e103

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in a around inf 66.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 9.5 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.16 \cdot 10^{+24} \lor \neg \left(c \cdot i \leq 1.05 \cdot 10^{+83}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.16e+24) (not (<= (* c i) 1.05e+83))) (* 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) <= -2.16e+24) || !((c * i) <= 1.05e+83)) {
		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) <= (-2.16d+24)) .or. (.not. ((c * i) <= 1.05d+83))) 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) <= -2.16e+24) || !((c * i) <= 1.05e+83)) {
		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) <= -2.16e+24) or not ((c * i) <= 1.05e+83):
		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) <= -2.16e+24) || !(Float64(c * i) <= 1.05e+83))
		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) <= -2.16e+24) || ~(((c * i) <= 1.05e+83)))
		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], -2.16e+24], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.05e+83]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.1599999999999999e24 or 1.05000000000000001e83 < (*.f64 c i)

   1. Initial program 89.6%

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

   3. Taylor expanded in c around inf 58.9%

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

   if -2.1599999999999999e24 < (*.f64 c i) < 1.05000000000000001e83

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 41.8%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.16 \cdot 10^{+24} \lor \neg \left(c \cdot i \leq 1.05 \cdot 10^{+83}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.0% 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 93.4%

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

3. Taylor expanded in a around inf 29.7%

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

Reproduce

herbie shell --seed 2024131 
(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)))