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

Percentage Accurate: 95.9% → 98.0%

Time: 10.1s

Alternatives: 15

Speedup: 0.4×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.3%

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

   3. associate-+l+ 97.3%

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

   4. fma-define 98.8%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.3%

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

   3. +-commutative 97.3%

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

   4. fma-define 98.0%

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

   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. Add Preprocessing

Alternative 3: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* x y) -4.2e+146)
     (* x y)
     (if (<= (* x y) -1.65e-113)
       t_1
       (if (<= (* x y) 1.15e-80)
         (+ (* a b) (* c i))
         (if (<= (* x y) 4.7e+116) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -4.2e+146) {
		tmp = x * y;
	} else if ((x * y) <= -1.65e-113) {
		tmp = t_1;
	} else if ((x * y) <= 1.15e-80) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.7e+116) {
		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 = (c * i) + (z * t)
    if ((x * y) <= (-4.2d+146)) then
        tmp = x * y
    else if ((x * y) <= (-1.65d-113)) then
        tmp = t_1
    else if ((x * y) <= 1.15d-80) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 4.7d+116) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -4.2e+146) {
		tmp = x * y;
	} else if ((x * y) <= -1.65e-113) {
		tmp = t_1;
	} else if ((x * y) <= 1.15e-80) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.7e+116) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (x * y) <= -4.2e+146:
		tmp = x * y
	elif (x * y) <= -1.65e-113:
		tmp = t_1
	elif (x * y) <= 1.15e-80:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 4.7e+116:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -4.2e+146)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.65e-113)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.15e-80)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 4.7e+116)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -4.2e+146)
		tmp = x * y;
	elseif ((x * y) <= -1.65e-113)
		tmp = t_1;
	elseif ((x * y) <= 1.15e-80)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 4.7e+116)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.2e+146], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.65e-113], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.15e-80], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.7e+116], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.2000000000000001e146 or 4.7000000000000003e116 < (*.f64 x y)

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 75.1%

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

   4. Taylor expanded in y around inf 73.0%

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

      1. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in y around inf 65.3%

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

   if -4.2000000000000001e146 < (*.f64 x y) < -1.6500000000000001e-113 or 1.1499999999999999e-80 < (*.f64 x y) < 4.7000000000000003e116

   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 z around inf 64.1%

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

   if -1.6500000000000001e-113 < (*.f64 x y) < 1.1499999999999999e-80

   1. Initial program 98.9%

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

   3. Taylor expanded in a around inf 78.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-113}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{+116}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(t + N[(N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision] + N[(c * N[(i / z), $MachinePrecision]), $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 33.3%

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

   4. Taylor expanded in z around inf 22.2%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 98.8%

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

Alternative 5: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{-16}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+125)
   (* y (+ x (* c (/ i y))))
   (if (<= (* x y) -1e+16)
     (+ (* a b) (* z t))
     (if (<= (* x y) 1e-16) (+ (* a b) (* c i)) (* z (+ t (/ (* x y) z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+125) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= -1e+16) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1e-16) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * (t + ((x * y) / z));
	}
	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) <= (-2d+125)) then
        tmp = y * (x + (c * (i / y)))
    else if ((x * y) <= (-1d+16)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 1d-16) then
        tmp = (a * b) + (c * i)
    else
        tmp = z * (t + ((x * y) / z))
    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) <= -2e+125) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= -1e+16) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1e-16) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * (t + ((x * y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+125:
		tmp = y * (x + (c * (i / y)))
	elif (x * y) <= -1e+16:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 1e-16:
		tmp = (a * b) + (c * i)
	else:
		tmp = z * (t + ((x * y) / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+125)
		tmp = Float64(y * Float64(x + Float64(c * Float64(i / y))));
	elseif (Float64(x * y) <= -1e+16)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 1e-16)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(z * Float64(t + Float64(Float64(x * y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+125)
		tmp = y * (x + (c * (i / y)));
	elseif ((x * y) <= -1e+16)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 1e-16)
		tmp = (a * b) + (c * i);
	else
		tmp = z * (t + ((x * y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+125], N[(y * N[(x + N[(c * N[(i / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e+16], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-16], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999998e125

   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 x around inf 78.4%

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

   4. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   if -1.9999999999999998e125 < (*.f64 x y) < -1e16

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 79.8%

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

   4. Taylor expanded in z around inf 67.1%

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

   5. Taylor expanded in c around 0 63.1%

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

   6. Taylor expanded in z around 0 71.5%

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

   if -1e16 < (*.f64 x y) < 9.9999999999999998e-17

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 74.0%

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

   if 9.9999999999999998e-17 < (*.f64 x y)

   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 a around 0 84.8%

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

   4. Taylor expanded in z around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 68.7%

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

      3. associate-/l* 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in c around 0 63.4%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{x \cdot y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{-16}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+125)
   (* y (+ x (* c (/ i y))))
   (if (<= (* x y) -1e+16)
     (+ (* a b) (* z t))
     (if (<= (* x y) 5e-81) (+ (* a b) (* c i)) (+ (* 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 ((x * y) <= -2e+125) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= -1e+16) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 5e-81) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (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) <= (-2d+125)) then
        tmp = y * (x + (c * (i / y)))
    else if ((x * y) <= (-1d+16)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 5d-81) then
        tmp = (a * b) + (c * i)
    else
        tmp = (x * y) + (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) <= -2e+125) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= -1e+16) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 5e-81) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+125:
		tmp = y * (x + (c * (i / y)))
	elif (x * y) <= -1e+16:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 5e-81:
		tmp = (a * b) + (c * i)
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+125)
		tmp = Float64(y * Float64(x + Float64(c * Float64(i / y))));
	elseif (Float64(x * y) <= -1e+16)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 5e-81)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(x * y) + 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) <= -2e+125)
		tmp = y * (x + (c * (i / y)));
	elseif ((x * y) <= -1e+16)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 5e-81)
		tmp = (a * b) + (c * i);
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+125], N[(y * N[(x + N[(c * N[(i / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e+16], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-81], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999998e125

   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 x around inf 78.4%

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

   4. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   if -1.9999999999999998e125 < (*.f64 x y) < -1e16

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 79.8%

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

   4. Taylor expanded in z around inf 67.1%

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

   5. Taylor expanded in c around 0 63.1%

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

   6. Taylor expanded in z around 0 71.5%

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

   if -1e16 < (*.f64 x y) < 4.99999999999999981e-81

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 74.4%

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

   if 4.99999999999999981e-81 < (*.f64 x y)

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf 66.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -26500000000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= (* x y) -5.6e+124)
     t_1
     (if (<= (* x y) -26500000000000.0)
       (+ (* a b) (* z t))
       (if (<= (* x y) 1.15e-77) (+ (* a b) (* c i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -5.6e+124) {
		tmp = t_1;
	} else if ((x * y) <= -26500000000000.0) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.15e-77) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (c * i)
    if ((x * y) <= (-5.6d+124)) then
        tmp = t_1
    else if ((x * y) <= (-26500000000000.0d0)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 1.15d-77) then
        tmp = (a * b) + (c * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -5.6e+124) {
		tmp = t_1;
	} else if ((x * y) <= -26500000000000.0) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.15e-77) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if (x * y) <= -5.6e+124:
		tmp = t_1
	elif (x * y) <= -26500000000000.0:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 1.15e-77:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -5.6e+124)
		tmp = t_1;
	elseif (Float64(x * y) <= -26500000000000.0)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 1.15e-77)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -5.6e+124)
		tmp = t_1;
	elseif ((x * y) <= -26500000000000.0)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 1.15e-77)
		tmp = (a * b) + (c * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5.6e+124], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -26500000000000.0], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.15e-77], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.59999999999999999e124 or 1.14999999999999999e-77 < (*.f64 x y)

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -5.59999999999999999e124 < (*.f64 x y) < -2.65e13

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 79.8%

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

   4. Taylor expanded in z around inf 67.1%

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

   5. Taylor expanded in c around 0 63.1%

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

   6. Taylor expanded in z around 0 71.5%

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

   if -2.65e13 < (*.f64 x y) < 1.14999999999999999e-77

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 74.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+124}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -26500000000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.2 \cdot 10^{+144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -9.2e+144)
   (* x y)
   (if (<= (* x y) -1.65e+15)
     (+ (* a b) (* z t))
     (if (<= (* x y) 2.5e+46) (+ (* a b) (* c i)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -9.2e+144) {
		tmp = x * y;
	} else if ((x * y) <= -1.65e+15) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.5e+46) {
		tmp = (a * b) + (c * i);
	} 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) <= (-9.2d+144)) then
        tmp = x * y
    else if ((x * y) <= (-1.65d+15)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 2.5d+46) then
        tmp = (a * b) + (c * i)
    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) <= -9.2e+144) {
		tmp = x * y;
	} else if ((x * y) <= -1.65e+15) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.5e+46) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -9.2e+144:
		tmp = x * y
	elif (x * y) <= -1.65e+15:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 2.5e+46:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -9.2e+144)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.65e+15)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 2.5e+46)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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) <= -9.2e+144)
		tmp = x * y;
	elseif ((x * y) <= -1.65e+15)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 2.5e+46)
		tmp = (a * b) + (c * i);
	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], -9.2e+144], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.65e+15], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+46], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.2000000000000006e144 or 2.5000000000000001e46 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 71.2%

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

   4. Taylor expanded in y around inf 69.4%

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

      1. associate-/l* 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around inf 60.9%

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

   if -9.2000000000000006e144 < (*.f64 x y) < -1.65e15

   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 x around 0 79.4%

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

   4. Taylor expanded in z around inf 68.7%

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

   5. Taylor expanded in c around 0 58.4%

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

   6. Taylor expanded in z around 0 65.5%

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

   if -1.65e15 < (*.f64 x y) < 2.5000000000000001e46

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 73.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.2 \cdot 10^{+144}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+46}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-128}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+150) (not (<= (* x y) 5e-128)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+150) || !((x * y) <= 5e-128)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+150)) .or. (.not. ((x * y) <= 5d-128))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+150) || !((x * y) <= 5e-128)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+150) or not ((x * y) <= 5e-128):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+150) || !(Float64(x * y) <= 5e-128))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+150) || ~(((x * y) <= 5e-128)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+150], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-128]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999996e150 or 5.0000000000000001e-128 < (*.f64 x y)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 81.5%

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

   if -1.99999999999999996e150 < (*.f64 x y) < 5.0000000000000001e-128

   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 x around 0 93.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-128}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-126}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+150)
   (+ (* c i) (+ (* a b) (* x y)))
   (if (<= (* x y) 1e-126)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* 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 ((x * y) <= -2e+150) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((x * y) <= 1e-126) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((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 ((x * y) <= (-2d+150)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if ((x * y) <= 1d-126) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((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 ((x * y) <= -2e+150) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((x * y) <= 1e-126) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+150:
		tmp = (c * i) + ((a * b) + (x * y))
	elif (x * y) <= 1e-126:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+150)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (Float64(x * y) <= 1e-126)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 ((x * y) <= -2e+150)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif ((x * y) <= 1e-126)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+150], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-126], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999996e150

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 92.4%

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

   if -1.99999999999999996e150 < (*.f64 x y) < 9.9999999999999995e-127

   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 x around 0 93.3%

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

   if 9.9999999999999995e-127 < (*.f64 x y)

   1. Initial program 92.7%

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

   3. Taylor expanded in a around 0 83.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-126}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+150)
   (* y (+ x (* c (/ i y))))
   (if (<= (* x y) 5e+115)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* 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 ((x * y) <= -2e+150) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= 5e+115) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (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) <= (-2d+150)) then
        tmp = y * (x + (c * (i / y)))
    else if ((x * y) <= 5d+115) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (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) <= -2e+150) {
		tmp = y * (x + (c * (i / y)));
	} else if ((x * y) <= 5e+115) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+150:
		tmp = y * (x + (c * (i / y)))
	elif (x * y) <= 5e+115:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+150)
		tmp = Float64(y * Float64(x + Float64(c * Float64(i / y))));
	elseif (Float64(x * y) <= 5e+115)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + 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) <= -2e+150)
		tmp = y * (x + (c * (i / y)));
	elseif ((x * y) <= 5e+115)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+150], N[(y * N[(x + N[(c * N[(i / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+115], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999996e150

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 80.8%

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

   4. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

   if -1.99999999999999996e150 < (*.f64 x y) < 5.00000000000000008e115

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 89.1%

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

   if 5.00000000000000008e115 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf 71.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(x + c \cdot \frac{i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+115}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8800000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 850000:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.1e+124)
   (* x y)
   (if (<= (* x y) -8800000000000.0)
     (* z t)
     (if (<= (* x y) 850000.0) (* c i) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.1e+124) {
		tmp = x * y;
	} else if ((x * y) <= -8800000000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 850000.0) {
		tmp = c * i;
	} 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) <= (-3.1d+124)) then
        tmp = x * y
    else if ((x * y) <= (-8800000000000.0d0)) then
        tmp = z * t
    else if ((x * y) <= 850000.0d0) then
        tmp = c * i
    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) <= -3.1e+124) {
		tmp = x * y;
	} else if ((x * y) <= -8800000000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 850000.0) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.1e+124:
		tmp = x * y
	elif (x * y) <= -8800000000000.0:
		tmp = z * t
	elif (x * y) <= 850000.0:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.1e+124)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -8800000000000.0)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 850000.0)
		tmp = Float64(c * i);
	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) <= -3.1e+124)
		tmp = x * y;
	elseif ((x * y) <= -8800000000000.0)
		tmp = z * t;
	elseif ((x * y) <= 850000.0)
		tmp = c * i;
	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], -3.1e+124], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8800000000000.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 850000.0], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.1000000000000002e124 or 8.5e5 < (*.f64 x y)

   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 x around inf 70.5%

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

   4. Taylor expanded in y around inf 68.0%

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

      1. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in y around inf 59.0%

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

   if -3.1000000000000002e124 < (*.f64 x y) < -8.8e12

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 61.9%

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

   4. Taylor expanded in t around inf 57.6%

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

      1. associate-/l* 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in t around inf 53.8%

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

   if -8.8e12 < (*.f64 x y) < 8.5e5

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 41.2%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8800000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 850000:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.8 \cdot 10^{+291} \lor \neg \left(x \cdot y \leq 2.5 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -7.8e+291) (not (<= (* x y) 2.5e+46)))
   (* 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) <= -7.8e+291) || !((x * y) <= 2.5e+46)) {
		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) <= (-7.8d+291)) .or. (.not. ((x * y) <= 2.5d+46))) 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) <= -7.8e+291) || !((x * y) <= 2.5e+46)) {
		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) <= -7.8e+291) or not ((x * y) <= 2.5e+46):
		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) <= -7.8e+291) || !(Float64(x * y) <= 2.5e+46))
		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) <= -7.8e+291) || ~(((x * y) <= 2.5e+46)))
		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], -7.8e+291], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.5e+46]], $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) < -7.79999999999999962e291 or 2.5000000000000001e46 < (*.f64 x y)

   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 x around inf 70.7%

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

   4. Taylor expanded in y around inf 69.6%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in y around inf 64.9%

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

   if -7.79999999999999962e291 < (*.f64 x y) < 2.5000000000000001e46

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 64.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.8 \cdot 10^{+291} \lor \neg \left(x \cdot y \leq 2.5 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3 \lor \neg \left(c \cdot i \leq 3.4 \cdot 10^{+58}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.3) (not (<= (* c i) 3.4e+58))) (* c i) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.3) || !((c * i) <= 3.4e+58)) {
		tmp = c * i;
	} else {
		tmp = 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) <= (-2.3d0)) .or. (.not. ((c * i) <= 3.4d+58))) then
        tmp = c * i
    else
        tmp = 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) <= -2.3) || !((c * i) <= 3.4e+58)) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.3) or not ((c * i) <= 3.4e+58):
		tmp = c * i
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.3) || !(Float64(c * i) <= 3.4e+58))
		tmp = Float64(c * i);
	else
		tmp = 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) <= -2.3) || ~(((c * i) <= 3.4e+58)))
		tmp = c * i;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.3], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.4e+58]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.2999999999999998 or 3.4000000000000001e58 < (*.f64 c i)

   1. Initial program 94.0%

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

   3. Taylor expanded in c around inf 56.5%

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

   if -2.2999999999999998 < (*.f64 c i) < 3.4000000000000001e58

   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 z around inf 33.0%

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

   4. Taylor expanded in t around inf 33.0%

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

      1. associate-/l* 33.0%

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

   6. Simplified 33.0%

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

   7. Taylor expanded in t around inf 30.8%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3 \lor \neg \left(c \cdot i \leq 3.4 \cdot 10^{+58}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ c \cdot i \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(c * i), $MachinePrecision]

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in c around inf 28.2%

   \[\leadsto \color{blue}{c \cdot i} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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)))