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

Percentage Accurate: 95.6% → 97.9%

Time: 6.2s

Alternatives: 13

Speedup: 0.5×

• 41.5% 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: 95.6% 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: 97.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4e+143)
   (fma c i (fma x y (fma z t (* a b))))
   (fma x y (fma z t (fma a b (* c i))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4e+143) {
		tmp = fma(c, i, fma(x, y, fma(z, t, (a * b))));
	} else {
		tmp = fma(x, y, fma(z, t, fma(a, b, (c * i))));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4e+143)
		tmp = fma(c, i, fma(x, y, fma(z, t, Float64(a * b))));
	else
		tmp = fma(x, y, fma(z, t, fma(a, b, Float64(c * i))));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4e+143], N[(c * i + N[(x * y + N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(z * t + N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000001e143

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. fma-def 97.8%

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

      3. associate-+l+ 97.8%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

   if -4.0000000000000001e143 < x

   1. Initial program 94.7%

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

      1. associate-+l+ 94.7%

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

      2. associate-+l+ 94.7%

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

      3. fma-def 96.2%

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

      4. fma-def 97.6%

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

      5. fma-def 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma c i (fma x y (fma z t (* a b)))))

C

assert(x < y);
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

x, y = sort([x, y])
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

NOTE: x and y should be sorted in increasing order before calling this function.
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 94.1%

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

   1. +-commutative 94.1%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 97.3%

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

   5. fma-def 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 3: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + \left(a \cdot b + t_1\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, t_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (+ (* a b) t_1))))
   (if (<= t_2 INFINITY) t_2 (fma c i t_1))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma(c, i, t_1);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(Float64(a * b) + t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = fma(c, i, t_1);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(c * i + t$95$1), $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%

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 33.3%

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

      3. associate-+l+ 33.3%

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

      4. fma-def 53.3%

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

      5. fma-def 60.0%

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

   3. Simplified 60.0%

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

      1. fma-udef 40.0%

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

      2. fma-udef 33.3%

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

      3. associate-+l+ 33.3%

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

      4. +-commutative 33.3%

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

      5. associate-+r+ 33.3%

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

   5. Applied egg-rr 33.3%

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

   6. Taylor expanded in a around 0 40.0%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{y \cdot x + t \cdot z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

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

Alternative 4: 96.7% accurate, 0.1× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma c i (+ (+ (* a b) (* x y)) (* z t))))

C

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

Julia

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(c * i + N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

   1. +-commutative 94.1%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 97.3%

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

   5. fma-def 97.7%

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

3. Simplified 97.7%

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

   1. fma-udef 96.5%

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

   2. fma-udef 96.1%

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

   3. associate-+l+ 96.1%

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

   4. +-commutative 96.1%

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

   5. associate-+r+ 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 5: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2.05 \cdot 10^{-190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.6 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.95 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* a b) -1.35e+109)
     (* a b)
     (if (<= (* a b) -2.2e+14)
       (* x y)
       (if (<= (* a b) -1.9e-111)
         t_1
         (if (<= (* a b) -2.05e-190)
           (* x y)
           (if (<= (* a b) 1.6e-262)
             t_1
             (if (<= (* a b) 2.6e-248)
               (* x y)
               (if (<= (* a b) 2.95e+158) t_1 (* a b))))))))))

C

assert(x < y);
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 ((a * b) <= -1.35e+109) {
		tmp = a * b;
	} else if ((a * b) <= -2.2e+14) {
		tmp = x * y;
	} else if ((a * b) <= -1.9e-111) {
		tmp = t_1;
	} else if ((a * b) <= -2.05e-190) {
		tmp = x * y;
	} else if ((a * b) <= 1.6e-262) {
		tmp = t_1;
	} else if ((a * b) <= 2.6e-248) {
		tmp = x * y;
	} else if ((a * b) <= 2.95e+158) {
		tmp = t_1;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 ((a * b) <= (-1.35d+109)) then
        tmp = a * b
    else if ((a * b) <= (-2.2d+14)) then
        tmp = x * y
    else if ((a * b) <= (-1.9d-111)) then
        tmp = t_1
    else if ((a * b) <= (-2.05d-190)) then
        tmp = x * y
    else if ((a * b) <= 1.6d-262) then
        tmp = t_1
    else if ((a * b) <= 2.6d-248) then
        tmp = x * y
    else if ((a * b) <= 2.95d+158) then
        tmp = t_1
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y;
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 ((a * b) <= -1.35e+109) {
		tmp = a * b;
	} else if ((a * b) <= -2.2e+14) {
		tmp = x * y;
	} else if ((a * b) <= -1.9e-111) {
		tmp = t_1;
	} else if ((a * b) <= -2.05e-190) {
		tmp = x * y;
	} else if ((a * b) <= 1.6e-262) {
		tmp = t_1;
	} else if ((a * b) <= 2.6e-248) {
		tmp = x * y;
	} else if ((a * b) <= 2.95e+158) {
		tmp = t_1;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -1.35e+109:
		tmp = a * b
	elif (a * b) <= -2.2e+14:
		tmp = x * y
	elif (a * b) <= -1.9e-111:
		tmp = t_1
	elif (a * b) <= -2.05e-190:
		tmp = x * y
	elif (a * b) <= 1.6e-262:
		tmp = t_1
	elif (a * b) <= 2.6e-248:
		tmp = x * y
	elif (a * b) <= 2.95e+158:
		tmp = t_1
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1.35e+109)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.2e+14)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -1.9e-111)
		tmp = t_1;
	elseif (Float64(a * b) <= -2.05e-190)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.6e-262)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.6e-248)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.95e+158)
		tmp = t_1;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1.35e+109)
		tmp = a * b;
	elseif ((a * b) <= -2.2e+14)
		tmp = x * y;
	elseif ((a * b) <= -1.9e-111)
		tmp = t_1;
	elseif ((a * b) <= -2.05e-190)
		tmp = x * y;
	elseif ((a * b) <= 1.6e-262)
		tmp = t_1;
	elseif ((a * b) <= 2.6e-248)
		tmp = x * y;
	elseif ((a * b) <= 2.95e+158)
		tmp = t_1;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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[(a * b), $MachinePrecision], -1.35e+109], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.2e+14], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.9e-111], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2.05e-190], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.6e-262], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.6e-248], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.95e+158], t$95$1, N[(a * b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.35000000000000001e109 or 2.94999999999999987e158 < (*.f64 a b)

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 72.0%

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

   if -1.35000000000000001e109 < (*.f64 a b) < -2.2e14 or -1.90000000000000011e-111 < (*.f64 a b) < -2.0500000000000001e-190 or 1.6e-262 < (*.f64 a b) < 2.60000000000000007e-248

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.4%

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

   if -2.2e14 < (*.f64 a b) < -1.90000000000000011e-111 or -2.0500000000000001e-190 < (*.f64 a b) < 1.6e-262 or 2.60000000000000007e-248 < (*.f64 a b) < 2.94999999999999987e158

   1. Initial program 95.8%

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

   2. Taylor expanded in a around 0 88.6%

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

   3. Taylor expanded in y around 0 61.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2.05 \cdot 10^{-190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.6 \cdot 10^{-262}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{-248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.95 \cdot 10^{+158}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 6: 42.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -69000000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-128}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3e+108)
   (* a b)
   (if (<= (* a b) -69000000000000.0)
     (* x y)
     (if (<= (* a b) -4.8e-106)
       (* c i)
       (if (<= (* a b) 5.2e-208)
         (* x y)
         (if (<= (* a b) 3.9e-128)
           (* z t)
           (if (<= (* a b) 1.05e-105)
             (* x y)
             (if (<= (* a b) 3.8e+128) (* z t) (* a b)))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3e+108) {
		tmp = a * b;
	} else if ((a * b) <= -69000000000000.0) {
		tmp = x * y;
	} else if ((a * b) <= -4.8e-106) {
		tmp = c * i;
	} else if ((a * b) <= 5.2e-208) {
		tmp = x * y;
	} else if ((a * b) <= 3.9e-128) {
		tmp = z * t;
	} else if ((a * b) <= 1.05e-105) {
		tmp = x * y;
	} else if ((a * b) <= 3.8e+128) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) <= (-3d+108)) then
        tmp = a * b
    else if ((a * b) <= (-69000000000000.0d0)) then
        tmp = x * y
    else if ((a * b) <= (-4.8d-106)) then
        tmp = c * i
    else if ((a * b) <= 5.2d-208) then
        tmp = x * y
    else if ((a * b) <= 3.9d-128) then
        tmp = z * t
    else if ((a * b) <= 1.05d-105) then
        tmp = x * y
    else if ((a * b) <= 3.8d+128) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y;
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) <= -3e+108) {
		tmp = a * b;
	} else if ((a * b) <= -69000000000000.0) {
		tmp = x * y;
	} else if ((a * b) <= -4.8e-106) {
		tmp = c * i;
	} else if ((a * b) <= 5.2e-208) {
		tmp = x * y;
	} else if ((a * b) <= 3.9e-128) {
		tmp = z * t;
	} else if ((a * b) <= 1.05e-105) {
		tmp = x * y;
	} else if ((a * b) <= 3.8e+128) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -3e+108:
		tmp = a * b
	elif (a * b) <= -69000000000000.0:
		tmp = x * y
	elif (a * b) <= -4.8e-106:
		tmp = c * i
	elif (a * b) <= 5.2e-208:
		tmp = x * y
	elif (a * b) <= 3.9e-128:
		tmp = z * t
	elif (a * b) <= 1.05e-105:
		tmp = x * y
	elif (a * b) <= 3.8e+128:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -3e+108)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -69000000000000.0)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -4.8e-106)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 5.2e-208)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.9e-128)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.05e-105)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.8e+128)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -3e+108)
		tmp = a * b;
	elseif ((a * b) <= -69000000000000.0)
		tmp = x * y;
	elseif ((a * b) <= -4.8e-106)
		tmp = c * i;
	elseif ((a * b) <= 5.2e-208)
		tmp = x * y;
	elseif ((a * b) <= 3.9e-128)
		tmp = z * t;
	elseif ((a * b) <= 1.05e-105)
		tmp = x * y;
	elseif ((a * b) <= 3.8e+128)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -3e+108], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -69000000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.8e-106], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.2e-208], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.9e-128], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.05e-105], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+128], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.99999999999999984e108 or 3.7999999999999999e128 < (*.f64 a b)

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 68.9%

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

   if -2.99999999999999984e108 < (*.f64 a b) < -6.9e13 or -4.7999999999999995e-106 < (*.f64 a b) < 5.20000000000000034e-208 or 3.89999999999999997e-128 < (*.f64 a b) < 1.05e-105

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 57.0%

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

   if -6.9e13 < (*.f64 a b) < -4.7999999999999995e-106

   1. Initial program 92.3%

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

   2. Taylor expanded in c around inf 56.0%

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

   if 5.20000000000000034e-208 < (*.f64 a b) < 3.89999999999999997e-128 or 1.05e-105 < (*.f64 a b) < 3.7999999999999999e128

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 49.1%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -69000000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-128}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 7: 96.8% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (* c i))))

C

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

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * i), $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%

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

   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. Taylor expanded in c around inf 34.0%

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

4. Final simplification 96.1%

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

Alternative 8: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -1.58 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* a b) -1.8e+109)
     (* a b)
     (if (<= (* a b) -5800000000000.0)
       t_1
       (if (<= (* a b) -1.58e-105)
         t_2
         (if (<= (* a b) 4e-69)
           t_1
           (if (<= (* a b) 2.05e+157) t_2 (* a b))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -1.8e+109) {
		tmp = a * b;
	} else if ((a * b) <= -5800000000000.0) {
		tmp = t_1;
	} else if ((a * b) <= -1.58e-105) {
		tmp = t_2;
	} else if ((a * b) <= 4e-69) {
		tmp = t_1;
	} else if ((a * b) <= 2.05e+157) {
		tmp = t_2;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (c * i) + (z * t)
    if ((a * b) <= (-1.8d+109)) then
        tmp = a * b
    else if ((a * b) <= (-5800000000000.0d0)) then
        tmp = t_1
    else if ((a * b) <= (-1.58d-105)) then
        tmp = t_2
    else if ((a * b) <= 4d-69) then
        tmp = t_1
    else if ((a * b) <= 2.05d+157) then
        tmp = t_2
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -1.8e+109) {
		tmp = a * b;
	} else if ((a * b) <= -5800000000000.0) {
		tmp = t_1;
	} else if ((a * b) <= -1.58e-105) {
		tmp = t_2;
	} else if ((a * b) <= 4e-69) {
		tmp = t_1;
	} else if ((a * b) <= 2.05e+157) {
		tmp = t_2;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -1.8e+109:
		tmp = a * b
	elif (a * b) <= -5800000000000.0:
		tmp = t_1
	elif (a * b) <= -1.58e-105:
		tmp = t_2
	elif (a * b) <= 4e-69:
		tmp = t_1
	elif (a * b) <= 2.05e+157:
		tmp = t_2
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1.8e+109)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -5800000000000.0)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.58e-105)
		tmp = t_2;
	elseif (Float64(a * b) <= 4e-69)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.05e+157)
		tmp = t_2;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1.8e+109)
		tmp = a * b;
	elseif ((a * b) <= -5800000000000.0)
		tmp = t_1;
	elseif ((a * b) <= -1.58e-105)
		tmp = t_2;
	elseif ((a * b) <= 4e-69)
		tmp = t_1;
	elseif ((a * b) <= 2.05e+157)
		tmp = t_2;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.8e+109], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5800000000000.0], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.58e-105], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 4e-69], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.05e+157], t$95$2, N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.8e109 or 2.05000000000000008e157 < (*.f64 a b)

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 72.0%

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

   if -1.8e109 < (*.f64 a b) < -5.8e12 or -1.57999999999999997e-105 < (*.f64 a b) < 3.9999999999999999e-69

   1. Initial program 97.6%

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

   2. Taylor expanded in a around 0 96.8%

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

   3. Taylor expanded in c around 0 80.3%

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

   if -5.8e12 < (*.f64 a b) < -1.57999999999999997e-105 or 3.9999999999999999e-69 < (*.f64 a b) < 2.05000000000000008e157

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 73.5%

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

   3. Taylor expanded in y around 0 65.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+109}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5800000000000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.58 \cdot 10^{-105}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-69}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.05 \cdot 10^{+157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+108} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot b + t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* a b) -7.8e+108) (not (<= (* a b) 1.85e+43)))
     (+ (* a b) t_1)
     (+ (* c i) t_1))))

C

assert(x < y);
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 (((a * b) <= -7.8e+108) || !((a * b) <= 1.85e+43)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 (((a * b) <= (-7.8d+108)) .or. (.not. ((a * b) <= 1.85d+43))) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + t_1
    end if
    code = tmp
end function

Java

assert x < y;
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 (((a * b) <= -7.8e+108) || !((a * b) <= 1.85e+43)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((a * b) <= -7.8e+108) or not ((a * b) <= 1.85e+43):
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -7.8e+108) || !(Float64(a * b) <= 1.85e+43))
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((a * b) <= -7.8e+108) || ~(((a * b) <= 1.85e+43)))
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -7.8e+108], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.85e+43]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.79999999999999969e108 or 1.85e43 < (*.f64 a b)

   1. Initial program 90.0%

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

   2. Taylor expanded in c around 0 84.3%

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

   if -7.79999999999999969e108 < (*.f64 a b) < 1.85e43

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0 93.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+108} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 10: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+258}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.5e+195)
   (+ (* c i) (* z t))
   (if (<= (* c i) 4.5e+258) (+ (* a b) (+ (* x y) (* z t))) (* c i))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+195) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 4.5e+258) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.5d+195)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 4.5d+258) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+195) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 4.5e+258) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.5e+195:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 4.5e+258:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = c * i
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.5e+195)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 4.5e+258)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.5e+195)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 4.5e+258)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.5e+195], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.5e+258], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.5000000000000002e195

   1. Initial program 84.6%

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

   2. Taylor expanded in a around 0 81.0%

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

   3. Taylor expanded in y around 0 77.2%

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

   if -3.5000000000000002e195 < (*.f64 c i) < 4.5000000000000004e258

   1. Initial program 97.6%

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

   2. Taylor expanded in c around 0 88.7%

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

   if 4.5000000000000004e258 < (*.f64 c i)

   1. Initial program 71.4%

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

   2. Taylor expanded in c around inf 81.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+258}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 11: 42.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{+151}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.75e+103)
   (* a b)
   (if (<= (* a b) 7.4e+151) (* c i) (* a b))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.75e+103) {
		tmp = a * b;
	} else if ((a * b) <= 7.4e+151) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.75d+103)) then
        tmp = a * b
    else if ((a * b) <= 7.4d+151) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.75e+103) {
		tmp = a * b;
	} else if ((a * b) <= 7.4e+151) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.75e+103:
		tmp = a * b
	elif (a * b) <= 7.4e+151:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.75e+103)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 7.4e+151)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.75e+103)
		tmp = a * b;
	elseif ((a * b) <= 7.4e+151)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.75e+103], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.4e+151], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.75e103 or 7.3999999999999995e151 < (*.f64 a b)

   1. Initial program 89.1%

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

   2. Taylor expanded in a around inf 70.8%

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

   if -1.75e103 < (*.f64 a b) < 7.3999999999999995e151

   1. Initial program 96.5%

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

   2. Taylor expanded in c around inf 28.5%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{+151}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 12: 43.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 6 \cdot 10^{+127}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.7e+103) (* a b) (if (<= (* a b) 6e+127) (* z t) (* a b))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+103) {
		tmp = a * b;
	} else if ((a * b) <= 6e+127) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.7d+103)) then
        tmp = a * b
    else if ((a * b) <= 6d+127) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+103) {
		tmp = a * b;
	} else if ((a * b) <= 6e+127) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.7e+103:
		tmp = a * b
	elif (a * b) <= 6e+127:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.7e+103)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 6e+127)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.7e+103)
		tmp = a * b;
	elseif ((a * b) <= 6e+127)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.7e+103], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6e+127], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.6999999999999999e103 or 6.0000000000000005e127 < (*.f64 a b)

   1. Initial program 88.6%

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

   2. Taylor expanded in a around inf 68.2%

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

   if -1.6999999999999999e103 < (*.f64 a b) < 6.0000000000000005e127

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 32.2%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 6 \cdot 10^{+127}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 27.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ a \cdot b \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (* a b))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a * b;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

2. Taylor expanded in a around inf 27.8%

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

3. Final simplification 27.8%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023195 
(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)))