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

Percentage Accurate: 95.4% → 97.4%

Time: 12.9s

Alternatives: 17

Speedup: 0.4×

• 42.1% 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: 95.4% 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: 97.4% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (fma c i (* 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) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(c, i, (x * y));
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 33.3%

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

   4. Taylor expanded in a around 0 50.1%

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

      1. fma-define 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 99.2%

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

Alternative 2: 97.7% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 98.4%

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

   3. associate-+l+ 98.4%

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

   4. fma-define 98.4%

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

   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. Final simplification 98.8%

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

Alternative 3: 97.7% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 98.4%

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

   3. +-commutative 98.4%

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

   4. fma-define 98.8%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 4: 97.2% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 98.4%

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

   3. associate-+l+ 98.4%

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

   4. fma-define 98.4%

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

   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. Step-by-step derivation

   1. fma-undefine 98.4%

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

6. Applied egg-rr 98.4%

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

7. Final simplification 98.4%

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

Alternative 5: 96.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 98.4%

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

   3. +-commutative 98.4%

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

   4. fma-define 98.8%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

   1. fma-undefine 98.4%

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

   2. fma-define 98.4%

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

   3. associate-+r+ 98.4%

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

6. Applied egg-rr 98.4%

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

7. Final simplification 98.4%

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

Alternative 6: 42.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-145}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-177}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{+117}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.5e+42)
   (* a b)
   (if (<= (* a b) -2.1e-145)
     (* c i)
     (if (<= (* a b) -4e-177)
       (* x y)
       (if (<= (* a b) 0.0)
         (* z t)
         (if (<= (* a b) 1.5e-60)
           (* x y)
           (if (<= (* a b) 8.2e+117) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.5e+42) {
		tmp = a * b;
	} else if ((a * b) <= -2.1e-145) {
		tmp = c * i;
	} else if ((a * b) <= -4e-177) {
		tmp = x * y;
	} else if ((a * b) <= 0.0) {
		tmp = z * t;
	} else if ((a * b) <= 1.5e-60) {
		tmp = x * y;
	} else if ((a * b) <= 8.2e+117) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-2.5d+42)) then
        tmp = a * b
    else if ((a * b) <= (-2.1d-145)) then
        tmp = c * i
    else if ((a * b) <= (-4d-177)) then
        tmp = x * y
    else if ((a * b) <= 0.0d0) then
        tmp = z * t
    else if ((a * b) <= 1.5d-60) then
        tmp = x * y
    else if ((a * b) <= 8.2d+117) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.5e+42) {
		tmp = a * b;
	} else if ((a * b) <= -2.1e-145) {
		tmp = c * i;
	} else if ((a * b) <= -4e-177) {
		tmp = x * y;
	} else if ((a * b) <= 0.0) {
		tmp = z * t;
	} else if ((a * b) <= 1.5e-60) {
		tmp = x * y;
	} else if ((a * b) <= 8.2e+117) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -2.5e+42:
		tmp = a * b
	elif (a * b) <= -2.1e-145:
		tmp = c * i
	elif (a * b) <= -4e-177:
		tmp = x * y
	elif (a * b) <= 0.0:
		tmp = z * t
	elif (a * b) <= 1.5e-60:
		tmp = x * y
	elif (a * b) <= 8.2e+117:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -2.5e+42)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.1e-145)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= -4e-177)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.5e-60)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8.2e+117)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -2.5e+42)
		tmp = a * b;
	elseif ((a * b) <= -2.1e-145)
		tmp = c * i;
	elseif ((a * b) <= -4e-177)
		tmp = x * y;
	elseif ((a * b) <= 0.0)
		tmp = z * t;
	elseif ((a * b) <= 1.5e-60)
		tmp = x * y;
	elseif ((a * b) <= 8.2e+117)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.5e+42], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.1e-145], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4e-177], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.5e-60], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.2e+117], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.50000000000000003e42 or 8.1999999999999999e117 < (*.f64 a b)

   1. Initial program 95.9%

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

   3. Taylor expanded in a around inf 64.2%

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

   if -2.50000000000000003e42 < (*.f64 a b) < -2.09999999999999991e-145

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 39.5%

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

   if -2.09999999999999991e-145 < (*.f64 a b) < -3.99999999999999981e-177 or 0.0 < (*.f64 a b) < 1.50000000000000009e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.0%

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

   if -3.99999999999999981e-177 < (*.f64 a b) < 0.0 or 1.50000000000000009e-60 < (*.f64 a b) < 8.1999999999999999e117

   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 inf 45.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-145}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-177}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{-60}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{+117}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.56 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.56e+112)
     (* x y)
     (if (<= (* x y) 2.2e-81)
       t_1
       (if (<= (* x y) 1.6e-45)
         (* z t)
         (if (<= (* x y) 3.4e+130) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.56e+112) {
		tmp = x * y;
	} else if ((x * y) <= 2.2e-81) {
		tmp = t_1;
	} else if ((x * y) <= 1.6e-45) {
		tmp = z * t;
	} else if ((x * y) <= 3.4e+130) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-1.56d+112)) then
        tmp = x * y
    else if ((x * y) <= 2.2d-81) then
        tmp = t_1
    else if ((x * y) <= 1.6d-45) then
        tmp = z * t
    else if ((x * y) <= 3.4d+130) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.56e+112) {
		tmp = x * y;
	} else if ((x * y) <= 2.2e-81) {
		tmp = t_1;
	} else if ((x * y) <= 1.6e-45) {
		tmp = z * t;
	} else if ((x * y) <= 3.4e+130) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.56e+112:
		tmp = x * y
	elif (x * y) <= 2.2e-81:
		tmp = t_1
	elif (x * y) <= 1.6e-45:
		tmp = z * t
	elif (x * y) <= 3.4e+130:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.56e+112)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.2e-81)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.6e-45)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 3.4e+130)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.56e+112)
		tmp = x * y;
	elseif ((x * y) <= 2.2e-81)
		tmp = t_1;
	elseif ((x * y) <= 1.6e-45)
		tmp = z * t;
	elseif ((x * y) <= 3.4e+130)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.56e+112], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-81], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.6e-45], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+130], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.55999999999999992e112 or 3.4000000000000001e130 < (*.f64 x y)

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 72.2%

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

   if -1.55999999999999992e112 < (*.f64 x y) < 2.1999999999999999e-81 or 1.60000000000000004e-45 < (*.f64 x y) < 3.4000000000000001e130

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 69.4%

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

   4. Taylor expanded in x around 0 62.3%

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

   if 2.1999999999999999e-81 < (*.f64 x y) < 1.60000000000000004e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 70.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.56 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-81}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+130}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.0% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (+ (* a b) (* 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) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 33.3%

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

      1. +-commutative 33.3%

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

      2. *-commutative 33.3%

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

      3. fma-define 33.3%

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

   5. Applied egg-rr 33.3%

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

   6. Taylor expanded in c around 0 66.7%

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

4. Final simplification 99.2%

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

Alternative 9: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.9e+248) (not (<= (* c i) 9e+200)))
   (+ (* x y) (* c i))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 9e+200)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.9d+248)) .or. (.not. ((c * i) <= 9d+200))) then
        tmp = (x * y) + (c * i)
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 9e+200)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.9e+248) or not ((c * i) <= 9e+200):
		tmp = (x * y) + (c * i)
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.9e+248) || !(Float64(c * i) <= 9e+200))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.9e+248) || ~(((c * i) <= 9e+200)))
		tmp = (x * y) + (c * i);
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.9e+248], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9e+200]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8999999999999999e248 or 8.99999999999999939e200 < (*.f64 c i)

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 91.6%

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

   4. Taylor expanded in a around 0 91.9%

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

   if -3.8999999999999999e248 < (*.f64 c i) < 8.99999999999999939e200

   1. Initial program 99.5%

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

   3. Taylor expanded in c around 0 94.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.8e+121)
   (+ (* c i) (+ (* a b) (* z t)))
   (if (<= (* c i) 2.7e+195)
     (+ (* a b) (+ (* x y) (* 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 ((c * i) <= -3.8e+121) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 2.7e+195) {
		tmp = (a * b) + ((x * y) + (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 ((c * i) <= (-3.8d+121)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((c * i) <= 2.7d+195) then
        tmp = (a * b) + ((x * y) + (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 ((c * i) <= -3.8e+121) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 2.7e+195) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.8e+121:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (c * i) <= 2.7e+195:
		tmp = (a * b) + ((x * y) + (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(c * i) <= -3.8e+121)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(c * i) <= 2.7e+195)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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 ((c * i) <= -3.8e+121)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((c * i) <= 2.7e+195)
		tmp = (a * b) + ((x * y) + (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[(c * i), $MachinePrecision], -3.8e+121], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e+195], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $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 c i) < -3.8e121

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -3.8e121 < (*.f64 c i) < 2.7000000000000002e195

   1. Initial program 99.4%

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

   3. Taylor expanded in c around 0 95.6%

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

   if 2.7000000000000002e195 < (*.f64 c i)

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 92.3%

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

   4. Taylor expanded in a around 0 89.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.4 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.4e+121)
   (+ (* c i) (+ (* a b) (* z t)))
   (if (<= (* c i) 1.5e+153)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (+ (* a b) (* x y)) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5.4e+121) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 1.5e+153) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = ((a * b) + (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 ((c * i) <= (-5.4d+121)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((c * i) <= 1.5d+153) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = ((a * b) + (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 ((c * i) <= -5.4e+121) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 1.5e+153) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = ((a * b) + (x * y)) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.4e+121:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (c * i) <= 1.5e+153:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = ((a * b) + (x * y)) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5.4e+121)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(c * i) <= 1.5e+153)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(a * b) + 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 ((c * i) <= -5.4e+121)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((c * i) <= 1.5e+153)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = ((a * b) + (x * y)) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5.4e+121], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.5e+153], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.4000000000000004e121

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 88.8%

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

   if -5.4000000000000004e121 < (*.f64 c i) < 1.50000000000000009e153

   1. Initial program 99.4%

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

   3. Taylor expanded in c around 0 96.1%

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

   if 1.50000000000000009e153 < (*.f64 c i)

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 90.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.4 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 2.15 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -9e+102) (not (<= (* x y) 2.15e+39)))
   (* x y)
   (+ (* 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) <= -9e+102) || !((x * y) <= 2.15e+39)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-9d+102)) .or. (.not. ((x * y) <= 2.15d+39))) then
        tmp = x * y
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -9e+102) || !((x * y) <= 2.15e+39)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -9e+102) or not ((x * y) <= 2.15e+39):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -9e+102) || !(Float64(x * y) <= 2.15e+39))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -9e+102) || ~(((x * y) <= 2.15e+39)))
		tmp = x * y;
	else
		tmp = (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], -9e+102], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.15e+39]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.00000000000000042e102 or 2.15e39 < (*.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 68.2%

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

   if -9.00000000000000042e102 < (*.f64 x y) < 2.15e39

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 92.7%

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

   4. Taylor expanded in c around 0 72.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 2.15 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 6.4 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -7.5e+89) (not (<= (* x y) 6.4e+28)))
   (+ (* a b) (* x y))
   (+ (* 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) <= -7.5e+89) || !((x * y) <= 6.4e+28)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-7.5d+89)) .or. (.not. ((x * y) <= 6.4d+28))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -7.5e+89) || !((x * y) <= 6.4e+28)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -7.5e+89) or not ((x * y) <= 6.4e+28):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -7.5e+89) || !(Float64(x * y) <= 6.4e+28))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -7.5e+89) || ~(((x * y) <= 6.4e+28)))
		tmp = (a * b) + (x * y);
	else
		tmp = (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], -7.5e+89], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6.4e+28]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -7.49999999999999947e89 or 6.4000000000000001e28 < (*.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. *-commutative 91.0%

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

      3. fma-define 91.0%

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

   5. Applied egg-rr 91.0%

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

   6. Taylor expanded in c around 0 76.3%

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

   if -7.49999999999999947e89 < (*.f64 x y) < 6.4000000000000001e28

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 93.1%

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

   4. Taylor expanded in c around 0 72.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 6.4 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 1.65 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5.5e+102) (not (<= (* x y) 1.65e+28)))
   (+ (* 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) <= -5.5e+102) || !((x * y) <= 1.65e+28)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-5.5d+102)) .or. (.not. ((x * y) <= 1.65d+28))) then
        tmp = (x * y) + (c * i)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -5.5e+102) || !((x * y) <= 1.65e+28)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -5.5e+102) or not ((x * y) <= 1.65e+28):
		tmp = (x * y) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -5.5e+102) || !(Float64(x * y) <= 1.65e+28))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -5.5e+102) || ~(((x * y) <= 1.65e+28)))
		tmp = (x * y) + (c * i);
	else
		tmp = (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], -5.5e+102], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.65e+28]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.49999999999999981e102 or 1.65e28 < (*.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 91.6%

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

   4. Taylor expanded in a around 0 83.9%

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

   if -5.49999999999999981e102 < (*.f64 x y) < 1.65e28

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 92.7%

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

   4. Taylor expanded in c around 0 72.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 1.65 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 2.1 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.9e+248) (not (<= (* c i) 2.1e+191))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 2.1e+191)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.9d+248)) .or. (.not. ((c * i) <= 2.1d+191))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 2.1e+191)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.9e+248) or not ((c * i) <= 2.1e+191):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.9e+248) || !(Float64(c * i) <= 2.1e+191))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.9e+248) || ~(((c * i) <= 2.1e+191)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.9e+248], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.1e+191]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8999999999999999e248 or 2.1000000000000001e191 < (*.f64 c i)

   1. Initial program 91.1%

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

   3. Taylor expanded in c around inf 84.9%

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

   if -3.8999999999999999e248 < (*.f64 c i) < 2.1000000000000001e191

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 33.3%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 2.1 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.5 \cdot 10^{+33} \lor \neg \left(a \cdot b \leq 4.6 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -7.5e+33) (not (<= (* a b) 4.6e+119))) (* 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 (((a * b) <= -7.5e+33) || !((a * b) <= 4.6e+119)) {
		tmp = a * b;
	} 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 (((a * b) <= (-7.5d+33)) .or. (.not. ((a * b) <= 4.6d+119))) then
        tmp = a * b
    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 (((a * b) <= -7.5e+33) || !((a * b) <= 4.6e+119)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -7.5e+33) or not ((a * b) <= 4.6e+119):
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -7.5e+33) || !(Float64(a * b) <= 4.6e+119))
		tmp = Float64(a * b);
	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 (((a * b) <= -7.5e+33) || ~(((a * b) <= 4.6e+119)))
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -7.5e+33], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.6e+119]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.50000000000000046e33 or 4.6000000000000001e119 < (*.f64 a b)

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 63.0%

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

   if -7.50000000000000046e33 < (*.f64 a b) < 4.6000000000000001e119

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 38.3%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.5 \cdot 10^{+33} \lor \neg \left(a \cdot b \leq 4.6 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in a around inf 28.4%

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

4. Final simplification 28.4%

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

Reproduce

herbie shell --seed 2024043 
(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)))