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

Percentage Accurate: 96.2% → 97.6%

Time: 10.7s

Alternatives: 16

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.5× speedup

Math

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

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) (* z t)))))

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) + (z * t);
	}
	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) + (z * t);
	}
	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) + (z * t)
	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(z * t));
	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) + (z * t);
	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[(z * t), $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%

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

   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 0 33.3%

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

   3. Taylor expanded in t around inf 55.6%

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

4. Final simplification 98.4%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. +-commutative 96.5%

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

   3. associate-+l+ 96.5%

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

   4. fma-def 97.6%

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

   5. associate-+r+ 97.6%

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

   6. +-commutative 97.6%

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

   7. fma-def 98.4%

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

   8. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 98.3% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. associate-+l+ 96.5%

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

   3. fma-def 96.9%

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

   4. associate-+l+ 96.9%

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

   5. fma-def 97.7%

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

   6. +-commutative 97.7%

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

   7. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 4: 96.6% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. fma-def 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 5: 43.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.35 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.35e+89)
   (* c i)
   (if (<= (* c i) -1.3e+19)
     (* x y)
     (if (<= (* c i) -1.3e-22)
       (* a b)
       (if (<= (* c i) -1.8e-105)
         (* x y)
         (if (<= (* c i) 3.7e-209)
           (* z t)
           (if (<= (* c i) 1.15e+111) (* 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) <= -2.35e+89) {
		tmp = c * i;
	} else if ((c * i) <= -1.3e+19) {
		tmp = x * y;
	} else if ((c * i) <= -1.3e-22) {
		tmp = a * b;
	} else if ((c * i) <= -1.8e-105) {
		tmp = x * y;
	} else if ((c * i) <= 3.7e-209) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e+111) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.35d+89)) then
        tmp = c * i
    else if ((c * i) <= (-1.3d+19)) then
        tmp = x * y
    else if ((c * i) <= (-1.3d-22)) then
        tmp = a * b
    else if ((c * i) <= (-1.8d-105)) then
        tmp = x * y
    else if ((c * i) <= 3.7d-209) then
        tmp = z * t
    else if ((c * i) <= 1.15d+111) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.35e+89) {
		tmp = c * i;
	} else if ((c * i) <= -1.3e+19) {
		tmp = x * y;
	} else if ((c * i) <= -1.3e-22) {
		tmp = a * b;
	} else if ((c * i) <= -1.8e-105) {
		tmp = x * y;
	} else if ((c * i) <= 3.7e-209) {
		tmp = z * t;
	} else if ((c * i) <= 1.15e+111) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.35e+89:
		tmp = c * i
	elif (c * i) <= -1.3e+19:
		tmp = x * y
	elif (c * i) <= -1.3e-22:
		tmp = a * b
	elif (c * i) <= -1.8e-105:
		tmp = x * y
	elif (c * i) <= 3.7e-209:
		tmp = z * t
	elif (c * i) <= 1.15e+111:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.35e+89)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.3e+19)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -1.3e-22)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -1.8e-105)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 3.7e-209)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.15e+111)
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.35e+89)
		tmp = c * i;
	elseif ((c * i) <= -1.3e+19)
		tmp = x * y;
	elseif ((c * i) <= -1.3e-22)
		tmp = a * b;
	elseif ((c * i) <= -1.8e-105)
		tmp = x * y;
	elseif ((c * i) <= 3.7e-209)
		tmp = z * t;
	elseif ((c * i) <= 1.15e+111)
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.35e+89], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.3e+19], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.3e-22], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.8e-105], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.7e-209], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.15e+111], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.35000000000000011e89 or 1.15000000000000001e111 < (*.f64 c i)

   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 c around inf 69.4%

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

   if -2.35000000000000011e89 < (*.f64 c i) < -1.3e19 or -1.3e-22 < (*.f64 c i) < -1.79999999999999982e-105 or 3.6999999999999998e-209 < (*.f64 c i) < 1.15000000000000001e111

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf 46.4%

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

   if -1.3e19 < (*.f64 c i) < -1.3e-22

   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 a around inf 68.6%

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

   if -1.79999999999999982e-105 < (*.f64 c i) < 3.6999999999999998e-209

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 48.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.35 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 6: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.75 \cdot 10^{-306}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -1.4e+47)
     t_2
     (if (<= (* x y) -3.1e-107)
       t_1
       (if (<= (* x y) -2.75e-306)
         (+ (* a b) (* z t))
         (if (<= (* x y) 2.2e-105)
           t_1
           (if (<= (* x y) 7e+67) (+ (* a b) (* c i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -1.4e+47) {
		tmp = t_2;
	} else if ((x * y) <= -3.1e-107) {
		tmp = t_1;
	} else if ((x * y) <= -2.75e-306) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.2e-105) {
		tmp = t_1;
	} else if ((x * y) <= 7e+67) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-1.4d+47)) then
        tmp = t_2
    else if ((x * y) <= (-3.1d-107)) then
        tmp = t_1
    else if ((x * y) <= (-2.75d-306)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 2.2d-105) then
        tmp = t_1
    else if ((x * y) <= 7d+67) then
        tmp = (a * b) + (c * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -1.4e+47) {
		tmp = t_2;
	} else if ((x * y) <= -3.1e-107) {
		tmp = t_1;
	} else if ((x * y) <= -2.75e-306) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.2e-105) {
		tmp = t_1;
	} else if ((x * y) <= 7e+67) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -1.4e+47:
		tmp = t_2
	elif (x * y) <= -3.1e-107:
		tmp = t_1
	elif (x * y) <= -2.75e-306:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 2.2e-105:
		tmp = t_1
	elif (x * y) <= 7e+67:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.4e+47)
		tmp = t_2;
	elseif (Float64(x * y) <= -3.1e-107)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.75e-306)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 2.2e-105)
		tmp = t_1;
	elseif (Float64(x * y) <= 7e+67)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.4e+47)
		tmp = t_2;
	elseif ((x * y) <= -3.1e-107)
		tmp = t_1;
	elseif ((x * y) <= -2.75e-306)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 2.2e-105)
		tmp = t_1;
	elseif ((x * y) <= 7e+67)
		tmp = (a * b) + (c * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.4e+47], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -3.1e-107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.75e-306], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-105], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7e+67], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.39999999999999994e47 or 7e67 < (*.f64 x y)

   1. Initial program 92.7%

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

   2. Taylor expanded in c around 0 86.1%

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

   3. Taylor expanded in t around 0 77.9%

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

   if -1.39999999999999994e47 < (*.f64 x y) < -3.10000000000000022e-107 or -2.74999999999999996e-306 < (*.f64 x y) < 2.20000000000000004e-105

   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 a around 0 86.0%

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

   3. Taylor expanded in t around inf 80.4%

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

   if -3.10000000000000022e-107 < (*.f64 x y) < -2.74999999999999996e-306

   1. Initial program 95.7%

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

   2. Taylor expanded in c around 0 85.5%

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

   3. Taylor expanded in t around inf 85.4%

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

   if 2.20000000000000004e-105 < (*.f64 x y) < 7e67

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+l+ 96.9%

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

      3. fma-def 97.0%

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

      4. associate-+l+ 97.0%

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

      5. fma-def 97.0%

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

      6. +-commutative 97.0%

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

      7. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 88.2%

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

   5. Taylor expanded in x around 0 85.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-107}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.75 \cdot 10^{-306}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-105}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 7: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.7 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{-192}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1e+259)
     (* x y)
     (if (<= (* x y) 3.7e-268)
       t_1
       (if (<= (* x y) 1.45e-192)
         (* z t)
         (if (<= (* x y) 1.8e+129) 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) <= -1e+259) {
		tmp = x * y;
	} else if ((x * y) <= 3.7e-268) {
		tmp = t_1;
	} else if ((x * y) <= 1.45e-192) {
		tmp = z * t;
	} else if ((x * y) <= 1.8e+129) {
		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) <= (-1d+259)) then
        tmp = x * y
    else if ((x * y) <= 3.7d-268) then
        tmp = t_1
    else if ((x * y) <= 1.45d-192) then
        tmp = z * t
    else if ((x * y) <= 1.8d+129) 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) <= -1e+259) {
		tmp = x * y;
	} else if ((x * y) <= 3.7e-268) {
		tmp = t_1;
	} else if ((x * y) <= 1.45e-192) {
		tmp = z * t;
	} else if ((x * y) <= 1.8e+129) {
		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) <= -1e+259:
		tmp = x * y
	elif (x * y) <= 3.7e-268:
		tmp = t_1
	elif (x * y) <= 1.45e-192:
		tmp = z * t
	elif (x * y) <= 1.8e+129:
		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) <= -1e+259)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 3.7e-268)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.45e-192)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.8e+129)
		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) <= -1e+259)
		tmp = x * y;
	elseif ((x * y) <= 3.7e-268)
		tmp = t_1;
	elseif ((x * y) <= 1.45e-192)
		tmp = z * t;
	elseif ((x * y) <= 1.8e+129)
		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], -1e+259], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.7e-268], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.45e-192], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.8e+129], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.999999999999999e258 or 1.8000000000000001e129 < (*.f64 x y)

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 83.8%

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

   if -9.999999999999999e258 < (*.f64 x y) < 3.70000000000000018e-268 or 1.45000000000000008e-192 < (*.f64 x y) < 1.8000000000000001e129

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+l+ 96.9%

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

      3. fma-def 97.4%

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

      4. associate-+l+ 97.4%

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

      5. fma-def 97.4%

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

      6. +-commutative 97.4%

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

      7. fma-def 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 73.4%

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

   5. Taylor expanded in x around 0 63.2%

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

   if 3.70000000000000018e-268 < (*.f64 x y) < 1.45000000000000008e-192

   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 z around inf 78.3%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.7 \cdot 10^{-268}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{-192}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{+129}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{-190}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.1e+259)
     (* x y)
     (if (<= (* x y) -2.4e-80)
       t_1
       (if (<= (* x y) 1.05e-190)
         (+ (* a b) (* z t))
         (if (<= (* x y) 2.5e+129) 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) <= -1.1e+259) {
		tmp = x * y;
	} else if ((x * y) <= -2.4e-80) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e-190) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.5e+129) {
		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) <= (-1.1d+259)) then
        tmp = x * y
    else if ((x * y) <= (-2.4d-80)) then
        tmp = t_1
    else if ((x * y) <= 1.05d-190) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 2.5d+129) 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) <= -1.1e+259) {
		tmp = x * y;
	} else if ((x * y) <= -2.4e-80) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e-190) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 2.5e+129) {
		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) <= -1.1e+259:
		tmp = x * y
	elif (x * y) <= -2.4e-80:
		tmp = t_1
	elif (x * y) <= 1.05e-190:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 2.5e+129:
		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) <= -1.1e+259)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.4e-80)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.05e-190)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 2.5e+129)
		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) <= -1.1e+259)
		tmp = x * y;
	elseif ((x * y) <= -2.4e-80)
		tmp = t_1;
	elseif ((x * y) <= 1.05e-190)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 2.5e+129)
		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], -1.1e+259], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.4e-80], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.05e-190], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+129], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.09999999999999996e259 or 2.5000000000000001e129 < (*.f64 x y)

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 83.8%

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

   if -1.09999999999999996e259 < (*.f64 x y) < -2.3999999999999999e-80 or 1.04999999999999996e-190 < (*.f64 x y) < 2.5000000000000001e129

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-+l+ 95.6%

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

      3. fma-def 96.5%

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

      4. associate-+l+ 96.5%

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

      5. fma-def 96.5%

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

      6. +-commutative 96.5%

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

      7. fma-def 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 82.6%

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

   5. Taylor expanded in x around 0 65.8%

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

   if -2.3999999999999999e-80 < (*.f64 x y) < 1.04999999999999996e-190

   1. Initial program 98.8%

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

   2. Taylor expanded in c around 0 70.3%

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

   3. Taylor expanded in t around inf 69.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+259}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{-190}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -7e+48)
     t_2
     (if (<= (* x y) -2.3e-84)
       t_1
       (if (<= (* x y) 3.8e-184)
         (+ (* a b) (* z t))
         (if (<= (* x y) 1.5e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7e+48) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-84) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e-184) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.5e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-7d+48)) then
        tmp = t_2
    else if ((x * y) <= (-2.3d-84)) then
        tmp = t_1
    else if ((x * y) <= 3.8d-184) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 1.5d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7e+48) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-84) {
		tmp = t_1;
	} else if ((x * y) <= 3.8e-184) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.5e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -7e+48:
		tmp = t_2
	elif (x * y) <= -2.3e-84:
		tmp = t_1
	elif (x * y) <= 3.8e-184:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 1.5e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -7e+48)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.3e-84)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.8e-184)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 1.5e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -7e+48)
		tmp = t_2;
	elseif ((x * y) <= -2.3e-84)
		tmp = t_1;
	elseif ((x * y) <= 3.8e-184)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 1.5e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7e+48], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e-84], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e-184], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.5e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.9999999999999995e48 or 1.50000000000000005e67 < (*.f64 x y)

   1. Initial program 92.7%

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

   2. Taylor expanded in c around 0 86.0%

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

   3. Taylor expanded in t around 0 77.7%

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

   if -6.9999999999999995e48 < (*.f64 x y) < -2.29999999999999981e-84 or 3.80000000000000017e-184 < (*.f64 x y) < 1.50000000000000005e67

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+l+ 98.6%

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

      3. fma-def 98.6%

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

      4. associate-+l+ 98.6%

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

      5. fma-def 98.6%

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

      6. +-commutative 98.6%

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

      7. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 84.2%

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

   5. Taylor expanded in x around 0 76.4%

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

   if -2.29999999999999981e-84 < (*.f64 x y) < 3.80000000000000017e-184

   1. Initial program 98.8%

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

   2. Taylor expanded in c around 0 70.3%

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

   3. Taylor expanded in t around inf 69.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+48}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-84}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 10: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{-66}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.22 \cdot 10^{-306}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{-106}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.05e-66)
   (+ (* c i) (* x y))
   (if (<= (* x y) -1.22e-306)
     (+ (* a b) (* z t))
     (if (<= (* x y) 4.4e-106)
       (+ (* c i) (* z t))
       (if (<= (* x y) 2.2e+67) (+ (* a b) (* c i)) (+ (* a b) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.05e-66) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= -1.22e-306) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 4.4e-106) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2.2e+67) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-2.05d-66)) then
        tmp = (c * i) + (x * y)
    else if ((x * y) <= (-1.22d-306)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 4.4d-106) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 2.2d+67) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2.05e-66) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= -1.22e-306) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 4.4e-106) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2.2e+67) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2.05e-66:
		tmp = (c * i) + (x * y)
	elif (x * y) <= -1.22e-306:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 4.4e-106:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 2.2e+67:
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2.05e-66)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(x * y) <= -1.22e-306)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 4.4e-106)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 2.2e+67)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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)
	tmp = 0.0;
	if ((x * y) <= -2.05e-66)
		tmp = (c * i) + (x * y);
	elseif ((x * y) <= -1.22e-306)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 4.4e-106)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 2.2e+67)
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.05e-66], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.22e-306], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.4e-106], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e+67], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2.04999999999999999e-66

   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 83.6%

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

   3. Taylor expanded in t around 0 68.5%

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

   if -2.04999999999999999e-66 < (*.f64 x y) < -1.21999999999999995e-306

   1. Initial program 96.7%

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

   2. Taylor expanded in c around 0 85.6%

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

   3. Taylor expanded in t around inf 82.3%

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

   if -1.21999999999999995e-306 < (*.f64 x y) < 4.39999999999999989e-106

   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 a around 0 84.5%

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

   3. Taylor expanded in t around inf 84.5%

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

   if 4.39999999999999989e-106 < (*.f64 x y) < 2.2e67

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-+l+ 96.9%

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

      3. fma-def 97.0%

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

      4. associate-+l+ 97.0%

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

      5. fma-def 97.0%

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

      6. +-commutative 97.0%

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

      7. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 88.2%

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

   5. Taylor expanded in x around 0 85.1%

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

   if 2.2e67 < (*.f64 x y)

   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 0 86.7%

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

   3. Taylor expanded in t around 0 86.5%

      \[\leadsto a \cdot b + \color{blue}{x \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{-66}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.22 \cdot 10^{-306}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{-106}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 11: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+140} \lor \neg \left(c \cdot i \leq 4.4 \cdot 10^{+101}\right):\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.5e+140) (not (<= (* c i) 4.4e+101)))
   (+ (* c i) (* x y))
   (+ (* 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) <= -3.5e+140) || !((c * i) <= 4.4e+101)) {
		tmp = (c * i) + (x * y);
	} 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) <= (-3.5d+140)) .or. (.not. ((c * i) <= 4.4d+101))) then
        tmp = (c * i) + (x * y)
    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) <= -3.5e+140) || !((c * i) <= 4.4e+101)) {
		tmp = (c * i) + (x * y);
	} 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) <= -3.5e+140) or not ((c * i) <= 4.4e+101):
		tmp = (c * i) + (x * y)
	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) <= -3.5e+140) || !(Float64(c * i) <= 4.4e+101))
		tmp = Float64(Float64(c * i) + Float64(x * y));
	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) <= -3.5e+140) || ~(((c * i) <= 4.4e+101)))
		tmp = (c * i) + (x * y);
	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], -3.5e+140], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4.4e+101]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(x * y), $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) < -3.49999999999999989e140 or 4.4000000000000001e101 < (*.f64 c i)

   1. Initial program 93.3%

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

   2. Taylor expanded in a around 0 91.9%

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

   3. Taylor expanded in t around 0 86.9%

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

   if -3.49999999999999989e140 < (*.f64 c i) < 4.4000000000000001e101

   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 c around 0 89.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+140} \lor \neg \left(c \cdot i \leq 4.4 \cdot 10^{+101}\right):\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 12: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+110} \lor \neg \left(c \cdot i \leq 5.3 \cdot 10^{+94}\right):\\ \;\;\;\;c \cdot i + t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* c i) -3.2e+110) (not (<= (* c i) 5.3e+94)))
     (+ (* c i) t_1)
     (+ (* a b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((c * i) <= -3.2e+110) || !((c * i) <= 5.3e+94)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (((c * i) <= (-3.2d+110)) .or. (.not. ((c * i) <= 5.3d+94))) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((c * i) <= -3.2e+110) || !((c * i) <= 5.3e+94)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((c * i) <= -3.2e+110) or not ((c * i) <= 5.3e+94):
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(c * i) <= -3.2e+110) || !(Float64(c * i) <= 5.3e+94))
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((c * i) <= -3.2e+110) || ~(((c * i) <= 5.3e+94)))
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.2e+110], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.3e+94]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.19999999999999994e110 or 5.30000000000000003e94 < (*.f64 c i)

   1. Initial program 93.9%

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

   2. Taylor expanded in a around 0 90.5%

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

   if -3.19999999999999994e110 < (*.f64 c i) < 5.30000000000000003e94

   1. Initial program 97.7%

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

   2. Taylor expanded in c around 0 90.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+110} \lor \neg \left(c \cdot i \leq 5.3 \cdot 10^{+94}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 13: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{-12}:\\ \;\;\;\;c \cdot i + t_1\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* x y) -1.5e-12)
     (+ (* c i) t_1)
     (if (<= (* x y) 1.9e+71)
       (+ (* c i) (+ (* a b) (* z t)))
       (+ (* a b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -1.5e-12) {
		tmp = (c * i) + t_1;
	} else if ((x * y) <= 1.9e+71) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((x * y) <= (-1.5d-12)) then
        tmp = (c * i) + t_1
    else if ((x * y) <= 1.9d+71) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -1.5e-12) {
		tmp = (c * i) + t_1;
	} else if ((x * y) <= 1.9e+71) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -1.5e-12:
		tmp = (c * i) + t_1
	elif (x * y) <= 1.9e+71:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1.5e-12)
		tmp = Float64(Float64(c * i) + t_1);
	elseif (Float64(x * y) <= 1.9e+71)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -1.5e-12)
		tmp = (c * i) + t_1;
	elseif ((x * y) <= 1.9e+71)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-12], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+71], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.5000000000000001e-12

   1. Initial program 95.0%

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

   2. Taylor expanded in a around 0 83.5%

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

   if -1.5000000000000001e-12 < (*.f64 x y) < 1.9e71

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 97.2%

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

   if 1.9e71 < (*.f64 x y)

   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 0 86.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{-12}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 14: 43.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{-102}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.5e+117)
   (* c i)
   (if (<= (* c i) -8e-102)
     (* a b)
     (if (<= (* c i) 7.5e+107) (* z t) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5.5e+117) {
		tmp = c * i;
	} else if ((c * i) <= -8e-102) {
		tmp = a * b;
	} else if ((c * i) <= 7.5e+107) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-5.5d+117)) then
        tmp = c * i
    else if ((c * i) <= (-8d-102)) then
        tmp = a * b
    else if ((c * i) <= 7.5d+107) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5.5e+117) {
		tmp = c * i;
	} else if ((c * i) <= -8e-102) {
		tmp = a * b;
	} else if ((c * i) <= 7.5e+107) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.5e+117:
		tmp = c * i
	elif (c * i) <= -8e-102:
		tmp = a * b
	elif (c * i) <= 7.5e+107:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5.5e+117)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -8e-102)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 7.5e+107)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -5.5e+117)
		tmp = c * i;
	elseif ((c * i) <= -8e-102)
		tmp = a * b;
	elseif ((c * i) <= 7.5e+107)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5.5e+117], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -8e-102], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.5e+107], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.49999999999999965e117 or 7.4999999999999996e107 < (*.f64 c i)

   1. Initial program 93.5%

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

   2. Taylor expanded in c around inf 72.5%

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

   if -5.49999999999999965e117 < (*.f64 c i) < -7.99999999999999946e-102

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 38.3%

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

   if -7.99999999999999946e-102 < (*.f64 c i) < 7.4999999999999996e107

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 38.7%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{-102}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 42.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+117} \lor \neg \left(c \cdot i \leq 7 \cdot 10^{+107}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.8e+117) (not (<= (* c i) 7e+107))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.8e+117) || !((c * i) <= 7e+107)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.8d+117)) .or. (.not. ((c * i) <= 7d+107))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.8e+117) || !((c * i) <= 7e+107)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.8e+117) or not ((c * i) <= 7e+107):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.8e+117) || !(Float64(c * i) <= 7e+107))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.8e+117) || ~(((c * i) <= 7e+107)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.8e+117], N[Not[LessEqual[N[(c * i), $MachinePrecision], 7e+107]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8000000000000002e117 or 6.9999999999999995e107 < (*.f64 c i)

   1. Initial program 93.5%

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

   2. Taylor expanded in c around inf 72.5%

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

   if -3.8000000000000002e117 < (*.f64 c i) < 6.9999999999999995e107

   1. Initial program 97.7%

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

   2. Taylor expanded in a around inf 32.0%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+117} \lor \neg \left(c \cdot i \leq 7 \cdot 10^{+107}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 16: 26.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in a around inf 25.1%

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

3. Final simplification 25.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023310 
(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)))