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

Percentage Accurate: 95.8% → 97.6%

Time: 7.9s

Alternatives: 13

Speedup: 0.5×

• 41.4% 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: 95.8% 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, 0.1× speedup

Math

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

FPCore

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

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)) + (a * b)) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(a, b, (c * i));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * b + N[(c * i), $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 z around 0 25.0%

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

   3. Taylor expanded in x around 0 62.5%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]
   4. Step-by-step derivation

      1. fma-def 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 99.6%

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

Alternative 2: 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 96.9%

   \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
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 97.7%

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

   4. associate-+l+ 97.7%

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

   5. fma-def 98.4%

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

   6. +-commutative 98.4%

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

   7. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 97.0% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 62.7%

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

4. Final simplification 98.8%

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

Alternative 4: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* x y) -8.5e+293)
     (* x y)
     (if (<= (* x y) -3.2e-100)
       t_1
       (if (<= (* x y) 1.55e-246)
         t_2
         (if (<= (* x y) 3.5e-21)
           t_1
           (if (<= (* x y) 3.1e+156) t_2 (* 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 t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -8.5e+293) {
		tmp = x * y;
	} else if ((x * y) <= -3.2e-100) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-246) {
		tmp = t_2;
	} else if ((x * y) <= 3.5e-21) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+156) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (a * b) + (z * t)
    if ((x * y) <= (-8.5d+293)) then
        tmp = x * y
    else if ((x * y) <= (-3.2d-100)) then
        tmp = t_1
    else if ((x * y) <= 1.55d-246) then
        tmp = t_2
    else if ((x * y) <= 3.5d-21) then
        tmp = t_1
    else if ((x * y) <= 3.1d+156) then
        tmp = t_2
    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 t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -8.5e+293) {
		tmp = x * y;
	} else if ((x * y) <= -3.2e-100) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-246) {
		tmp = t_2;
	} else if ((x * y) <= 3.5e-21) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+156) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -8.5e+293:
		tmp = x * y
	elif (x * y) <= -3.2e-100:
		tmp = t_1
	elif (x * y) <= 1.55e-246:
		tmp = t_2
	elif (x * y) <= 3.5e-21:
		tmp = t_1
	elif (x * y) <= 3.1e+156:
		tmp = t_2
	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))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+293)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.2e-100)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.55e-246)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.5e-21)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.1e+156)
		tmp = t_2;
	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);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -8.5e+293)
		tmp = x * y;
	elseif ((x * y) <= -3.2e-100)
		tmp = t_1;
	elseif ((x * y) <= 1.55e-246)
		tmp = t_2;
	elseif ((x * y) <= 3.5e-21)
		tmp = t_1;
	elseif ((x * y) <= 3.1e+156)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e+293], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.2e-100], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e-246], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-21], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e+156], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.5000000000000001e293 or 3.1000000000000002e156 < (*.f64 x y)

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 77.6%

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

   if -8.5000000000000001e293 < (*.f64 x y) < -3.20000000000000017e-100 or 1.55e-246 < (*.f64 x y) < 3.5000000000000003e-21

   1. Initial program 97.9%

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

   2. Taylor expanded in z around 0 83.7%

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

   3. Taylor expanded in x around 0 71.2%

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

   if -3.20000000000000017e-100 < (*.f64 x y) < 1.55e-246 or 3.5000000000000003e-21 < (*.f64 x y) < 3.1000000000000002e156

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 90.6%

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

      1. fma-def 91.6%

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

      2. fma-def 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in c around 0 72.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-100}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-246}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-21}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ t_3 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -3.05 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* x y) (* a b))))
   (if (<= (* x y) -2.3e+84)
     t_3
     (if (<= (* x y) -3.05e-100)
       t_1
       (if (<= (* x y) 1e-246)
         t_2
         (if (<= (* x y) 3.9e-22) t_1 (if (<= (* x y) 4.1e+36) t_2 t_3)))))))

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) + (z * t);
	double t_3 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.3e+84) {
		tmp = t_3;
	} else if ((x * y) <= -3.05e-100) {
		tmp = t_1;
	} else if ((x * y) <= 1e-246) {
		tmp = t_2;
	} else if ((x * y) <= 3.9e-22) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+36) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (a * b) + (z * t)
    t_3 = (x * y) + (a * b)
    if ((x * y) <= (-2.3d+84)) then
        tmp = t_3
    else if ((x * y) <= (-3.05d-100)) then
        tmp = t_1
    else if ((x * y) <= 1d-246) then
        tmp = t_2
    else if ((x * y) <= 3.9d-22) then
        tmp = t_1
    else if ((x * y) <= 4.1d+36) then
        tmp = t_2
    else
        tmp = t_3
    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) + (z * t);
	double t_3 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.3e+84) {
		tmp = t_3;
	} else if ((x * y) <= -3.05e-100) {
		tmp = t_1;
	} else if ((x * y) <= 1e-246) {
		tmp = t_2;
	} else if ((x * y) <= 3.9e-22) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+36) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (z * t)
	t_3 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -2.3e+84:
		tmp = t_3
	elif (x * y) <= -3.05e-100:
		tmp = t_1
	elif (x * y) <= 1e-246:
		tmp = t_2
	elif (x * y) <= 3.9e-22:
		tmp = t_1
	elif (x * y) <= 4.1e+36:
		tmp = t_2
	else:
		tmp = t_3
	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(z * t))
	t_3 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -2.3e+84)
		tmp = t_3;
	elseif (Float64(x * y) <= -3.05e-100)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-246)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.9e-22)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e+36)
		tmp = t_2;
	else
		tmp = t_3;
	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) + (z * t);
	t_3 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -2.3e+84)
		tmp = t_3;
	elseif ((x * y) <= -3.05e-100)
		tmp = t_1;
	elseif ((x * y) <= 1e-246)
		tmp = t_2;
	elseif ((x * y) <= 3.9e-22)
		tmp = t_1;
	elseif ((x * y) <= 4.1e+36)
		tmp = t_2;
	else
		tmp = t_3;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e+84], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -3.05e-100], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-246], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.9e-22], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+36], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.2999999999999999e84 or 4.10000000000000013e36 < (*.f64 x y)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 84.6%

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

   3. Taylor expanded in c around 0 74.4%

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

   if -2.2999999999999999e84 < (*.f64 x y) < -3.05e-100 or 9.99999999999999956e-247 < (*.f64 x y) < 3.89999999999999998e-22

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 83.2%

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

   3. Taylor expanded in x around 0 80.3%

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

   if -3.05e-100 < (*.f64 x y) < 9.99999999999999956e-247 or 3.89999999999999998e-22 < (*.f64 x y) < 4.10000000000000013e36

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 95.3%

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

      1. fma-def 96.5%

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

      2. fma-def 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in c around 0 75.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.05 \cdot 10^{-100}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 10^{-246}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]

Alternative 6: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 450000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -9e+293)
     (* x y)
     (if (<= (* x y) 2.7e-24)
       t_1
       (if (<= (* x y) 450000000.0)
         (* z t)
         (if (<= (* x y) 4.6e+150) 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) <= -9e+293) {
		tmp = x * y;
	} else if ((x * y) <= 2.7e-24) {
		tmp = t_1;
	} else if ((x * y) <= 450000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 4.6e+150) {
		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) <= (-9d+293)) then
        tmp = x * y
    else if ((x * y) <= 2.7d-24) then
        tmp = t_1
    else if ((x * y) <= 450000000.0d0) then
        tmp = z * t
    else if ((x * y) <= 4.6d+150) 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) <= -9e+293) {
		tmp = x * y;
	} else if ((x * y) <= 2.7e-24) {
		tmp = t_1;
	} else if ((x * y) <= 450000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 4.6e+150) {
		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) <= -9e+293:
		tmp = x * y
	elif (x * y) <= 2.7e-24:
		tmp = t_1
	elif (x * y) <= 450000000.0:
		tmp = z * t
	elif (x * y) <= 4.6e+150:
		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) <= -9e+293)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.7e-24)
		tmp = t_1;
	elseif (Float64(x * y) <= 450000000.0)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 4.6e+150)
		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) <= -9e+293)
		tmp = x * y;
	elseif ((x * y) <= 2.7e-24)
		tmp = t_1;
	elseif ((x * y) <= 450000000.0)
		tmp = z * t;
	elseif ((x * y) <= 4.6e+150)
		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], -9e+293], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.7e-24], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 450000000.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.6e+150], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.99999999999999932e293 or 4.60000000000000002e150 < (*.f64 x y)

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 77.6%

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

   if -8.99999999999999932e293 < (*.f64 x y) < 2.70000000000000007e-24 or 4.5e8 < (*.f64 x y) < 4.60000000000000002e150

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 76.3%

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

   3. Taylor expanded in x around 0 66.6%

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

   if 2.70000000000000007e-24 < (*.f64 x y) < 4.5e8

   1. Initial program 87.5%

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

   2. Taylor expanded in z around inf 63.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-24}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 450000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -2.1 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -9 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* a b) -2.1e-7)
     t_2
     (if (<= (* a b) -9e-297)
       t_1
       (if (<= (* a b) 6.2e-118)
         (+ (* x y) (* c i))
         (if (<= (* a b) 1.5e+140) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -2.1e-7) {
		tmp = t_2;
	} else if ((a * b) <= -9e-297) {
		tmp = t_1;
	} else if ((a * b) <= 6.2e-118) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 1.5e+140) {
		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 = (c * i) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((a * b) <= (-2.1d-7)) then
        tmp = t_2
    else if ((a * b) <= (-9d-297)) then
        tmp = t_1
    else if ((a * b) <= 6.2d-118) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 1.5d+140) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -2.1e-7) {
		tmp = t_2;
	} else if ((a * b) <= -9e-297) {
		tmp = t_1;
	} else if ((a * b) <= 6.2e-118) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 1.5e+140) {
		tmp = t_1;
	} 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 = (x * y) + (a * b)
	tmp = 0
	if (a * b) <= -2.1e-7:
		tmp = t_2
	elif (a * b) <= -9e-297:
		tmp = t_1
	elif (a * b) <= 6.2e-118:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 1.5e+140:
		tmp = t_1
	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(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -2.1e-7)
		tmp = t_2;
	elseif (Float64(a * b) <= -9e-297)
		tmp = t_1;
	elseif (Float64(a * b) <= 6.2e-118)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 1.5e+140)
		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 = (c * i) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -2.1e-7)
		tmp = t_2;
	elseif ((a * b) <= -9e-297)
		tmp = t_1;
	elseif ((a * b) <= 6.2e-118)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 1.5e+140)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.1e-7], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -9e-297], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 6.2e-118], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.5e+140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.1e-7 or 1.49999999999999998e140 < (*.f64 a b)

   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 z around 0 87.9%

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

   3. Taylor expanded in c around 0 81.9%

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

   if -2.1e-7 < (*.f64 a b) < -8.99999999999999951e-297 or 6.2000000000000002e-118 < (*.f64 a b) < 1.49999999999999998e140

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 84.9%

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

      1. fma-def 85.0%

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

      2. fma-def 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in a around 0 74.2%

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

   if -8.99999999999999951e-297 < (*.f64 a b) < 6.2000000000000002e-118

   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 0 73.7%

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

   3. Taylor expanded in a around 0 72.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -9 \cdot 10^{-297}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]

Alternative 8: 43.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.8 \cdot 10^{-218}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.18 \cdot 10^{+148}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -9.8e+68)
   (* a b)
   (if (<= (* a b) -8e-8)
     (* x y)
     (if (<= (* a b) 1.8e-218)
       (* z t)
       (if (<= (* a b) 1.18e+148) (* 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 ((a * b) <= -9.8e+68) {
		tmp = a * b;
	} else if ((a * b) <= -8e-8) {
		tmp = x * y;
	} else if ((a * b) <= 1.8e-218) {
		tmp = z * t;
	} else if ((a * b) <= 1.18e+148) {
		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 ((a * b) <= (-9.8d+68)) then
        tmp = a * b
    else if ((a * b) <= (-8d-8)) then
        tmp = x * y
    else if ((a * b) <= 1.8d-218) then
        tmp = z * t
    else if ((a * b) <= 1.18d+148) 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 ((a * b) <= -9.8e+68) {
		tmp = a * b;
	} else if ((a * b) <= -8e-8) {
		tmp = x * y;
	} else if ((a * b) <= 1.8e-218) {
		tmp = z * t;
	} else if ((a * b) <= 1.18e+148) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -9.8e+68:
		tmp = a * b
	elif (a * b) <= -8e-8:
		tmp = x * y
	elif (a * b) <= 1.8e-218:
		tmp = z * t
	elif (a * b) <= 1.18e+148:
		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(a * b) <= -9.8e+68)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -8e-8)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.8e-218)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.18e+148)
		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 ((a * b) <= -9.8e+68)
		tmp = a * b;
	elseif ((a * b) <= -8e-8)
		tmp = x * y;
	elseif ((a * b) <= 1.8e-218)
		tmp = z * t;
	elseif ((a * b) <= 1.18e+148)
		tmp = c * i;
	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], -9.8e+68], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8e-8], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.8e-218], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.18e+148], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -9.79999999999999956e68 or 1.18e148 < (*.f64 a b)

   1. Initial program 92.2%

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

   2. Taylor expanded in a around inf 69.8%

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

   if -9.79999999999999956e68 < (*.f64 a b) < -8.0000000000000002e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 77.4%

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

   if -8.0000000000000002e-8 < (*.f64 a b) < 1.80000000000000006e-218

   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 41.8%

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

   if 1.80000000000000006e-218 < (*.f64 a b) < 1.18e148

   1. Initial program 98.5%

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

   2. Taylor expanded in c around inf 39.8%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.8 \cdot 10^{-218}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.18 \cdot 10^{+148}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+36}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.15e+90) (not (<= (* x y) 1.75e+36)))
   (+ (* c i) (+ (* x y) (* a b)))
   (+ (* 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) <= -1.15e+90) || !((x * y) <= 1.75e+36)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.15d+90)) .or. (.not. ((x * y) <= 1.75d+36))) then
        tmp = (c * i) + ((x * y) + (a * b))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.15e+90) || !((x * y) <= 1.75e+36)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.15e+90) or not ((x * y) <= 1.75e+36):
		tmp = (c * i) + ((x * y) + (a * b))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.15e+90) || !(Float64(x * y) <= 1.75e+36))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.15e+90) || ~(((x * y) <= 1.75e+36)))
		tmp = (c * i) + ((x * y) + (a * b));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.15e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.75e+36]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.15e90 or 1.7499999999999999e36 < (*.f64 x y)

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 85.4%

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

   if -1.15e90 < (*.f64 x y) < 1.7499999999999999e36

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0 94.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+36}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 10: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+285}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.2e+285)
   (+ (* x y) (* a b))
   (if (<= (* x y) 4.2e+143)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.2e+285) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= 4.2e+143) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-3.2d+285)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= 4.2d+143) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.2e+285) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= 4.2e+143) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.2e+285:
		tmp = (x * y) + (a * b)
	elif (x * y) <= 4.2e+143:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+285)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= 4.2e+143)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -3.2e+285)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= 4.2e+143)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+285], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.2e+143], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.20000000000000025e285

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0 90.0%

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

   3. Taylor expanded in c around 0 90.0%

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

   if -3.20000000000000025e285 < (*.f64 x y) < 4.19999999999999975e143

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 88.6%

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

   if 4.19999999999999975e143 < (*.f64 x y)

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 82.8%

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

   3. Taylor expanded in a around 0 80.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+285}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+143}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]

Alternative 11: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{-7} \lor \neg \left(a \cdot b \leq 1.15 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.6e-7) (not (<= (* a b) 1.15e+140)))
   (+ (* x y) (* a b))
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.6e-7) || !((a * b) <= 1.15e+140)) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (c * i) + (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) <= (-1.6d-7)) .or. (.not. ((a * b) <= 1.15d+140))) then
        tmp = (x * y) + (a * b)
    else
        tmp = (c * i) + (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) <= -1.6e-7) || !((a * b) <= 1.15e+140)) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.6e-7) or not ((a * b) <= 1.15e+140):
		tmp = (x * y) + (a * b)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.6e-7) || !(Float64(a * b) <= 1.15e+140))
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = Float64(Float64(c * i) + 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) <= -1.6e-7) || ~(((a * b) <= 1.15e+140)))
		tmp = (x * y) + (a * b);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.6e-7], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.15e+140]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.6e-7 or 1.14999999999999995e140 < (*.f64 a b)

   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 z around 0 87.9%

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

   3. Taylor expanded in c around 0 81.9%

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

   if -1.6e-7 < (*.f64 a b) < 1.14999999999999995e140

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. fma-def 76.5%

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

      2. fma-def 76.5%

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

   4. Simplified 76.5%

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

   5. Taylor expanded in a around 0 69.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{-7} \lor \neg \left(a \cdot b \leq 1.15 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 12: 43.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+51} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+147}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -3e+51) (not (<= (* a b) 2.1e+147))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -3e+51) || !((a * b) <= 2.1e+147)) {
		tmp = a * b;
	} 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 (((a * b) <= (-3d+51)) .or. (.not. ((a * b) <= 2.1d+147))) then
        tmp = a * b
    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 (((a * b) <= -3e+51) || !((a * b) <= 2.1e+147)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -3e+51) or not ((a * b) <= 2.1e+147):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -3e+51) || !(Float64(a * b) <= 2.1e+147))
		tmp = Float64(a * b);
	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 (((a * b) <= -3e+51) || ~(((a * b) <= 2.1e+147)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -3e+51], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.1e+147]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3e51 or 2.10000000000000006e147 < (*.f64 a b)

   1. Initial program 92.5%

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

   2. Taylor expanded in a around inf 67.7%

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

   if -3e51 < (*.f64 a b) < 2.10000000000000006e147

   1. Initial program 99.4%

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

   2. Taylor expanded in c around inf 36.9%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+51} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+147}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 13: 28.1% 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 96.9%

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

2. Taylor expanded in a around inf 30.1%

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

3. Final simplification 30.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023320 
(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)))