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

Percentage Accurate: 96.0% → 98.0%

Time: 10.2s

Alternatives: 14

Speedup: 1.3×

• 40.8% 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: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.3× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. associate-+l+ N/A

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

   4. lift-+.f64 N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. lift-*.f64 N/A

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

   8. lower-fma.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. lower-fma.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lower-fma.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 2: 43.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+107)
   (* z t)
   (if (<= (* z t) -2e-276)
     (* a b)
     (if (<= (* z t) 1e-316)
       (* c i)
       (if (<= (* z t) 2e-87)
         (* a b)
         (if (<= (* z t) 2e+79) (* 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 ((z * t) <= -5e+107) {
		tmp = z * t;
	} else if ((z * t) <= -2e-276) {
		tmp = a * b;
	} else if ((z * t) <= 1e-316) {
		tmp = c * i;
	} else if ((z * t) <= 2e-87) {
		tmp = a * b;
	} else if ((z * t) <= 2e+79) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+107)) then
        tmp = z * t
    else if ((z * t) <= (-2d-276)) then
        tmp = a * b
    else if ((z * t) <= 1d-316) then
        tmp = c * i
    else if ((z * t) <= 2d-87) then
        tmp = a * b
    else if ((z * t) <= 2d+79) then
        tmp = x * y
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+107) {
		tmp = z * t;
	} else if ((z * t) <= -2e-276) {
		tmp = a * b;
	} else if ((z * t) <= 1e-316) {
		tmp = c * i;
	} else if ((z * t) <= 2e-87) {
		tmp = a * b;
	} else if ((z * t) <= 2e+79) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+107:
		tmp = z * t
	elif (z * t) <= -2e-276:
		tmp = a * b
	elif (z * t) <= 1e-316:
		tmp = c * i
	elif (z * t) <= 2e-87:
		tmp = a * b
	elif (z * t) <= 2e+79:
		tmp = x * y
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+107)
		tmp = Float64(z * t);
	elseif (Float64(z * t) <= -2e-276)
		tmp = Float64(a * b);
	elseif (Float64(z * t) <= 1e-316)
		tmp = Float64(c * i);
	elseif (Float64(z * t) <= 2e-87)
		tmp = Float64(a * b);
	elseif (Float64(z * t) <= 2e+79)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+107)
		tmp = z * t;
	elseif ((z * t) <= -2e-276)
		tmp = a * b;
	elseif ((z * t) <= 1e-316)
		tmp = c * i;
	elseif ((z * t) <= 2e-87)
		tmp = a * b;
	elseif ((z * t) <= 2e+79)
		tmp = x * y;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+107], N[(z * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-276], N[(a * b), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-316], N[(c * i), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-87], N[(a * b), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+79], N[(x * y), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -5.0000000000000002e107 or 1.99999999999999993e79 < (*.f64 z t)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -5.0000000000000002e107 < (*.f64 z t) < -2e-276 or 9.999999837e-317 < (*.f64 z t) < 2.00000000000000004e-87

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   if -2e-276 < (*.f64 z t) < 9.999999837e-317

   1. Initial program 86.2%

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

   3. Taylor expanded in c around inf

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

      1. lower-*.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if 2.00000000000000004e-87 < (*.f64 z t) < 1.99999999999999993e79

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 45.4

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

   5. Applied rewrites 45.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+201}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+107)
   (* z t)
   (if (<= (* z t) -2e-276)
     (* a b)
     (if (<= (* z t) 1e-316)
       (* c i)
       (if (<= (* z t) 2e-87)
         (* a b)
         (if (<= (* z t) 5e+201) (* 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 ((z * t) <= -5e+107) {
		tmp = z * t;
	} else if ((z * t) <= -2e-276) {
		tmp = a * b;
	} else if ((z * t) <= 1e-316) {
		tmp = c * i;
	} else if ((z * t) <= 2e-87) {
		tmp = a * b;
	} else if ((z * t) <= 5e+201) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+107)) then
        tmp = z * t
    else if ((z * t) <= (-2d-276)) then
        tmp = a * b
    else if ((z * t) <= 1d-316) then
        tmp = c * i
    else if ((z * t) <= 2d-87) then
        tmp = a * b
    else if ((z * t) <= 5d+201) then
        tmp = c * i
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+107) {
		tmp = z * t;
	} else if ((z * t) <= -2e-276) {
		tmp = a * b;
	} else if ((z * t) <= 1e-316) {
		tmp = c * i;
	} else if ((z * t) <= 2e-87) {
		tmp = a * b;
	} else if ((z * t) <= 5e+201) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+107:
		tmp = z * t
	elif (z * t) <= -2e-276:
		tmp = a * b
	elif (z * t) <= 1e-316:
		tmp = c * i
	elif (z * t) <= 2e-87:
		tmp = a * b
	elif (z * t) <= 5e+201:
		tmp = c * i
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+107)
		tmp = Float64(z * t);
	elseif (Float64(z * t) <= -2e-276)
		tmp = Float64(a * b);
	elseif (Float64(z * t) <= 1e-316)
		tmp = Float64(c * i);
	elseif (Float64(z * t) <= 2e-87)
		tmp = Float64(a * b);
	elseif (Float64(z * t) <= 5e+201)
		tmp = Float64(c * i);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+107)
		tmp = z * t;
	elseif ((z * t) <= -2e-276)
		tmp = a * b;
	elseif ((z * t) <= 1e-316)
		tmp = c * i;
	elseif ((z * t) <= 2e-87)
		tmp = a * b;
	elseif ((z * t) <= 5e+201)
		tmp = c * i;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+107], N[(z * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-276], N[(a * b), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-316], N[(c * i), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-87], N[(a * b), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+201], N[(c * i), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.0000000000000002e107 or 4.9999999999999995e201 < (*.f64 z t)

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -5.0000000000000002e107 < (*.f64 z t) < -2e-276 or 9.999999837e-317 < (*.f64 z t) < 2.00000000000000004e-87

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

   if -2e-276 < (*.f64 z t) < 9.999999837e-317 or 2.00000000000000004e-87 < (*.f64 z t) < 4.9999999999999995e201

   1. Initial program 92.7%

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

   3. Taylor expanded in c around inf

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

      1. lower-*.f64 45.5

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

   5. Applied rewrites 45.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-276}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 10^{-316}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+201}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t, x \cdot y\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma z t (* x y))) (t_2 (+ (* x y) (* z t))))
   (if (<= t_2 -1e+107) t_1 (if (<= t_2 2e+193) (fma a b (* c i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(z, t, (x * y));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+193) {
		tmp = fma(a, b, (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(z, t, Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+193)
		tmp = fma(a, b, Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+107], t$95$1, If[LessEqual[t$95$2, 2e+193], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < -9.9999999999999997e106 or 2.00000000000000013e193 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 90.3%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 96.8

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 85.0

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

   7. Applied rewrites 85.0%

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

   if -9.9999999999999997e106 < (+.f64 (*.f64 x y) (*.f64 z t)) < 2.00000000000000013e193

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 41.8

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

   5. Applied rewrites 41.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 88.9

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

   8. Applied rewrites 88.9%

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

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 79.2%

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

Alternative 5: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, t, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -2e+92)
   (fma z t (* c i))
   (if (<= (* z t) 2e-87)
     (fma a b (* c i))
     (if (<= (* z t) 5e+25) (fma i c (* x y)) (fma i c (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -2e+92) {
		tmp = fma(z, t, (c * i));
	} else if ((z * t) <= 2e-87) {
		tmp = fma(a, b, (c * i));
	} else if ((z * t) <= 5e+25) {
		tmp = fma(i, c, (x * y));
	} else {
		tmp = fma(i, c, (z * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -2e+92)
		tmp = fma(z, t, Float64(c * i));
	elseif (Float64(z * t) <= 2e-87)
		tmp = fma(a, b, Float64(c * i));
	elseif (Float64(z * t) <= 5e+25)
		tmp = fma(i, c, Float64(x * y));
	else
		tmp = fma(i, c, Float64(z * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+92], N[(z * t + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-87], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+25], N[(i * c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -2.0000000000000001e92

   1. Initial program 91.5%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   5. Taylor expanded in c around inf

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

      1. lower-*.f64 74.7

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

   7. Applied rewrites 74.7%

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

   if -2.0000000000000001e92 < (*.f64 z t) < 2.00000000000000004e-87

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 42.2

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

   5. Applied rewrites 42.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 75.2

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

   8. Applied rewrites 75.2%

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

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 72.0%

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

   if 2.00000000000000004e-87 < (*.f64 z t) < 5.00000000000000024e25

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 81.0

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

   7. Applied rewrites 81.0%

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

   if 5.00000000000000024e25 < (*.f64 z t)

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 36.1

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

   5. Applied rewrites 36.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 36.1

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

   7. Applied rewrites 36.1%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 79.0

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

   10. Applied rewrites 79.0%

       \[\leadsto \mathsf{fma}\left(i, c, \color{blue}{t \cdot z}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, t, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* z t))))
   (if (<= (* z t) -2e+92)
     t_1
     (if (<= (* z t) 2e-87)
       (fma a b (* c i))
       (if (<= (* z t) 5e+25) (fma i c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, c, (z * t));
	double tmp;
	if ((z * t) <= -2e+92) {
		tmp = t_1;
	} else if ((z * t) <= 2e-87) {
		tmp = fma(a, b, (c * i));
	} else if ((z * t) <= 5e+25) {
		tmp = fma(i, c, (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -2e+92)
		tmp = t_1;
	elseif (Float64(z * t) <= 2e-87)
		tmp = fma(a, b, Float64(c * i));
	elseif (Float64(z * t) <= 5e+25)
		tmp = fma(i, c, Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+92], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 2e-87], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+25], N[(i * c + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -2.0000000000000001e92 or 5.00000000000000024e25 < (*.f64 z t)

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 29.6

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

   5. Applied rewrites 29.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 29.6

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

   7. Applied rewrites 29.6%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 76.2

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

   10. Applied rewrites 76.2%

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

   if -2.0000000000000001e92 < (*.f64 z t) < 2.00000000000000004e-87

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 42.2

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

   5. Applied rewrites 42.2%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 75.2

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

   8. Applied rewrites 75.2%

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

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 72.0%

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

   if 2.00000000000000004e-87 < (*.f64 z t) < 5.00000000000000024e25

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 81.0

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

   7. Applied rewrites 81.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(i, c, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma z t (fma x y (* a b)))))
   (if (<= (* x y) -1e+107)
     t_1
     (if (<= (* x y) 1e+112) (fma a b (fma c i (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(z, t, fma(x, y, (a * b)));
	double tmp;
	if ((x * y) <= -1e+107) {
		tmp = t_1;
	} else if ((x * y) <= 1e+112) {
		tmp = fma(a, b, fma(c, i, (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(z, t, fma(x, y, Float64(a * b)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+107)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+112)
		tmp = fma(a, b, fma(c, i, Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z * t + N[(x * y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+112], N[(a * b + N[(c * i + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999997e106 or 9.9999999999999993e111 < (*.f64 x y)

   1. Initial program 85.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 95.9

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 93.4

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

   7. Applied rewrites 93.4%

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

   if -9.9999999999999997e106 < (*.f64 x y) < 9.9999999999999993e111

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 31.8

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

   5. Applied rewrites 31.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 93.6

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

   8. Applied rewrites 93.6%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x y (fma a b (* z t)))))
   (if (<= (* x y) -1e+107)
     t_1
     (if (<= (* x y) 1e+112) (fma a b (fma c i (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(x, y, fma(a, b, (z * t)));
	double tmp;
	if ((x * y) <= -1e+107) {
		tmp = t_1;
	} else if ((x * y) <= 1e+112) {
		tmp = fma(a, b, fma(c, i, (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, y, fma(a, b, Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+107)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+112)
		tmp = fma(a, b, fma(c, i, Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * y + N[(a * b + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+112], N[(a * b + N[(c * i + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999997e106 or 9.9999999999999993e111 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in c around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 88.0

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

   5. Applied rewrites 88.0%

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

   if -9.9999999999999997e106 < (*.f64 x y) < 9.9999999999999993e111

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 31.8

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

   5. Applied rewrites 31.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 93.6

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

   8. Applied rewrites 93.6%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+107)
   (fma z t (* x y))
   (if (<= (* z t) 5e+25)
     (fma a b (fma c i (* x y)))
     (fma a b (fma 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 ((z * t) <= -5e+107) {
		tmp = fma(z, t, (x * y));
	} else if ((z * t) <= 5e+25) {
		tmp = fma(a, b, fma(c, i, (x * y)));
	} else {
		tmp = fma(a, b, fma(c, i, (z * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+107)
		tmp = fma(z, t, Float64(x * y));
	elseif (Float64(z * t) <= 5e+25)
		tmp = fma(a, b, fma(c, i, Float64(x * y)));
	else
		tmp = fma(a, b, fma(c, i, Float64(z * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+107], N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+25], N[(a * b + N[(c * i + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * b + N[(c * i + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.0000000000000002e107

   1. Initial program 91.3%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 87.3

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

   7. Applied rewrites 87.3%

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

   if -5.0000000000000002e107 < (*.f64 z t) < 5.00000000000000024e25

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 93.3

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

   5. Applied rewrites 93.3%

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

   if 5.00000000000000024e25 < (*.f64 z t)

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 16.4

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 90.5

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

   8. Applied rewrites 90.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma z t (* x y))))
   (if (<= (* x y) -1.15e+107)
     t_1
     (if (<= (* x y) 5.6e+123) (fma a b (fma c i (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(z, t, (x * y));
	double tmp;
	if ((x * y) <= -1.15e+107) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e+123) {
		tmp = fma(a, b, fma(c, i, (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(z, t, Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.15e+107)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.6e+123)
		tmp = fma(a, b, fma(c, i, Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z * t + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.15e+107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.6e+123], N[(a * b + N[(c * i + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.15e107 or 5.60000000000000023e123 < (*.f64 x y)

   1. Initial program 85.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lower-fma.f64 95.9

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 85.5

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

   7. Applied rewrites 85.5%

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

   if -1.15e107 < (*.f64 x y) < 5.60000000000000023e123

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 31.8

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

   5. Applied rewrites 31.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 93.6

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

   8. Applied rewrites 93.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(a, b, \mathsf{fma}\left(c, i, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, t, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i c (* z t))))
   (if (<= (* z t) -2e+92) t_1 (if (<= (* z t) 0.02) (fma a b (* c i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, c, (z * t));
	double tmp;
	if ((z * t) <= -2e+92) {
		tmp = t_1;
	} else if ((z * t) <= 0.02) {
		tmp = fma(a, b, (c * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, c, Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -2e+92)
		tmp = t_1;
	elseif (Float64(z * t) <= 0.02)
		tmp = fma(a, b, Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * c + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -2e+92], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 0.02], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.0000000000000001e92 or 0.0200000000000000004 < (*.f64 z t)

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 30.5

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

   5. Applied rewrites 30.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 30.5

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

   7. Applied rewrites 30.5%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 74.0

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

   10. Applied rewrites 74.0%

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

   if -2.0000000000000001e92 < (*.f64 z t) < 0.0200000000000000004

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 39.6

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

   5. Applied rewrites 39.6%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 73.0

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

   8. Applied rewrites 73.0%

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

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 69.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, c, z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+201}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+107)
   (* z t)
   (if (<= (* z t) 5e+201) (fma 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 ((z * t) <= -5e+107) {
		tmp = z * t;
	} else if ((z * t) <= 5e+201) {
		tmp = fma(a, b, (c * i));
	} else {
		tmp = z * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+107)
		tmp = Float64(z * t);
	elseif (Float64(z * t) <= 5e+201)
		tmp = fma(a, b, Float64(c * i));
	else
		tmp = Float64(z * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+107], N[(z * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+201], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000002e107 or 4.9999999999999995e201 < (*.f64 z t)

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -5.0000000000000002e107 < (*.f64 z t) < 4.9999999999999995e201

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 35.4

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

   5. Applied rewrites 35.4%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 73.8

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

   8. Applied rewrites 73.8%

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

   9. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(a, b, c \cdot i\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 66.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+107}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+201}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+106}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.4e+106)
   (* a b)
   (if (<= (* a b) 3.05e+119) (* 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) <= -4.4e+106) {
		tmp = a * b;
	} else if ((a * b) <= 3.05e+119) {
		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) <= (-4.4d+106)) then
        tmp = a * b
    else if ((a * b) <= 3.05d+119) 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) <= -4.4e+106) {
		tmp = a * b;
	} else if ((a * b) <= 3.05e+119) {
		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) <= -4.4e+106:
		tmp = a * b
	elif (a * b) <= 3.05e+119:
		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) <= -4.4e+106)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 3.05e+119)
		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) <= -4.4e+106)
		tmp = a * b;
	elseif ((a * b) <= 3.05e+119)
		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], -4.4e+106], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.05e+119], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.39999999999999983e106 or 3.05e119 < (*.f64 a b)

   1. Initial program 90.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

   if -4.39999999999999983e106 < (*.f64 a b) < 3.05e119

   1. Initial program 96.5%

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

   3. Taylor expanded in c around inf

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

      1. lower-*.f64 34.5

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

   5. Applied rewrites 34.5%

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

Alternative 14: 26.9% 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 94.5%

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

3. Taylor expanded in a around inf

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

   1. lower-*.f64 27.1

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

5. Applied rewrites 27.1%

   \[\leadsto \color{blue}{a \cdot b} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024220 
(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)))