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

Percentage Accurate: 95.7% → 97.9%

Time: 12.0s

Alternatives: 15

Speedup: 0.4×

• 42.4% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. +-commutative 93.3%

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

   2. fma-define 94.9%

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

   3. +-commutative 94.9%

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

   4. fma-define 96.5%

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

   5. fma-define 97.2%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 2: 65.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + z \cdot t\\ t_3 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-306}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-37}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 8.4 \cdot 10^{+15} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{+94}\right) \land x \cdot y \leq 3.3 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* x y) (* z t)))
        (t_3 (+ (* a b) (* z t))))
   (if (<= (* x y) -1.8e+51)
     t_2
     (if (<= (* x y) -4.1e-193)
       (+ (* a b) (* c i))
       (if (<= (* x y) 4.1e-306)
         t_3
         (if (<= (* x y) 3.5e-141)
           t_1
           (if (<= (* x y) 5.6e-37)
             t_3
             (if (or (<= (* x y) 8.4e+15)
                     (and (not (<= (* x y) 2.1e+94)) (<= (* x y) 3.3e+138)))
               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) + (z * t);
	double t_3 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -1.8e+51) {
		tmp = t_2;
	} else if ((x * y) <= -4.1e-193) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.1e-306) {
		tmp = t_3;
	} else if ((x * y) <= 3.5e-141) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-37) {
		tmp = t_3;
	} else if (((x * y) <= 8.4e+15) || (!((x * y) <= 2.1e+94) && ((x * y) <= 3.3e+138))) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (x * y) + (z * t)
    t_3 = (a * b) + (z * t)
    if ((x * y) <= (-1.8d+51)) then
        tmp = t_2
    else if ((x * y) <= (-4.1d-193)) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 4.1d-306) then
        tmp = t_3
    else if ((x * y) <= 3.5d-141) then
        tmp = t_1
    else if ((x * y) <= 5.6d-37) then
        tmp = t_3
    else if (((x * y) <= 8.4d+15) .or. (.not. ((x * y) <= 2.1d+94)) .and. ((x * y) <= 3.3d+138)) 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) + (z * t);
	double t_3 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -1.8e+51) {
		tmp = t_2;
	} else if ((x * y) <= -4.1e-193) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 4.1e-306) {
		tmp = t_3;
	} else if ((x * y) <= 3.5e-141) {
		tmp = t_1;
	} else if ((x * y) <= 5.6e-37) {
		tmp = t_3;
	} else if (((x * y) <= 8.4e+15) || (!((x * y) <= 2.1e+94) && ((x * y) <= 3.3e+138))) {
		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) + (z * t)
	t_3 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -1.8e+51:
		tmp = t_2
	elif (x * y) <= -4.1e-193:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 4.1e-306:
		tmp = t_3
	elif (x * y) <= 3.5e-141:
		tmp = t_1
	elif (x * y) <= 5.6e-37:
		tmp = t_3
	elif ((x * y) <= 8.4e+15) or (not ((x * y) <= 2.1e+94) and ((x * y) <= 3.3e+138)):
		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(z * t))
	t_3 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1.8e+51)
		tmp = t_2;
	elseif (Float64(x * y) <= -4.1e-193)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 4.1e-306)
		tmp = t_3;
	elseif (Float64(x * y) <= 3.5e-141)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.6e-37)
		tmp = t_3;
	elseif ((Float64(x * y) <= 8.4e+15) || (!(Float64(x * y) <= 2.1e+94) && (Float64(x * y) <= 3.3e+138)))
		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) + (z * t);
	t_3 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -1.8e+51)
		tmp = t_2;
	elseif ((x * y) <= -4.1e-193)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 4.1e-306)
		tmp = t_3;
	elseif ((x * y) <= 3.5e-141)
		tmp = t_1;
	elseif ((x * y) <= 5.6e-37)
		tmp = t_3;
	elseif (((x * y) <= 8.4e+15) || (~(((x * y) <= 2.1e+94)) && ((x * y) <= 3.3e+138)))
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e+51], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -4.1e-193], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.1e-306], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-141], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.6e-37], t$95$3, If[Or[LessEqual[N[(x * y), $MachinePrecision], 8.4e+15], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.1e+94]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 3.3e+138]]], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.80000000000000005e51 or 8.4e15 < (*.f64 x y) < 2.09999999999999989e94 or 3.29999999999999978e138 < (*.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in c around 0 84.1%

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

   4. Taylor expanded in a around 0 80.5%

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

   if -1.80000000000000005e51 < (*.f64 x y) < -4.10000000000000003e-193

   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 85.8%

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

   4. Taylor expanded in a around inf 73.4%

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

   if -4.10000000000000003e-193 < (*.f64 x y) < 4.09999999999999985e-306 or 3.5000000000000003e-141 < (*.f64 x y) < 5.6000000000000002e-37

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 97.1%

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

   4. Taylor expanded in c around 0 84.6%

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

   if 4.09999999999999985e-306 < (*.f64 x y) < 3.5000000000000003e-141 or 5.6000000000000002e-37 < (*.f64 x y) < 8.4e15 or 2.09999999999999989e94 < (*.f64 x y) < 3.29999999999999978e138

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf 84.3%

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

   4. Taylor expanded in z around inf 74.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-306}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-141}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-37}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.4 \cdot 10^{+15} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{+94}\right) \land x \cdot y \leq 3.3 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x + \frac{c \cdot i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-309}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* x y) -4e+108)
     (* y (+ x (/ (* c i) y)))
     (if (<= (* x y) -1e-10)
       t_2
       (if (<= (* x y) -1e-76)
         t_1
         (if (<= (* x y) 2e-309)
           t_2
           (if (<= (* x y) 4e-149)
             t_1
             (if (<= (* x y) 1e-30)
               (* z (+ t (/ (* a b) z)))
               (+ (* x y) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -4e+108) {
		tmp = y * (x + ((c * i) / y));
	} else if ((x * y) <= -1e-10) {
		tmp = t_2;
	} else if ((x * y) <= -1e-76) {
		tmp = t_1;
	} else if ((x * y) <= 2e-309) {
		tmp = t_2;
	} else if ((x * y) <= 4e-149) {
		tmp = t_1;
	} else if ((x * y) <= 1e-30) {
		tmp = z * (t + ((a * b) / z));
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((x * y) <= (-4d+108)) then
        tmp = y * (x + ((c * i) / y))
    else if ((x * y) <= (-1d-10)) then
        tmp = t_2
    else if ((x * y) <= (-1d-76)) then
        tmp = t_1
    else if ((x * y) <= 2d-309) then
        tmp = t_2
    else if ((x * y) <= 4d-149) then
        tmp = t_1
    else if ((x * y) <= 1d-30) then
        tmp = z * (t + ((a * b) / z))
    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 t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -4e+108) {
		tmp = y * (x + ((c * i) / y));
	} else if ((x * y) <= -1e-10) {
		tmp = t_2;
	} else if ((x * y) <= -1e-76) {
		tmp = t_1;
	} else if ((x * y) <= 2e-309) {
		tmp = t_2;
	} else if ((x * y) <= 4e-149) {
		tmp = t_1;
	} else if ((x * y) <= 1e-30) {
		tmp = z * (t + ((a * b) / z));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -4e+108:
		tmp = y * (x + ((c * i) / y))
	elif (x * y) <= -1e-10:
		tmp = t_2
	elif (x * y) <= -1e-76:
		tmp = t_1
	elif (x * y) <= 2e-309:
		tmp = t_2
	elif (x * y) <= 4e-149:
		tmp = t_1
	elif (x * y) <= 1e-30:
		tmp = z * (t + ((a * b) / z))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -4e+108)
		tmp = Float64(y * Float64(x + Float64(Float64(c * i) / y)));
	elseif (Float64(x * y) <= -1e-10)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e-76)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-309)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-149)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(z * Float64(t + Float64(Float64(a * b) / z)));
	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)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -4e+108)
		tmp = y * (x + ((c * i) / y));
	elseif ((x * y) <= -1e-10)
		tmp = t_2;
	elseif ((x * y) <= -1e-76)
		tmp = t_1;
	elseif ((x * y) <= 2e-309)
		tmp = t_2;
	elseif ((x * y) <= 4e-149)
		tmp = t_1;
	elseif ((x * y) <= 1e-30)
		tmp = z * (t + ((a * b) / z));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+108], N[(y * N[(x + N[(N[(c * i), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-10], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e-76], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-309], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-149], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(z * N[(t + N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.0000000000000001e108

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 89.0%

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

   4. Taylor expanded in y around inf 87.0%

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

   5. Taylor expanded in a around 0 81.1%

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

   if -4.0000000000000001e108 < (*.f64 x y) < -1.00000000000000004e-10 or -9.99999999999999927e-77 < (*.f64 x y) < 1.9999999999999988e-309

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 93.4%

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

   4. Taylor expanded in c around 0 78.1%

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

   if -1.00000000000000004e-10 < (*.f64 x y) < -9.99999999999999927e-77 or 1.9999999999999988e-309 < (*.f64 x y) < 3.99999999999999992e-149

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 91.7%

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

   4. Taylor expanded in z around inf 76.7%

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

   if 3.99999999999999992e-149 < (*.f64 x y) < 1e-30

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 93.4%

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

   4. Taylor expanded in x around 0 89.9%

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

   5. Taylor expanded in c around 0 83.1%

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

   if 1e-30 < (*.f64 x y)

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 79.3%

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

   4. Taylor expanded in x around inf 72.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x + \frac{c \cdot i}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-309}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;z \cdot \left(t + \frac{a \cdot b}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.8 \cdot 10^{-192}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* x y) -2.3e+122)
     (+ (* x y) (* a b))
     (if (<= (* x y) -3.8e-192)
       (+ (* a b) (* c i))
       (if (<= (* x y) 2.2e-293)
         t_2
         (if (<= (* x y) 8.6e-142)
           t_1
           (if (<= (* x y) 4.3e-36)
             t_2
             (if (<= (* x y) 1.2e+141) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -2.3e+122) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -3.8e-192) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.2e-293) {
		tmp = t_2;
	} else if ((x * y) <= 8.6e-142) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-36) {
		tmp = t_2;
	} else if ((x * y) <= 1.2e+141) {
		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) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((x * y) <= (-2.3d+122)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= (-3.8d-192)) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2.2d-293) then
        tmp = t_2
    else if ((x * y) <= 8.6d-142) then
        tmp = t_1
    else if ((x * y) <= 4.3d-36) then
        tmp = t_2
    else if ((x * y) <= 1.2d+141) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -2.3e+122) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -3.8e-192) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.2e-293) {
		tmp = t_2;
	} else if ((x * y) <= 8.6e-142) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e-36) {
		tmp = t_2;
	} else if ((x * y) <= 1.2e+141) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -2.3e+122:
		tmp = (x * y) + (a * b)
	elif (x * y) <= -3.8e-192:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2.2e-293:
		tmp = t_2
	elif (x * y) <= 8.6e-142:
		tmp = t_1
	elif (x * y) <= 4.3e-36:
		tmp = t_2
	elif (x * y) <= 1.2e+141:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2.3e+122)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= -3.8e-192)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2.2e-293)
		tmp = t_2;
	elseif (Float64(x * y) <= 8.6e-142)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.3e-36)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.2e+141)
		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 = (c * i) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -2.3e+122)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= -3.8e-192)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2.2e-293)
		tmp = t_2;
	elseif ((x * y) <= 8.6e-142)
		tmp = t_1;
	elseif ((x * y) <= 4.3e-36)
		tmp = t_2;
	elseif ((x * y) <= 1.2e+141)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e+122], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.8e-192], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-293], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8.6e-142], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.3e-36], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.2e+141], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2.3000000000000001e122

   1. Initial program 92.3%

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

   3. Taylor expanded in c around 0 85.0%

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

   4. Taylor expanded in t around 0 77.5%

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

   if -2.3000000000000001e122 < (*.f64 x y) < -3.8000000000000001e-192

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 85.7%

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

   4. Taylor expanded in a around inf 67.4%

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

   if -3.8000000000000001e-192 < (*.f64 x y) < 2.2e-293 or 8.5999999999999995e-142 < (*.f64 x y) < 4.3000000000000002e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 97.1%

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

   4. Taylor expanded in c around 0 84.6%

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

   if 2.2e-293 < (*.f64 x y) < 8.5999999999999995e-142 or 4.3000000000000002e-36 < (*.f64 x y) < 1.19999999999999999e141

   1. Initial program 89.1%

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

   3. Taylor expanded in z around inf 85.9%

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

   4. Taylor expanded in z around inf 67.9%

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

   if 1.19999999999999999e141 < (*.f64 x y)

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 78.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.8 \cdot 10^{-192}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-293}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-142}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{-36}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+141}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.65 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+183}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

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) -1.9e+125)
     (* x y)
     (if (<= (* x y) -2.55e-194)
       t_1
       (if (<= (* x y) 2.65e-48)
         t_2
         (if (<= (* x y) 2.1e+15)
           t_1
           (if (<= (* x y) 8e+183) 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) <= -1.9e+125) {
		tmp = x * y;
	} else if ((x * y) <= -2.55e-194) {
		tmp = t_1;
	} else if ((x * y) <= 2.65e-48) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e+15) {
		tmp = t_1;
	} else if ((x * y) <= 8e+183) {
		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) <= (-1.9d+125)) then
        tmp = x * y
    else if ((x * y) <= (-2.55d-194)) then
        tmp = t_1
    else if ((x * y) <= 2.65d-48) then
        tmp = t_2
    else if ((x * y) <= 2.1d+15) then
        tmp = t_1
    else if ((x * y) <= 8d+183) 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) <= -1.9e+125) {
		tmp = x * y;
	} else if ((x * y) <= -2.55e-194) {
		tmp = t_1;
	} else if ((x * y) <= 2.65e-48) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e+15) {
		tmp = t_1;
	} else if ((x * y) <= 8e+183) {
		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) <= -1.9e+125:
		tmp = x * y
	elif (x * y) <= -2.55e-194:
		tmp = t_1
	elif (x * y) <= 2.65e-48:
		tmp = t_2
	elif (x * y) <= 2.1e+15:
		tmp = t_1
	elif (x * y) <= 8e+183:
		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) <= -1.9e+125)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.55e-194)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.65e-48)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.1e+15)
		tmp = t_1;
	elseif (Float64(x * y) <= 8e+183)
		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) <= -1.9e+125)
		tmp = x * y;
	elseif ((x * y) <= -2.55e-194)
		tmp = t_1;
	elseif ((x * y) <= 2.65e-48)
		tmp = t_2;
	elseif ((x * y) <= 2.1e+15)
		tmp = t_1;
	elseif ((x * y) <= 8e+183)
		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], -1.9e+125], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.55e-194], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.65e-48], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.1e+15], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8e+183], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.90000000000000001e125 or 7.99999999999999957e183 < (*.f64 x y)

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 77.1%

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

   if -1.90000000000000001e125 < (*.f64 x y) < -2.5499999999999999e-194 or 2.65e-48 < (*.f64 x y) < 2.1e15

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf 81.5%

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

   4. Taylor expanded in a around inf 67.8%

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

   if -2.5499999999999999e-194 < (*.f64 x y) < 2.65e-48 or 2.1e15 < (*.f64 x y) < 7.99999999999999957e183

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in c around 0 72.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.55 \cdot 10^{-194}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.65 \cdot 10^{-48}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+183}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1.26 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.8 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

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) -1.26e+122)
     (+ (* x y) (* a b))
     (if (<= (* x y) -4.8e-197)
       t_1
       (if (<= (* x y) 3.2e-49)
         t_2
         (if (<= (* x y) 9.5e+14)
           t_1
           (if (<= (* x y) 1.55e+184) 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) <= -1.26e+122) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -4.8e-197) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-49) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e+14) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e+184) {
		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) <= (-1.26d+122)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= (-4.8d-197)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-49) then
        tmp = t_2
    else if ((x * y) <= 9.5d+14) then
        tmp = t_1
    else if ((x * y) <= 1.55d+184) 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) <= -1.26e+122) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -4.8e-197) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-49) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e+14) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e+184) {
		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) <= -1.26e+122:
		tmp = (x * y) + (a * b)
	elif (x * y) <= -4.8e-197:
		tmp = t_1
	elif (x * y) <= 3.2e-49:
		tmp = t_2
	elif (x * y) <= 9.5e+14:
		tmp = t_1
	elif (x * y) <= 1.55e+184:
		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) <= -1.26e+122)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= -4.8e-197)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-49)
		tmp = t_2;
	elseif (Float64(x * y) <= 9.5e+14)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.55e+184)
		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) <= -1.26e+122)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= -4.8e-197)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-49)
		tmp = t_2;
	elseif ((x * y) <= 9.5e+14)
		tmp = t_1;
	elseif ((x * y) <= 1.55e+184)
		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], -1.26e+122], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.8e-197], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-49], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9.5e+14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e+184], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.25999999999999991e122

   1. Initial program 92.3%

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

   3. Taylor expanded in c around 0 85.0%

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

   4. Taylor expanded in t around 0 77.5%

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

   if -1.25999999999999991e122 < (*.f64 x y) < -4.8000000000000002e-197 or 3.20000000000000002e-49 < (*.f64 x y) < 9.5e14

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf 81.5%

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

   4. Taylor expanded in a around inf 67.8%

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

   if -4.8000000000000002e-197 < (*.f64 x y) < 3.20000000000000002e-49 or 9.5e14 < (*.f64 x y) < 1.5499999999999999e184

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in c around 0 72.1%

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

   if 1.5499999999999999e184 < (*.f64 x y)

   1. Initial program 89.2%

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

   3. Taylor expanded in x around inf 81.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.26 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.8 \cdot 10^{-197}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-49}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+184}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.95 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-106}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.95 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -6.5e+87)
   (* x y)
   (if (<= (* x y) -1.95e-220)
     (* a b)
     (if (<= (* x y) 6.6e-106)
       (* z t)
       (if (<= (* x y) 2.95e-80)
         (* a b)
         (if (<= (* x y) 1.42e+19) (* c i) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -6.5e+87) {
		tmp = x * y;
	} else if ((x * y) <= -1.95e-220) {
		tmp = a * b;
	} else if ((x * y) <= 6.6e-106) {
		tmp = z * t;
	} else if ((x * y) <= 2.95e-80) {
		tmp = a * b;
	} else if ((x * y) <= 1.42e+19) {
		tmp = c * i;
	} 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) :: tmp
    if ((x * y) <= (-6.5d+87)) then
        tmp = x * y
    else if ((x * y) <= (-1.95d-220)) then
        tmp = a * b
    else if ((x * y) <= 6.6d-106) then
        tmp = z * t
    else if ((x * y) <= 2.95d-80) then
        tmp = a * b
    else if ((x * y) <= 1.42d+19) then
        tmp = c * i
    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 tmp;
	if ((x * y) <= -6.5e+87) {
		tmp = x * y;
	} else if ((x * y) <= -1.95e-220) {
		tmp = a * b;
	} else if ((x * y) <= 6.6e-106) {
		tmp = z * t;
	} else if ((x * y) <= 2.95e-80) {
		tmp = a * b;
	} else if ((x * y) <= 1.42e+19) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -6.5e+87:
		tmp = x * y
	elif (x * y) <= -1.95e-220:
		tmp = a * b
	elif (x * y) <= 6.6e-106:
		tmp = z * t
	elif (x * y) <= 2.95e-80:
		tmp = a * b
	elif (x * y) <= 1.42e+19:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -6.5e+87)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.95e-220)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 6.6e-106)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.95e-80)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.42e+19)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -6.5e+87)
		tmp = x * y;
	elseif ((x * y) <= -1.95e-220)
		tmp = a * b;
	elseif ((x * y) <= 6.6e-106)
		tmp = z * t;
	elseif ((x * y) <= 2.95e-80)
		tmp = a * b;
	elseif ((x * y) <= 1.42e+19)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -6.5e+87], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.95e-220], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.6e-106], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.95e-80], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.42e+19], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -6.5000000000000002e87 or 1.42e19 < (*.f64 x y)

   1. Initial program 92.4%

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

   3. Taylor expanded in x around inf 64.2%

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

   if -6.5000000000000002e87 < (*.f64 x y) < -1.95000000000000001e-220 or 6.60000000000000031e-106 < (*.f64 x y) < 2.95e-80

   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 43.6%

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

   if -1.95000000000000001e-220 < (*.f64 x y) < 6.60000000000000031e-106

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 46.9%

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

   if 2.95e-80 < (*.f64 x y) < 1.42e19

   1. Initial program 81.0%

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

   3. Taylor expanded in c around inf 44.0%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.95 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{-106}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.95 \cdot 10^{-80}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.46 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-305}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.46e+125)
     (* x y)
     (if (<= (* x y) -1.9e-220)
       t_1
       (if (<= (* x y) -5.5e-305)
         (* z t)
         (if (<= (* x y) 2.1e+182) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.46e+125) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-220) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-305) {
		tmp = z * t;
	} else if ((x * y) <= 2.1e+182) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-1.46d+125)) then
        tmp = x * y
    else if ((x * y) <= (-1.9d-220)) then
        tmp = t_1
    else if ((x * y) <= (-5.5d-305)) then
        tmp = z * t
    else if ((x * y) <= 2.1d+182) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.46e+125) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-220) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-305) {
		tmp = z * t;
	} else if ((x * y) <= 2.1e+182) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.46e+125:
		tmp = x * y
	elif (x * y) <= -1.9e-220:
		tmp = t_1
	elif (x * y) <= -5.5e-305:
		tmp = z * t
	elif (x * y) <= 2.1e+182:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.46e+125)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.9e-220)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.5e-305)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.1e+182)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.46e+125)
		tmp = x * y;
	elseif ((x * y) <= -1.9e-220)
		tmp = t_1;
	elseif ((x * y) <= -5.5e-305)
		tmp = z * t;
	elseif ((x * y) <= 2.1e+182)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.46e+125], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-220], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-305], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.1e+182], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.45999999999999999e125 or 2.0999999999999999e182 < (*.f64 x y)

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 77.1%

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

   if -1.45999999999999999e125 < (*.f64 x y) < -1.90000000000000004e-220 or -5.5e-305 < (*.f64 x y) < 2.0999999999999999e182

   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 89.3%

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

   4. Taylor expanded in a around inf 59.8%

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

   if -1.90000000000000004e-220 < (*.f64 x y) < -5.5e-305

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.46 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-305}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+182}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-247}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* c i))))
   (if (<= (* c i) -2e+179)
     t_2
     (if (<= (* c i) -5e-182)
       t_1
       (if (<= (* c i) -2e-247)
         (+ (* x y) (* z t))
         (if (<= (* c i) 4e-31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2e+179) {
		tmp = t_2;
	} else if ((c * i) <= -5e-182) {
		tmp = t_1;
	} else if ((c * i) <= -2e-247) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 4e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (c * i)
    if ((c * i) <= (-2d+179)) then
        tmp = t_2
    else if ((c * i) <= (-5d-182)) then
        tmp = t_1
    else if ((c * i) <= (-2d-247)) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 4d-31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((c * i) <= -2e+179) {
		tmp = t_2;
	} else if ((c * i) <= -5e-182) {
		tmp = t_1;
	} else if ((c * i) <= -2e-247) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 4e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (c * i)
	tmp = 0
	if (c * i) <= -2e+179:
		tmp = t_2
	elif (c * i) <= -5e-182:
		tmp = t_1
	elif (c * i) <= -2e-247:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 4e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -2e+179)
		tmp = t_2;
	elseif (Float64(c * i) <= -5e-182)
		tmp = t_1;
	elseif (Float64(c * i) <= -2e-247)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 4e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -2e+179)
		tmp = t_2;
	elseif ((c * i) <= -5e-182)
		tmp = t_1;
	elseif ((c * i) <= -2e-247)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 4e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2e+179], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -5e-182], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2e-247], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.99999999999999996e179 or 4e-31 < (*.f64 c i)

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 78.4%

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

   4. Taylor expanded in x around inf 75.5%

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

   if -1.99999999999999996e179 < (*.f64 c i) < -5.00000000000000024e-182 or -2e-247 < (*.f64 c i) < 4e-31

   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 0 76.3%

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

   4. Taylor expanded in c around 0 72.2%

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

   if -5.00000000000000024e-182 < (*.f64 c i) < -2e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in c around 0 100.0%

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

   4. Taylor expanded in a around 0 96.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-182}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-247}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{-31}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 23.5%

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

   4. Taylor expanded in y around inf 29.4%

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

   5. Taylor expanded in a around 0 47.8%

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

4. Final simplification 96.5%

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

Alternative 11: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+237}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+79} \lor \neg \left(z \leq -1.45 \cdot 10^{-46}\right) \land z \leq 8.6 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7.5e+237)
   (+ (* c i) (* z t))
   (if (or (<= z -1.85e+79) (and (not (<= z -1.45e-46)) (<= z 8.6e-13)))
     (+ (* a b) (+ (* x y) (* c i)))
     (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+237) {
		tmp = (c * i) + (z * t);
	} else if ((z <= -1.85e+79) || (!(z <= -1.45e-46) && (z <= 8.6e-13))) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-7.5d+237)) then
        tmp = (c * i) + (z * t)
    else if ((z <= (-1.85d+79)) .or. (.not. (z <= (-1.45d-46))) .and. (z <= 8.6d-13)) then
        tmp = (a * b) + ((x * y) + (c * i))
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+237) {
		tmp = (c * i) + (z * t);
	} else if ((z <= -1.85e+79) || (!(z <= -1.45e-46) && (z <= 8.6e-13))) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7.5e+237:
		tmp = (c * i) + (z * t)
	elif (z <= -1.85e+79) or (not (z <= -1.45e-46) and (z <= 8.6e-13)):
		tmp = (a * b) + ((x * y) + (c * i))
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7.5e+237)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif ((z <= -1.85e+79) || (!(z <= -1.45e-46) && (z <= 8.6e-13)))
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(c * i)));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7.5e+237)
		tmp = (c * i) + (z * t);
	elseif ((z <= -1.85e+79) || (~((z <= -1.45e-46)) && (z <= 8.6e-13)))
		tmp = (a * b) + ((x * y) + (c * i));
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7.5e+237], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.85e+79], And[N[Not[LessEqual[z, -1.45e-46]], $MachinePrecision], LessEqual[z, 8.6e-13]]], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e237

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in z around inf 90.0%

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

   if -7.5e237 < z < -1.85000000000000005e79 or -1.45000000000000002e-46 < z < 8.5999999999999997e-13

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 85.3%

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

   if -1.85000000000000005e79 < z < -1.45000000000000002e-46 or 8.5999999999999997e-13 < z

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 79.2%

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

   4. Taylor expanded in c around 0 63.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+237}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+79} \lor \neg \left(z \leq -1.45 \cdot 10^{-46}\right) \land z \leq 8.6 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.5 \cdot 10^{+216}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{-161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 600000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.5e+216)
   (* c i)
   (if (<= (* c i) 2.7e-308)
     (* z t)
     (if (<= (* c i) 2.7e-161)
       (* a b)
       (if (<= (* c i) 600000000.0) (* z t) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.5e+216) {
		tmp = c * i;
	} else if ((c * i) <= 2.7e-308) {
		tmp = z * t;
	} else if ((c * i) <= 2.7e-161) {
		tmp = a * b;
	} else if ((c * i) <= 600000000.0) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.5d+216)) then
        tmp = c * i
    else if ((c * i) <= 2.7d-308) then
        tmp = z * t
    else if ((c * i) <= 2.7d-161) then
        tmp = a * b
    else if ((c * i) <= 600000000.0d0) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.5e+216) {
		tmp = c * i;
	} else if ((c * i) <= 2.7e-308) {
		tmp = z * t;
	} else if ((c * i) <= 2.7e-161) {
		tmp = a * b;
	} else if ((c * i) <= 600000000.0) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.5e+216:
		tmp = c * i
	elif (c * i) <= 2.7e-308:
		tmp = z * t
	elif (c * i) <= 2.7e-161:
		tmp = a * b
	elif (c * i) <= 600000000.0:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.5e+216)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.7e-308)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.7e-161)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 600000000.0)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.5e+216)
		tmp = c * i;
	elseif ((c * i) <= 2.7e-308)
		tmp = z * t;
	elseif ((c * i) <= 2.7e-161)
		tmp = a * b;
	elseif ((c * i) <= 600000000.0)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.5e+216], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e-308], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e-161], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 600000000.0], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.4999999999999999e216 or 6e8 < (*.f64 c i)

   1. Initial program 87.6%

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

   3. Taylor expanded in c around inf 58.3%

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

   if -1.4999999999999999e216 < (*.f64 c i) < 2.70000000000000015e-308 or 2.6999999999999999e-161 < (*.f64 c i) < 6e8

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 40.0%

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

   if 2.70000000000000015e-308 < (*.f64 c i) < 2.6999999999999999e-161

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 48.0%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.5 \cdot 10^{+216}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{-161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 600000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+217}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+56}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4e+217)
   (+ (* c i) (* z t))
   (if (<= (* c i) 1e+56)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* a b) (+ (* x y) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4e+217) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1e+56) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (c * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-4d+217)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 1d+56) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (a * b) + ((x * y) + (c * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4e+217) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1e+56) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4e+217:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 1e+56:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + ((x * y) + (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4e+217)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 1e+56)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4e+217)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 1e+56)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4e+217], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+56], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.99999999999999984e217

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 63.3%

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

   4. Taylor expanded in z around inf 86.1%

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

   if -3.99999999999999984e217 < (*.f64 c i) < 1.00000000000000009e56

   1. Initial program 97.1%

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

   3. Taylor expanded in c around 0 89.7%

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

   if 1.00000000000000009e56 < (*.f64 c i)

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 84.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+217}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+56}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+214} \lor \neg \left(c \cdot i \leq 5.8 \cdot 10^{-29}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -7.5e+214) (not (<= (* c i) 5.8e-29))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.5e+214) || !((c * i) <= 5.8e-29)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-7.5d+214)) .or. (.not. ((c * i) <= 5.8d-29))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.5e+214) || !((c * i) <= 5.8e-29)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -7.5e+214) or not ((c * i) <= 5.8e-29):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -7.5e+214) || !(Float64(c * i) <= 5.8e-29))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -7.5e+214) || ~(((c * i) <= 5.8e-29)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -7.5e+214], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.8e-29]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -7.4999999999999998e214 or 5.80000000000000048e-29 < (*.f64 c i)

   1. Initial program 88.4%

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

   3. Taylor expanded in c around inf 55.5%

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

   if -7.4999999999999998e214 < (*.f64 c i) < 5.80000000000000048e-29

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 35.1%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+214} \lor \neg \left(c \cdot i \leq 5.8 \cdot 10^{-29}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.8% 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 93.3%

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

3. Taylor expanded in a around inf 25.9%

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

4. Final simplification 25.9%

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

Reproduce

herbie shell --seed 2024077 
(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)))