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

Percentage Accurate: 95.5% → 98.1%

Time: 12.9s

Alternatives: 16

Speedup: 0.4×

• 41.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% 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: 98.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-define 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-define 98.4%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 98.0% 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 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-define 98.0%

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

   3. +-commutative 98.0%

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

   4. fma-define 98.4%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

Alternative 3: 65.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+166}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (<= (* x y) -2.8e+166)
     t_2
     (if (<= (* x y) -9e-272)
       t_1
       (if (<= (* x y) 2e-316)
         (+ (* c i) (* z t))
         (if (<= (* x y) 3.5e-108)
           t_1
           (if (<= (* x y) 1.55e+125)
             (+ (* a b) (* c i))
             (if (<= (* x y) 1.75e+207) (* z (+ t (/ (* x y) z))) 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 ((x * y) <= -2.8e+166) {
		tmp = t_2;
	} else if ((x * y) <= -9e-272) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3.5e-108) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e+125) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.75e+207) {
		tmp = z * (t + ((x * y) / z));
	} 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 ((x * y) <= (-2.8d+166)) then
        tmp = t_2
    else if ((x * y) <= (-9d-272)) then
        tmp = t_1
    else if ((x * y) <= 2d-316) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 3.5d-108) then
        tmp = t_1
    else if ((x * y) <= 1.55d+125) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.75d+207) then
        tmp = z * (t + ((x * y) / z))
    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 ((x * y) <= -2.8e+166) {
		tmp = t_2;
	} else if ((x * y) <= -9e-272) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3.5e-108) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e+125) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.75e+207) {
		tmp = z * (t + ((x * y) / z));
	} 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 (x * y) <= -2.8e+166:
		tmp = t_2
	elif (x * y) <= -9e-272:
		tmp = t_1
	elif (x * y) <= 2e-316:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 3.5e-108:
		tmp = t_1
	elif (x * y) <= 1.55e+125:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.75e+207:
		tmp = z * (t + ((x * y) / z))
	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(x * y) <= -2.8e+166)
		tmp = t_2;
	elseif (Float64(x * y) <= -9e-272)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-316)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 3.5e-108)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.55e+125)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.75e+207)
		tmp = Float64(z * Float64(t + Float64(Float64(x * y) / z)));
	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 ((x * y) <= -2.8e+166)
		tmp = t_2;
	elseif ((x * y) <= -9e-272)
		tmp = t_1;
	elseif ((x * y) <= 2e-316)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 3.5e-108)
		tmp = t_1;
	elseif ((x * y) <= 1.55e+125)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.75e+207)
		tmp = z * (t + ((x * y) / z));
	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[(x * y), $MachinePrecision], -2.8e+166], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -9e-272], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-316], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-108], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e+125], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.75e+207], N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2.79999999999999996e166 or 1.75000000000000014e207 < (*.f64 x y)

   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 a around 0 86.7%

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

   4. Taylor expanded in t around 0 85.4%

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

   if -2.79999999999999996e166 < (*.f64 x y) < -8.9999999999999995e-272 or 2.000000017e-316 < (*.f64 x y) < 3.4999999999999999e-108

   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 92.2%

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

   4. Taylor expanded in z around inf 88.0%

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

   5. Taylor expanded in c around 0 77.7%

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

   if -8.9999999999999995e-272 < (*.f64 x y) < 2.000000017e-316

   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 0 82.6%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 3.4999999999999999e-108 < (*.f64 x y) < 1.55e125

   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 b around inf 92.1%

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

      1. associate-/l* 86.5%

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

      2. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in b around inf 69.2%

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

   if 1.55e125 < (*.f64 x y) < 1.75000000000000014e207

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 84.8%

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

   4. Taylor expanded in a around 0 77.6%

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

   5. Taylor expanded in c around 0 70.0%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{x \cdot y}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+166}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-272}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (<= (* x y) -5.8e+165)
     t_2
     (if (<= (* x y) -7.5e-271)
       t_1
       (if (<= (* x y) 2e-316)
         (+ (* c i) (* z t))
         (if (<= (* x y) 3e-115)
           t_1
           (if (<= (* x y) 3.2e+149)
             (+ (* a b) (* c i))
             (if (<= (* x y) 1.9e+199) 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 ((x * y) <= -5.8e+165) {
		tmp = t_2;
	} else if ((x * y) <= -7.5e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3e-115) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.9e+199) {
		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 ((x * y) <= (-5.8d+165)) then
        tmp = t_2
    else if ((x * y) <= (-7.5d-271)) then
        tmp = t_1
    else if ((x * y) <= 2d-316) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 3d-115) then
        tmp = t_1
    else if ((x * y) <= 3.2d+149) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.9d+199) 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 ((x * y) <= -5.8e+165) {
		tmp = t_2;
	} else if ((x * y) <= -7.5e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 3e-115) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.9e+199) {
		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 (x * y) <= -5.8e+165:
		tmp = t_2
	elif (x * y) <= -7.5e-271:
		tmp = t_1
	elif (x * y) <= 2e-316:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 3e-115:
		tmp = t_1
	elif (x * y) <= 3.2e+149:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.9e+199:
		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(x * y) <= -5.8e+165)
		tmp = t_2;
	elseif (Float64(x * y) <= -7.5e-271)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-316)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 3e-115)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e+149)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.9e+199)
		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 ((x * y) <= -5.8e+165)
		tmp = t_2;
	elseif ((x * y) <= -7.5e-271)
		tmp = t_1;
	elseif ((x * y) <= 2e-316)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 3e-115)
		tmp = t_1;
	elseif ((x * y) <= 3.2e+149)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.9e+199)
		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[(x * y), $MachinePrecision], -5.8e+165], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -7.5e-271], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-316], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e-115], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+149], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+199], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.80000000000000011e165 or 1.9e199 < (*.f64 x y)

   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 a around 0 86.7%

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

   4. Taylor expanded in t around 0 85.4%

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

   if -5.80000000000000011e165 < (*.f64 x y) < -7.50000000000000031e-271 or 2.000000017e-316 < (*.f64 x y) < 3.0000000000000002e-115 or 3.2000000000000002e149 < (*.f64 x y) < 1.9e199

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 91.8%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in c around 0 78.3%

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

   if -7.50000000000000031e-271 < (*.f64 x y) < 2.000000017e-316

   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 0 82.6%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 3.0000000000000002e-115 < (*.f64 x y) < 3.2000000000000002e149

   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 b around inf 90.9%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in b around inf 66.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+165}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-271}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+199}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -5e+225)
     (* x y)
     (if (<= (* x y) -5.2e-271)
       t_1
       (if (<= (* x y) 2e-316)
         (+ (* c i) (* z t))
         (if (<= (* x y) 1.95e-110)
           t_1
           (if (<= (* x y) 4.8e+148)
             (+ (* a b) (* c i))
             (if (<= (* x y) 1.02e+200) 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) + (z * t);
	double tmp;
	if ((x * y) <= -5e+225) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.95e-110) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e+148) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.02e+200) {
		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) + (z * t)
    if ((x * y) <= (-5d+225)) then
        tmp = x * y
    else if ((x * y) <= (-5.2d-271)) then
        tmp = t_1
    else if ((x * y) <= 2d-316) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 1.95d-110) then
        tmp = t_1
    else if ((x * y) <= 4.8d+148) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.02d+200) 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) + (z * t);
	double tmp;
	if ((x * y) <= -5e+225) {
		tmp = x * y;
	} else if ((x * y) <= -5.2e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.95e-110) {
		tmp = t_1;
	} else if ((x * y) <= 4.8e+148) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.02e+200) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -5e+225:
		tmp = x * y
	elif (x * y) <= -5.2e-271:
		tmp = t_1
	elif (x * y) <= 2e-316:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 1.95e-110:
		tmp = t_1
	elif (x * y) <= 4.8e+148:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.02e+200:
		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(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -5e+225)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.2e-271)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-316)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 1.95e-110)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.8e+148)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.02e+200)
		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) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -5e+225)
		tmp = x * y;
	elseif ((x * y) <= -5.2e-271)
		tmp = t_1;
	elseif ((x * y) <= 2e-316)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 1.95e-110)
		tmp = t_1;
	elseif ((x * y) <= 4.8e+148)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.02e+200)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+225], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.2e-271], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-316], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.95e-110], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.8e+148], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.02e+200], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.99999999999999981e225 or 1.02000000000000001e200 < (*.f64 x y)

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 82.9%

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

   if -4.99999999999999981e225 < (*.f64 x y) < -5.2e-271 or 2.000000017e-316 < (*.f64 x y) < 1.95e-110 or 4.79999999999999989e148 < (*.f64 x y) < 1.02000000000000001e200

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 90.1%

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

   4. Taylor expanded in z around inf 85.7%

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

   5. Taylor expanded in c around 0 75.9%

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

   if -5.2e-271 < (*.f64 x y) < 2.000000017e-316

   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 0 82.6%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 1.95e-110 < (*.f64 x y) < 4.79999999999999989e148

   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 b around inf 90.9%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in b around inf 66.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{-271}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-110}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+200}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-148}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.8 \cdot 10^{+141}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -6.2e+138)
   (* a b)
   (if (<= (* a b) -6.2e-176)
     (* x y)
     (if (<= (* a b) 1e-148)
       (* z t)
       (if (<= (* a b) 1.55e-64)
         (* x y)
         (if (<= (* a b) 7.8e+141) (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6.2e+138) {
		tmp = a * b;
	} else if ((a * b) <= -6.2e-176) {
		tmp = x * y;
	} else if ((a * b) <= 1e-148) {
		tmp = z * t;
	} else if ((a * b) <= 1.55e-64) {
		tmp = x * y;
	} else if ((a * b) <= 7.8e+141) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-6.2d+138)) then
        tmp = a * b
    else if ((a * b) <= (-6.2d-176)) then
        tmp = x * y
    else if ((a * b) <= 1d-148) then
        tmp = z * t
    else if ((a * b) <= 1.55d-64) then
        tmp = x * y
    else if ((a * b) <= 7.8d+141) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6.2e+138) {
		tmp = a * b;
	} else if ((a * b) <= -6.2e-176) {
		tmp = x * y;
	} else if ((a * b) <= 1e-148) {
		tmp = z * t;
	} else if ((a * b) <= 1.55e-64) {
		tmp = x * y;
	} else if ((a * b) <= 7.8e+141) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -6.2e+138:
		tmp = a * b
	elif (a * b) <= -6.2e-176:
		tmp = x * y
	elif (a * b) <= 1e-148:
		tmp = z * t
	elif (a * b) <= 1.55e-64:
		tmp = x * y
	elif (a * b) <= 7.8e+141:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -6.2e+138)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -6.2e-176)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1e-148)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.55e-64)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 7.8e+141)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -6.2e+138)
		tmp = a * b;
	elseif ((a * b) <= -6.2e-176)
		tmp = x * y;
	elseif ((a * b) <= 1e-148)
		tmp = z * t;
	elseif ((a * b) <= 1.55e-64)
		tmp = x * y;
	elseif ((a * b) <= 7.8e+141)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -6.2e+138], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6.2e-176], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-148], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.55e-64], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.8e+141], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.1999999999999995e138 or 7.79999999999999983e141 < (*.f64 a b)

   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 a around inf 74.0%

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

   if -6.1999999999999995e138 < (*.f64 a b) < -6.19999999999999983e-176 or 9.99999999999999936e-149 < (*.f64 a b) < 1.55000000000000012e-64

   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 inf 50.8%

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

   if -6.19999999999999983e-176 < (*.f64 a b) < 9.99999999999999936e-149 or 1.55000000000000012e-64 < (*.f64 a b) < 7.79999999999999983e141

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 45.8%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.2 \cdot 10^{+138}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{-148}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.8 \cdot 10^{+141}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.65e+225)
     (* x y)
     (if (<= (* x y) -1e-108)
       t_1
       (if (<= (* x y) -4.5e-169)
         (* z t)
         (if (<= (* x y) 2.6e+132) 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) <= -1.65e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1e-108) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e-169) {
		tmp = z * t;
	} else if ((x * y) <= 2.6e+132) {
		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) <= (-1.65d+225)) then
        tmp = x * y
    else if ((x * y) <= (-1d-108)) then
        tmp = t_1
    else if ((x * y) <= (-4.5d-169)) then
        tmp = z * t
    else if ((x * y) <= 2.6d+132) 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) <= -1.65e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1e-108) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e-169) {
		tmp = z * t;
	} else if ((x * y) <= 2.6e+132) {
		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) <= -1.65e+225:
		tmp = x * y
	elif (x * y) <= -1e-108:
		tmp = t_1
	elif (x * y) <= -4.5e-169:
		tmp = z * t
	elif (x * y) <= 2.6e+132:
		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) <= -1.65e+225)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1e-108)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.5e-169)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.6e+132)
		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) <= -1.65e+225)
		tmp = x * y;
	elseif ((x * y) <= -1e-108)
		tmp = t_1;
	elseif ((x * y) <= -4.5e-169)
		tmp = z * t;
	elseif ((x * y) <= 2.6e+132)
		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], -1.65e+225], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-108], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e-169], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.6e+132], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.65e225 or 2.6e132 < (*.f64 x y)

   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 x around inf 74.3%

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

   if -1.65e225 < (*.f64 x y) < -1.00000000000000004e-108 or -4.4999999999999999e-169 < (*.f64 x y) < 2.6e132

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 89.6%

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

      1. associate-/l* 85.6%

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

      2. associate-/l* 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in b around inf 62.4%

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

   if -1.00000000000000004e-108 < (*.f64 x y) < -4.4999999999999999e-169

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 82.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-108}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+132}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $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 inf 10.0%

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

   4. Taylor expanded in a around 0 20.0%

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

   5. Taylor expanded in c around 0 50.4%

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

4. Final simplification 98.0%

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

Alternative 9: 42.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4e+23)
   (* a b)
   (if (<= (* a b) 1.05e-8)
     (* z t)
     (if (<= (* a b) 9.8e+32)
       (* c i)
       (if (<= (* a b) 1.25e+140) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4e+23) {
		tmp = a * b;
	} else if ((a * b) <= 1.05e-8) {
		tmp = z * t;
	} else if ((a * b) <= 9.8e+32) {
		tmp = c * i;
	} else if ((a * b) <= 1.25e+140) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-4d+23)) then
        tmp = a * b
    else if ((a * b) <= 1.05d-8) then
        tmp = z * t
    else if ((a * b) <= 9.8d+32) then
        tmp = c * i
    else if ((a * b) <= 1.25d+140) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4e+23) {
		tmp = a * b;
	} else if ((a * b) <= 1.05e-8) {
		tmp = z * t;
	} else if ((a * b) <= 9.8e+32) {
		tmp = c * i;
	} else if ((a * b) <= 1.25e+140) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4e+23:
		tmp = a * b
	elif (a * b) <= 1.05e-8:
		tmp = z * t
	elif (a * b) <= 9.8e+32:
		tmp = c * i
	elif (a * b) <= 1.25e+140:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4e+23)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.05e-8)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 9.8e+32)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.25e+140)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -4e+23)
		tmp = a * b;
	elseif ((a * b) <= 1.05e-8)
		tmp = z * t;
	elseif ((a * b) <= 9.8e+32)
		tmp = c * i;
	elseif ((a * b) <= 1.25e+140)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+23], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.05e-8], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.8e+32], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.25e+140], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.9999999999999997e23 or 1.25000000000000002e140 < (*.f64 a b)

   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 a around inf 64.5%

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

   if -3.9999999999999997e23 < (*.f64 a b) < 1.04999999999999997e-8 or 9.8000000000000003e32 < (*.f64 a b) < 1.25000000000000002e140

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 40.8%

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

   if 1.04999999999999997e-8 < (*.f64 a b) < 9.8000000000000003e32

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 64.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + b \cdot \left(a + x \cdot \frac{y}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* a b) -1e-95)
     (+ (* a b) t_1)
     (if (<= (* a b) 2e+140)
       (+ (* c i) t_1)
       (+ (* c i) (* b (+ a (* x (/ y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -1e-95) {
		tmp = (a * b) + t_1;
	} else if ((a * b) <= 2e+140) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (c * i) + (b * (a + (x * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a * b) <= (-1d-95)) then
        tmp = (a * b) + t_1
    else if ((a * b) <= 2d+140) then
        tmp = (c * i) + t_1
    else
        tmp = (c * i) + (b * (a + (x * (y / 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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -1e-95) {
		tmp = (a * b) + t_1;
	} else if ((a * b) <= 2e+140) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (c * i) + (b * (a + (x * (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -1e-95:
		tmp = (a * b) + t_1
	elif (a * b) <= 2e+140:
		tmp = (c * i) + t_1
	else:
		tmp = (c * i) + (b * (a + (x * (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1e-95)
		tmp = Float64(Float64(a * b) + t_1);
	elseif (Float64(a * b) <= 2e+140)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(c * i) + Float64(b * Float64(a + Float64(x * Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1e-95)
		tmp = (a * b) + t_1;
	elseif ((a * b) <= 2e+140)
		tmp = (c * i) + t_1;
	else
		tmp = (c * i) + (b * (a + (x * (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e-95], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+140], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(b * N[(a + N[(x * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999989e-96

   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 c around 0 86.7%

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

   if -9.99999999999999989e-96 < (*.f64 a b) < 2.00000000000000012e140

   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 0 94.4%

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

   if 2.00000000000000012e140 < (*.f64 a b)

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf 93.4%

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

      1. associate-/l* 95.6%

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

      2. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in t around 0 97.6%

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

      1. associate-*r/ 97.6%

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

   8. Simplified 97.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-95}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + b \cdot \left(a + x \cdot \frac{y}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.28 \cdot 10^{-12} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+56}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.28e-12) (not (<= (* x y) 3.9e+56)))
   (+ (* a b) (+ (* x y) (* z t)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.28e-12) || !((x * y) <= 3.9e+56)) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.28d-12)) .or. (.not. ((x * y) <= 3.9d+56))) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.28e-12) || !((x * y) <= 3.9e+56)) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.28e-12) or not ((x * y) <= 3.9e+56):
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.28e-12) || !(Float64(x * y) <= 3.9e+56))
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.28e-12) || ~(((x * y) <= 3.9e+56)))
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.28e-12], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.9e+56]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.28e-12 or 3.89999999999999994e56 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in c around 0 88.5%

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

   if -1.28e-12 < (*.f64 x y) < 3.89999999999999994e56

   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 x around 0 92.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.28 \cdot 10^{-12} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+56}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{elif}\;c \cdot i \leq 10^{-52}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -2e+119)
     (+ (* c i) t_1)
     (if (<= (* c i) 1e-52) (+ (* a b) t_1) (+ (* 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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2e+119) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1e-52) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-2d+119)) then
        tmp = (c * i) + t_1
    else if ((c * i) <= 1d-52) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2e+119) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1e-52) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -2e+119:
		tmp = (c * i) + t_1
	elif (c * i) <= 1e-52:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -2e+119)
		tmp = Float64(Float64(c * i) + t_1);
	elseif (Float64(c * i) <= 1e-52)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2e+119)
		tmp = (c * i) + t_1;
	elseif ((c * i) <= 1e-52)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2e+119], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e-52], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.99999999999999989e119

   1. Initial program 92.5%

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

   3. Taylor expanded in a around 0 85.3%

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

   if -1.99999999999999989e119 < (*.f64 c i) < 1e-52

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 95.2%

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

   if 1e-52 < (*.f64 c i)

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 84.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{-52}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+193}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e+119)
   (+ (* x y) (* c i))
   (if (<= (* c i) 2e+193)
     (+ (* a b) (+ (* 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) {
	double tmp;
	if ((c * i) <= -2e+119) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 2e+193) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (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) <= (-2d+119)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 2d+193) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (a * b) + (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) <= -2e+119) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 2e+193) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2e+119:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 2e+193:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e+119)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 2e+193)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + 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) <= -2e+119)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 2e+193)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e+119], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+193], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.99999999999999989e119

   1. Initial program 92.5%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in t around 0 80.6%

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

   if -1.99999999999999989e119 < (*.f64 c i) < 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 c around 0 92.4%

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

   if 2.00000000000000013e193 < (*.f64 c i)

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 83.3%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in b around inf 83.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+193}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+56} \lor \neg \left(c \cdot i \leq 9500000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -6.8e+56) (not (<= (* c i) 9500000000.0)))
   (+ (* a b) (* c i))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -6.8e+56) || !((c * i) <= 9500000000.0)) {
		tmp = (a * b) + (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 (((c * i) <= (-6.8d+56)) .or. (.not. ((c * i) <= 9500000000.0d0))) then
        tmp = (a * b) + (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 (((c * i) <= -6.8e+56) || !((c * i) <= 9500000000.0)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -6.8e+56) or not ((c * i) <= 9500000000.0):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -6.8e+56) || !(Float64(c * i) <= 9500000000.0))
		tmp = Float64(Float64(a * b) + 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 (((c * i) <= -6.8e+56) || ~(((c * i) <= 9500000000.0)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -6.8e+56], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9500000000.0]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -6.80000000000000002e56 or 9.5e9 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 87.5%

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

      1. associate-/l* 83.6%

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

      2. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in b around inf 72.5%

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

   if -6.80000000000000002e56 < (*.f64 c i) < 9.5e9

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 88.2%

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

   4. Taylor expanded in z around inf 68.3%

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

   5. Taylor expanded in c around 0 66.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+56} \lor \neg \left(c \cdot i \leq 9500000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{+24} \lor \neg \left(a \cdot b \leq 1.3 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.05e+24) (not (<= (* a b) 1.3e+125))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.05e+24) || !((a * b) <= 1.3e+125)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-1.05d+24)) .or. (.not. ((a * b) <= 1.3d+125))) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.05e+24) || !((a * b) <= 1.3e+125)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.05e+24) or not ((a * b) <= 1.3e+125):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.05e+24) || !(Float64(a * b) <= 1.3e+125))
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -1.05e+24) || ~(((a * b) <= 1.3e+125)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.05e+24], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.3e+125]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.0500000000000001e24 or 1.30000000000000002e125 < (*.f64 a b)

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf 64.2%

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

   if -1.0500000000000001e24 < (*.f64 a b) < 1.30000000000000002e125

   1. Initial program 97.5%

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

   3. Taylor expanded in c around inf 30.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{+24} \lor \neg \left(a \cdot b \leq 1.3 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 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 a around inf 28.6%

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

Reproduce

herbie shell --seed 2024096 
(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)))