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

Percentage Accurate: 95.5% → 98.0%

Time: 10.4s

Alternatives: 14

Speedup: 0.4×

• 41.7% 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: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(c * i + N[(a * b + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t + N[(c * N[(i / z), $MachinePrecision]), $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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   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 61.6%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 98.8%

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

Alternative 2: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{-157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))))
   (if (<= (* a b) -5e+23)
     (+ (* a b) (* c i))
     (if (<= (* a b) -1e-33)
       t_1
       (if (<= (* a b) 1e-157)
         (+ (* c i) (* z t))
         (if (<= (* a b) 5e-15) t_1 (* i (+ c (/ (* a b) i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5e+23) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -1e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1e-157) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 5e-15) {
		tmp = t_1;
	} else {
		tmp = i * (c + ((a * b) / 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) :: tmp
    t_1 = (x * y) + (c * i)
    if ((a * b) <= (-5d+23)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= (-1d-33)) then
        tmp = t_1
    else if ((a * b) <= 1d-157) then
        tmp = (c * i) + (z * t)
    else if ((a * b) <= 5d-15) then
        tmp = t_1
    else
        tmp = i * (c + ((a * b) / 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 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5e+23) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= -1e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1e-157) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 5e-15) {
		tmp = t_1;
	} else {
		tmp = i * (c + ((a * b) / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	tmp = 0
	if (a * b) <= -5e+23:
		tmp = (a * b) + (c * i)
	elif (a * b) <= -1e-33:
		tmp = t_1
	elif (a * b) <= 1e-157:
		tmp = (c * i) + (z * t)
	elif (a * b) <= 5e-15:
		tmp = t_1
	else:
		tmp = i * (c + ((a * b) / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5e+23)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= -1e-33)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e-157)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(a * b) <= 5e-15)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(c + Float64(Float64(a * b) / i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -5e+23)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= -1e-33)
		tmp = t_1;
	elseif ((a * b) <= 1e-157)
		tmp = (c * i) + (z * t);
	elseif ((a * b) <= 5e-15)
		tmp = t_1;
	else
		tmp = i * (c + ((a * b) / i));
	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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+23], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-33], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e-157], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e-15], t$95$1, N[(i * N[(c + N[(N[(a * b), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.9999999999999999e23

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 77.4%

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

   if -4.9999999999999999e23 < (*.f64 a b) < -1.0000000000000001e-33 or 9.99999999999999943e-158 < (*.f64 a b) < 4.99999999999999999e-15

   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 x around inf 73.9%

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

   if -1.0000000000000001e-33 < (*.f64 a b) < 9.99999999999999943e-158

   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 z around inf 64.9%

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

   if 4.99999999999999999e-15 < (*.f64 a b)

   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 inf 64.9%

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

   4. Taylor expanded in i around inf 62.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{-157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (* x (+ y (/ (* a b) x)))))
   (if (<= (* x y) -4e-23)
     t_2
     (if (<= (* x y) -1e-294)
       t_1
       (if (<= (* x y) 5e-297)
         (+ (* c i) (* z t))
         (if (<= (* x y) 2e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = x * (y + ((a * b) / x));
	double tmp;
	if ((x * y) <= -4e-23) {
		tmp = t_2;
	} else if ((x * y) <= -1e-294) {
		tmp = t_1;
	} else if ((x * y) <= 5e-297) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = x * (y + ((a * b) / x))
    if ((x * y) <= (-4d-23)) then
        tmp = t_2
    else if ((x * y) <= (-1d-294)) then
        tmp = t_1
    else if ((x * y) <= 5d-297) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 2d+112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = x * (y + ((a * b) / x));
	double tmp;
	if ((x * y) <= -4e-23) {
		tmp = t_2;
	} else if ((x * y) <= -1e-294) {
		tmp = t_1;
	} else if ((x * y) <= 5e-297) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = x * (y + ((a * b) / x))
	tmp = 0
	if (x * y) <= -4e-23:
		tmp = t_2
	elif (x * y) <= -1e-294:
		tmp = t_1
	elif (x * y) <= 5e-297:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 2e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(x * Float64(y + Float64(Float64(a * b) / x)))
	tmp = 0.0
	if (Float64(x * y) <= -4e-23)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e-294)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-297)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 2e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = x * (y + ((a * b) / x));
	tmp = 0.0;
	if ((x * y) <= -4e-23)
		tmp = t_2;
	elseif ((x * y) <= -1e-294)
		tmp = t_1;
	elseif ((x * y) <= 5e-297)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 2e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y + N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-23], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e-294], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-297], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999984e-23 or 1.9999999999999999e112 < (*.f64 x y)

   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 x around inf 92.3%

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

   4. Taylor expanded in t around 0 80.3%

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

   5. Taylor expanded in c around 0 75.4%

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

   if -3.99999999999999984e-23 < (*.f64 x y) < -1.00000000000000002e-294 or 5e-297 < (*.f64 x y) < 1.9999999999999999e112

   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 a around inf 70.1%

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

   if -1.00000000000000002e-294 < (*.f64 x y) < 5e-297

   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 70.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -4e-23)
     (* x (+ y (/ (* a b) x)))
     (if (<= (* x y) -1e-294)
       t_1
       (if (<= (* x y) 5e-297)
         (+ (* c i) (* z t))
         (if (<= (* x y) 5e+108) 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 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -4e-23) {
		tmp = x * (y + ((a * b) / x));
	} else if ((x * y) <= -1e-294) {
		tmp = t_1;
	} else if ((x * y) <= 5e-297) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5e+108) {
		tmp = t_1;
	} else {
		tmp = z * (t + ((x * y) / z));
	}
	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) <= (-4d-23)) then
        tmp = x * (y + ((a * b) / x))
    else if ((x * y) <= (-1d-294)) then
        tmp = t_1
    else if ((x * y) <= 5d-297) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 5d+108) then
        tmp = t_1
    else
        tmp = z * (t + ((x * y) / z))
    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) <= -4e-23) {
		tmp = x * (y + ((a * b) / x));
	} else if ((x * y) <= -1e-294) {
		tmp = t_1;
	} else if ((x * y) <= 5e-297) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5e+108) {
		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 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -4e-23:
		tmp = x * (y + ((a * b) / x))
	elif (x * y) <= -1e-294:
		tmp = t_1
	elif (x * y) <= 5e-297:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 5e+108:
		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(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -4e-23)
		tmp = Float64(x * Float64(y + Float64(Float64(a * b) / x)));
	elseif (Float64(x * y) <= -1e-294)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-297)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 5e+108)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -4e-23)
		tmp = x * (y + ((a * b) / x));
	elseif ((x * y) <= -1e-294)
		tmp = t_1;
	elseif ((x * y) <= 5e-297)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 5e+108)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-23], N[(x * N[(y + N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-294], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-297], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+108], t$95$1, N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.99999999999999984e-23

   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 inf 89.9%

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

   4. Taylor expanded in t around 0 80.2%

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

   5. Taylor expanded in c around 0 73.4%

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

   if -3.99999999999999984e-23 < (*.f64 x y) < -1.00000000000000002e-294 or 5e-297 < (*.f64 x y) < 4.99999999999999991e108

   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 a around inf 70.7%

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

   if -1.00000000000000002e-294 < (*.f64 x y) < 5e-297

   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 70.4%

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

   if 4.99999999999999991e108 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 85.0%

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

   4. Taylor expanded in a around 0 80.5%

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

   5. Taylor expanded in c around 0 80.5%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{x \cdot y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + c \cdot i\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{-157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* c i))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* a b) -5e+23)
     t_2
     (if (<= (* a b) -1e-33)
       t_1
       (if (<= (* a b) 1e-157)
         (+ (* c i) (* z t))
         (if (<= (* a b) 5e-15) 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 = (x * y) + (c * i);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -5e+23) {
		tmp = t_2;
	} else if ((a * b) <= -1e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1e-157) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 5e-15) {
		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 = (x * y) + (c * i)
    t_2 = (a * b) + (c * i)
    if ((a * b) <= (-5d+23)) then
        tmp = t_2
    else if ((a * b) <= (-1d-33)) then
        tmp = t_1
    else if ((a * b) <= 1d-157) then
        tmp = (c * i) + (z * t)
    else if ((a * b) <= 5d-15) 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 = (x * y) + (c * i);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -5e+23) {
		tmp = t_2;
	} else if ((a * b) <= -1e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1e-157) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 5e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (c * i)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -5e+23:
		tmp = t_2
	elif (a * b) <= -1e-33:
		tmp = t_1
	elif (a * b) <= 1e-157:
		tmp = (c * i) + (z * t)
	elif (a * b) <= 5e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5e+23)
		tmp = t_2;
	elseif (Float64(a * b) <= -1e-33)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e-157)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(a * b) <= 5e-15)
		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 = (x * y) + (c * i);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -5e+23)
		tmp = t_2;
	elseif ((a * b) <= -1e-33)
		tmp = t_1;
	elseif ((a * b) <= 1e-157)
		tmp = (c * i) + (z * t);
	elseif ((a * b) <= 5e-15)
		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[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+23], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1e-33], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e-157], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e-15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e23 or 4.99999999999999999e-15 < (*.f64 a b)

   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 a around inf 70.9%

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

   if -4.9999999999999999e23 < (*.f64 a b) < -1.0000000000000001e-33 or 9.99999999999999943e-158 < (*.f64 a b) < 4.99999999999999999e-15

   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 x around inf 73.9%

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

   if -1.0000000000000001e-33 < (*.f64 a b) < 9.99999999999999943e-158

   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 z around inf 64.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 10^{-157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.4× speedup

Math

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

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 (* z (+ t (* c (/ i z)))))))

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 = z * (t + (c * (i / 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 = ((a * b) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (t + (c * (i / z)));
	}
	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 = z * (t + (c * (i / z)))
	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(z * Float64(t + Float64(c * Float64(i / z))));
	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 = z * (t + (c * (i / z)));
	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[(z * N[(t + N[(c * N[(i / z), $MachinePrecision]), $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 61.6%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 98.8%

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

Alternative 7: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119} \lor \neg \left(x \cdot y \leq 10^{+173}\right):\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+119) (not (<= (* x y) 1e+173)))
   (* x (+ y (/ (* a b) x)))
   (+ (* 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) <= -5e+119) || !((x * y) <= 1e+173)) {
		tmp = x * (y + ((a * b) / x));
	} 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) <= (-5d+119)) .or. (.not. ((x * y) <= 1d+173))) then
        tmp = x * (y + ((a * b) / x))
    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) <= -5e+119) || !((x * y) <= 1e+173)) {
		tmp = x * (y + ((a * b) / x));
	} 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) <= -5e+119) or not ((x * y) <= 1e+173):
		tmp = x * (y + ((a * b) / x))
	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) <= -5e+119) || !(Float64(x * y) <= 1e+173))
		tmp = Float64(x * Float64(y + Float64(Float64(a * b) / x)));
	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) <= -5e+119) || ~(((x * y) <= 1e+173)))
		tmp = x * (y + ((a * b) / x));
	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], -5e+119], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+173]], $MachinePrecision]], N[(x * N[(y + N[(N[(a * b), $MachinePrecision] / x), $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) < -4.9999999999999999e119 or 1e173 < (*.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 94.6%

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

   4. Taylor expanded in t around 0 89.2%

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

   5. Taylor expanded in c around 0 86.5%

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

   if -4.9999999999999999e119 < (*.f64 x y) < 1e173

   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 x around 0 88.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119} \lor \neg \left(x \cdot y \leq 10^{+173}\right):\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+173}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+119)
   (+ (* c i) (+ (* x y) (* a b)))
   (if (<= (* x y) 1e+173)
     (+ (* c i) (+ (* a b) (* z t)))
     (* x (+ y (/ (* a b) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+119) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((x * y) <= 1e+173) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = x * (y + ((a * b) / x));
	}
	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) <= (-5d+119)) then
        tmp = (c * i) + ((x * y) + (a * b))
    else if ((x * y) <= 1d+173) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = x * (y + ((a * b) / x))
    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) <= -5e+119) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((x * y) <= 1e+173) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = x * (y + ((a * b) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+119:
		tmp = (c * i) + ((x * y) + (a * b))
	elif (x * y) <= 1e+173:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = x * (y + ((a * b) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+119)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	elseif (Float64(x * y) <= 1e+173)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(x * Float64(y + Float64(Float64(a * b) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+119)
		tmp = (c * i) + ((x * y) + (a * b));
	elseif ((x * y) <= 1e+173)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = x * (y + ((a * b) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+119], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+173], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e119

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 89.3%

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

   if -4.9999999999999999e119 < (*.f64 x y) < 1e173

   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 x around 0 88.6%

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

   if 1e173 < (*.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 94.7%

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

   4. Taylor expanded in t around 0 86.4%

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

   5. Taylor expanded in c around 0 83.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+173}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+119)
   (+ (* c i) (+ (* x y) (* a b)))
   (if (<= (* x y) 5e+108)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* x y) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+119) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((x * y) <= 5e+108) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-5d+119)) then
        tmp = (c * i) + ((x * y) + (a * b))
    else if ((x * y) <= 5d+108) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+119) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((x * y) <= 5e+108) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+119:
		tmp = (c * i) + ((x * y) + (a * b))
	elif (x * y) <= 5e+108:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+119)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	elseif (Float64(x * y) <= 5e+108)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+119)
		tmp = (c * i) + ((x * y) + (a * b));
	elseif ((x * y) <= 5e+108)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+119], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+108], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e119

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 89.3%

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

   if -4.9999999999999999e119 < (*.f64 x y) < 4.99999999999999991e108

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0 89.9%

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

   if 4.99999999999999991e108 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 88.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+119)
   (+ (* c i) (* x (+ y (/ (* a b) x))))
   (if (<= (* x y) 5e+108)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* x y) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+119) {
		tmp = (c * i) + (x * (y + ((a * b) / x)));
	} else if ((x * y) <= 5e+108) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-5d+119)) then
        tmp = (c * i) + (x * (y + ((a * b) / x)))
    else if ((x * y) <= 5d+108) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+119) {
		tmp = (c * i) + (x * (y + ((a * b) / x)));
	} else if ((x * y) <= 5e+108) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+119:
		tmp = (c * i) + (x * (y + ((a * b) / x)))
	elif (x * y) <= 5e+108:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+119)
		tmp = Float64(Float64(c * i) + Float64(x * Float64(y + Float64(Float64(a * b) / x))));
	elseif (Float64(x * y) <= 5e+108)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+119)
		tmp = (c * i) + (x * (y + ((a * b) / x)));
	elseif ((x * y) <= 5e+108)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+119], N[(N[(c * i), $MachinePrecision] + N[(x * N[(y + N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+108], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e119

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf 94.5%

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

   4. Taylor expanded in t around 0 92.0%

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

   if -4.9999999999999999e119 < (*.f64 x y) < 4.99999999999999991e108

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0 89.9%

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

   if 4.99999999999999991e108 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 88.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + x \cdot \left(y + \frac{a \cdot b}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -36000000 \lor \neg \left(a \cdot b \leq 5.6 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -36000000.0) (not (<= (* a b) 5.6e+36)))
   (+ (* a b) (* c i))
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -36000000.0) || !((a * b) <= 5.6e+36)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-36000000.0d0)) .or. (.not. ((a * b) <= 5.6d+36))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -36000000.0) || !((a * b) <= 5.6e+36)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -36000000.0) or not ((a * b) <= 5.6e+36):
		tmp = (a * b) + (c * i)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -36000000.0) || !(Float64(a * b) <= 5.6e+36))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -36000000.0) || ~(((a * b) <= 5.6e+36)))
		tmp = (a * b) + (c * i);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -36000000.0], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5.6e+36]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.6e7 or 5.6000000000000001e36 < (*.f64 a b)

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 73.3%

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

   if -3.6e7 < (*.f64 a b) < 5.6000000000000001e36

   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 z around inf 58.8%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -36000000 \lor \neg \left(a \cdot b \leq 5.6 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 1.76 \cdot 10^{+146}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.9e+248) (not (<= (* c i) 1.76e+146))) (* c i) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 1.76e+146)) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.9d+248)) .or. (.not. ((c * i) <= 1.76d+146))) then
        tmp = c * i
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.9e+248) || !((c * i) <= 1.76e+146)) {
		tmp = c * i;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.9e+248) or not ((c * i) <= 1.76e+146):
		tmp = c * i
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.9e+248) || !(Float64(c * i) <= 1.76e+146))
		tmp = Float64(c * i);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.9e+248) || ~(((c * i) <= 1.76e+146)))
		tmp = c * i;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.9e+248], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.76e+146]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.8999999999999999e248 or 1.76000000000000007e146 < (*.f64 c i)

   1. Initial program 87.1%

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

   3. Taylor expanded in c around inf 77.2%

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

   if -3.8999999999999999e248 < (*.f64 c i) < 1.76000000000000007e146

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 36.9%

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

   4. Taylor expanded in z around inf 35.9%

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

      1. associate-/l* 36.4%

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

   6. Simplified 36.4%

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

      1. clear-num 36.3%

         \[\leadsto z \cdot \left(t + c \cdot \color{blue}{\frac{1}{\frac{z}{i}}}\right) \]

      2. un-div-inv 35.8%

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

   8. Applied egg-rr 35.8%

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

   9. Taylor expanded in z around inf 31.9%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+248} \lor \neg \left(c \cdot i \leq 1.76 \cdot 10^{+146}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{+236}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t 1.45e+236) (+ (* a b) (* c i)) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= 1.45e+236) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (t <= 1.45d+236) then
        tmp = (a * b) + (c * i)
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= 1.45e+236) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= 1.45e+236:
		tmp = (a * b) + (c * i)
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= 1.45e+236)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (t <= 1.45e+236)
		tmp = (a * b) + (c * i);
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, 1.45e+236], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.45e236

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 53.2%

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

   if 1.45e236 < t

   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 inf 75.3%

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

   4. Taylor expanded in z around inf 68.9%

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

      1. associate-/l* 68.9%

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

   6. Simplified 68.9%

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

      1. clear-num 68.9%

         \[\leadsto z \cdot \left(t + c \cdot \color{blue}{\frac{1}{\frac{z}{i}}}\right) \]

      2. un-div-inv 68.9%

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

   8. Applied egg-rr 68.9%

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

   9. Taylor expanded in z around inf 62.6%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{+236}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ c \cdot i \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 c around inf 24.2%

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

4. Final simplification 24.2%

   \[\leadsto c \cdot i \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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)))