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

Percentage Accurate: 95.7% → 98.3%

Time: 10.9s

Alternatives: 16

Speedup: 0.4×

• 41.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.4× speedup

Math

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

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 (* x (+ y (+ (* a (/ b x)) (* c (/ i x))))))))

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 = x * (y + ((a * (b / x)) + (c * (i / x))));
	}
	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 = x * (y + ((a * (b / x)) + (c * (i / x))));
	}
	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 = x * (y + ((a * (b / x)) + (c * (i / x))))
	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(x * Float64(y + Float64(Float64(a * Float64(b / x)) + Float64(c * Float64(i / x)))));
	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 = x * (y + ((a * (b / x)) + (c * (i / x))));
	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[(x * N[(y + N[(N[(a * N[(b / x), $MachinePrecision]), $MachinePrecision] + N[(c * N[(i / x), $MachinePrecision]), $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 x around inf 18.2%

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

      1. associate-/l* 27.3%

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

      2. associate-/l* 45.5%

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

      3. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 45.5%

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

      1. associate-/l* 54.5%

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

      2. associate-*r/ 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 98.8%

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

Alternative 2: 98.0% 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 95.7%

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

   1. +-commutative 95.7%

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

   2. fma-define 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-define 97.3%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

Alternative 3: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. +-commutative 95.7%

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

   2. fma-define 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-define 97.3%

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

   5. fma-define 97.7%

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

3. Simplified 97.7%

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

Alternative 4: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-309}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 400000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* c i) -1e+206)
     (* i (+ c (/ (* a b) i)))
     (if (<= (* c i) -2e+70)
       t_2
       (if (<= (* c i) -5e-25)
         t_1
         (if (<= (* c i) -1e-309)
           (+ (* a b) (* z t))
           (if (<= (* c i) 400000000.0)
             t_2
             (if (<= (* c i) 1e+30) t_1 (+ (* c i) (* z t))))))))))

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) + (z * t);
	double tmp;
	if ((c * i) <= -1e+206) {
		tmp = i * (c + ((a * b) / i));
	} else if ((c * i) <= -2e+70) {
		tmp = t_2;
	} else if ((c * i) <= -5e-25) {
		tmp = t_1;
	} else if ((c * i) <= -1e-309) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 400000000.0) {
		tmp = t_2;
	} else if ((c * i) <= 1e+30) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (x * y) + (z * t)
    if ((c * i) <= (-1d+206)) then
        tmp = i * (c + ((a * b) / i))
    else if ((c * i) <= (-2d+70)) then
        tmp = t_2
    else if ((c * i) <= (-5d-25)) then
        tmp = t_1
    else if ((c * i) <= (-1d-309)) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 400000000.0d0) then
        tmp = t_2
    else if ((c * i) <= 1d+30) then
        tmp = t_1
    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 t_1 = (a * b) + (c * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -1e+206) {
		tmp = i * (c + ((a * b) / i));
	} else if ((c * i) <= -2e+70) {
		tmp = t_2;
	} else if ((c * i) <= -5e-25) {
		tmp = t_1;
	} else if ((c * i) <= -1e-309) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 400000000.0) {
		tmp = t_2;
	} else if ((c * i) <= 1e+30) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -1e+206:
		tmp = i * (c + ((a * b) / i))
	elif (c * i) <= -2e+70:
		tmp = t_2
	elif (c * i) <= -5e-25:
		tmp = t_1
	elif (c * i) <= -1e-309:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 400000000.0:
		tmp = t_2
	elif (c * i) <= 1e+30:
		tmp = t_1
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1e+206)
		tmp = Float64(i * Float64(c + Float64(Float64(a * b) / i)));
	elseif (Float64(c * i) <= -2e+70)
		tmp = t_2;
	elseif (Float64(c * i) <= -5e-25)
		tmp = t_1;
	elseif (Float64(c * i) <= -1e-309)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 400000000.0)
		tmp = t_2;
	elseif (Float64(c * i) <= 1e+30)
		tmp = t_1;
	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)
	t_1 = (a * b) + (c * i);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1e+206)
		tmp = i * (c + ((a * b) / i));
	elseif ((c * i) <= -2e+70)
		tmp = t_2;
	elseif ((c * i) <= -5e-25)
		tmp = t_1;
	elseif ((c * i) <= -1e-309)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 400000000.0)
		tmp = t_2;
	elseif ((c * i) <= 1e+30)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1e+206], N[(i * N[(c + N[(N[(a * b), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e+70], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -5e-25], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1e-309], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 400000000.0], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1e+30], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -1e206

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0 93.3%

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

   4. Taylor expanded in a around inf 89.9%

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

   5. Taylor expanded in i around inf 96.7%

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

   if -1e206 < (*.f64 c i) < -2.00000000000000015e70 or -1.000000000000002e-309 < (*.f64 c i) < 4e8

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 83.9%

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

   4. Taylor expanded in c around 0 76.4%

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

   if -2.00000000000000015e70 < (*.f64 c i) < -4.99999999999999962e-25 or 4e8 < (*.f64 c i) < 1e30

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in a around inf 83.4%

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

   if -4.99999999999999962e-25 < (*.f64 c i) < -1.000000000000002e-309

   1. Initial program 95.9%

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

   3. Taylor expanded in c around 0 93.9%

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

   4. Taylor expanded in x around 0 72.4%

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

   if 1e30 < (*.f64 c i)

   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 a around 0 88.3%

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

   4. Taylor expanded in x around 0 81.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-309}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 400000000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+30}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -1.22 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -5.5 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-309}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 340000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.25 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -5.2e+205)
     t_2
     (if (<= (* c i) -1.22e+70)
       t_1
       (if (<= (* c i) -5.5e-25)
         t_2
         (if (<= (* c i) -1e-309)
           (+ (* a b) (* z t))
           (if (<= (* c i) 340000000.0)
             t_1
             (if (<= (* c i) 1.25e+30) t_2 (+ (* c i) (* 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 t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.2e+205) {
		tmp = t_2;
	} else if ((c * i) <= -1.22e+70) {
		tmp = t_1;
	} else if ((c * i) <= -5.5e-25) {
		tmp = t_2;
	} else if ((c * i) <= -1e-309) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 340000000.0) {
		tmp = t_1;
	} else if ((c * i) <= 1.25e+30) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-5.2d+205)) then
        tmp = t_2
    else if ((c * i) <= (-1.22d+70)) then
        tmp = t_1
    else if ((c * i) <= (-5.5d-25)) then
        tmp = t_2
    else if ((c * i) <= (-1d-309)) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 340000000.0d0) then
        tmp = t_1
    else if ((c * i) <= 1.25d+30) then
        tmp = t_2
    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 t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.2e+205) {
		tmp = t_2;
	} else if ((c * i) <= -1.22e+70) {
		tmp = t_1;
	} else if ((c * i) <= -5.5e-25) {
		tmp = t_2;
	} else if ((c * i) <= -1e-309) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 340000000.0) {
		tmp = t_1;
	} else if ((c * i) <= 1.25e+30) {
		tmp = t_2;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -5.2e+205:
		tmp = t_2
	elif (c * i) <= -1.22e+70:
		tmp = t_1
	elif (c * i) <= -5.5e-25:
		tmp = t_2
	elif (c * i) <= -1e-309:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 340000000.0:
		tmp = t_1
	elif (c * i) <= 1.25e+30:
		tmp = t_2
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -5.2e+205)
		tmp = t_2;
	elseif (Float64(c * i) <= -1.22e+70)
		tmp = t_1;
	elseif (Float64(c * i) <= -5.5e-25)
		tmp = t_2;
	elseif (Float64(c * i) <= -1e-309)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 340000000.0)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.25e+30)
		tmp = t_2;
	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)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -5.2e+205)
		tmp = t_2;
	elseif ((c * i) <= -1.22e+70)
		tmp = t_1;
	elseif ((c * i) <= -5.5e-25)
		tmp = t_2;
	elseif ((c * i) <= -1e-309)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 340000000.0)
		tmp = t_1;
	elseif ((c * i) <= 1.25e+30)
		tmp = t_2;
	else
		tmp = (c * i) + (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]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5.2e+205], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1.22e+70], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5.5e-25], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1e-309], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 340000000.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.25e+30], t$95$2, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -5.1999999999999998e205 or -1.22e70 < (*.f64 c i) < -5.50000000000000004e-25 or 3.4e8 < (*.f64 c i) < 1.25e30

   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 0 89.4%

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

   4. Taylor expanded in a around inf 87.4%

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

   if -5.1999999999999998e205 < (*.f64 c i) < -1.22e70 or -1.000000000000002e-309 < (*.f64 c i) < 3.4e8

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 83.9%

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

   4. Taylor expanded in c around 0 76.4%

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

   if -5.50000000000000004e-25 < (*.f64 c i) < -1.000000000000002e-309

   1. Initial program 95.9%

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

   3. Taylor expanded in c around 0 93.9%

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

   4. Taylor expanded in x around 0 72.4%

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

   if 1.25e30 < (*.f64 c i)

   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 a around 0 88.3%

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

   4. Taylor expanded in x around 0 81.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+205}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.22 \cdot 10^{+70}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -5.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1 \cdot 10^{-309}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 340000000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.25 \cdot 10^{+30}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.2 \cdot 10^{+135}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -0.56:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-265}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 340000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.2e+135)
   (* c i)
   (if (<= (* c i) -2e+70)
     (* z t)
     (if (<= (* c i) -0.56)
       (* a b)
       (if (<= (* c i) 7e-265)
         (* z t)
         (if (<= (* c i) 340000000.0)
           (* x y)
           (if (<= (* c i) 8.2e+38) (* 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) <= -4.2e+135) {
		tmp = c * i;
	} else if ((c * i) <= -2e+70) {
		tmp = z * t;
	} else if ((c * i) <= -0.56) {
		tmp = a * b;
	} else if ((c * i) <= 7e-265) {
		tmp = z * t;
	} else if ((c * i) <= 340000000.0) {
		tmp = x * y;
	} else if ((c * i) <= 8.2e+38) {
		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 ((c * i) <= (-4.2d+135)) then
        tmp = c * i
    else if ((c * i) <= (-2d+70)) then
        tmp = z * t
    else if ((c * i) <= (-0.56d0)) then
        tmp = a * b
    else if ((c * i) <= 7d-265) then
        tmp = z * t
    else if ((c * i) <= 340000000.0d0) then
        tmp = x * y
    else if ((c * i) <= 8.2d+38) 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 ((c * i) <= -4.2e+135) {
		tmp = c * i;
	} else if ((c * i) <= -2e+70) {
		tmp = z * t;
	} else if ((c * i) <= -0.56) {
		tmp = a * b;
	} else if ((c * i) <= 7e-265) {
		tmp = z * t;
	} else if ((c * i) <= 340000000.0) {
		tmp = x * y;
	} else if ((c * i) <= 8.2e+38) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.2e+135:
		tmp = c * i
	elif (c * i) <= -2e+70:
		tmp = z * t
	elif (c * i) <= -0.56:
		tmp = a * b
	elif (c * i) <= 7e-265:
		tmp = z * t
	elif (c * i) <= 340000000.0:
		tmp = x * y
	elif (c * i) <= 8.2e+38:
		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(c * i) <= -4.2e+135)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2e+70)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -0.56)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 7e-265)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 340000000.0)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 8.2e+38)
		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 ((c * i) <= -4.2e+135)
		tmp = c * i;
	elseif ((c * i) <= -2e+70)
		tmp = z * t;
	elseif ((c * i) <= -0.56)
		tmp = a * b;
	elseif ((c * i) <= 7e-265)
		tmp = z * t;
	elseif ((c * i) <= 340000000.0)
		tmp = x * y;
	elseif ((c * i) <= 8.2e+38)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.2e+135], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e+70], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -0.56], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7e-265], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 340000000.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e+38], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.20000000000000019e135 or 8.2000000000000007e38 < (*.f64 c i)

   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 67.0%

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

   if -4.20000000000000019e135 < (*.f64 c i) < -2.00000000000000015e70 or -0.56000000000000005 < (*.f64 c i) < 7.00000000000000031e-265

   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 z around inf 40.5%

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

   if -2.00000000000000015e70 < (*.f64 c i) < -0.56000000000000005 or 3.4e8 < (*.f64 c i) < 8.2000000000000007e38

   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 a around inf 57.4%

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

   if 7.00000000000000031e-265 < (*.f64 c i) < 3.4e8

   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 53.0%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.2 \cdot 10^{+135}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -0.56:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-265}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 340000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.02 \cdot 10^{-197}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -8.5e+123)
     (+ (* x y) (* c i))
     (if (<= (* c i) 6.2e-263)
       t_1
       (if (<= (* c i) 1.02e-197)
         (* x y)
         (if (<= (* c i) 4.8e+35) t_1 (+ (* c i) (* z t))))))))

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 ((c * i) <= -8.5e+123) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 6.2e-263) {
		tmp = t_1;
	} else if ((c * i) <= 1.02e-197) {
		tmp = x * y;
	} else if ((c * i) <= 4.8e+35) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-8.5d+123)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 6.2d-263) then
        tmp = t_1
    else if ((c * i) <= 1.02d-197) then
        tmp = x * y
    else if ((c * i) <= 4.8d+35) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -8.5e+123) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 6.2e-263) {
		tmp = t_1;
	} else if ((c * i) <= 1.02e-197) {
		tmp = x * y;
	} else if ((c * i) <= 4.8e+35) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -8.5e+123:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 6.2e-263:
		tmp = t_1
	elif (c * i) <= 1.02e-197:
		tmp = x * y
	elif (c * i) <= 4.8e+35:
		tmp = t_1
	else:
		tmp = (c * i) + (z * t)
	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(c * i) <= -8.5e+123)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 6.2e-263)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.02e-197)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 4.8e+35)
		tmp = t_1;
	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)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -8.5e+123)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 6.2e-263)
		tmp = t_1;
	elseif ((c * i) <= 1.02e-197)
		tmp = x * y;
	elseif ((c * i) <= 4.8e+35)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	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[(c * i), $MachinePrecision], -8.5e+123], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-263], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.02e-197], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.8e+35], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -8.5e123

   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 0 85.8%

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

   4. Taylor expanded in t around 0 80.7%

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

   if -8.5e123 < (*.f64 c i) < 6.20000000000000008e-263 or 1.0199999999999999e-197 < (*.f64 c i) < 4.80000000000000029e35

   1. Initial program 95.8%

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

   3. Taylor expanded in c around 0 88.7%

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

   4. Taylor expanded in x around 0 66.0%

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

   if 6.20000000000000008e-263 < (*.f64 c i) < 1.0199999999999999e-197

   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 84.9%

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

   if 4.80000000000000029e35 < (*.f64 c i)

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 90.3%

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

   4. Taylor expanded in x around 0 82.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.02 \cdot 10^{-197}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.8 \cdot 10^{+35}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+134}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -5e+134)
     (+ (* a b) (* c i))
     (if (<= (* c i) 6.2e-263)
       t_1
       (if (<= (* c i) 3.6e-201)
         (* x y)
         (if (<= (* c i) 1.9e+39) t_1 (+ (* c i) (* z t))))))))

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 ((c * i) <= -5e+134) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 6.2e-263) {
		tmp = t_1;
	} else if ((c * i) <= 3.6e-201) {
		tmp = x * y;
	} else if ((c * i) <= 1.9e+39) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-5d+134)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 6.2d-263) then
        tmp = t_1
    else if ((c * i) <= 3.6d-201) then
        tmp = x * y
    else if ((c * i) <= 1.9d+39) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -5e+134) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 6.2e-263) {
		tmp = t_1;
	} else if ((c * i) <= 3.6e-201) {
		tmp = x * y;
	} else if ((c * i) <= 1.9e+39) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -5e+134:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 6.2e-263:
		tmp = t_1
	elif (c * i) <= 3.6e-201:
		tmp = x * y
	elif (c * i) <= 1.9e+39:
		tmp = t_1
	else:
		tmp = (c * i) + (z * t)
	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(c * i) <= -5e+134)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 6.2e-263)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.6e-201)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1.9e+39)
		tmp = t_1;
	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)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -5e+134)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 6.2e-263)
		tmp = t_1;
	elseif ((c * i) <= 3.6e-201)
		tmp = x * y;
	elseif ((c * i) <= 1.9e+39)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	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[(c * i), $MachinePrecision], -5e+134], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-263], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.6e-201], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.9e+39], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.99999999999999981e134

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around inf 81.6%

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

   if -4.99999999999999981e134 < (*.f64 c i) < 6.20000000000000008e-263 or 3.60000000000000031e-201 < (*.f64 c i) < 1.8999999999999999e39

   1. Initial program 95.9%

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

   3. Taylor expanded in c around 0 88.8%

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

   4. Taylor expanded in x around 0 65.6%

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

   if 6.20000000000000008e-263 < (*.f64 c i) < 3.60000000000000031e-201

   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 84.9%

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

   if 1.8999999999999999e39 < (*.f64 c i)

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 90.3%

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

   4. Taylor expanded in x around 0 82.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+134}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-263}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 380000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -3.3e+136)
     t_2
     (if (<= (* c i) 1.5e-265)
       t_1
       (if (<= (* c i) 3.6e-201)
         (* x y)
         (if (<= (* c i) 380000000.0) 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 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.3e+136) {
		tmp = t_2;
	} else if ((c * i) <= 1.5e-265) {
		tmp = t_1;
	} else if ((c * i) <= 3.6e-201) {
		tmp = x * y;
	} else if ((c * i) <= 380000000.0) {
		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 = (a * b) + (c * i)
    if ((c * i) <= (-3.3d+136)) then
        tmp = t_2
    else if ((c * i) <= 1.5d-265) then
        tmp = t_1
    else if ((c * i) <= 3.6d-201) then
        tmp = x * y
    else if ((c * i) <= 380000000.0d0) 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 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.3e+136) {
		tmp = t_2;
	} else if ((c * i) <= 1.5e-265) {
		tmp = t_1;
	} else if ((c * i) <= 3.6e-201) {
		tmp = x * y;
	} else if ((c * i) <= 380000000.0) {
		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 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -3.3e+136:
		tmp = t_2
	elif (c * i) <= 1.5e-265:
		tmp = t_1
	elif (c * i) <= 3.6e-201:
		tmp = x * y
	elif (c * i) <= 380000000.0:
		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(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -3.3e+136)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.5e-265)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.6e-201)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 380000000.0)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -3.3e+136)
		tmp = t_2;
	elseif ((c * i) <= 1.5e-265)
		tmp = t_1;
	elseif ((c * i) <= 3.6e-201)
		tmp = x * y;
	elseif ((c * i) <= 380000000.0)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.3e+136], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.5e-265], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.6e-201], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 380000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.29999999999999992e136 or 3.8e8 < (*.f64 c i)

   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 x around 0 88.6%

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

   4. Taylor expanded in a around inf 75.9%

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

   if -3.29999999999999992e136 < (*.f64 c i) < 1.4999999999999999e-265 or 3.60000000000000031e-201 < (*.f64 c i) < 3.8e8

   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 c around 0 89.8%

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

   4. Taylor expanded in x around 0 64.9%

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

   if 1.4999999999999999e-265 < (*.f64 c i) < 3.60000000000000031e-201

   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 84.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+136}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 380000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= y -1.7e+46)
     (* x y)
     (if (<= y 4.5e+50)
       t_1
       (if (<= y 9.6e+84) (* z t) (if (<= y 2.4e+176) 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 (y <= -1.7e+46) {
		tmp = x * y;
	} else if (y <= 4.5e+50) {
		tmp = t_1;
	} else if (y <= 9.6e+84) {
		tmp = z * t;
	} else if (y <= 2.4e+176) {
		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 (y <= (-1.7d+46)) then
        tmp = x * y
    else if (y <= 4.5d+50) then
        tmp = t_1
    else if (y <= 9.6d+84) then
        tmp = z * t
    else if (y <= 2.4d+176) 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 (y <= -1.7e+46) {
		tmp = x * y;
	} else if (y <= 4.5e+50) {
		tmp = t_1;
	} else if (y <= 9.6e+84) {
		tmp = z * t;
	} else if (y <= 2.4e+176) {
		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 y <= -1.7e+46:
		tmp = x * y
	elif y <= 4.5e+50:
		tmp = t_1
	elif y <= 9.6e+84:
		tmp = z * t
	elif y <= 2.4e+176:
		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 (y <= -1.7e+46)
		tmp = Float64(x * y);
	elseif (y <= 4.5e+50)
		tmp = t_1;
	elseif (y <= 9.6e+84)
		tmp = Float64(z * t);
	elseif (y <= 2.4e+176)
		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 (y <= -1.7e+46)
		tmp = x * y;
	elseif (y <= 4.5e+50)
		tmp = t_1;
	elseif (y <= 9.6e+84)
		tmp = z * t;
	elseif (y <= 2.4e+176)
		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[y, -1.7e+46], N[(x * y), $MachinePrecision], If[LessEqual[y, 4.5e+50], t$95$1, If[LessEqual[y, 9.6e+84], N[(z * t), $MachinePrecision], If[LessEqual[y, 2.4e+176], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e46 or 2.4000000000000001e176 < y

   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 x around inf 51.1%

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

   if -1.6999999999999999e46 < y < 4.50000000000000014e50 or 9.5999999999999999e84 < y < 2.4000000000000001e176

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 86.2%

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

   4. Taylor expanded in a around inf 62.8%

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

   if 4.50000000000000014e50 < y < 9.5999999999999999e84

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+47} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+47) (not (<= (* x y) 5e-29)))
   (+ (* c i) (+ (* 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) <= -5e+47) || !((x * y) <= 5e-29)) {
		tmp = (c * i) + ((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) <= (-5d+47)) .or. (.not. ((x * y) <= 5d-29))) then
        tmp = (c * i) + ((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) <= -5e+47) || !((x * y) <= 5e-29)) {
		tmp = (c * i) + ((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) <= -5e+47) or not ((x * y) <= 5e-29):
		tmp = (c * i) + ((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) <= -5e+47) || !(Float64(x * y) <= 5e-29))
		tmp = Float64(Float64(c * i) + 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) <= -5e+47) || ~(((x * y) <= 5e-29)))
		tmp = (c * i) + ((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], -5e+47], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-29]], $MachinePrecision]], N[(N[(c * i), $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) < -5.00000000000000022e47 or 4.99999999999999986e-29 < (*.f64 x y)

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0 86.0%

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

   if -5.00000000000000022e47 < (*.f64 x y) < 4.99999999999999986e-29

   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 x around 0 96.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+47} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+65} \lor \neg \left(c \cdot i \leq 400000000\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -4e+65) (not (<= (* c i) 400000000.0)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* a b) (+ (* 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 (((c * i) <= -4e+65) || !((c * i) <= 400000000.0)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((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 (((c * i) <= (-4d+65)) .or. (.not. ((c * i) <= 400000000.0d0))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + ((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 (((c * i) <= -4e+65) || !((c * i) <= 400000000.0)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -4e+65) or not ((c * i) <= 400000000.0):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -4e+65) || !(Float64(c * i) <= 400000000.0))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + 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 (((c * i) <= -4e+65) || ~(((c * i) <= 400000000.0)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -4e+65], N[Not[LessEqual[N[(c * i), $MachinePrecision], 400000000.0]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4e65 or 4e8 < (*.f64 c i)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0 87.3%

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

   if -4e65 < (*.f64 c i) < 4e8

   1. Initial program 96.2%

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

   3. Taylor expanded in c around 0 93.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+65} \lor \neg \left(c \cdot i \leq 400000000\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+61}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+206)
   (* i (+ c (/ (* a b) i)))
   (if (<= (* c i) 2e+61)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* 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) <= -1e+206) {
		tmp = i * (c + ((a * b) / i));
	} else if ((c * i) <= 2e+61) {
		tmp = (a * b) + ((x * y) + (z * t));
	} 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 ((c * i) <= (-1d+206)) then
        tmp = i * (c + ((a * b) / i))
    else if ((c * i) <= 2d+61) then
        tmp = (a * b) + ((x * y) + (z * t))
    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 ((c * i) <= -1e+206) {
		tmp = i * (c + ((a * b) / i));
	} else if ((c * i) <= 2e+61) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+206:
		tmp = i * (c + ((a * b) / i))
	elif (c * i) <= 2e+61:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+206)
		tmp = Float64(i * Float64(c + Float64(Float64(a * b) / i)));
	elseif (Float64(c * i) <= 2e+61)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	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 ((c * i) <= -1e+206)
		tmp = i * (c + ((a * b) / i));
	elseif ((c * i) <= 2e+61)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1e+206], N[(i * N[(c + N[(N[(a * b), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+61], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1e206

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0 93.3%

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

   4. Taylor expanded in a around inf 89.9%

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

   5. Taylor expanded in i around inf 96.7%

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

   if -1e206 < (*.f64 c i) < 1.9999999999999999e61

   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 c around 0 87.8%

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

   if 1.9999999999999999e61 < (*.f64 c i)

   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 0 89.7%

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

   4. Taylor expanded in x around 0 84.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(c + \frac{a \cdot b}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+61}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-86}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.55e-86)
   (* c i)
   (if (<= i 4.8e-161) (* a b) (if (<= i 1.6e+121) (* z t) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.55e-86) {
		tmp = c * i;
	} else if (i <= 4.8e-161) {
		tmp = a * b;
	} else if (i <= 1.6e+121) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-1.55d-86)) then
        tmp = c * i
    else if (i <= 4.8d-161) then
        tmp = a * b
    else if (i <= 1.6d+121) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.55e-86) {
		tmp = c * i;
	} else if (i <= 4.8e-161) {
		tmp = a * b;
	} else if (i <= 1.6e+121) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.55e-86:
		tmp = c * i
	elif i <= 4.8e-161:
		tmp = a * b
	elif i <= 1.6e+121:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.55e-86)
		tmp = Float64(c * i);
	elseif (i <= 4.8e-161)
		tmp = Float64(a * b);
	elseif (i <= 1.6e+121)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.55e-86)
		tmp = c * i;
	elseif (i <= 4.8e-161)
		tmp = a * b;
	elseif (i <= 1.6e+121)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.55e-86], N[(c * i), $MachinePrecision], If[LessEqual[i, 4.8e-161], N[(a * b), $MachinePrecision], If[LessEqual[i, 1.6e+121], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.54999999999999994e-86 or 1.6e121 < i

   1. Initial program 95.3%

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

   3. Taylor expanded in c around inf 50.3%

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

   if -1.54999999999999994e-86 < i < 4.79999999999999998e-161

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 35.0%

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

   if 4.79999999999999998e-161 < i < 1.6e121

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 41.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-86}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{-21} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.35e-21) (not (<= (* a b) 4.5e+93))) (* 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) <= -1.35e-21) || !((a * b) <= 4.5e+93)) {
		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) <= (-1.35d-21)) .or. (.not. ((a * b) <= 4.5d+93))) 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) <= -1.35e-21) || !((a * b) <= 4.5e+93)) {
		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) <= -1.35e-21) or not ((a * b) <= 4.5e+93):
		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) <= -1.35e-21) || !(Float64(a * b) <= 4.5e+93))
		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) <= -1.35e-21) || ~(((a * b) <= 4.5e+93)))
		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], -1.35e-21], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.5e+93]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.3500000000000001e-21 or 4.49999999999999991e93 < (*.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 a around inf 54.7%

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

   if -1.3500000000000001e-21 < (*.f64 a b) < 4.49999999999999991e93

   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 c around inf 41.9%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.35 \cdot 10^{-21} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.0% 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 95.7%

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

3. Taylor expanded in a around inf 25.5%

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

Reproduce

herbie shell --seed 2024108 
(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)))