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

Percentage Accurate: 96.0% → 98.4%

Time: 12.0s

Alternatives: 14

Speedup: 0.4×

• 41.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.4× speedup

Math

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

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (x + ((a * (b / y)) + (c * (i / y))));
	}
	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 = y * (x + ((a * (b / y)) + (c * (i / y))))
	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(y * Float64(x + Float64(Float64(a * Float64(b / y)) + Float64(c * Float64(i / y)))));
	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 = y * (x + ((a * (b / y)) + (c * (i / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(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[(y * N[(x + N[(N[(a * N[(b / y), $MachinePrecision]), $MachinePrecision] + N[(c * N[(i / y), $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 z around 0 8.3%

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

   4. Taylor expanded in y around inf 25.0%

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

      1. associate-/l* 58.3%

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

      2. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 98.8%

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

Alternative 2: 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 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-define 96.1%

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

   3. +-commutative 96.1%

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

   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 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+181}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 12500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+106}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 10^{+145}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.35e+181)
     (* x y)
     (if (<= (* x y) 12500.0)
       t_1
       (if (<= (* x y) 2.1e+106)
         (* z t)
         (if (or (<= (* x y) 5.4e+124) (not (<= (* x y) 1e+145)))
           (* x y)
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.35e+181) {
		tmp = x * y;
	} else if ((x * y) <= 12500.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.1e+106) {
		tmp = z * t;
	} else if (((x * y) <= 5.4e+124) || !((x * y) <= 1e+145)) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-1.35d+181)) then
        tmp = x * y
    else if ((x * y) <= 12500.0d0) then
        tmp = t_1
    else if ((x * y) <= 2.1d+106) then
        tmp = z * t
    else if (((x * y) <= 5.4d+124) .or. (.not. ((x * y) <= 1d+145))) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.35e+181) {
		tmp = x * y;
	} else if ((x * y) <= 12500.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.1e+106) {
		tmp = z * t;
	} else if (((x * y) <= 5.4e+124) || !((x * y) <= 1e+145)) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.35e+181:
		tmp = x * y
	elif (x * y) <= 12500.0:
		tmp = t_1
	elif (x * y) <= 2.1e+106:
		tmp = z * t
	elif ((x * y) <= 5.4e+124) or not ((x * y) <= 1e+145):
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.35e+181)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 12500.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.1e+106)
		tmp = Float64(z * t);
	elseif ((Float64(x * y) <= 5.4e+124) || !(Float64(x * y) <= 1e+145))
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.35e+181)
		tmp = x * y;
	elseif ((x * y) <= 12500.0)
		tmp = t_1;
	elseif ((x * y) <= 2.1e+106)
		tmp = z * t;
	elseif (((x * y) <= 5.4e+124) || ~(((x * y) <= 1e+145)))
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.35e+181], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 12500.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.1e+106], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 5.4e+124], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+145]], $MachinePrecision]], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.35000000000000004e181 or 2.10000000000000005e106 < (*.f64 x y) < 5.39999999999999956e124 or 9.9999999999999999e144 < (*.f64 x y)

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf 74.6%

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

   if -1.35000000000000004e181 < (*.f64 x y) < 12500 or 5.39999999999999956e124 < (*.f64 x y) < 9.9999999999999999e144

   1. Initial program 98.7%

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

   3. Taylor expanded in a around inf 91.0%

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

      1. associate-+r+ 91.0%

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

      2. associate-/l* 86.7%

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

      3. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in a around inf 66.1%

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

   if 12500 < (*.f64 x y) < 2.10000000000000005e106

   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 62.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+181}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 12500:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+106}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 10^{+145}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* x y) -3.8e+179)
     t_2
     (if (<= (* x y) 9e-301)
       t_1
       (if (<= (* x y) 1.1e-127)
         (+ (* a b) (* c i))
         (if (<= (* x y) 6.2e+97) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -3.8e+179) {
		tmp = t_2;
	} else if ((x * y) <= 9e-301) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e-127) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.2e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((x * y) <= (-3.8d+179)) then
        tmp = t_2
    else if ((x * y) <= 9d-301) then
        tmp = t_1
    else if ((x * y) <= 1.1d-127) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 6.2d+97) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -3.8e+179) {
		tmp = t_2;
	} else if ((x * y) <= 9e-301) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e-127) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.2e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -3.8e+179:
		tmp = t_2
	elif (x * y) <= 9e-301:
		tmp = t_1
	elif (x * y) <= 1.1e-127:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 6.2e+97:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -3.8e+179)
		tmp = t_2;
	elseif (Float64(x * y) <= 9e-301)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.1e-127)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 6.2e+97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -3.8e+179)
		tmp = t_2;
	elseif ((x * y) <= 9e-301)
		tmp = t_1;
	elseif ((x * y) <= 1.1e-127)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 6.2e+97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.8e+179], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9e-301], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.1e-127], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.2e+97], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.8e179 or 6.19999999999999962e97 < (*.f64 x y)

   1. Initial program 88.1%

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

   3. Taylor expanded in c around 0 83.3%

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

   4. Taylor expanded in t around 0 77.6%

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

   if -3.8e179 < (*.f64 x y) < 9.00000000000000039e-301 or 1.1000000000000001e-127 < (*.f64 x y) < 6.19999999999999962e97

   1. Initial program 98.6%

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

   3. Taylor expanded in c around 0 73.9%

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

   4. Taylor expanded in x around 0 67.9%

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

   if 9.00000000000000039e-301 < (*.f64 x y) < 1.1000000000000001e-127

   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 96.3%

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

      1. associate-+r+ 96.3%

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

      2. associate-/l* 92.7%

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

      3. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in a around inf 89.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-301}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177} \lor \neg \left(a \cdot b \leq 500000000000\right):\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* a b) -2e+177) (not (<= (* a b) 500000000000.0)))
     (+ (* a b) t_1)
     (+ (* c i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -2e+177) || !((a * b) <= 500000000000.0)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (((a * b) <= (-2d+177)) .or. (.not. ((a * b) <= 500000000000.0d0))) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -2e+177) || !((a * b) <= 500000000000.0)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((a * b) <= -2e+177) or not ((a * b) <= 500000000000.0):
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -2e+177) || !(Float64(a * b) <= 500000000000.0))
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((a * b) <= -2e+177) || ~(((a * b) <= 500000000000.0)))
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+177], N[Not[LessEqual[N[(a * b), $MachinePrecision], 500000000000.0]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2e177 or 5e11 < (*.f64 a b)

   1. Initial program 92.6%

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

   3. Taylor expanded in c around 0 86.6%

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

   if -2e177 < (*.f64 a b) < 5e11

   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 a around 0 92.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177} \lor \neg \left(a \cdot b \leq 500000000000\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+250}:\\ \;\;\;\;a \cdot \left(b + c \cdot \frac{i}{a}\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{+238}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+250)
   (* a (+ b (* c (/ i a))))
   (if (<= (* c i) 1e+238)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+250) {
		tmp = a * (b + (c * (i / a)));
	} else if ((c * i) <= 1e+238) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1d+250)) then
        tmp = a * (b + (c * (i / a)))
    else if ((c * i) <= 1d+238) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+250) {
		tmp = a * (b + (c * (i / a)));
	} else if ((c * i) <= 1e+238) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+250:
		tmp = a * (b + (c * (i / a)))
	elif (c * i) <= 1e+238:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+250)
		tmp = Float64(a * Float64(b + Float64(c * Float64(i / a))));
	elseif (Float64(c * i) <= 1e+238)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1e+250)
		tmp = a * (b + (c * (i / a)));
	elseif ((c * i) <= 1e+238)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1e+250], N[(a * N[(b + N[(c * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+238], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.9999999999999992e249

   1. Initial program 69.6%

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

   3. Taylor expanded in a around inf 73.9%

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

      1. associate-+r+ 73.9%

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

      2. associate-/l* 73.9%

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

      3. associate-/l* 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in a around inf 78.3%

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

   7. Taylor expanded in a around inf 82.9%

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

      1. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

   if -9.9999999999999992e249 < (*.f64 c i) < 1e238

   1. Initial program 97.6%

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

   3. Taylor expanded in c around 0 84.9%

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

   if 1e238 < (*.f64 c i)

   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 84.7%

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

      1. associate-+r+ 84.7%

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

      2. associate-/l* 84.7%

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

      3. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in x around inf 90.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+250}:\\ \;\;\;\;a \cdot \left(b + c \cdot \frac{i}{a}\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{+238}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000000:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* a b) -2e+177)
     (+ (* c i) (+ (* x y) (* a b)))
     (if (<= (* a b) 500000000000.0) (+ (* c i) t_1) (+ (* a b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -2e+177) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((a * b) <= 500000000000.0) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a * b) <= (-2d+177)) then
        tmp = (c * i) + ((x * y) + (a * b))
    else if ((a * b) <= 500000000000.0d0) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -2e+177) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((a * b) <= 500000000000.0) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -2e+177:
		tmp = (c * i) + ((x * y) + (a * b))
	elif (a * b) <= 500000000000.0:
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2e+177)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	elseif (Float64(a * b) <= 500000000000.0)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -2e+177)
		tmp = (c * i) + ((x * y) + (a * b));
	elseif ((a * b) <= 500000000000.0)
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+177], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 500000000000.0], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2e177

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 88.2%

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

   if -2e177 < (*.f64 a b) < 5e11

   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 a around 0 92.4%

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

   if 5e11 < (*.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 c around 0 88.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000000:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177}:\\ \;\;\;\;c \cdot i + a \cdot \left(b + x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000000:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* a b) -2e+177)
     (+ (* c i) (* a (+ b (* x (/ y a)))))
     (if (<= (* a b) 500000000000.0) (+ (* c i) t_1) (+ (* a b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -2e+177) {
		tmp = (c * i) + (a * (b + (x * (y / a))));
	} else if ((a * b) <= 500000000000.0) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a * b) <= (-2d+177)) then
        tmp = (c * i) + (a * (b + (x * (y / a))))
    else if ((a * b) <= 500000000000.0d0) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -2e+177) {
		tmp = (c * i) + (a * (b + (x * (y / a))));
	} else if ((a * b) <= 500000000000.0) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -2e+177:
		tmp = (c * i) + (a * (b + (x * (y / a))))
	elif (a * b) <= 500000000000.0:
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2e+177)
		tmp = Float64(Float64(c * i) + Float64(a * Float64(b + Float64(x * Float64(y / a)))));
	elseif (Float64(a * b) <= 500000000000.0)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -2e+177)
		tmp = (c * i) + (a * (b + (x * (y / a))));
	elseif ((a * b) <= 500000000000.0)
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+177], N[(N[(c * i), $MachinePrecision] + N[(a * N[(b + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 500000000000.0], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2e177

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. associate-+r+ 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 97.1%

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

      1. associate-*r/ 97.1%

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

   8. Simplified 97.1%

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

   if -2e177 < (*.f64 a b) < 5e11

   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 a around 0 92.4%

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

   if 5e11 < (*.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 c around 0 88.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+177}:\\ \;\;\;\;c \cdot i + a \cdot \left(b + x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;a \cdot b \leq 500000000000:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -4.5e-41)
   (* z t)
   (if (<= t 5.5e-251)
     (* c i)
     (if (<= t 1.5e-127) (* a b) (if (<= t 2.6e+109) (* 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 (t <= -4.5e-41) {
		tmp = z * t;
	} else if (t <= 5.5e-251) {
		tmp = c * i;
	} else if (t <= 1.5e-127) {
		tmp = a * b;
	} else if (t <= 2.6e+109) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (t <= (-4.5d-41)) then
        tmp = z * t
    else if (t <= 5.5d-251) then
        tmp = c * i
    else if (t <= 1.5d-127) then
        tmp = a * b
    else if (t <= 2.6d+109) then
        tmp = x * y
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -4.5e-41) {
		tmp = z * t;
	} else if (t <= 5.5e-251) {
		tmp = c * i;
	} else if (t <= 1.5e-127) {
		tmp = a * b;
	} else if (t <= 2.6e+109) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -4.5e-41:
		tmp = z * t
	elif t <= 5.5e-251:
		tmp = c * i
	elif t <= 1.5e-127:
		tmp = a * b
	elif t <= 2.6e+109:
		tmp = x * y
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -4.5e-41)
		tmp = Float64(z * t);
	elseif (t <= 5.5e-251)
		tmp = Float64(c * i);
	elseif (t <= 1.5e-127)
		tmp = Float64(a * b);
	elseif (t <= 2.6e+109)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (t <= -4.5e-41)
		tmp = z * t;
	elseif (t <= 5.5e-251)
		tmp = c * i;
	elseif (t <= 1.5e-127)
		tmp = a * b;
	elseif (t <= 2.6e+109)
		tmp = x * y;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -4.5e-41], N[(z * t), $MachinePrecision], If[LessEqual[t, 5.5e-251], N[(c * i), $MachinePrecision], If[LessEqual[t, 1.5e-127], N[(a * b), $MachinePrecision], If[LessEqual[t, 2.6e+109], N[(x * y), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5e-41 or 2.5999999999999998e109 < t

   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 z around inf 50.4%

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

   if -4.5e-41 < t < 5.5e-251

   1. Initial program 96.0%

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

   3. Taylor expanded in c around inf 40.7%

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

   if 5.5e-251 < t < 1.50000000000000004e-127

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 53.9%

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

   if 1.50000000000000004e-127 < t < 2.5999999999999998e109

   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 x around inf 52.6%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-251}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3300000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= t -1.02e-26)
     t_1
     (if (<= t 3300000.0)
       (+ (* a b) (* c i))
       (if (<= t 4.2e+67) (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if (t <= -1.02e-26) {
		tmp = t_1;
	} else if (t <= 3300000.0) {
		tmp = (a * b) + (c * i);
	} else if (t <= 4.2e+67) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	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 (t <= (-1.02d-26)) then
        tmp = t_1
    else if (t <= 3300000.0d0) then
        tmp = (a * b) + (c * i)
    else if (t <= 4.2d+67) then
        tmp = x * y
    else
        tmp = t_1
    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 (t <= -1.02e-26) {
		tmp = t_1;
	} else if (t <= 3300000.0) {
		tmp = (a * b) + (c * i);
	} else if (t <= 4.2e+67) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if t <= -1.02e-26:
		tmp = t_1
	elif t <= 3300000.0:
		tmp = (a * b) + (c * i)
	elif t <= 4.2e+67:
		tmp = x * y
	else:
		tmp = t_1
	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 (t <= -1.02e-26)
		tmp = t_1;
	elseif (t <= 3300000.0)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (t <= 4.2e+67)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	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 (t <= -1.02e-26)
		tmp = t_1;
	elseif (t <= 3300000.0)
		tmp = (a * b) + (c * i);
	elseif (t <= 4.2e+67)
		tmp = x * y;
	else
		tmp = t_1;
	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[t, -1.02e-26], t$95$1, If[LessEqual[t, 3300000.0], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+67], N[(x * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e-26 or 4.2000000000000003e67 < t

   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 c around 0 80.5%

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

   4. Taylor expanded in x around 0 65.8%

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

   if -1.02e-26 < t < 3.3e6

   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 a around inf 90.7%

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

      1. associate-+r+ 90.7%

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

      2. associate-/l* 86.0%

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

      3. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in a around inf 64.3%

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

   if 3.3e6 < t < 4.2000000000000003e67

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 73.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-26}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;t \leq 3300000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-246}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= t -7.4e-100)
     t_1
     (if (<= t 1.95e-246)
       (+ (* a b) (* c i))
       (if (<= t 3.4e+109) (+ (* x y) (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if (t <= -7.4e-100) {
		tmp = t_1;
	} else if (t <= 1.95e-246) {
		tmp = (a * b) + (c * i);
	} else if (t <= 3.4e+109) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	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 = (c * i) + (z * t)
    if (t <= (-7.4d-100)) then
        tmp = t_1
    else if (t <= 1.95d-246) then
        tmp = (a * b) + (c * i)
    else if (t <= 3.4d+109) then
        tmp = (x * y) + (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if (t <= -7.4e-100) {
		tmp = t_1;
	} else if (t <= 1.95e-246) {
		tmp = (a * b) + (c * i);
	} else if (t <= 3.4e+109) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if t <= -7.4e-100:
		tmp = t_1
	elif t <= 1.95e-246:
		tmp = (a * b) + (c * i)
	elif t <= 3.4e+109:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (t <= -7.4e-100)
		tmp = t_1;
	elseif (t <= 1.95e-246)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (t <= 3.4e+109)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if (t <= -7.4e-100)
		tmp = t_1;
	elseif (t <= 1.95e-246)
		tmp = (a * b) + (c * i);
	elseif (t <= 3.4e+109)
		tmp = (x * y) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e-100], t$95$1, If[LessEqual[t, 1.95e-246], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+109], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.40000000000000035e-100 or 3.40000000000000006e109 < t

   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 a around inf 79.1%

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

      1. associate-+r+ 79.1%

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

      2. associate-/l* 78.3%

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

      3. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in t around inf 63.6%

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

   if -7.40000000000000035e-100 < t < 1.94999999999999989e-246

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 91.3%

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

      1. associate-+r+ 91.3%

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

      2. associate-/l* 86.9%

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

      3. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in a around inf 72.0%

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

   if 1.94999999999999989e-246 < t < 3.40000000000000006e109

   1. Initial program 93.0%

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

   3. Taylor expanded in c around 0 76.2%

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

   4. Taylor expanded in t around 0 66.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-100}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-246}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-251}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -2.1e-35)
   (* z t)
   (if (<= t 5e-251) (* c i) (if (<= t 4.1e+108) (* 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 (t <= -2.1e-35) {
		tmp = z * t;
	} else if (t <= 5e-251) {
		tmp = c * i;
	} else if (t <= 4.1e+108) {
		tmp = a * b;
	} 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 <= (-2.1d-35)) then
        tmp = z * t
    else if (t <= 5d-251) then
        tmp = c * i
    else if (t <= 4.1d+108) then
        tmp = a * b
    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 <= -2.1e-35) {
		tmp = z * t;
	} else if (t <= 5e-251) {
		tmp = c * i;
	} else if (t <= 4.1e+108) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -2.1e-35:
		tmp = z * t
	elif t <= 5e-251:
		tmp = c * i
	elif t <= 4.1e+108:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -2.1e-35)
		tmp = Float64(z * t);
	elseif (t <= 5e-251)
		tmp = Float64(c * i);
	elseif (t <= 4.1e+108)
		tmp = Float64(a * b);
	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 <= -2.1e-35)
		tmp = z * t;
	elseif (t <= 5e-251)
		tmp = c * i;
	elseif (t <= 4.1e+108)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -2.1e-35], N[(z * t), $MachinePrecision], If[LessEqual[t, 5e-251], N[(c * i), $MachinePrecision], If[LessEqual[t, 4.1e+108], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e-35 or 4.0999999999999999e108 < t

   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 z around inf 51.2%

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

   if -2.1e-35 < t < 5.0000000000000003e-251

   1. Initial program 96.1%

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

   3. Taylor expanded in c around inf 39.7%

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

   if 5.0000000000000003e-251 < t < 4.0999999999999999e108

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 31.5%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-251}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+108}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{+150} \lor \neg \left(a \cdot b \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.3e+150) (not (<= (* a b) 2.8e+18))) (* 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) <= -2.3e+150) || !((a * b) <= 2.8e+18)) {
		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) <= (-2.3d+150)) .or. (.not. ((a * b) <= 2.8d+18))) 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) <= -2.3e+150) || !((a * b) <= 2.8e+18)) {
		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) <= -2.3e+150) or not ((a * b) <= 2.8e+18):
		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) <= -2.3e+150) || !(Float64(a * b) <= 2.8e+18))
		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) <= -2.3e+150) || ~(((a * b) <= 2.8e+18)))
		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], -2.3e+150], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.8e+18]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.30000000000000001e150 or 2.8e18 < (*.f64 a b)

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 60.5%

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

   if -2.30000000000000001e150 < (*.f64 a b) < 2.8e18

   1. Initial program 96.8%

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

   3. Taylor expanded in c around inf 33.1%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{+150} \lor \neg \left(a \cdot b \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.3% 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 95.3%

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

3. Taylor expanded in a around inf 26.6%

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

4. Final simplification 26.6%

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

Reproduce

herbie shell --seed 2024055 
(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)))