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

Percentage Accurate: 95.8% → 97.5%

Time: 7.6s

Alternatives: 15

Speedup: 0.5×

• 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) + t_1) <= ((double) INFINITY)) {
		tmp = fma(c, i, ((z * t) + ((a * b) + (x * y))));
	} else {
		tmp = t_1 + (c * i);
	}
	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(Float64(a * b) + t_1) <= Inf)
		tmp = fma(c, i, Float64(Float64(z * t) + Float64(Float64(a * b) + Float64(x * y))));
	else
		tmp = Float64(t_1 + Float64(c * i));
	end
	return 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[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(c * i + N[(N[(z * t), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. fma-def 99.6%

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

      3. associate-+l+ 99.6%

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

      4. fma-def 99.6%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-udef 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+r+ 99.6%

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

   5. Applied egg-rr 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0 55.6%

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

4. Final simplification 98.0%

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

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 94.1%

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

   1. +-commutative 94.1%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 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-def 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 3: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-def 33.3%

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

      3. associate-+l+ 33.3%

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

      4. fma-def 53.3%

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

      5. fma-def 60.0%

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

   3. Simplified 60.0%

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

      1. fma-udef 40.0%

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

      2. fma-udef 33.3%

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

      3. associate-+l+ 33.3%

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

      4. +-commutative 33.3%

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

      5. associate-+r+ 33.3%

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

   5. Applied egg-rr 33.3%

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

   6. Taylor expanded in z around inf 47.3%

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

4. Final simplification 96.9%

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

Alternative 4: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + c \cdot i\\ t_2 := a \cdot b + x \cdot y\\ t_3 := x \cdot y + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1.85 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-316}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* c i)))
        (t_2 (+ (* a b) (* x y)))
        (t_3 (+ (* x y) (* c i))))
   (if (<= (* a b) -2.6e+141)
     t_2
     (if (<= (* a b) -1.85e-125)
       t_1
       (if (<= (* a b) -2e-316)
         t_3
         (if (<= (* a b) 5.8e-218)
           t_1
           (if (<= (* a b) 1.4e-105)
             t_3
             (if (<= (* a b) 2.4e-73)
               t_1
               (if (<= (* a b) 7.2e+87) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (c * i);
	double t_2 = (a * b) + (x * y);
	double t_3 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -2.6e+141) {
		tmp = t_2;
	} else if ((a * b) <= -1.85e-125) {
		tmp = t_1;
	} else if ((a * b) <= -2e-316) {
		tmp = t_3;
	} else if ((a * b) <= 5.8e-218) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e-105) {
		tmp = t_3;
	} else if ((a * b) <= 2.4e-73) {
		tmp = t_1;
	} else if ((a * b) <= 7.2e+87) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) + (c * i)
    t_2 = (a * b) + (x * y)
    t_3 = (x * y) + (c * i)
    if ((a * b) <= (-2.6d+141)) then
        tmp = t_2
    else if ((a * b) <= (-1.85d-125)) then
        tmp = t_1
    else if ((a * b) <= (-2d-316)) then
        tmp = t_3
    else if ((a * b) <= 5.8d-218) then
        tmp = t_1
    else if ((a * b) <= 1.4d-105) then
        tmp = t_3
    else if ((a * b) <= 2.4d-73) then
        tmp = t_1
    else if ((a * b) <= 7.2d+87) then
        tmp = t_3
    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 = (z * t) + (c * i);
	double t_2 = (a * b) + (x * y);
	double t_3 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -2.6e+141) {
		tmp = t_2;
	} else if ((a * b) <= -1.85e-125) {
		tmp = t_1;
	} else if ((a * b) <= -2e-316) {
		tmp = t_3;
	} else if ((a * b) <= 5.8e-218) {
		tmp = t_1;
	} else if ((a * b) <= 1.4e-105) {
		tmp = t_3;
	} else if ((a * b) <= 2.4e-73) {
		tmp = t_1;
	} else if ((a * b) <= 7.2e+87) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (c * i)
	t_2 = (a * b) + (x * y)
	t_3 = (x * y) + (c * i)
	tmp = 0
	if (a * b) <= -2.6e+141:
		tmp = t_2
	elif (a * b) <= -1.85e-125:
		tmp = t_1
	elif (a * b) <= -2e-316:
		tmp = t_3
	elif (a * b) <= 5.8e-218:
		tmp = t_1
	elif (a * b) <= 1.4e-105:
		tmp = t_3
	elif (a * b) <= 2.4e-73:
		tmp = t_1
	elif (a * b) <= 7.2e+87:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	t_3 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -2.6e+141)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.85e-125)
		tmp = t_1;
	elseif (Float64(a * b) <= -2e-316)
		tmp = t_3;
	elseif (Float64(a * b) <= 5.8e-218)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.4e-105)
		tmp = t_3;
	elseif (Float64(a * b) <= 2.4e-73)
		tmp = t_1;
	elseif (Float64(a * b) <= 7.2e+87)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (c * i);
	t_2 = (a * b) + (x * y);
	t_3 = (x * y) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -2.6e+141)
		tmp = t_2;
	elseif ((a * b) <= -1.85e-125)
		tmp = t_1;
	elseif ((a * b) <= -2e-316)
		tmp = t_3;
	elseif ((a * b) <= 5.8e-218)
		tmp = t_1;
	elseif ((a * b) <= 1.4e-105)
		tmp = t_3;
	elseif ((a * b) <= 2.4e-73)
		tmp = t_1;
	elseif ((a * b) <= 7.2e+87)
		tmp = t_3;
	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[(z * t), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.6e+141], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.85e-125], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2e-316], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 5.8e-218], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.4e-105], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 2.4e-73], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 7.2e+87], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.5999999999999999e141 or 7.19999999999999988e87 < (*.f64 a b)

   1. Initial program 87.3%

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

   2. Taylor expanded in z around 0 75.9%

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

   3. Taylor expanded in c around 0 75.0%

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

   if -2.5999999999999999e141 < (*.f64 a b) < -1.85e-125 or -2.000000017e-316 < (*.f64 a b) < 5.8000000000000004e-218 or 1.4e-105 < (*.f64 a b) < 2.40000000000000006e-73

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 83.8%

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

   3. Taylor expanded in a around 0 79.4%

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

   if -1.85e-125 < (*.f64 a b) < -2.000000017e-316 or 5.8000000000000004e-218 < (*.f64 a b) < 1.4e-105 or 2.40000000000000006e-73 < (*.f64 a b) < 7.19999999999999988e87

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 91.6%

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

   3. Taylor expanded in t around 0 78.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.85 \cdot 10^{-125}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-316}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-218}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-73}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 5: 96.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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. Taylor expanded in a around inf 47.2%

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

4. Final simplification 96.9%

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

Alternative 6: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + c \cdot i\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.22 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* c i))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* a b) -1.15e+144)
     t_2
     (if (<= (* a b) 3.5e-33)
       t_1
       (if (<= (* a b) 1.22e+128)
         t_2
         (if (<= (* a b) 1.65e+143)
           t_1
           (if (<= (* a b) 3.2e+211) (+ (* a b) (* c i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1.15e+144) {
		tmp = t_2;
	} else if ((a * b) <= 3.5e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1.22e+128) {
		tmp = t_2;
	} else if ((a * b) <= 1.65e+143) {
		tmp = t_1;
	} else if ((a * b) <= 3.2e+211) {
		tmp = (a * b) + (c * i);
	} 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 = (z * t) + (c * i)
    t_2 = (a * b) + (x * y)
    if ((a * b) <= (-1.15d+144)) then
        tmp = t_2
    else if ((a * b) <= 3.5d-33) then
        tmp = t_1
    else if ((a * b) <= 1.22d+128) then
        tmp = t_2
    else if ((a * b) <= 1.65d+143) then
        tmp = t_1
    else if ((a * b) <= 3.2d+211) then
        tmp = (a * b) + (c * i)
    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 = (z * t) + (c * i);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1.15e+144) {
		tmp = t_2;
	} else if ((a * b) <= 3.5e-33) {
		tmp = t_1;
	} else if ((a * b) <= 1.22e+128) {
		tmp = t_2;
	} else if ((a * b) <= 1.65e+143) {
		tmp = t_1;
	} else if ((a * b) <= 3.2e+211) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (c * i)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (a * b) <= -1.15e+144:
		tmp = t_2
	elif (a * b) <= 3.5e-33:
		tmp = t_1
	elif (a * b) <= 1.22e+128:
		tmp = t_2
	elif (a * b) <= 1.65e+143:
		tmp = t_1
	elif (a * b) <= 3.2e+211:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -1.15e+144)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.5e-33)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.22e+128)
		tmp = t_2;
	elseif (Float64(a * b) <= 1.65e+143)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.2e+211)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (c * i);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -1.15e+144)
		tmp = t_2;
	elseif ((a * b) <= 3.5e-33)
		tmp = t_1;
	elseif ((a * b) <= 1.22e+128)
		tmp = t_2;
	elseif ((a * b) <= 1.65e+143)
		tmp = t_1;
	elseif ((a * b) <= 3.2e+211)
		tmp = (a * b) + (c * i);
	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[(z * t), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+144], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.5e-33], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.22e+128], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1.65e+143], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.2e+211], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.1500000000000001e144 or 3.4999999999999999e-33 < (*.f64 a b) < 1.22000000000000009e128 or 3.19999999999999977e211 < (*.f64 a b)

   1. Initial program 87.0%

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

   2. Taylor expanded in z around 0 79.2%

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

   3. Taylor expanded in c around 0 77.4%

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

   if -1.1500000000000001e144 < (*.f64 a b) < 3.4999999999999999e-33 or 1.22000000000000009e128 < (*.f64 a b) < 1.65e143

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 74.7%

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

   3. Taylor expanded in a around 0 70.2%

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

   if 1.65e143 < (*.f64 a b) < 3.19999999999999977e211

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.6%

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

   3. Taylor expanded in t around 0 81.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+144}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.22 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{+211}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 7: 43.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+138}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{-217}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9.5 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 6.8 \cdot 10^{+48}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.6e+138)
   (* a b)
   (if (<= (* a b) -1.6e-92)
     (* z t)
     (if (<= (* a b) 2.7e-217)
       (* c i)
       (if (<= (* a b) 9.5e-112)
         (* x y)
         (if (<= (* a b) 6.8e+48) (* c i) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.6e+138) {
		tmp = a * b;
	} else if ((a * b) <= -1.6e-92) {
		tmp = z * t;
	} else if ((a * b) <= 2.7e-217) {
		tmp = c * i;
	} else if ((a * b) <= 9.5e-112) {
		tmp = x * y;
	} else if ((a * b) <= 6.8e+48) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.6d+138)) then
        tmp = a * b
    else if ((a * b) <= (-1.6d-92)) then
        tmp = z * t
    else if ((a * b) <= 2.7d-217) then
        tmp = c * i
    else if ((a * b) <= 9.5d-112) then
        tmp = x * y
    else if ((a * b) <= 6.8d+48) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.6e+138) {
		tmp = a * b;
	} else if ((a * b) <= -1.6e-92) {
		tmp = z * t;
	} else if ((a * b) <= 2.7e-217) {
		tmp = c * i;
	} else if ((a * b) <= 9.5e-112) {
		tmp = x * y;
	} else if ((a * b) <= 6.8e+48) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.6e+138:
		tmp = a * b
	elif (a * b) <= -1.6e-92:
		tmp = z * t
	elif (a * b) <= 2.7e-217:
		tmp = c * i
	elif (a * b) <= 9.5e-112:
		tmp = x * y
	elif (a * b) <= 6.8e+48:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.6e+138)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.6e-92)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.7e-217)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 9.5e-112)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 6.8e+48)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.6e+138)
		tmp = a * b;
	elseif ((a * b) <= -1.6e-92)
		tmp = z * t;
	elseif ((a * b) <= 2.7e-217)
		tmp = c * i;
	elseif ((a * b) <= 9.5e-112)
		tmp = x * y;
	elseif ((a * b) <= 6.8e+48)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.6e+138], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.6e-92], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.7e-217], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.5e-112], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.8e+48], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.6000000000000001e138 or 6.8000000000000006e48 < (*.f64 a b)

   1. Initial program 87.9%

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

   2. Taylor expanded in a around inf 65.5%

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

   if -1.6000000000000001e138 < (*.f64 a b) < -1.5999999999999998e-92

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 47.3%

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

   if -1.5999999999999998e-92 < (*.f64 a b) < 2.70000000000000016e-217 or 9.50000000000000056e-112 < (*.f64 a b) < 6.8000000000000006e48

   1. Initial program 99.0%

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

   2. Taylor expanded in c around inf 43.8%

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

   if 2.70000000000000016e-217 < (*.f64 a b) < 9.50000000000000056e-112

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 56.4%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.6 \cdot 10^{+138}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.6 \cdot 10^{-92}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{-217}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9.5 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 6.8 \cdot 10^{+48}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + z \cdot t\right)\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+222}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (* z t)))) (t_2 (+ (* x y) (* c i))))
   (if (<= y -1.1e+48)
     t_2
     (if (<= y 7.4e+146)
       t_1
       (if (<= y 4.8e+222)
         (+ (* a b) (* x y))
         (if (<= y 1.6e+251) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (x * y) + (c * i);
	double tmp;
	if (y <= -1.1e+48) {
		tmp = t_2;
	} else if (y <= 7.4e+146) {
		tmp = t_1;
	} else if (y <= 4.8e+222) {
		tmp = (a * b) + (x * y);
	} else if (y <= 1.6e+251) {
		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 = (c * i) + ((a * b) + (z * t))
    t_2 = (x * y) + (c * i)
    if (y <= (-1.1d+48)) then
        tmp = t_2
    else if (y <= 7.4d+146) then
        tmp = t_1
    else if (y <= 4.8d+222) then
        tmp = (a * b) + (x * y)
    else if (y <= 1.6d+251) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + (z * t));
	double t_2 = (x * y) + (c * i);
	double tmp;
	if (y <= -1.1e+48) {
		tmp = t_2;
	} else if (y <= 7.4e+146) {
		tmp = t_1;
	} else if (y <= 4.8e+222) {
		tmp = (a * b) + (x * y);
	} else if (y <= 1.6e+251) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + (z * t))
	t_2 = (x * y) + (c * i)
	tmp = 0
	if y <= -1.1e+48:
		tmp = t_2
	elif y <= 7.4e+146:
		tmp = t_1
	elif y <= 4.8e+222:
		tmp = (a * b) + (x * y)
	elif y <= 1.6e+251:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)))
	t_2 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (y <= -1.1e+48)
		tmp = t_2;
	elseif (y <= 7.4e+146)
		tmp = t_1;
	elseif (y <= 4.8e+222)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (y <= 1.6e+251)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + (z * t));
	t_2 = (x * y) + (c * i);
	tmp = 0.0;
	if (y <= -1.1e+48)
		tmp = t_2;
	elseif (y <= 7.4e+146)
		tmp = t_1;
	elseif (y <= 4.8e+222)
		tmp = (a * b) + (x * y);
	elseif (y <= 1.6e+251)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+48], t$95$2, If[LessEqual[y, 7.4e+146], t$95$1, If[LessEqual[y, 4.8e+222], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+251], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e48 or 1.5999999999999999e251 < y

   1. Initial program 91.9%

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

   2. Taylor expanded in a around 0 74.8%

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

   3. Taylor expanded in t around 0 63.7%

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

   if -1.1e48 < y < 7.40000000000000009e146 or 4.8000000000000002e222 < y < 1.5999999999999999e251

   1. Initial program 95.1%

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

   2. Taylor expanded in x around 0 85.8%

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

   if 7.40000000000000009e146 < y < 4.8000000000000002e222

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0 90.0%

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

   3. Taylor expanded in c around 0 80.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+146}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+222}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+251}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]

Alternative 9: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-27} \lor \neg \left(z \leq 0.0029\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.8e+161)
   (+ (+ (* x y) (* z t)) (* c i))
   (if (or (<= z -1.2e-27) (not (<= z 0.0029)))
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+161) {
		tmp = ((x * y) + (z * t)) + (c * i);
	} else if ((z <= -1.2e-27) || !(z <= 0.0029)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.8d+161)) then
        tmp = ((x * y) + (z * t)) + (c * i)
    else if ((z <= (-1.2d-27)) .or. (.not. (z <= 0.0029d0))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+161) {
		tmp = ((x * y) + (z * t)) + (c * i);
	} else if ((z <= -1.2e-27) || !(z <= 0.0029)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+161:
		tmp = ((x * y) + (z * t)) + (c * i)
	elif (z <= -1.2e-27) or not (z <= 0.0029):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.8e+161)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) + Float64(c * i));
	elseif ((z <= -1.2e-27) || !(z <= 0.0029))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.8e+161)
		tmp = ((x * y) + (z * t)) + (c * i);
	elseif ((z <= -1.2e-27) || ~((z <= 0.0029)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.8e+161], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.2e-27], N[Not[LessEqual[z, 0.0029]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.80000000000000021e161

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 91.3%

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

   if -2.80000000000000021e161 < z < -1.20000000000000001e-27 or 0.0029 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 87.7%

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

   if -1.20000000000000001e-27 < z < 0.0029

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 91.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+161}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-27} \lor \neg \left(z \leq 0.0029\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 10: 43.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+141)
   (* a b)
   (if (<= (* a b) -1.4e-92)
     (* z t)
     (if (<= (* a b) 2.1e+50) (* c i) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = a * b;
	} else if ((a * b) <= -1.4e-92) {
		tmp = z * t;
	} else if ((a * b) <= 2.1e+50) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-5d+141)) then
        tmp = a * b
    else if ((a * b) <= (-1.4d-92)) then
        tmp = z * t
    else if ((a * b) <= 2.1d+50) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = a * b;
	} else if ((a * b) <= -1.4e-92) {
		tmp = z * t;
	} else if ((a * b) <= 2.1e+50) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5e+141:
		tmp = a * b
	elif (a * b) <= -1.4e-92:
		tmp = z * t
	elif (a * b) <= 2.1e+50:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5e+141)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.4e-92)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.1e+50)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5e+141)
		tmp = a * b;
	elseif ((a * b) <= -1.4e-92)
		tmp = z * t;
	elseif ((a * b) <= 2.1e+50)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+141], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.4e-92], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.1e+50], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000025e141 or 2.1e50 < (*.f64 a b)

   1. Initial program 87.9%

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

   2. Taylor expanded in a around inf 65.5%

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

   if -5.00000000000000025e141 < (*.f64 a b) < -1.4e-92

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 47.3%

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

   if -1.4e-92 < (*.f64 a b) < 2.1e50

   1. Initial program 99.2%

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

   2. Taylor expanded in c around inf 41.2%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 11: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5200 \lor \neg \left(c \cdot i \leq 8.5 \cdot 10^{+218}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5200.0) (not (<= (* c i) 8.5e+218)))
   (+ (* a b) (* c i))
   (+ (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5200.0) || !((c * i) <= 8.5e+218)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-5200.0d0)) .or. (.not. ((c * i) <= 8.5d+218))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5200.0) || !((c * i) <= 8.5e+218)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -5200.0) or not ((c * i) <= 8.5e+218):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -5200.0) || !(Float64(c * i) <= 8.5e+218))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -5200.0) || ~(((c * i) <= 8.5e+218)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -5200.0], N[Not[LessEqual[N[(c * i), $MachinePrecision], 8.5e+218]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5200 or 8.50000000000000041e218 < (*.f64 c i)

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 86.3%

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

   3. Taylor expanded in t around 0 77.1%

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

   if -5200 < (*.f64 c i) < 8.50000000000000041e218

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 68.1%

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

   3. Taylor expanded in c around 0 63.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5200 \lor \neg \left(c \cdot i \leq 8.5 \cdot 10^{+218}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 12: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-73} \lor \neg \left(t \leq 1.1 \cdot 10^{+82}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -2.8e-73) (not (<= t 1.1e+82)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -2.8e-73) || !(t <= 1.1e+82)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-2.8d-73)) .or. (.not. (t <= 1.1d+82))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -2.8e-73) || !(t <= 1.1e+82)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -2.8e-73) or not (t <= 1.1e+82):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -2.8e-73) || !(t <= 1.1e+82))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -2.8e-73) || ~((t <= 1.1e+82)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -2.8e-73], N[Not[LessEqual[t, 1.1e+82]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000012e-73 or 1.1000000000000001e82 < t

   1. Initial program 91.7%

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

   2. Taylor expanded in x around 0 80.4%

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

   if -2.80000000000000012e-73 < t < 1.1000000000000001e82

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 86.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-73} \lor \neg \left(t \leq 1.1 \cdot 10^{+82}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 13: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+99}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+235}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1e+99)
   (* c i)
   (if (<= (* c i) 3.6e+235) (+ (* a b) (* x y)) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1e+99) {
		tmp = c * i;
	} else if ((c * i) <= 3.6e+235) {
		tmp = (a * b) + (x * y);
	} 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) <= (-1d+99)) then
        tmp = c * i
    else if ((c * i) <= 3.6d+235) then
        tmp = (a * b) + (x * y)
    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) <= -1e+99) {
		tmp = c * i;
	} else if ((c * i) <= 3.6e+235) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1e+99:
		tmp = c * i
	elif (c * i) <= 3.6e+235:
		tmp = (a * b) + (x * y)
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1e+99)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3.6e+235)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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) <= -1e+99)
		tmp = c * i;
	elseif ((c * i) <= 3.6e+235)
		tmp = (a * b) + (x * y);
	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], -1e+99], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.6e+235], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.9999999999999997e98 or 3.59999999999999985e235 < (*.f64 c i)

   1. Initial program 86.3%

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

   2. Taylor expanded in c around inf 70.7%

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

   if -9.9999999999999997e98 < (*.f64 c i) < 3.59999999999999985e235

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 70.2%

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

   3. Taylor expanded in c around 0 63.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+99}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+235}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 14: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3.2e+38) (* a b) (if (<= (* a b) 3e+46) (* c i) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3.2e+38) {
		tmp = a * b;
	} else if ((a * b) <= 3e+46) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-3.2d+38)) then
        tmp = a * b
    else if ((a * b) <= 3d+46) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3.2e+38) {
		tmp = a * b;
	} else if ((a * b) <= 3e+46) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -3.2e+38:
		tmp = a * b
	elif (a * b) <= 3e+46:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -3.2e+38)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 3e+46)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -3.2e+38)
		tmp = a * b;
	elseif ((a * b) <= 3e+46)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -3.2e+38], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3e+46], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.19999999999999985e38 or 3.00000000000000023e46 < (*.f64 a b)

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 61.9%

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

   if -3.19999999999999985e38 < (*.f64 a b) < 3.00000000000000023e46

   1. Initial program 98.6%

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

   2. Taylor expanded in c around inf 40.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 15: 27.7% 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 94.1%

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

2. Taylor expanded in a around inf 31.7%

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

3. Final simplification 31.7%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023182 
(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)))