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

Percentage Accurate: 96.0% → 97.2%

Time: 12.8s

Alternatives: 16

Speedup: 0.5×

• 41.3% 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: 97.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq 8.2 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i 8.2e+261)
   (fma c i (fma x y (fma z t (* a b))))
   (+ (* c i) (+ (* a b) (* z t)))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= 8.2e+261) {
		tmp = fma(c, i, fma(x, y, fma(z, t, (a * b))));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= 8.2e+261)
		tmp = fma(c, i, fma(x, y, fma(z, t, Float64(a * b))));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, 8.2e+261], N[(c * i + N[(x * y + N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 8.1999999999999999e261

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. fma-def 97.1%

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

      3. associate-+l+ 97.1%

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

      4. fma-def 97.5%

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

      5. fma-def 97.5%

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

   3. Simplified 97.5%

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

   if 8.1999999999999999e261 < i

   1. Initial program 83.3%

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

   2. Taylor expanded in x around 0 100.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 8.2 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t, a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma x y (fma z t (fma a b (* c i)))))

C

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

Julia

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

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(x * y + N[(z * t + N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

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

   1. associate-+l+ 95.7%

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

   2. associate-+l+ 95.7%

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

   3. fma-def 98.0%

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

   4. fma-def 98.0%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 97.7% accurate, 0.1× speedup

Math

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

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (* c i) (+ (* a b) (+ (* z t) (* x y)))) INFINITY)
   (+ (fma z t (* a b)) (+ (* c i) (* x y)))
   (fma x y (+ (* c i) (* z t)))))

C

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

Julia

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

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   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. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 54.5%

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

      4. fma-def 54.5%

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

      5. fma-def 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in a around 0 72.7%

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

4. Final simplification 98.8%

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

Alternative 4: 97.7% accurate, 0.1× speedup

Math

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

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (if (<= t_1 INFINITY) t_1 (fma x y (+ (* c i) (* z t))))))

C

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

Julia

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

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * y + N[(N[(c * i), $MachinePrecision] + N[(z * t), $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%

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

   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. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 54.5%

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

      4. fma-def 54.5%

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

      5. fma-def 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in a around 0 72.7%

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

4. Final simplification 98.8%

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

Alternative 5: 97.5% accurate, 0.5× speedup

Math

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

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (if (<= t_1 INFINITY) t_1 (+ (* c i) (* z t)))))

C

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

Java

assert c < i;
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) + (x * y)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + ((z * t) + (x * y)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(c * i), $MachinePrecision] + 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. Taylor expanded in a around 0 27.3%

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

      1. +-commutative 27.3%

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

      2. *-commutative 27.3%

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

      3. fma-udef 27.3%

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

      4. *-commutative 27.3%

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

   4. Simplified 27.3%

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

   5. Taylor expanded in y around 0 64.3%

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

4. Final simplification 98.4%

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

Alternative 6: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := c \cdot i + a \cdot b\\ t_3 := z \cdot t + x \cdot y\\ t_4 := a \cdot b + x \cdot y\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* c i) (* a b)))
        (t_3 (+ (* z t) (* x y)))
        (t_4 (+ (* a b) (* x y))))
   (if (<= z -6.6e+202)
     t_3
     (if (<= z -3.7e+80)
       t_1
       (if (<= z -7.2e+56)
         t_4
         (if (<= z -3.3e+14)
           t_1
           (if (<= z -2.4e-74)
             t_4
             (if (<= z -4e-194)
               t_2
               (if (<= z 3.6e-280) t_4 (if (<= z 4.2e+32) t_2 t_3))))))))))

C

assert(c < i);
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 t_2 = (c * i) + (a * b);
	double t_3 = (z * t) + (x * y);
	double t_4 = (a * b) + (x * y);
	double tmp;
	if (z <= -6.6e+202) {
		tmp = t_3;
	} else if (z <= -3.7e+80) {
		tmp = t_1;
	} else if (z <= -7.2e+56) {
		tmp = t_4;
	} else if (z <= -3.3e+14) {
		tmp = t_1;
	} else if (z <= -2.4e-74) {
		tmp = t_4;
	} else if (z <= -4e-194) {
		tmp = t_2;
	} else if (z <= 3.6e-280) {
		tmp = t_4;
	} else if (z <= 4.2e+32) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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) :: t_4
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (c * i) + (a * b)
    t_3 = (z * t) + (x * y)
    t_4 = (a * b) + (x * y)
    if (z <= (-6.6d+202)) then
        tmp = t_3
    else if (z <= (-3.7d+80)) then
        tmp = t_1
    else if (z <= (-7.2d+56)) then
        tmp = t_4
    else if (z <= (-3.3d+14)) then
        tmp = t_1
    else if (z <= (-2.4d-74)) then
        tmp = t_4
    else if (z <= (-4d-194)) then
        tmp = t_2
    else if (z <= 3.6d-280) then
        tmp = t_4
    else if (z <= 4.2d+32) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert c < i;
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 t_2 = (c * i) + (a * b);
	double t_3 = (z * t) + (x * y);
	double t_4 = (a * b) + (x * y);
	double tmp;
	if (z <= -6.6e+202) {
		tmp = t_3;
	} else if (z <= -3.7e+80) {
		tmp = t_1;
	} else if (z <= -7.2e+56) {
		tmp = t_4;
	} else if (z <= -3.3e+14) {
		tmp = t_1;
	} else if (z <= -2.4e-74) {
		tmp = t_4;
	} else if (z <= -4e-194) {
		tmp = t_2;
	} else if (z <= 3.6e-280) {
		tmp = t_4;
	} else if (z <= 4.2e+32) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (c * i) + (a * b)
	t_3 = (z * t) + (x * y)
	t_4 = (a * b) + (x * y)
	tmp = 0
	if z <= -6.6e+202:
		tmp = t_3
	elif z <= -3.7e+80:
		tmp = t_1
	elif z <= -7.2e+56:
		tmp = t_4
	elif z <= -3.3e+14:
		tmp = t_1
	elif z <= -2.4e-74:
		tmp = t_4
	elif z <= -4e-194:
		tmp = t_2
	elif z <= 3.6e-280:
		tmp = t_4
	elif z <= 4.2e+32:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(a * b))
	t_3 = Float64(Float64(z * t) + Float64(x * y))
	t_4 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (z <= -6.6e+202)
		tmp = t_3;
	elseif (z <= -3.7e+80)
		tmp = t_1;
	elseif (z <= -7.2e+56)
		tmp = t_4;
	elseif (z <= -3.3e+14)
		tmp = t_1;
	elseif (z <= -2.4e-74)
		tmp = t_4;
	elseif (z <= -4e-194)
		tmp = t_2;
	elseif (z <= 3.6e-280)
		tmp = t_4;
	elseif (z <= 4.2e+32)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (c * i) + (a * b);
	t_3 = (z * t) + (x * y);
	t_4 = (a * b) + (x * y);
	tmp = 0.0;
	if (z <= -6.6e+202)
		tmp = t_3;
	elseif (z <= -3.7e+80)
		tmp = t_1;
	elseif (z <= -7.2e+56)
		tmp = t_4;
	elseif (z <= -3.3e+14)
		tmp = t_1;
	elseif (z <= -2.4e-74)
		tmp = t_4;
	elseif (z <= -4e-194)
		tmp = t_2;
	elseif (z <= 3.6e-280)
		tmp = t_4;
	elseif (z <= 4.2e+32)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+202], t$95$3, If[LessEqual[z, -3.7e+80], t$95$1, If[LessEqual[z, -7.2e+56], t$95$4, If[LessEqual[z, -3.3e+14], t$95$1, If[LessEqual[z, -2.4e-74], t$95$4, If[LessEqual[z, -4e-194], t$95$2, If[LessEqual[z, 3.6e-280], t$95$4, If[LessEqual[z, 4.2e+32], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999998e202 or 4.2000000000000001e32 < z

   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 c around 0 79.4%

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

   3. Taylor expanded in a around 0 64.5%

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

   if -6.5999999999999998e202 < z < -3.69999999999999996e80 or -7.19999999999999996e56 < z < -3.3e14

   1. Initial program 94.9%

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

   2. Taylor expanded in a around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. fma-udef 85.2%

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

      4. *-commutative 85.2%

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

   4. Simplified 85.2%

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

   5. Taylor expanded in y around 0 76.9%

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

   if -3.69999999999999996e80 < z < -7.19999999999999996e56 or -3.3e14 < z < -2.3999999999999999e-74 or -4.00000000000000007e-194 < z < 3.59999999999999994e-280

   1. Initial program 97.8%

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

   2. Taylor expanded in c around 0 83.2%

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

   3. Taylor expanded in t around 0 76.9%

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

   if -2.3999999999999999e-74 < z < -4.00000000000000007e-194 or 3.59999999999999994e-280 < z < 4.2000000000000001e32

   1. Initial program 94.4%

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

   2. Taylor expanded in x around 0 68.9%

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

   3. Taylor expanded in t around 0 62.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+202}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+14}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-194}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \]

Alternative 7: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ t_3 := c \cdot i + a \cdot b\\ \mathbf{if}\;z \leq -6 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3200000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 520000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* a b) (* x y)))
        (t_3 (+ (* c i) (* a b))))
   (if (<= z -6e+84)
     t_1
     (if (<= z -1.35e+47)
       t_2
       (if (<= z -3200000000000.0)
         t_1
         (if (<= z -2.8e-75)
           t_2
           (if (<= z -9e-194)
             t_3
             (if (<= z 4.8e-280)
               t_2
               (if (<= z 520000.0) t_3 (+ (* a b) (* z t)))))))))))

C

assert(c < i);
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 t_2 = (a * b) + (x * y);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if (z <= -6e+84) {
		tmp = t_1;
	} else if (z <= -1.35e+47) {
		tmp = t_2;
	} else if (z <= -3200000000000.0) {
		tmp = t_1;
	} else if (z <= -2.8e-75) {
		tmp = t_2;
	} else if (z <= -9e-194) {
		tmp = t_3;
	} else if (z <= 4.8e-280) {
		tmp = t_2;
	} else if (z <= 520000.0) {
		tmp = t_3;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    t_3 = (c * i) + (a * b)
    if (z <= (-6d+84)) then
        tmp = t_1
    else if (z <= (-1.35d+47)) then
        tmp = t_2
    else if (z <= (-3200000000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.8d-75)) then
        tmp = t_2
    else if (z <= (-9d-194)) then
        tmp = t_3
    else if (z <= 4.8d-280) then
        tmp = t_2
    else if (z <= 520000.0d0) then
        tmp = t_3
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

assert c < i;
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 t_2 = (a * b) + (x * y);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if (z <= -6e+84) {
		tmp = t_1;
	} else if (z <= -1.35e+47) {
		tmp = t_2;
	} else if (z <= -3200000000000.0) {
		tmp = t_1;
	} else if (z <= -2.8e-75) {
		tmp = t_2;
	} else if (z <= -9e-194) {
		tmp = t_3;
	} else if (z <= 4.8e-280) {
		tmp = t_2;
	} else if (z <= 520000.0) {
		tmp = t_3;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	t_3 = (c * i) + (a * b)
	tmp = 0
	if z <= -6e+84:
		tmp = t_1
	elif z <= -1.35e+47:
		tmp = t_2
	elif z <= -3200000000000.0:
		tmp = t_1
	elif z <= -2.8e-75:
		tmp = t_2
	elif z <= -9e-194:
		tmp = t_3
	elif z <= 4.8e-280:
		tmp = t_2
	elif z <= 520000.0:
		tmp = t_3
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	t_3 = Float64(Float64(c * i) + Float64(a * b))
	tmp = 0.0
	if (z <= -6e+84)
		tmp = t_1;
	elseif (z <= -1.35e+47)
		tmp = t_2;
	elseif (z <= -3200000000000.0)
		tmp = t_1;
	elseif (z <= -2.8e-75)
		tmp = t_2;
	elseif (z <= -9e-194)
		tmp = t_3;
	elseif (z <= 4.8e-280)
		tmp = t_2;
	elseif (z <= 520000.0)
		tmp = t_3;
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	t_3 = (c * i) + (a * b);
	tmp = 0.0;
	if (z <= -6e+84)
		tmp = t_1;
	elseif (z <= -1.35e+47)
		tmp = t_2;
	elseif (z <= -3200000000000.0)
		tmp = t_1;
	elseif (z <= -2.8e-75)
		tmp = t_2;
	elseif (z <= -9e-194)
		tmp = t_3;
	elseif (z <= 4.8e-280)
		tmp = t_2;
	elseif (z <= 520000.0)
		tmp = t_3;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+84], t$95$1, If[LessEqual[z, -1.35e+47], t$95$2, If[LessEqual[z, -3200000000000.0], t$95$1, If[LessEqual[z, -2.8e-75], t$95$2, If[LessEqual[z, -9e-194], t$95$3, If[LessEqual[z, 4.8e-280], t$95$2, If[LessEqual[z, 520000.0], t$95$3, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.99999999999999992e84 or -1.34999999999999998e47 < z < -3.2e12

   1. Initial program 94.8%

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

   2. Taylor expanded in a around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. fma-udef 86.2%

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

      4. *-commutative 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in y around 0 78.9%

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

   if -5.99999999999999992e84 < z < -1.34999999999999998e47 or -3.2e12 < z < -2.79999999999999998e-75 or -8.9999999999999997e-194 < z < 4.7999999999999996e-280

   1. Initial program 97.8%

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

   2. Taylor expanded in c around 0 83.2%

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

   3. Taylor expanded in t around 0 76.9%

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

   if -2.79999999999999998e-75 < z < -8.9999999999999997e-194 or 4.7999999999999996e-280 < z < 5.2e5

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0 67.5%

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

   3. Taylor expanded in t around 0 61.3%

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

   if 5.2e5 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in c around 0 76.2%

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

   3. Taylor expanded in y around 0 64.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+84}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq -3200000000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-75}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-194}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-280}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;z \leq 520000:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 8: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.06 \cdot 10^{+77} \lor \neg \left(c \cdot i \leq 1.3 \cdot 10^{+80}\right):\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.06e+77) (not (<= (* c i) 1.3e+80)))
   (+ (* c i) (* a b))
   (+ (* a b) (+ (* z t) (* x y)))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.06e+77) || !((c * i) <= 1.3e+80)) {
		tmp = (c * i) + (a * b);
	} else {
		tmp = (a * b) + ((z * t) + (x * y));
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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) <= (-1.06d+77)) .or. (.not. ((c * i) <= 1.3d+80))) then
        tmp = (c * i) + (a * b)
    else
        tmp = (a * b) + ((z * t) + (x * y))
    end if
    code = tmp
end function

Java

assert c < i;
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) <= -1.06e+77) || !((c * i) <= 1.3e+80)) {
		tmp = (c * i) + (a * b);
	} else {
		tmp = (a * b) + ((z * t) + (x * y));
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.06e+77) or not ((c * i) <= 1.3e+80):
		tmp = (c * i) + (a * b)
	else:
		tmp = (a * b) + ((z * t) + (x * y))
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.06e+77) || !(Float64(c * i) <= 1.3e+80))
		tmp = Float64(Float64(c * i) + Float64(a * b));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.06e+77) || ~(((c * i) <= 1.3e+80)))
		tmp = (c * i) + (a * b);
	else
		tmp = (a * b) + ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.06e+77], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.3e+80]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.06000000000000003e77 or 1.29999999999999991e80 < (*.f64 c i)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 87.0%

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

   3. Taylor expanded in t around 0 77.6%

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

   if -1.06000000000000003e77 < (*.f64 c i) < 1.29999999999999991e80

   1. Initial program 98.7%

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

   2. Taylor expanded in c around 0 92.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.06 \cdot 10^{+77} \lor \neg \left(c \cdot i \leq 1.3 \cdot 10^{+80}\right):\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 9: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.6 \cdot 10^{+76} \lor \neg \left(c \cdot i \leq 1.35 \cdot 10^{+80}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -8.6e+76) (not (<= (* c i) 1.35e+80)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* a b) (+ (* z t) (* x y)))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -8.6e+76) || !((c * i) <= 1.35e+80)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((z * t) + (x * y));
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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) <= (-8.6d+76)) .or. (.not. ((c * i) <= 1.35d+80))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + ((z * t) + (x * y))
    end if
    code = tmp
end function

Java

assert c < i;
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) <= -8.6e+76) || !((c * i) <= 1.35e+80)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((z * t) + (x * y));
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -8.6e+76) or not ((c * i) <= 1.35e+80):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + ((z * t) + (x * y))
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -8.6e+76) || !(Float64(c * i) <= 1.35e+80))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -8.6e+76) || ~(((c * i) <= 1.35e+80)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -8.6e+76], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.35e+80]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -8.59999999999999957e76 or 1.34999999999999991e80 < (*.f64 c i)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 87.0%

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

   if -8.59999999999999957e76 < (*.f64 c i) < 1.34999999999999991e80

   1. Initial program 98.7%

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

   2. Taylor expanded in c around 0 92.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.6 \cdot 10^{+76} \lor \neg \left(c \cdot i \leq 1.35 \cdot 10^{+80}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 10: 39.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-194}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.3e+98)
   (* z t)
   (if (<= z -3.6e+14)
     (* c i)
     (if (<= z -1.9e-67)
       (* x y)
       (if (<= z -1.12e-194)
         (* c i)
         (if (<= z 1.15e-279)
           (* x y)
           (if (<= z 3800000.0) (* a b) (* z t))))))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+98) {
		tmp = z * t;
	} else if (z <= -3.6e+14) {
		tmp = c * i;
	} else if (z <= -1.9e-67) {
		tmp = x * y;
	} else if (z <= -1.12e-194) {
		tmp = c * i;
	} else if (z <= 1.15e-279) {
		tmp = x * y;
	} else if (z <= 3800000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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 <= (-4.3d+98)) then
        tmp = z * t
    else if (z <= (-3.6d+14)) then
        tmp = c * i
    else if (z <= (-1.9d-67)) then
        tmp = x * y
    else if (z <= (-1.12d-194)) then
        tmp = c * i
    else if (z <= 1.15d-279) then
        tmp = x * y
    else if (z <= 3800000.0d0) then
        tmp = a * b
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

assert c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+98) {
		tmp = z * t;
	} else if (z <= -3.6e+14) {
		tmp = c * i;
	} else if (z <= -1.9e-67) {
		tmp = x * y;
	} else if (z <= -1.12e-194) {
		tmp = c * i;
	} else if (z <= 1.15e-279) {
		tmp = x * y;
	} else if (z <= 3800000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.3e+98:
		tmp = z * t
	elif z <= -3.6e+14:
		tmp = c * i
	elif z <= -1.9e-67:
		tmp = x * y
	elif z <= -1.12e-194:
		tmp = c * i
	elif z <= 1.15e-279:
		tmp = x * y
	elif z <= 3800000.0:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.3e+98)
		tmp = Float64(z * t);
	elseif (z <= -3.6e+14)
		tmp = Float64(c * i);
	elseif (z <= -1.9e-67)
		tmp = Float64(x * y);
	elseif (z <= -1.12e-194)
		tmp = Float64(c * i);
	elseif (z <= 1.15e-279)
		tmp = Float64(x * y);
	elseif (z <= 3800000.0)
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.3e+98)
		tmp = z * t;
	elseif (z <= -3.6e+14)
		tmp = c * i;
	elseif (z <= -1.9e-67)
		tmp = x * y;
	elseif (z <= -1.12e-194)
		tmp = c * i;
	elseif (z <= 1.15e-279)
		tmp = x * y;
	elseif (z <= 3800000.0)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.3e+98], N[(z * t), $MachinePrecision], If[LessEqual[z, -3.6e+14], N[(c * i), $MachinePrecision], If[LessEqual[z, -1.9e-67], N[(x * y), $MachinePrecision], If[LessEqual[z, -1.12e-194], N[(c * i), $MachinePrecision], If[LessEqual[z, 1.15e-279], N[(x * y), $MachinePrecision], If[LessEqual[z, 3800000.0], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3000000000000001e98 or 3.8e6 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 52.7%

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

   if -4.3000000000000001e98 < z < -3.6e14 or -1.89999999999999994e-67 < z < -1.12000000000000001e-194

   1. Initial program 95.9%

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

   2. Taylor expanded in c around inf 36.3%

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

   if -3.6e14 < z < -1.89999999999999994e-67 or -1.12000000000000001e-194 < z < 1.14999999999999998e-279

   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 inf 41.6%

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

   if 1.14999999999999998e-279 < z < 3.8e6

   1. Initial program 93.0%

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

   2. Taylor expanded in a around inf 29.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-194}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 11: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+52} \lor \neg \left(c \cdot i \leq 48000000\right):\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.45e+52) (not (<= (* c i) 48000000.0)))
   (+ (* c i) (* a b))
   (+ (* a b) (* z t))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.45e+52) || !((c * i) <= 48000000.0)) {
		tmp = (c * i) + (a * b);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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) <= (-1.45d+52)) .or. (.not. ((c * i) <= 48000000.0d0))) then
        tmp = (c * i) + (a * b)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

assert c < i;
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) <= -1.45e+52) || !((c * i) <= 48000000.0)) {
		tmp = (c * i) + (a * b);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.45e+52) or not ((c * i) <= 48000000.0):
		tmp = (c * i) + (a * b)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.45e+52) || !(Float64(c * i) <= 48000000.0))
		tmp = Float64(Float64(c * i) + Float64(a * b));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.45e+52) || ~(((c * i) <= 48000000.0)))
		tmp = (c * i) + (a * b);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.45e+52], N[Not[LessEqual[N[(c * i), $MachinePrecision], 48000000.0]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.45e52 or 4.8e7 < (*.f64 c i)

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 81.4%

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

   3. Taylor expanded in t around 0 71.5%

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

   if -1.45e52 < (*.f64 c i) < 4.8e7

   1. Initial program 99.3%

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

   2. Taylor expanded in c around 0 95.8%

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

   3. Taylor expanded in y around 0 67.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+52} \lor \neg \left(c \cdot i \leq 48000000\right):\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 12: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.3e+221)
   (* c i)
   (if (<= (* c i) 3.5e+82) (+ (* a b) (* z t)) (* c i))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.3e+221) {
		tmp = c * i;
	} else if ((c * i) <= 3.5e+82) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.3d+221)) then
        tmp = c * i
    else if ((c * i) <= 3.5d+82) then
        tmp = (a * b) + (z * t)
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

assert c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.3e+221) {
		tmp = c * i;
	} else if ((c * i) <= 3.5e+82) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.3e+221:
		tmp = c * i
	elif (c * i) <= 3.5e+82:
		tmp = (a * b) + (z * t)
	else:
		tmp = c * i
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.3e+221)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3.5e+82)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.3e+221)
		tmp = c * i;
	elseif ((c * i) <= 3.5e+82)
		tmp = (a * b) + (z * t);
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.3e+221], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.5e+82], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.29999999999999991e221 or 3.5e82 < (*.f64 c i)

   1. Initial program 87.1%

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

   2. Taylor expanded in c around inf 68.9%

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

   if -3.29999999999999991e221 < (*.f64 c i) < 3.5e82

   1. Initial program 98.9%

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

   2. Taylor expanded in c around 0 88.6%

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

   3. Taylor expanded in y around 0 61.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 13: 62.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+14} \lor \neg \left(z \leq 15000000\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -9.2e+14) (not (<= z 15000000.0)))
   (+ (* a b) (* z t))
   (+ (* a b) (* x y))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -9.2e+14) || !(z <= 15000000.0)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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 <= (-9.2d+14)) .or. (.not. (z <= 15000000.0d0))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

assert c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -9.2e+14) || !(z <= 15000000.0)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -9.2e+14) or not (z <= 15000000.0):
		tmp = (a * b) + (z * t)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -9.2e+14) || !(z <= 15000000.0))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -9.2e+14) || ~((z <= 15000000.0)))
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -9.2e+14], N[Not[LessEqual[z, 15000000.0]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e14 or 1.5e7 < z

   1. Initial program 95.2%

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

   2. Taylor expanded in c around 0 77.6%

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

   3. Taylor expanded in y around 0 65.8%

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

   if -9.2e14 < z < 1.5e7

   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 c around 0 71.6%

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

   3. Taylor expanded in t around 0 64.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+14} \lor \neg \left(z \leq 15000000\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 14: 42.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+41}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.7e+153)
   (* a b)
   (if (<= (* a b) 1.05e+41) (* c i) (* a b))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4.7e+153) {
		tmp = a * b;
	} else if ((a * b) <= 1.05e+41) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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) <= (-4.7d+153)) then
        tmp = a * b
    else if ((a * b) <= 1.05d+41) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert c < i;
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) <= -4.7e+153) {
		tmp = a * b;
	} else if ((a * b) <= 1.05e+41) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4.7e+153:
		tmp = a * b
	elif (a * b) <= 1.05e+41:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4.7e+153)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.05e+41)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -4.7e+153)
		tmp = a * b;
	elseif ((a * b) <= 1.05e+41)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4.7e+153], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.05e+41], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.69999999999999968e153 or 1.05e41 < (*.f64 a b)

   1. Initial program 93.2%

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

   2. Taylor expanded in a around inf 63.4%

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

   if -4.69999999999999968e153 < (*.f64 a b) < 1.05e41

   1. Initial program 97.0%

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

   2. Taylor expanded in c around inf 37.7%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+41}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 15: 38.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-228}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 6800000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.3e+98)
   (* z t)
   (if (<= z 2.3e-228) (* c i) (if (<= z 6800000.0) (* a b) (* z t)))))

C

assert(c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+98) {
		tmp = z * t;
	} else if (z <= 2.3e-228) {
		tmp = c * i;
	} else if (z <= 6800000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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 <= (-4.3d+98)) then
        tmp = z * t
    else if (z <= 2.3d-228) then
        tmp = c * i
    else if (z <= 6800000.0d0) then
        tmp = a * b
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

assert c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+98) {
		tmp = z * t;
	} else if (z <= 2.3e-228) {
		tmp = c * i;
	} else if (z <= 6800000.0) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

[c, i] = sort([c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.3e+98:
		tmp = z * t
	elif z <= 2.3e-228:
		tmp = c * i
	elif z <= 6800000.0:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

c, i = sort([c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.3e+98)
		tmp = Float64(z * t);
	elseif (z <= 2.3e-228)
		tmp = Float64(c * i);
	elseif (z <= 6800000.0)
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.3e+98)
		tmp = z * t;
	elseif (z <= 2.3e-228)
		tmp = c * i;
	elseif (z <= 6800000.0)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.3e+98], N[(z * t), $MachinePrecision], If[LessEqual[z, 2.3e-228], N[(c * i), $MachinePrecision], If[LessEqual[z, 6800000.0], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3000000000000001e98 or 6.8e6 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 52.7%

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

   if -4.3000000000000001e98 < z < 2.2999999999999999e-228

   1. Initial program 98.0%

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

   2. Taylor expanded in c around inf 32.0%

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

   if 2.2999999999999999e-228 < z < 6.8e6

   1. Initial program 91.1%

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

   2. Taylor expanded in a around inf 32.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-228}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;z \leq 6800000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 16: 28.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} [c, i] = \mathsf{sort}([c, i])\\ \\ a \cdot b \end{array} \]

FPCore

NOTE: c and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (* a b))

C

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

Fortran

NOTE: c and i should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

c, i = num2cell(sort([c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a * b;
end

Wolfram

NOTE: c and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 95.7%

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

2. Taylor expanded in a around inf 27.7%

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

3. Final simplification 27.7%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023274 
(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)))