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

Percentage Accurate: 96.0% → 98.1%

Time: 8.2s

Alternatives: 16

Speedup: 0.5×

• 40.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

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

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 96.5%

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

   1. associate-+l+ 96.5%

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

   2. associate-+l+ 96.5%

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

   3. fma-def 97.6%

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

   4. fma-def 98.8%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 97.9% 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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-def 98.0%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * c + N[(a * b), $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. fma-def 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in x around 0 33.3%

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

   5. Taylor expanded in t around 0 55.6%

      \[\leadsto \color{blue}{c \cdot i + a \cdot b} \]
   6. Step-by-step derivation

      1. *-commutative 55.6%

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

      2. fma-def 55.6%

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

   7. Applied egg-rr 55.6%

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

4. Final simplification 98.4%

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

Alternative 4: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. fma-def 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 5: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ t_3 := c \cdot i + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -7.4 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 1.4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* c i) (* a b))))
   (if (<= (* c i) -7.4e+45)
     t_3
     (if (<= (* c i) -1.9e-20)
       t_1
       (if (<= (* c i) -1.9e-191)
         t_2
         (if (<= (* c i) 1.4e-304)
           t_1
           (if (<= (* c i) 4.7e-119)
             t_2
             (if (<= (* c i) 4.3e+25) t_1 t_3))))))))

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);
	double t_2 = (a * b) + (z * t);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -7.4e+45) {
		tmp = t_3;
	} else if ((c * i) <= -1.9e-20) {
		tmp = t_1;
	} else if ((c * i) <= -1.9e-191) {
		tmp = t_2;
	} else if ((c * i) <= 1.4e-304) {
		tmp = t_1;
	} else if ((c * i) <= 4.7e-119) {
		tmp = t_2;
	} else if ((c * i) <= 4.3e+25) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = (a * b) + (x * y)
    t_2 = (a * b) + (z * t)
    t_3 = (c * i) + (a * b)
    if ((c * i) <= (-7.4d+45)) then
        tmp = t_3
    else if ((c * i) <= (-1.9d-20)) then
        tmp = t_1
    else if ((c * i) <= (-1.9d-191)) then
        tmp = t_2
    else if ((c * i) <= 1.4d-304) then
        tmp = t_1
    else if ((c * i) <= 4.7d-119) then
        tmp = t_2
    else if ((c * i) <= 4.3d+25) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (z * t);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -7.4e+45) {
		tmp = t_3;
	} else if ((c * i) <= -1.9e-20) {
		tmp = t_1;
	} else if ((c * i) <= -1.9e-191) {
		tmp = t_2;
	} else if ((c * i) <= 1.4e-304) {
		tmp = t_1;
	} else if ((c * i) <= 4.7e-119) {
		tmp = t_2;
	} else if ((c * i) <= 4.3e+25) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (z * t)
	t_3 = (c * i) + (a * b)
	tmp = 0
	if (c * i) <= -7.4e+45:
		tmp = t_3
	elif (c * i) <= -1.9e-20:
		tmp = t_1
	elif (c * i) <= -1.9e-191:
		tmp = t_2
	elif (c * i) <= 1.4e-304:
		tmp = t_1
	elif (c * i) <= 4.7e-119:
		tmp = t_2
	elif (c * i) <= 4.3e+25:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	t_3 = Float64(Float64(c * i) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -7.4e+45)
		tmp = t_3;
	elseif (Float64(c * i) <= -1.9e-20)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.9e-191)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.4e-304)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.7e-119)
		tmp = t_2;
	elseif (Float64(c * i) <= 4.3e+25)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (a * b) + (z * t);
	t_3 = (c * i) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -7.4e+45)
		tmp = t_3;
	elseif ((c * i) <= -1.9e-20)
		tmp = t_1;
	elseif ((c * i) <= -1.9e-191)
		tmp = t_2;
	elseif ((c * i) <= 1.4e-304)
		tmp = t_1;
	elseif ((c * i) <= 4.7e-119)
		tmp = t_2;
	elseif ((c * i) <= 4.3e+25)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -7.4e+45], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -1.9e-20], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.9e-191], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.4e-304], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.7e-119], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 4.3e+25], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -7.39999999999999954e45 or 4.29999999999999998e25 < (*.f64 c i)

   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. associate-+l+ 94.1%

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

      2. fma-def 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 83.8%

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

   5. Taylor expanded in t around 0 74.7%

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

   if -7.39999999999999954e45 < (*.f64 c i) < -1.8999999999999999e-20 or -1.8999999999999999e-191 < (*.f64 c i) < 1.3999999999999999e-304 or 4.70000000000000002e-119 < (*.f64 c i) < 4.29999999999999998e25

   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 93.8%

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

   3. Taylor expanded in t around 0 74.7%

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

   if -1.8999999999999999e-20 < (*.f64 c i) < -1.8999999999999999e-191 or 1.3999999999999999e-304 < (*.f64 c i) < 4.70000000000000002e-119

   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 c around 0 95.1%

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

   3. Taylor expanded in y around 0 76.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.4 \cdot 10^{+45}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-191}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.4 \cdot 10^{-304}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{-119}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 6: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + x \cdot y\\ t_2 := c \cdot i + z \cdot t\\ t_3 := c \cdot i + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -1.2 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.55 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 5.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* x y)))
        (t_2 (+ (* c i) (* z t)))
        (t_3 (+ (* c i) (* a b))))
   (if (<= (* a b) -5.4e+172)
     t_3
     (if (<= (* a b) -1.2e+157)
       t_2
       (if (<= (* a b) -1.65e-39)
         (+ (* a b) (* x y))
         (if (<= (* a b) 2.55e-230)
           t_1
           (if (<= (* a b) 1.25e-179)
             t_2
             (if (<= (* a b) 5.5e+95) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double t_2 = (c * i) + (z * t);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if ((a * b) <= -5.4e+172) {
		tmp = t_3;
	} else if ((a * b) <= -1.2e+157) {
		tmp = t_2;
	} else if ((a * b) <= -1.65e-39) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 2.55e-230) {
		tmp = t_1;
	} else if ((a * b) <= 1.25e-179) {
		tmp = t_2;
	} else if ((a * b) <= 5.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = (c * i) + (x * y)
    t_2 = (c * i) + (z * t)
    t_3 = (c * i) + (a * b)
    if ((a * b) <= (-5.4d+172)) then
        tmp = t_3
    else if ((a * b) <= (-1.2d+157)) then
        tmp = t_2
    else if ((a * b) <= (-1.65d-39)) then
        tmp = (a * b) + (x * y)
    else if ((a * b) <= 2.55d-230) then
        tmp = t_1
    else if ((a * b) <= 1.25d-179) then
        tmp = t_2
    else if ((a * b) <= 5.5d+95) then
        tmp = t_1
    else
        tmp = t_3
    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) + (x * y);
	double t_2 = (c * i) + (z * t);
	double t_3 = (c * i) + (a * b);
	double tmp;
	if ((a * b) <= -5.4e+172) {
		tmp = t_3;
	} else if ((a * b) <= -1.2e+157) {
		tmp = t_2;
	} else if ((a * b) <= -1.65e-39) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 2.55e-230) {
		tmp = t_1;
	} else if ((a * b) <= 1.25e-179) {
		tmp = t_2;
	} else if ((a * b) <= 5.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (x * y)
	t_2 = (c * i) + (z * t)
	t_3 = (c * i) + (a * b)
	tmp = 0
	if (a * b) <= -5.4e+172:
		tmp = t_3
	elif (a * b) <= -1.2e+157:
		tmp = t_2
	elif (a * b) <= -1.65e-39:
		tmp = (a * b) + (x * y)
	elif (a * b) <= 2.55e-230:
		tmp = t_1
	elif (a * b) <= 1.25e-179:
		tmp = t_2
	elif (a * b) <= 5.5e+95:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(x * y))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	t_3 = Float64(Float64(c * i) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -5.4e+172)
		tmp = t_3;
	elseif (Float64(a * b) <= -1.2e+157)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.65e-39)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(a * b) <= 2.55e-230)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.25e-179)
		tmp = t_2;
	elseif (Float64(a * b) <= 5.5e+95)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (x * y);
	t_2 = (c * i) + (z * t);
	t_3 = (c * i) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -5.4e+172)
		tmp = t_3;
	elseif ((a * b) <= -1.2e+157)
		tmp = t_2;
	elseif ((a * b) <= -1.65e-39)
		tmp = (a * b) + (x * y);
	elseif ((a * b) <= 2.55e-230)
		tmp = t_1;
	elseif ((a * b) <= 1.25e-179)
		tmp = t_2;
	elseif ((a * b) <= 5.5e+95)
		tmp = t_1;
	else
		tmp = t_3;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.4e+172], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -1.2e+157], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.65e-39], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.55e-230], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.25e-179], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5.5e+95], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.4e172 or 5.4999999999999997e95 < (*.f64 a b)

   1. Initial program 92.2%

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

      1. associate-+l+ 92.3%

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

      2. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 91.1%

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

   5. Taylor expanded in t around 0 85.3%

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

   if -5.4e172 < (*.f64 a b) < -1.2e157 or 2.5499999999999999e-230 < (*.f64 a b) < 1.2499999999999999e-179

   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. associate-+l+ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in a around 0 93.7%

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

   if -1.2e157 < (*.f64 a b) < -1.64999999999999992e-39

   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 88.1%

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

   3. Taylor expanded in t around 0 70.5%

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

   if -1.64999999999999992e-39 < (*.f64 a b) < 2.5499999999999999e-230 or 1.2499999999999999e-179 < (*.f64 a b) < 5.4999999999999997e95

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 75.6%

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

   3. Taylor expanded in a around 0 74.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+172}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.2 \cdot 10^{+157}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.55 \cdot 10^{-230}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.5 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 7: 97.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(a * b), $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. fma-def 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in x around 0 33.3%

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

   5. Taylor expanded in t around 0 55.6%

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

4. Final simplification 98.4%

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

Alternative 8: 42.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.1 \cdot 10^{+118}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.02 \cdot 10^{-154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-256}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.4e+176)
   (* a b)
   (if (<= (* a b) -7.1e+118)
     (* z t)
     (if (<= (* a b) -1.3e+70)
       (* a b)
       (if (<= (* a b) -1.02e-154)
         (* x y)
         (if (<= (* a b) 7.2e-256)
           (* c i)
           (if (<= (* a b) 7e+95) (* x y) (* 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) <= -5.4e+176) {
		tmp = a * b;
	} else if ((a * b) <= -7.1e+118) {
		tmp = z * t;
	} else if ((a * b) <= -1.3e+70) {
		tmp = a * b;
	} else if ((a * b) <= -1.02e-154) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-256) {
		tmp = c * i;
	} else if ((a * b) <= 7e+95) {
		tmp = x * y;
	} 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) <= (-5.4d+176)) then
        tmp = a * b
    else if ((a * b) <= (-7.1d+118)) then
        tmp = z * t
    else if ((a * b) <= (-1.3d+70)) then
        tmp = a * b
    else if ((a * b) <= (-1.02d-154)) then
        tmp = x * y
    else if ((a * b) <= 7.2d-256) then
        tmp = c * i
    else if ((a * b) <= 7d+95) then
        tmp = x * y
    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) <= -5.4e+176) {
		tmp = a * b;
	} else if ((a * b) <= -7.1e+118) {
		tmp = z * t;
	} else if ((a * b) <= -1.3e+70) {
		tmp = a * b;
	} else if ((a * b) <= -1.02e-154) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-256) {
		tmp = c * i;
	} else if ((a * b) <= 7e+95) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5.4e+176:
		tmp = a * b
	elif (a * b) <= -7.1e+118:
		tmp = z * t
	elif (a * b) <= -1.3e+70:
		tmp = a * b
	elif (a * b) <= -1.02e-154:
		tmp = x * y
	elif (a * b) <= 7.2e-256:
		tmp = c * i
	elif (a * b) <= 7e+95:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5.4e+176)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -7.1e+118)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -1.3e+70)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.02e-154)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 7.2e-256)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 7e+95)
		tmp = Float64(x * y);
	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) <= -5.4e+176)
		tmp = a * b;
	elseif ((a * b) <= -7.1e+118)
		tmp = z * t;
	elseif ((a * b) <= -1.3e+70)
		tmp = a * b;
	elseif ((a * b) <= -1.02e-154)
		tmp = x * y;
	elseif ((a * b) <= 7.2e-256)
		tmp = c * i;
	elseif ((a * b) <= 7e+95)
		tmp = x * y;
	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], -5.4e+176], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.1e+118], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.3e+70], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.02e-154], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.2e-256], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7e+95], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.39999999999999959e176 or -7.0999999999999997e118 < (*.f64 a b) < -1.3e70 or 6.99999999999999999e95 < (*.f64 a b)

   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 a around inf 69.4%

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

   if -5.39999999999999959e176 < (*.f64 a b) < -7.0999999999999997e118

   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 z around inf 55.8%

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

   if -1.3e70 < (*.f64 a b) < -1.01999999999999992e-154 or 7.2000000000000004e-256 < (*.f64 a b) < 6.99999999999999999e95

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 47.8%

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

   if -1.01999999999999992e-154 < (*.f64 a b) < 7.2000000000000004e-256

   1. Initial program 98.1%

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

   2. Taylor expanded in c around inf 46.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.1 \cdot 10^{+118}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.02 \cdot 10^{-154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-256}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -2.5 \cdot 10^{-293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -1.55e+62)
     (* c i)
     (if (<= (* c i) -1.75e-250)
       t_1
       (if (<= (* c i) -2.5e-293)
         (* x y)
         (if (<= (* c i) 3.5e+113) 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 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.55e+62) {
		tmp = c * i;
	} else if ((c * i) <= -1.75e-250) {
		tmp = t_1;
	} else if ((c * i) <= -2.5e-293) {
		tmp = x * y;
	} else if ((c * i) <= 3.5e+113) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-1.55d+62)) then
        tmp = c * i
    else if ((c * i) <= (-1.75d-250)) then
        tmp = t_1
    else if ((c * i) <= (-2.5d-293)) then
        tmp = x * y
    else if ((c * i) <= 3.5d+113) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.55e+62) {
		tmp = c * i;
	} else if ((c * i) <= -1.75e-250) {
		tmp = t_1;
	} else if ((c * i) <= -2.5e-293) {
		tmp = x * y;
	} else if ((c * i) <= 3.5e+113) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -1.55e+62:
		tmp = c * i
	elif (c * i) <= -1.75e-250:
		tmp = t_1
	elif (c * i) <= -2.5e-293:
		tmp = x * y
	elif (c * i) <= 3.5e+113:
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.55e+62)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.75e-250)
		tmp = t_1;
	elseif (Float64(c * i) <= -2.5e-293)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 3.5e+113)
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.55e+62)
		tmp = c * i;
	elseif ((c * i) <= -1.75e-250)
		tmp = t_1;
	elseif ((c * i) <= -2.5e-293)
		tmp = x * y;
	elseif ((c * i) <= 3.5e+113)
		tmp = t_1;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.55e+62], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.75e-250], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2.5e-293], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.5e+113], t$95$1, N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.55000000000000007e62 or 3.5000000000000001e113 < (*.f64 c i)

   1. Initial program 95.0%

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

   2. Taylor expanded in c around inf 67.6%

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

   if -1.55000000000000007e62 < (*.f64 c i) < -1.7499999999999999e-250 or -2.5000000000000001e-293 < (*.f64 c i) < 3.5000000000000001e113

   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 0 90.9%

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

   3. Taylor expanded in y around 0 62.8%

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

   if -1.7499999999999999e-250 < (*.f64 c i) < -2.5000000000000001e-293

   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 78.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-250}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.5 \cdot 10^{-293}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+113}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.95 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 6.1 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.95e+46)
   (+ (* c i) (+ (* a b) (* x y)))
   (if (<= (* c i) 6.1e+25)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* a b) (+ (* c i) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.95e+46) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((c * i) <= 6.1e+25) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.95d+46)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if ((c * i) <= 6.1d+25) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (a * b) + ((c * i) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.95e+46) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((c * i) <= 6.1e+25) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.95e+46:
		tmp = (c * i) + ((a * b) + (x * y))
	elif (c * i) <= 6.1e+25:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + ((c * i) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.95e+46)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (Float64(c * i) <= 6.1e+25)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.95e+46)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif ((c * i) <= 6.1e+25)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + ((c * i) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.95e+46], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.1e+25], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.94999999999999997e46

   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 92.7%

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

   if -1.94999999999999997e46 < (*.f64 c i) < 6.1000000000000003e25

   1. Initial program 98.1%

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

   2. Taylor expanded in c around 0 94.4%

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

   if 6.1000000000000003e25 < (*.f64 c i)

   1. Initial program 91.7%

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

      1. associate-+l+ 91.8%

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

      2. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in x around 0 87.5%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.95 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 6.1 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \]

Alternative 11: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+248} \lor \neg \left(y \leq 2.8 \cdot 10^{+258}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= y -4.2e-53)
     (+ (* c i) (* x y))
     (if (<= y 7.5e+90)
       (+ (* a b) t_1)
       (if (or (<= y 1.7e+248) (not (<= y 2.8e+258)))
         (+ (* a b) (* x y))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if (y <= -4.2e-53) {
		tmp = (c * i) + (x * y);
	} else if (y <= 7.5e+90) {
		tmp = (a * b) + t_1;
	} else if ((y <= 1.7e+248) || !(y <= 2.8e+258)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if (y <= (-4.2d-53)) then
        tmp = (c * i) + (x * y)
    else if (y <= 7.5d+90) then
        tmp = (a * b) + t_1
    else if ((y <= 1.7d+248) .or. (.not. (y <= 2.8d+258))) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if (y <= -4.2e-53) {
		tmp = (c * i) + (x * y);
	} else if (y <= 7.5e+90) {
		tmp = (a * b) + t_1;
	} else if ((y <= 1.7e+248) || !(y <= 2.8e+258)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if y <= -4.2e-53:
		tmp = (c * i) + (x * y)
	elif y <= 7.5e+90:
		tmp = (a * b) + t_1
	elif (y <= 1.7e+248) or not (y <= 2.8e+258):
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (y <= -4.2e-53)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (y <= 7.5e+90)
		tmp = Float64(Float64(a * b) + t_1);
	elseif ((y <= 1.7e+248) || !(y <= 2.8e+258))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if (y <= -4.2e-53)
		tmp = (c * i) + (x * y);
	elseif (y <= 7.5e+90)
		tmp = (a * b) + t_1;
	elseif ((y <= 1.7e+248) || ~((y <= 2.8e+258)))
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e-53], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+90], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[y, 1.7e+248], N[Not[LessEqual[y, 2.8e+258]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.19999999999999955e-53

   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 0 77.5%

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

   3. Taylor expanded in a around 0 61.8%

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

   if -4.19999999999999955e-53 < y < 7.50000000000000014e90

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 7.50000000000000014e90 < y < 1.7e248 or 2.79999999999999982e258 < y

   1. Initial program 93.8%

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

   2. Taylor expanded in c around 0 81.8%

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

   3. Taylor expanded in t around 0 82.0%

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

   if 1.7e248 < y < 2.79999999999999982e258

   1. Initial program 66.7%

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

      1. associate-+l+ 66.7%

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

      2. fma-def 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in x around 0 66.7%

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

   5. Taylor expanded in a around 0 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-53}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+248} \lor \neg \left(y \leq 2.8 \cdot 10^{+258}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 12: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;y \leq -1.82 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-308}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= y -1.82e-56)
     t_2
     (if (<= y -5e-260)
       t_1
       (if (<= y -8.3e-308) (* c i) (if (<= y 9.6e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if (y <= -1.82e-56) {
		tmp = t_2;
	} else if (y <= -5e-260) {
		tmp = t_1;
	} else if (y <= -8.3e-308) {
		tmp = c * i;
	} else if (y <= 9.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    if (y <= (-1.82d-56)) then
        tmp = t_2
    else if (y <= (-5d-260)) then
        tmp = t_1
    else if (y <= (-8.3d-308)) then
        tmp = c * i
    else if (y <= 9.6d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if (y <= -1.82e-56) {
		tmp = t_2;
	} else if (y <= -5e-260) {
		tmp = t_1;
	} else if (y <= -8.3e-308) {
		tmp = c * i;
	} else if (y <= 9.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if y <= -1.82e-56:
		tmp = t_2
	elif y <= -5e-260:
		tmp = t_1
	elif y <= -8.3e-308:
		tmp = c * i
	elif y <= 9.6e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (y <= -1.82e-56)
		tmp = t_2;
	elseif (y <= -5e-260)
		tmp = t_1;
	elseif (y <= -8.3e-308)
		tmp = Float64(c * i);
	elseif (y <= 9.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if (y <= -1.82e-56)
		tmp = t_2;
	elseif (y <= -5e-260)
		tmp = t_1;
	elseif (y <= -8.3e-308)
		tmp = c * i;
	elseif (y <= 9.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.82e-56], t$95$2, If[LessEqual[y, -5e-260], t$95$1, If[LessEqual[y, -8.3e-308], N[(c * i), $MachinePrecision], If[LessEqual[y, 9.6e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.82000000000000007e-56 or 9.59999999999999958e45 < y

   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 c around 0 78.6%

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

   3. Taylor expanded in t around 0 65.5%

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

   if -1.82000000000000007e-56 < y < -5.0000000000000003e-260 or -8.30000000000000033e-308 < y < 9.59999999999999958e45

   1. Initial program 98.1%

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

   2. Taylor expanded in c around 0 73.8%

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

   3. Taylor expanded in y around 0 59.0%

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

   if -5.0000000000000003e-260 < y < -8.30000000000000033e-308

   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 c around inf 46.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-56}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-260}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;y \leq -8.3 \cdot 10^{-308}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+45}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 13: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+135}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-35}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -6.2e+135)
   (+ (* a b) (+ (* c i) (* z t)))
   (if (<= c 1.15e-35) (+ (* a b) (+ (* x y) (* z t))) (+ (* c i) (* 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 <= -6.2e+135) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else if (c <= 1.15e-35) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (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 <= (-6.2d+135)) then
        tmp = (a * b) + ((c * i) + (z * t))
    else if (c <= 1.15d-35) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (c * i) + (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 <= -6.2e+135) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else if (c <= 1.15e-35) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -6.2e+135:
		tmp = (a * b) + ((c * i) + (z * t))
	elif c <= 1.15e-35:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -6.2e+135)
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	elseif (c <= 1.15e-35)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 <= -6.2e+135)
		tmp = (a * b) + ((c * i) + (z * t));
	elseif (c <= 1.15e-35)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -6.2e+135], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-35], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.20000000000000044e135

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around 0 86.4%

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

   if -6.20000000000000044e135 < c < 1.1499999999999999e-35

   1. Initial program 96.7%

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

   2. Taylor expanded in c around 0 86.8%

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

   if 1.1499999999999999e-35 < c

   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 0 82.0%

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

   3. Taylor expanded in a around 0 61.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+135}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-35}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 14: 36.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+136}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-257}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 10^{-35}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -7.5e+136)
   (* c i)
   (if (<= c -1.8e-48)
     (* a b)
     (if (<= c 1.75e-257) (* z t) (if (<= c 1e-35) (* a b) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -7.5e+136) {
		tmp = c * i;
	} else if (c <= -1.8e-48) {
		tmp = a * b;
	} else if (c <= 1.75e-257) {
		tmp = z * t;
	} else if (c <= 1e-35) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-7.5d+136)) then
        tmp = c * i
    else if (c <= (-1.8d-48)) then
        tmp = a * b
    else if (c <= 1.75d-257) then
        tmp = z * t
    else if (c <= 1d-35) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -7.5e+136) {
		tmp = c * i;
	} else if (c <= -1.8e-48) {
		tmp = a * b;
	} else if (c <= 1.75e-257) {
		tmp = z * t;
	} else if (c <= 1e-35) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -7.5e+136:
		tmp = c * i
	elif c <= -1.8e-48:
		tmp = a * b
	elif c <= 1.75e-257:
		tmp = z * t
	elif c <= 1e-35:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -7.5e+136)
		tmp = Float64(c * i);
	elseif (c <= -1.8e-48)
		tmp = Float64(a * b);
	elseif (c <= 1.75e-257)
		tmp = Float64(z * t);
	elseif (c <= 1e-35)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -7.5e+136)
		tmp = c * i;
	elseif (c <= -1.8e-48)
		tmp = a * b;
	elseif (c <= 1.75e-257)
		tmp = z * t;
	elseif (c <= 1e-35)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -7.5e+136], N[(c * i), $MachinePrecision], If[LessEqual[c, -1.8e-48], N[(a * b), $MachinePrecision], If[LessEqual[c, 1.75e-257], N[(z * t), $MachinePrecision], If[LessEqual[c, 1e-35], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.5000000000000002e136 or 1.00000000000000001e-35 < c

   1. Initial program 96.0%

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

   2. Taylor expanded in c around inf 47.3%

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

   if -7.5000000000000002e136 < c < -1.8000000000000001e-48 or 1.75000000000000015e-257 < c < 1.00000000000000001e-35

   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 a around inf 38.0%

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

   if -1.8000000000000001e-48 < c < 1.75000000000000015e-257

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 40.8%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+136}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-257}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 10^{-35}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 43.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+55}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.9e+55) (* c i) (if (<= (* c i) 8.2e+112) (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.9e+55) {
		tmp = c * i;
	} else if ((c * i) <= 8.2e+112) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.9d+55)) then
        tmp = c * i
    else if ((c * i) <= 8.2d+112) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.9e+55) {
		tmp = c * i;
	} else if ((c * i) <= 8.2e+112) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.9e+55:
		tmp = c * i
	elif (c * i) <= 8.2e+112:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.9e+55)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 8.2e+112)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.9e+55)
		tmp = c * i;
	elseif ((c * i) <= 8.2e+112)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.9e+55], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e+112], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.90000000000000027e55 or 8.19999999999999951e112 < (*.f64 c i)

   1. Initial program 95.0%

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

   2. Taylor expanded in c around inf 67.6%

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

   if -3.90000000000000027e55 < (*.f64 c i) < 8.19999999999999951e112

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 35.5%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+55}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 16: 27.2% 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 96.5%

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

2. Taylor expanded in a around inf 28.8%

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

3. Final simplification 28.8%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023238 
(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)))