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

Percentage Accurate: 95.5% → 97.8%

Time: 12.6s

Alternatives: 18

Speedup: 0.4×

• 40.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% 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: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. +-commutative 96.8%

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

   2. fma-define 97.6%

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

   3. +-commutative 97.6%

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

   4. fma-define 98.8%

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

   5. fma-define 99.2%

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

3. Simplified 99.2%

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

Alternative 2: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + N[(N[(z * t), $MachinePrecision] / x), $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. 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-define 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. Add Preprocessing

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 25.0%

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

      3. +-commutative 25.0%

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

      4. fma-define 62.5%

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

      5. fma-define 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in a around 0 37.5%

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

   6. Taylor expanded in t around inf 37.5%

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

      1. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in x around inf 50.0%

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

       1. associate-/l* 50.0%

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

   11. Simplified 50.0%

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

   12. Taylor expanded in c around 0 75.0%

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

4. Final simplification 99.2%

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

Alternative 3: 88.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + a \cdot \frac{b}{x}\right) + c \cdot \frac{i}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* x y) -5e+207)
     (+ (* c i) t_1)
     (if (<= (* x y) -100000000000.0)
       (+ (* a b) t_1)
       (if (<= (* x y) 5e+41)
         (+ (* a b) (+ (* c i) (* z t)))
         (* x (+ (+ y (* a (/ b x))) (* c (/ i x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -5e+207) {
		tmp = (c * i) + t_1;
	} else if ((x * y) <= -100000000000.0) {
		tmp = (a * b) + t_1;
	} else if ((x * y) <= 5e+41) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else {
		tmp = x * ((y + (a * (b / x))) + (c * (i / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((x * y) <= (-5d+207)) then
        tmp = (c * i) + t_1
    else if ((x * y) <= (-100000000000.0d0)) then
        tmp = (a * b) + t_1
    else if ((x * y) <= 5d+41) then
        tmp = (a * b) + ((c * i) + (z * t))
    else
        tmp = x * ((y + (a * (b / x))) + (c * (i / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -5e+207) {
		tmp = (c * i) + t_1;
	} else if ((x * y) <= -100000000000.0) {
		tmp = (a * b) + t_1;
	} else if ((x * y) <= 5e+41) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else {
		tmp = x * ((y + (a * (b / x))) + (c * (i / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -5e+207:
		tmp = (c * i) + t_1
	elif (x * y) <= -100000000000.0:
		tmp = (a * b) + t_1
	elif (x * y) <= 5e+41:
		tmp = (a * b) + ((c * i) + (z * t))
	else:
		tmp = x * ((y + (a * (b / x))) + (c * (i / x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -5e+207)
		tmp = Float64(Float64(c * i) + t_1);
	elseif (Float64(x * y) <= -100000000000.0)
		tmp = Float64(Float64(a * b) + t_1);
	elseif (Float64(x * y) <= 5e+41)
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	else
		tmp = Float64(x * Float64(Float64(y + Float64(a * Float64(b / x))) + Float64(c * Float64(i / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -5e+207)
		tmp = (c * i) + t_1;
	elseif ((x * y) <= -100000000000.0)
		tmp = (a * b) + t_1;
	elseif ((x * y) <= 5e+41)
		tmp = (a * b) + ((c * i) + (z * t));
	else
		tmp = x * ((y + (a * (b / x))) + (c * (i / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+207], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -100000000000.0], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+41], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + N[(a * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(i / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.9999999999999999e207

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. fma-define 87.5%

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

      3. +-commutative 87.5%

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

      4. fma-define 95.8%

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

      5. fma-define 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in a around 0 95.8%

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

   if -4.9999999999999999e207 < (*.f64 x y) < -1e11

   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-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in c around 0 95.9%

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

   if -1e11 < (*.f64 x y) < 5.00000000000000022e41

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 93.8%

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

   if 5.00000000000000022e41 < (*.f64 x y)

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-define 95.0%

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

      3. +-commutative 95.0%

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

      4. fma-define 96.7%

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

      5. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 93.4%

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

      1. associate-/l* 93.6%

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

      2. +-commutative 93.6%

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

      3. associate-/l* 93.6%

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

      4. associate-/l* 91.9%

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

   7. Simplified 91.9%

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

   8. Taylor expanded in t around 0 87.3%

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

      1. associate-+r+ 87.3%

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

      2. associate-/l* 87.5%

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

      3. associate-*r/ 85.8%

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

   10. Simplified 85.8%

       \[\leadsto \color{blue}{x \cdot \left(\left(y + a \cdot \frac{b}{x}\right) + c \cdot \frac{i}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + a \cdot \frac{b}{x}\right) + c \cdot \frac{i}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 25.0%

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

      3. +-commutative 25.0%

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

      4. fma-define 62.5%

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

      5. fma-define 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in a around 0 37.5%

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

   6. Taylor expanded in t around inf 37.5%

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

      1. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in x around inf 50.0%

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

       1. associate-/l* 50.0%

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

   11. Simplified 50.0%

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

   12. Taylor expanded in c around 0 75.0%

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

4. Final simplification 99.2%

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

Alternative 5: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + t\_1\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+181}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) t_1)))
   (if (<= (* x y) -5e+207)
     t_2
     (if (<= (* x y) -100000000000.0)
       (+ (* a b) t_1)
       (if (<= (* x y) 2e+181) (+ (* a b) (+ (* c i) (* z t))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (c * i) + t_1;
	double tmp;
	if ((x * y) <= -5e+207) {
		tmp = t_2;
	} else if ((x * y) <= -100000000000.0) {
		tmp = (a * b) + t_1;
	} else if ((x * y) <= 2e+181) {
		tmp = (a * b) + ((c * i) + (z * t));
	} 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 = (x * y) + (z * t)
    t_2 = (c * i) + t_1
    if ((x * y) <= (-5d+207)) then
        tmp = t_2
    else if ((x * y) <= (-100000000000.0d0)) then
        tmp = (a * b) + t_1
    else if ((x * y) <= 2d+181) then
        tmp = (a * b) + ((c * i) + (z * t))
    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 = (x * y) + (z * t);
	double t_2 = (c * i) + t_1;
	double tmp;
	if ((x * y) <= -5e+207) {
		tmp = t_2;
	} else if ((x * y) <= -100000000000.0) {
		tmp = (a * b) + t_1;
	} else if ((x * y) <= 2e+181) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + t_1
	tmp = 0
	if (x * y) <= -5e+207:
		tmp = t_2
	elif (x * y) <= -100000000000.0:
		tmp = (a * b) + t_1
	elif (x * y) <= 2e+181:
		tmp = (a * b) + ((c * i) + (z * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + t_1)
	tmp = 0.0
	if (Float64(x * y) <= -5e+207)
		tmp = t_2;
	elseif (Float64(x * y) <= -100000000000.0)
		tmp = Float64(Float64(a * b) + t_1);
	elseif (Float64(x * y) <= 2e+181)
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (c * i) + t_1;
	tmp = 0.0;
	if ((x * y) <= -5e+207)
		tmp = t_2;
	elseif ((x * y) <= -100000000000.0)
		tmp = (a * b) + t_1;
	elseif ((x * y) <= 2e+181)
		tmp = (a * b) + ((c * i) + (z * t));
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+207], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -100000000000.0], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+181], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999999e207 or 1.9999999999999998e181 < (*.f64 x y)

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. fma-define 91.8%

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

      3. +-commutative 91.8%

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

      4. fma-define 96.7%

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

      5. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around 0 93.4%

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

   if -4.9999999999999999e207 < (*.f64 x y) < -1e11

   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-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in c around 0 95.9%

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

   if -1e11 < (*.f64 x y) < 1.9999999999999998e181

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-define 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 91.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+181}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y + \frac{z \cdot t}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-218}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+76}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e-11)
   (* x (+ y (/ (* z t) x)))
   (if (<= (* x y) 1e-218)
     (+ (* a b) (* z t))
     (if (<= (* x y) 5e+76) (+ (* c i) (* z t)) (+ (* 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 ((x * y) <= -1e-11) {
		tmp = x * (y + ((z * t) / x));
	} else if ((x * y) <= 1e-218) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 5e+76) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (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 ((x * y) <= (-1d-11)) then
        tmp = x * (y + ((z * t) / x))
    else if ((x * y) <= 1d-218) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 5d+76) then
        tmp = (c * i) + (z * t)
    else
        tmp = (x * y) + (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 ((x * y) <= -1e-11) {
		tmp = x * (y + ((z * t) / x));
	} else if ((x * y) <= 1e-218) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 5e+76) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e-11:
		tmp = x * (y + ((z * t) / x))
	elif (x * y) <= 1e-218:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 5e+76:
		tmp = (c * i) + (z * t)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e-11)
		tmp = Float64(x * Float64(y + Float64(Float64(z * t) / x)));
	elseif (Float64(x * y) <= 1e-218)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 5e+76)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e-11)
		tmp = x * (y + ((z * t) / x));
	elseif ((x * y) <= 1e-218)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 5e+76)
		tmp = (c * i) + (z * t);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-11], N[(x * N[(y + N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-218], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+76], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999939e-12

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. fma-define 94.8%

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

      3. +-commutative 94.8%

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

      4. fma-define 98.3%

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

      5. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around 0 84.9%

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

   6. Taylor expanded in t around inf 72.0%

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

      1. associate-/l* 63.5%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in x around inf 84.8%

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

       1. associate-/l* 84.8%

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

   11. Simplified 84.8%

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

   12. Taylor expanded in c around 0 74.7%

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

   if -9.99999999999999939e-12 < (*.f64 x y) < 1e-218

   1. Initial program 97.9%

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

      1. +-commutative 97.9%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 94.8%

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

   6. Taylor expanded in c around 0 76.6%

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

   if 1e-218 < (*.f64 x y) < 4.99999999999999991e76

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-define 97.8%

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

      3. +-commutative 97.8%

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

      4. fma-define 97.8%

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

      5. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 91.8%

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

   6. Taylor expanded in a around 0 74.2%

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

   if 4.99999999999999991e76 < (*.f64 x y)

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. fma-define 96.4%

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

      3. +-commutative 96.4%

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

      4. fma-define 98.2%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in c around 0 80.9%

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

   6. Taylor expanded in t around 0 73.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y + \frac{z \cdot t}{x}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-218}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+76}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{-204}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4.5e+143)
   (+ (* x y) (* c i))
   (if (<= (* x y) 1.36e-204)
     (+ (* a b) (* z t))
     (if (<= (* x y) 7.5e+78) (+ (* c i) (* z t)) (+ (* 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 ((x * y) <= -4.5e+143) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 1.36e-204) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 7.5e+78) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (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 ((x * y) <= (-4.5d+143)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 1.36d-204) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 7.5d+78) then
        tmp = (c * i) + (z * t)
    else
        tmp = (x * y) + (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 ((x * y) <= -4.5e+143) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 1.36e-204) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 7.5e+78) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4.5e+143:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 1.36e-204:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 7.5e+78:
		tmp = (c * i) + (z * t)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4.5e+143)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 1.36e-204)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 7.5e+78)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4.5e+143)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 1.36e-204)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 7.5e+78)
		tmp = (c * i) + (z * t);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+143], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.36e-204], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+78], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.4999999999999997e143

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. fma-define 89.3%

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

      3. +-commutative 89.3%

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

      4. fma-define 96.4%

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

      5. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in a around 0 96.4%

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

   6. Taylor expanded in t around 0 92.9%

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

   if -4.4999999999999997e143 < (*.f64 x y) < 1.3600000000000001e-204

   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. +-commutative 98.4%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 88.3%

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

   6. Taylor expanded in c around 0 71.9%

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

   if 1.3600000000000001e-204 < (*.f64 x y) < 7.49999999999999934e78

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-define 97.8%

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

      3. +-commutative 97.8%

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

      4. fma-define 97.8%

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

      5. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 91.8%

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

   6. Taylor expanded in a around 0 74.2%

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

   if 7.49999999999999934e78 < (*.f64 x y)

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. fma-define 96.4%

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

      3. +-commutative 96.4%

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

      4. fma-define 98.2%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in c around 0 80.9%

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

   6. Taylor expanded in t around 0 73.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+143}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{-204}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-201}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* x y) -5.5e+69)
     t_1
     (if (<= (* x y) 1.1e-201)
       (+ (* a b) (* z t))
       (if (<= (* x y) 1.2e+77) (+ (* c i) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -5.5e+69) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e-201) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.2e+77) {
		tmp = (c * i) + (z * t);
	} 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 = (x * y) + (a * b)
    if ((x * y) <= (-5.5d+69)) then
        tmp = t_1
    else if ((x * y) <= 1.1d-201) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 1.2d+77) then
        tmp = (c * i) + (z * t)
    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 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -5.5e+69) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e-201) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.2e+77) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -5.5e+69:
		tmp = t_1
	elif (x * y) <= 1.1e-201:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 1.2e+77:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -5.5e+69)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.1e-201)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 1.2e+77)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -5.5e+69)
		tmp = t_1;
	elseif ((x * y) <= 1.1e-201)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 1.2e+77)
		tmp = (c * i) + (z * t);
	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[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+69], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.1e-201], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.2e+77], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.50000000000000002e69 or 1.1999999999999999e77 < (*.f64 x y)

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. fma-define 94.9%

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

      3. +-commutative 94.9%

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

      4. fma-define 97.9%

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

      5. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in c around 0 83.0%

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

   6. Taylor expanded in t around 0 74.7%

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

   if -5.50000000000000002e69 < (*.f64 x y) < 1.1e-201

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 92.0%

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

   6. Taylor expanded in c around 0 73.6%

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

   if 1.1e-201 < (*.f64 x y) < 1.1999999999999999e77

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-define 97.8%

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

      3. +-commutative 97.8%

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

      4. fma-define 97.8%

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

      5. fma-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 91.8%

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

   6. Taylor expanded in a around 0 74.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-201}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{-219}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* x y) -1e+66)
     t_1
     (if (<= (* x y) 4.7e-219)
       (+ (* a b) (* z t))
       (if (<= (* x y) 3.4e+110) (+ (* a b) (* c i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -1e+66) {
		tmp = t_1;
	} else if ((x * y) <= 4.7e-219) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 3.4e+110) {
		tmp = (a * b) + (c * i);
	} 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 = (x * y) + (a * b)
    if ((x * y) <= (-1d+66)) then
        tmp = t_1
    else if ((x * y) <= 4.7d-219) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 3.4d+110) then
        tmp = (a * b) + (c * i)
    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 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -1e+66) {
		tmp = t_1;
	} else if ((x * y) <= 4.7e-219) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 3.4e+110) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -1e+66:
		tmp = t_1
	elif (x * y) <= 4.7e-219:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 3.4e+110:
		tmp = (a * b) + (c * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -1e+66)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.7e-219)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 3.4e+110)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -1e+66)
		tmp = t_1;
	elseif ((x * y) <= 4.7e-219)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 3.4e+110)
		tmp = (a * b) + (c * i);
	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[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.7e-219], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+110], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999945e65 or 3.4000000000000001e110 < (*.f64 x y)

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. fma-define 94.5%

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

      3. +-commutative 94.5%

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

      4. fma-define 97.8%

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

      5. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in c around 0 85.0%

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

   6. Taylor expanded in t around 0 76.8%

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

   if -9.99999999999999945e65 < (*.f64 x y) < 4.7e-219

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.9%

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

   6. Taylor expanded in c around 0 73.3%

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

   if 4.7e-219 < (*.f64 x y) < 3.4000000000000001e110

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-define 98.1%

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

      3. +-commutative 98.1%

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

      4. fma-define 98.1%

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

      5. fma-define 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around 0 89.1%

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

   6. Taylor expanded in c around inf 67.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+66}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{-219}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+110}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-219}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+256}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.1e+145)
   (* x y)
   (if (<= (* x y) 5.3e-219)
     (+ (* a b) (* z t))
     (if (<= (* x y) 8.8e+256) (+ (* a b) (* 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 ((x * y) <= -3.1e+145) {
		tmp = x * y;
	} else if ((x * y) <= 5.3e-219) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 8.8e+256) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-3.1d+145)) then
        tmp = x * y
    else if ((x * y) <= 5.3d-219) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 8.8d+256) then
        tmp = (a * b) + (c * i)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.1e+145) {
		tmp = x * y;
	} else if ((x * y) <= 5.3e-219) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 8.8e+256) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.1e+145:
		tmp = x * y
	elif (x * y) <= 5.3e-219:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 8.8e+256:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.1e+145)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 5.3e-219)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 8.8e+256)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -3.1e+145)
		tmp = x * y;
	elseif ((x * y) <= 5.3e-219)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 8.8e+256)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.1e+145], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.3e-219], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.8e+256], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.09999999999999988e145 or 8.7999999999999997e256 < (*.f64 x y)

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. fma-define 90.7%

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

      3. +-commutative 90.7%

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

      4. fma-define 96.3%

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

      5. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in a around 0 94.4%

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

   6. Taylor expanded in t around 0 90.9%

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

   7. Taylor expanded in c around 0 85.7%

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

   if -3.09999999999999988e145 < (*.f64 x y) < 5.3000000000000003e-219

   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. +-commutative 98.4%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 88.2%

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

   6. Taylor expanded in c around 0 71.7%

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

   if 5.3000000000000003e-219 < (*.f64 x y) < 8.7999999999999997e256

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-define 98.6%

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

      3. +-commutative 98.6%

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

      4. fma-define 98.7%

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

      5. fma-define 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 82.2%

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

   6. Taylor expanded in c around inf 63.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.1 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-219}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{+256}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+39} \lor \neg \left(c \cdot i \leq 7.4 \cdot 10^{+47}\right):\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -7.6e+39) (not (<= (* c i) 7.4e+47)))
   (+ (* a b) (+ (* c i) (* z t)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.6e+39) || !((c * i) <= 7.4e+47)) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-7.6d+39)) .or. (.not. ((c * i) <= 7.4d+47))) then
        tmp = (a * b) + ((c * i) + (z * t))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.6e+39) || !((c * i) <= 7.4e+47)) {
		tmp = (a * b) + ((c * i) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -7.6e+39) or not ((c * i) <= 7.4e+47):
		tmp = (a * b) + ((c * i) + (z * t))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -7.6e+39) || !(Float64(c * i) <= 7.4e+47))
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -7.6e+39) || ~(((c * i) <= 7.4e+47)))
		tmp = (a * b) + ((c * i) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -7.6e+39], N[Not[LessEqual[N[(c * i), $MachinePrecision], 7.4e+47]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -7.5999999999999996e39 or 7.40000000000000081e47 < (*.f64 c i)

   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. +-commutative 97.1%

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

      2. fma-define 99.0%

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

      3. +-commutative 99.0%

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

      4. fma-define 99.0%

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

      5. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0 87.1%

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

   if -7.5999999999999996e39 < (*.f64 c i) < 7.40000000000000081e47

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. fma-define 96.6%

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

      3. +-commutative 96.6%

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

      4. fma-define 98.6%

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

      5. fma-define 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in c around 0 92.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+39} \lor \neg \left(c \cdot i \leq 7.4 \cdot 10^{+47}\right):\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+158} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+158) (not (<= (* x y) 2e+206)))
   (+ (* x y) (* c i))
   (+ (* 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 (((x * y) <= -5e+158) || !((x * y) <= 2e+206)) {
		tmp = (x * y) + (c * i);
	} 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 (((x * y) <= (-5d+158)) .or. (.not. ((x * y) <= 2d+206))) then
        tmp = (x * y) + (c * i)
    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 (((x * y) <= -5e+158) || !((x * y) <= 2e+206)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -5e+158) or not ((x * y) <= 2e+206):
		tmp = (x * y) + (c * i)
	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(x * y) <= -5e+158) || !(Float64(x * y) <= 2e+206))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	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 (((x * y) <= -5e+158) || ~(((x * y) <= 2e+206)))
		tmp = (x * y) + (c * i);
	else
		tmp = (a * b) + ((c * i) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+158], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+206]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e158 or 2.0000000000000001e206 < (*.f64 x y)

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. fma-define 92.0%

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

      3. +-commutative 92.0%

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

      4. fma-define 96.8%

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

      5. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around 0 93.6%

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

   6. Taylor expanded in t around 0 89.2%

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

   if -4.9999999999999996e158 < (*.f64 x y) < 2.0000000000000001e206

   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. +-commutative 98.4%

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

      2. fma-define 99.4%

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

      3. +-commutative 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 87.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+158} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+245}:\\ \;\;\;\;a \cdot b + i \cdot \left(c + t \cdot \frac{z}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -5e+245)
     (+ (* a b) (* i (+ c (* t (/ z i)))))
     (if (<= (* c i) 2e+94) (+ (* a b) t_1) (+ (* c i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -5e+245) {
		tmp = (a * b) + (i * (c + (t * (z / i))));
	} else if ((c * i) <= 2e+94) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-5d+245)) then
        tmp = (a * b) + (i * (c + (t * (z / i))))
    else if ((c * i) <= 2d+94) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -5e+245) {
		tmp = (a * b) + (i * (c + (t * (z / i))));
	} else if ((c * i) <= 2e+94) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -5e+245:
		tmp = (a * b) + (i * (c + (t * (z / i))))
	elif (c * i) <= 2e+94:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -5e+245)
		tmp = Float64(Float64(a * b) + Float64(i * Float64(c + Float64(t * Float64(z / i)))));
	elseif (Float64(c * i) <= 2e+94)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -5e+245)
		tmp = (a * b) + (i * (c + (t * (z / i))));
	elseif ((c * i) <= 2e+94)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5e+245], N[(N[(a * b), $MachinePrecision] + N[(i * N[(c + N[(t * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+94], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.00000000000000034e245

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-define 99.9%

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

      5. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.6%

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

   6. Taylor expanded in i around inf 99.9%

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

      1. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   if -5.00000000000000034e245 < (*.f64 c i) < 2e94

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. fma-define 96.7%

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

      3. +-commutative 96.7%

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

      4. fma-define 98.3%

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

      5. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in c around 0 89.9%

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

   if 2e94 < (*.f64 c i)

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. 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-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 91.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+245}:\\ \;\;\;\;a \cdot b + i \cdot \left(c + t \cdot \frac{z}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-202}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+110}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.95e+76)
   (* x y)
   (if (<= (* x y) 6.4e-202)
     (* z t)
     (if (<= (* x y) 5.5e+110) (* 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 ((x * y) <= -1.95e+76) {
		tmp = x * y;
	} else if ((x * y) <= 6.4e-202) {
		tmp = z * t;
	} else if ((x * y) <= 5.5e+110) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1.95d+76)) then
        tmp = x * y
    else if ((x * y) <= 6.4d-202) then
        tmp = z * t
    else if ((x * y) <= 5.5d+110) then
        tmp = c * i
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.95e+76) {
		tmp = x * y;
	} else if ((x * y) <= 6.4e-202) {
		tmp = z * t;
	} else if ((x * y) <= 5.5e+110) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.95e+76:
		tmp = x * y
	elif (x * y) <= 6.4e-202:
		tmp = z * t
	elif (x * y) <= 5.5e+110:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.95e+76)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 6.4e-202)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 5.5e+110)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.95e+76)
		tmp = x * y;
	elseif ((x * y) <= 6.4e-202)
		tmp = z * t;
	elseif ((x * y) <= 5.5e+110)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.95e+76], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.4e-202], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.5e+110], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.94999999999999995e76 or 5.49999999999999996e110 < (*.f64 x y)

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. fma-define 94.5%

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

      3. +-commutative 94.5%

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

      4. fma-define 97.8%

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

      5. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in a around 0 83.9%

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

   6. Taylor expanded in t around 0 75.6%

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

   7. Taylor expanded in c around 0 66.2%

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

   if -1.94999999999999995e76 < (*.f64 x y) < 6.4000000000000002e-202

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 92.0%

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

   6. Taylor expanded in c around 0 73.6%

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

   7. Taylor expanded in a around 0 39.2%

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

   if 6.4000000000000002e-202 < (*.f64 x y) < 5.49999999999999996e110

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-define 98.1%

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

      3. +-commutative 98.1%

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

      4. fma-define 98.1%

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

      5. fma-define 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in c around inf 44.4%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-202}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+110}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-188}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.12e+179)
   (* a b)
   (if (<= (* a b) 4.4e-188)
     (* z t)
     (if (<= (* a b) 9e+149) (* c i) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.12e+179) {
		tmp = a * b;
	} else if ((a * b) <= 4.4e-188) {
		tmp = z * t;
	} else if ((a * b) <= 9e+149) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.12d+179)) then
        tmp = a * b
    else if ((a * b) <= 4.4d-188) then
        tmp = z * t
    else if ((a * b) <= 9d+149) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.12e+179) {
		tmp = a * b;
	} else if ((a * b) <= 4.4e-188) {
		tmp = z * t;
	} else if ((a * b) <= 9e+149) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.12e+179:
		tmp = a * b
	elif (a * b) <= 4.4e-188:
		tmp = z * t
	elif (a * b) <= 9e+149:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.12e+179)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4.4e-188)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 9e+149)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.12e+179)
		tmp = a * b;
	elseif ((a * b) <= 4.4e-188)
		tmp = z * t;
	elseif ((a * b) <= 9e+149)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.12e+179], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-188], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9e+149], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.11999999999999997e179 or 8.99999999999999965e149 < (*.f64 a b)

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. fma-define 92.9%

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

      3. +-commutative 92.9%

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

      4. fma-define 97.2%

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

      5. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around inf 68.1%

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

   if -1.11999999999999997e179 < (*.f64 a b) < 4.3999999999999999e-188

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-define 99.1%

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

      3. +-commutative 99.1%

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

      4. fma-define 99.1%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 64.1%

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

   6. Taylor expanded in c around 0 43.9%

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

   7. Taylor expanded in a around 0 37.8%

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

   if 4.3999999999999999e-188 < (*.f64 a b) < 8.99999999999999965e149

   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-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in c around inf 36.7%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-188}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.25 \cdot 10^{+73} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+255}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.25e+73) (not (<= (* x y) 4e+255)))
   (* x y)
   (+ (* 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 (((x * y) <= -1.25e+73) || !((x * y) <= 4e+255)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (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 (((x * y) <= (-1.25d+73)) .or. (.not. ((x * y) <= 4d+255))) then
        tmp = x * y
    else
        tmp = (a * b) + (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 (((x * y) <= -1.25e+73) || !((x * y) <= 4e+255)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.25e+73) or not ((x * y) <= 4e+255):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.25e+73) || !(Float64(x * y) <= 4e+255))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.25e+73) || ~(((x * y) <= 4e+255)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.25e+73], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+255]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.24999999999999994e73 or 3.99999999999999995e255 < (*.f64 x y)

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. fma-define 92.6%

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

      3. +-commutative 92.6%

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

      4. fma-define 97.1%

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

      5. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in a around 0 88.4%

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

   6. Taylor expanded in t around 0 81.5%

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

   7. Taylor expanded in c around 0 77.4%

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

   if -1.24999999999999994e73 < (*.f64 x y) < 3.99999999999999995e255

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. fma-define 99.4%

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

      3. +-commutative 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 87.9%

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

   6. Taylor expanded in c around inf 60.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.25 \cdot 10^{+73} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+255}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+109} \lor \neg \left(c \cdot i \leq 4.9 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.2e+109) (not (<= (* c i) 4.9e+145))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.2e+109) || !((c * i) <= 4.9e+145)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-3.2d+109)) .or. (.not. ((c * i) <= 4.9d+145))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.2e+109) || !((c * i) <= 4.9e+145)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.2e+109) or not ((c * i) <= 4.9e+145):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.2e+109) || !(Float64(c * i) <= 4.9e+145))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.2e+109) || ~(((c * i) <= 4.9e+145)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.2e+109], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4.9e+145]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.2000000000000001e109 or 4.90000000000000003e145 < (*.f64 c i)

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-define 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-define 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in c around inf 60.6%

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

   if -3.2000000000000001e109 < (*.f64 c i) < 4.90000000000000003e145

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. fma-define 96.6%

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

      3. +-commutative 96.6%

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

      4. fma-define 98.3%

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

      5. fma-define 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in a around inf 35.3%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+109} \lor \neg \left(c \cdot i \leq 4.9 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 27.5% 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 96.8%

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

   1. +-commutative 96.8%

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

   2. fma-define 97.6%

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

   3. +-commutative 97.6%

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

   4. fma-define 98.8%

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

   5. fma-define 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in a around inf 27.1%

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

Reproduce

herbie shell --seed 2024154 
(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)))