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

Percentage Accurate: 95.5% → 96.9%

Time: 10.1s

Alternatives: 11

Speedup: 0.4×

• 41.6% 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: 96.9% accurate, 0.4× speedup

Math

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

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) (* c i)))))

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) + (c * i);
	}
	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) + (c * i);
	}
	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) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	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) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 50.0%

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

      1. associate-+r+ 50.0%

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

      2. associate-/l* 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in x around inf 67.1%

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

4. Final simplification 99.2%

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

Alternative 2: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-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 98.8%

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

3. Simplified 98.8%

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

Alternative 3: 42.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-180}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-307}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-281}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+147}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.1e+90)
   (* c i)
   (if (<= (* c i) -1.9e-180)
     (* z t)
     (if (<= (* c i) -1.75e-307)
       (* x y)
       (if (<= (* c i) 9.5e-281)
         (* z t)
         (if (<= (* c i) 4.5e+147) (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.1e+90) {
		tmp = c * i;
	} else if ((c * i) <= -1.9e-180) {
		tmp = z * t;
	} else if ((c * i) <= -1.75e-307) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e-281) {
		tmp = z * t;
	} else if ((c * i) <= 4.5e+147) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.1d+90)) then
        tmp = c * i
    else if ((c * i) <= (-1.9d-180)) then
        tmp = z * t
    else if ((c * i) <= (-1.75d-307)) then
        tmp = x * y
    else if ((c * i) <= 9.5d-281) then
        tmp = z * t
    else if ((c * i) <= 4.5d+147) then
        tmp = x * y
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.1e+90) {
		tmp = c * i;
	} else if ((c * i) <= -1.9e-180) {
		tmp = z * t;
	} else if ((c * i) <= -1.75e-307) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e-281) {
		tmp = z * t;
	} else if ((c * i) <= 4.5e+147) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.1e+90:
		tmp = c * i
	elif (c * i) <= -1.9e-180:
		tmp = z * t
	elif (c * i) <= -1.75e-307:
		tmp = x * y
	elif (c * i) <= 9.5e-281:
		tmp = z * t
	elif (c * i) <= 4.5e+147:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.1e+90)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.9e-180)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -1.75e-307)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 9.5e-281)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 4.5e+147)
		tmp = Float64(x * y);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.1e+90)
		tmp = c * i;
	elseif ((c * i) <= -1.9e-180)
		tmp = z * t;
	elseif ((c * i) <= -1.75e-307)
		tmp = x * y;
	elseif ((c * i) <= 9.5e-281)
		tmp = z * t;
	elseif ((c * i) <= 4.5e+147)
		tmp = x * y;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.1e+90], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.9e-180], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.75e-307], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e-281], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.5e+147], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.09999999999999988e90 or 4.50000000000000008e147 < (*.f64 c i)

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. fma-define 96.3%

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

      3. +-commutative 96.3%

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

      4. fma-define 96.3%

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

      5. fma-define 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in c around inf 73.1%

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

   if -3.09999999999999988e90 < (*.f64 c i) < -1.9e-180 or -1.7500000000000001e-307 < (*.f64 c i) < 9.5000000000000003e-281

   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 z around inf 47.1%

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

   if -1.9e-180 < (*.f64 c i) < -1.7500000000000001e-307 or 9.5000000000000003e-281 < (*.f64 c i) < 4.50000000000000008e147

   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 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 inf 52.7%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.9 \cdot 10^{-180}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-307}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-281}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+147}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+228} \lor \neg \left(x \cdot y \leq -2.6 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq -1.25 \cdot 10^{+90}\right) \land x \cdot y \leq 9 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.8e+228)
         (not
          (or (<= (* x y) -2.6e+175)
              (and (not (<= (* x y) -1.25e+90)) (<= (* x y) 9e+172)))))
   (* 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) <= -2.8e+228) || !(((x * y) <= -2.6e+175) || (!((x * y) <= -1.25e+90) && ((x * y) <= 9e+172)))) {
		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) <= (-2.8d+228)) .or. (.not. ((x * y) <= (-2.6d+175)) .or. (.not. ((x * y) <= (-1.25d+90))) .and. ((x * y) <= 9d+172))) 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) <= -2.8e+228) || !(((x * y) <= -2.6e+175) || (!((x * y) <= -1.25e+90) && ((x * y) <= 9e+172)))) {
		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) <= -2.8e+228) or not (((x * y) <= -2.6e+175) or (not ((x * y) <= -1.25e+90) and ((x * y) <= 9e+172))):
		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) <= -2.8e+228) || !((Float64(x * y) <= -2.6e+175) || (!(Float64(x * y) <= -1.25e+90) && (Float64(x * y) <= 9e+172))))
		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) <= -2.8e+228) || ~((((x * y) <= -2.6e+175) || (~(((x * y) <= -1.25e+90)) && ((x * y) <= 9e+172)))))
		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], -2.8e+228], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -2.6e+175], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -1.25e+90]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 9e+172]]]], $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) < -2.7999999999999999e228 or -2.6e175 < (*.f64 x y) < -1.2500000000000001e90 or 9.0000000000000004e172 < (*.f64 x y)

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. fma-define 98.7%

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

      3. +-commutative 98.7%

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

      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 inf 76.7%

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

   if -2.7999999999999999e228 < (*.f64 x y) < -2.6e175 or -1.2500000000000001e90 < (*.f64 x y) < 9.0000000000000004e172

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf 86.4%

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

      1. associate-+r+ 86.4%

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

      2. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in a around inf 60.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+228} \lor \neg \left(x \cdot y \leq -2.6 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq -1.25 \cdot 10^{+90}\right) \land x \cdot y \leq 9 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -6.2 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* c i) -6.8e+88)
     (+ (* x y) (* c i))
     (if (<= (* c i) -7.5e-118)
       t_1
       (if (<= (* c i) -6.2e-181)
         (* z t)
         (if (<= (* c i) 1.05e+146) t_1 (+ (* a b) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -6.8e+88) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -7.5e-118) {
		tmp = t_1;
	} else if ((c * i) <= -6.2e-181) {
		tmp = z * t;
	} else if ((c * i) <= 1.05e+146) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (a * b)
    if ((c * i) <= (-6.8d+88)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= (-7.5d-118)) then
        tmp = t_1
    else if ((c * i) <= (-6.2d-181)) then
        tmp = z * t
    else if ((c * i) <= 1.05d+146) then
        tmp = t_1
    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 t_1 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -6.8e+88) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -7.5e-118) {
		tmp = t_1;
	} else if ((c * i) <= -6.2e-181) {
		tmp = z * t;
	} else if ((c * i) <= 1.05e+146) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (c * i) <= -6.8e+88:
		tmp = (x * y) + (c * i)
	elif (c * i) <= -7.5e-118:
		tmp = t_1
	elif (c * i) <= -6.2e-181:
		tmp = z * t
	elif (c * i) <= 1.05e+146:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	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(c * i) <= -6.8e+88)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= -7.5e-118)
		tmp = t_1;
	elseif (Float64(c * i) <= -6.2e-181)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.05e+146)
		tmp = t_1;
	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)
	t_1 = (x * y) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -6.8e+88)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= -7.5e-118)
		tmp = t_1;
	elseif ((c * i) <= -6.2e-181)
		tmp = z * t;
	elseif ((c * i) <= 1.05e+146)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	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[(c * i), $MachinePrecision], -6.8e+88], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -7.5e-118], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -6.2e-181], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+146], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -6.80000000000000008e88

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 81.6%

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

      1. associate-+r+ 81.6%

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

      2. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in x around inf 80.1%

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

   if -6.80000000000000008e88 < (*.f64 c i) < -7.49999999999999978e-118 or -6.20000000000000043e-181 < (*.f64 c i) < 1.05e146

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 71.4%

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

   4. Taylor expanded in c around 0 66.9%

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

   if -7.49999999999999978e-118 < (*.f64 c i) < -6.20000000000000043e-181

   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 z around inf 82.1%

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

   if 1.05e146 < (*.f64 c i)

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 80.6%

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

      1. associate-+r+ 80.6%

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

      2. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in a around inf 89.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.5 \cdot 10^{-118}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -6.2 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -6.4 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -6.4e+87)
     t_2
     (if (<= (* c i) -4.2e-118)
       t_1
       (if (<= (* c i) -7e-181) (* z t) (if (<= (* c i) 7e+146) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.4e+87) {
		tmp = t_2;
	} else if ((c * i) <= -4.2e-118) {
		tmp = t_1;
	} else if ((c * i) <= -7e-181) {
		tmp = z * t;
	} else if ((c * i) <= 7e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (a * b)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-6.4d+87)) then
        tmp = t_2
    else if ((c * i) <= (-4.2d-118)) then
        tmp = t_1
    else if ((c * i) <= (-7d-181)) then
        tmp = z * t
    else if ((c * i) <= 7d+146) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.4e+87) {
		tmp = t_2;
	} else if ((c * i) <= -4.2e-118) {
		tmp = t_1;
	} else if ((c * i) <= -7e-181) {
		tmp = z * t;
	} else if ((c * i) <= 7e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -6.4e+87:
		tmp = t_2
	elif (c * i) <= -4.2e-118:
		tmp = t_1
	elif (c * i) <= -7e-181:
		tmp = z * t
	elif (c * i) <= 7e+146:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -6.4e+87)
		tmp = t_2;
	elseif (Float64(c * i) <= -4.2e-118)
		tmp = t_1;
	elseif (Float64(c * i) <= -7e-181)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 7e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -6.4e+87)
		tmp = t_2;
	elseif ((c * i) <= -4.2e-118)
		tmp = t_1;
	elseif ((c * i) <= -7e-181)
		tmp = z * t;
	elseif ((c * i) <= 7e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -6.4e+87], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -4.2e-118], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -7e-181], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7e+146], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.4000000000000001e87 or 7.0000000000000002e146 < (*.f64 c i)

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf 81.2%

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

      1. associate-+r+ 81.2%

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

      2. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in a around inf 82.5%

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

   if -6.4000000000000001e87 < (*.f64 c i) < -4.2e-118 or -6.99999999999999993e-181 < (*.f64 c i) < 7.0000000000000002e146

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 71.4%

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

   4. Taylor expanded in c around 0 66.9%

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

   if -4.2e-118 < (*.f64 c i) < -6.99999999999999993e-181

   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 z around inf 82.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.4 \cdot 10^{+87}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -7 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.8 \cdot 10^{-190}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+39}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.25e+92)
   (* c i)
   (if (<= (* c i) -4.8e-190)
     (* z t)
     (if (<= (* c i) 0.0) (* a b) (if (<= (* c i) 4e+39) (* z t) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.25e+92) {
		tmp = c * i;
	} else if ((c * i) <= -4.8e-190) {
		tmp = z * t;
	} else if ((c * i) <= 0.0) {
		tmp = a * b;
	} else if ((c * i) <= 4e+39) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.25d+92)) then
        tmp = c * i
    else if ((c * i) <= (-4.8d-190)) then
        tmp = z * t
    else if ((c * i) <= 0.0d0) then
        tmp = a * b
    else if ((c * i) <= 4d+39) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.25e+92) {
		tmp = c * i;
	} else if ((c * i) <= -4.8e-190) {
		tmp = z * t;
	} else if ((c * i) <= 0.0) {
		tmp = a * b;
	} else if ((c * i) <= 4e+39) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.25e+92:
		tmp = c * i
	elif (c * i) <= -4.8e-190:
		tmp = z * t
	elif (c * i) <= 0.0:
		tmp = a * b
	elif (c * i) <= 4e+39:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.25e+92)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -4.8e-190)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 0.0)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4e+39)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.25e+92)
		tmp = c * i;
	elseif ((c * i) <= -4.8e-190)
		tmp = z * t;
	elseif ((c * i) <= 0.0)
		tmp = a * b;
	elseif ((c * i) <= 4e+39)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.25e+92], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4.8e-190], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.0], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4e+39], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.25000000000000005e92 or 3.99999999999999976e39 < (*.f64 c i)

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. fma-define 96.1%

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

      3. +-commutative 96.1%

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

      4. fma-define 97.1%

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

      5. fma-define 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in c around inf 62.8%

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

   if -1.25000000000000005e92 < (*.f64 c i) < -4.8000000000000001e-190 or -0.0 < (*.f64 c i) < 3.99999999999999976e39

   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 98.2%

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

      3. +-commutative 98.2%

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

      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 z around inf 42.2%

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

   if -4.8000000000000001e-190 < (*.f64 c i) < -0.0

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-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 inf 45.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.8 \cdot 10^{-190}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4 \cdot 10^{+39}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.7 \cdot 10^{+89} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+37}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -8.7e+89) (not (<= (* c i) 2.4e+37)))
   (+ (* c i) (+ (* x y) (* a b)))
   (+ (* 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) <= -8.7e+89) || !((c * i) <= 2.4e+37)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} 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) <= (-8.7d+89)) .or. (.not. ((c * i) <= 2.4d+37))) then
        tmp = (c * i) + ((x * y) + (a * b))
    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) <= -8.7e+89) || !((c * i) <= 2.4e+37)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} 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) <= -8.7e+89) or not ((c * i) <= 2.4e+37):
		tmp = (c * i) + ((x * y) + (a * b))
	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) <= -8.7e+89) || !(Float64(c * i) <= 2.4e+37))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	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) <= -8.7e+89) || ~(((c * i) <= 2.4e+37)))
		tmp = (c * i) + ((x * y) + (a * b));
	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], -8.7e+89], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.4e+37]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $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) < -8.70000000000000019e89 or 2.4e37 < (*.f64 c i)

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 92.4%

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

   if -8.70000000000000019e89 < (*.f64 c i) < 2.4e37

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. fma-define 98.7%

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

      3. +-commutative 98.7%

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

      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 96.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.7 \cdot 10^{+89} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+37}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.2e+92)
   (+ (* x y) (* c i))
   (if (<= (* c i) 7.5e+171)
     (+ (* a b) (+ (* 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) {
	double tmp;
	if ((c * i) <= -5.2e+92) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 7.5e+171) {
		tmp = (a * b) + ((x * y) + (z * t));
	} 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 ((c * i) <= (-5.2d+92)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 7.5d+171) then
        tmp = (a * b) + ((x * y) + (z * t))
    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 ((c * i) <= -5.2e+92) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 7.5e+171) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.2e+92:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 7.5e+171:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5.2e+92)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 7.5e+171)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	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 ((c * i) <= -5.2e+92)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 7.5e+171)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5.2e+92], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.5e+171], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.1999999999999998e92

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf 81.2%

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

      1. associate-+r+ 81.2%

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

      2. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around inf 81.8%

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

   if -5.1999999999999998e92 < (*.f64 c i) < 7.4999999999999998e171

   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 98.3%

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

      3. +-commutative 98.3%

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

      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 93.7%

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

   if 7.4999999999999998e171 < (*.f64 c i)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 78.1%

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

      1. associate-+r+ 78.1%

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

      2. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around inf 97.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.46 \cdot 10^{+88} \lor \neg \left(c \cdot i \leq 9 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.46e+88) (not (<= (* c i) 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) <= -1.46e+88) || !((c * i) <= 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) <= (-1.46d+88)) .or. (.not. ((c * i) <= 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) <= -1.46e+88) || !((c * i) <= 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) <= -1.46e+88) or not ((c * i) <= 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) <= -1.46e+88) || !(Float64(c * i) <= 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) <= -1.46e+88) || ~(((c * i) <= 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], -1.46e+88], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9e+145]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.45999999999999999e88 or 8.9999999999999996e145 < (*.f64 c i)

   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 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 c around inf 72.3%

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

   if -1.45999999999999999e88 < (*.f64 c i) < 8.9999999999999996e145

   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 98.2%

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

      3. +-commutative 98.2%

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

      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 inf 29.6%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.46 \cdot 10^{+88} \lor \neg \left(c \cdot i \leq 9 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 27.6% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-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 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in a around inf 24.7%

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

Reproduce

herbie shell --seed 2024111 
(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)))