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

Percentage Accurate: 95.6% → 96.6%

Time: 9.4s

Alternatives: 12

Speedup: 0.4×

• 40.7% 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: 95.6% 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: 96.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 50.9%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 50.9%

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

4. Final simplification 97.7%

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

Alternative 2: 43.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-249}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{-113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.8e+94)
   (* c i)
   (if (<= (* c i) -1.8e-249)
     (* z t)
     (if (<= (* c i) 1.85e-113)
       (* x y)
       (if (<= (* c i) 6.2e-13)
         (* a b)
         (if (<= (* c i) 7.5e+93) (* 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) <= -4.8e+94) {
		tmp = c * i;
	} else if ((c * i) <= -1.8e-249) {
		tmp = z * t;
	} else if ((c * i) <= 1.85e-113) {
		tmp = x * y;
	} else if ((c * i) <= 6.2e-13) {
		tmp = a * b;
	} else if ((c * i) <= 7.5e+93) {
		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) <= (-4.8d+94)) then
        tmp = c * i
    else if ((c * i) <= (-1.8d-249)) then
        tmp = z * t
    else if ((c * i) <= 1.85d-113) then
        tmp = x * y
    else if ((c * i) <= 6.2d-13) then
        tmp = a * b
    else if ((c * i) <= 7.5d+93) 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) <= -4.8e+94) {
		tmp = c * i;
	} else if ((c * i) <= -1.8e-249) {
		tmp = z * t;
	} else if ((c * i) <= 1.85e-113) {
		tmp = x * y;
	} else if ((c * i) <= 6.2e-13) {
		tmp = a * b;
	} else if ((c * i) <= 7.5e+93) {
		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) <= -4.8e+94:
		tmp = c * i
	elif (c * i) <= -1.8e-249:
		tmp = z * t
	elif (c * i) <= 1.85e-113:
		tmp = x * y
	elif (c * i) <= 6.2e-13:
		tmp = a * b
	elif (c * i) <= 7.5e+93:
		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) <= -4.8e+94)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.8e-249)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.85e-113)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 6.2e-13)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 7.5e+93)
		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) <= -4.8e+94)
		tmp = c * i;
	elseif ((c * i) <= -1.8e-249)
		tmp = z * t;
	elseif ((c * i) <= 1.85e-113)
		tmp = x * y;
	elseif ((c * i) <= 6.2e-13)
		tmp = a * b;
	elseif ((c * i) <= 7.5e+93)
		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], -4.8e+94], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.8e-249], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.85e-113], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.2e-13], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.5e+93], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.79999999999999965e94 or 7.5000000000000002e93 < (*.f64 c i)

   1. Initial program 94.1%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.4%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 67.4%

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

   if -4.79999999999999965e94 < (*.f64 c i) < -1.79999999999999997e-249 or 6.1999999999999998e-13 < (*.f64 c i) < 7.5000000000000002e93

   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 z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 45.1%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 45.1%

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

   if -1.79999999999999997e-249 < (*.f64 c i) < 1.8499999999999999e-113

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 49.8%

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

   if 1.8499999999999999e-113 < (*.f64 c i) < 6.1999999999999998e-13

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 62.6%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 62.6%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-249}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{-113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -6.5e+50)
     t_2
     (if (<= (* c i) 4.3e-274)
       t_1
       (if (<= (* c i) 7e-13)
         (+ (* x y) (* a b))
         (if (<= (* c i) 3.8e+98) 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) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.5e+50) {
		tmp = t_2;
	} else if ((c * i) <= 4.3e-274) {
		tmp = t_1;
	} else if ((c * i) <= 7e-13) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 3.8e+98) {
		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) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-6.5d+50)) then
        tmp = t_2
    else if ((c * i) <= 4.3d-274) then
        tmp = t_1
    else if ((c * i) <= 7d-13) then
        tmp = (x * y) + (a * b)
    else if ((c * i) <= 3.8d+98) 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) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.5e+50) {
		tmp = t_2;
	} else if ((c * i) <= 4.3e-274) {
		tmp = t_1;
	} else if ((c * i) <= 7e-13) {
		tmp = (x * y) + (a * b);
	} else if ((c * i) <= 3.8e+98) {
		tmp = t_1;
	} 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 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -6.5e+50:
		tmp = t_2
	elif (c * i) <= 4.3e-274:
		tmp = t_1
	elif (c * i) <= 7e-13:
		tmp = (x * y) + (a * b)
	elif (c * i) <= 3.8e+98:
		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(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -6.5e+50)
		tmp = t_2;
	elseif (Float64(c * i) <= 4.3e-274)
		tmp = t_1;
	elseif (Float64(c * i) <= 7e-13)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(c * i) <= 3.8e+98)
		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) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -6.5e+50)
		tmp = t_2;
	elseif ((c * i) <= 4.3e-274)
		tmp = t_1;
	elseif ((c * i) <= 7e-13)
		tmp = (x * y) + (a * b);
	elseif ((c * i) <= 3.8e+98)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -6.5e+50], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 4.3e-274], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 7e-13], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.8e+98], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.5000000000000003e50 or 3.7999999999999999e98 < (*.f64 c i)

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.1%

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

   if -6.5000000000000003e50 < (*.f64 c i) < 4.29999999999999989e-274 or 7.0000000000000005e-13 < (*.f64 c i) < 3.7999999999999999e98

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z + x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot z\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      3. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   5. Simplified 81.4%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      4. *-lowering-*.f64 77.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 77.8%

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

   if 4.29999999999999989e-274 < (*.f64 c i) < 7.0000000000000005e-13

   1. Initial program 90.0%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 85.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      3. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 72.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{-274}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.6 \cdot 10^{-182}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* a b) -4.2e+248)
     t_1
     (if (<= (* a b) -1.15e+47)
       (+ (* x y) (* a b))
       (if (<= (* a b) -4.6e-182)
         (+ (* x y) (* c i))
         (if (<= (* a b) 7.5e+95) (+ (* 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -4.2e+248) {
		tmp = t_1;
	} else if ((a * b) <= -1.15e+47) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= -4.6e-182) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 7.5e+95) {
		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 = (a * b) + (c * i)
    if ((a * b) <= (-4.2d+248)) then
        tmp = t_1
    else if ((a * b) <= (-1.15d+47)) then
        tmp = (x * y) + (a * b)
    else if ((a * b) <= (-4.6d-182)) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 7.5d+95) 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -4.2e+248) {
		tmp = t_1;
	} else if ((a * b) <= -1.15e+47) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= -4.6e-182) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 7.5e+95) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -4.2e+248:
		tmp = t_1
	elif (a * b) <= -1.15e+47:
		tmp = (x * y) + (a * b)
	elif (a * b) <= -4.6e-182:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 7.5e+95:
		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(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -4.2e+248)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.15e+47)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(a * b) <= -4.6e-182)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 7.5e+95)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -4.2e+248)
		tmp = t_1;
	elseif ((a * b) <= -1.15e+47)
		tmp = (x * y) + (a * b);
	elseif ((a * b) <= -4.6e-182)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 7.5e+95)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4.2e+248], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+47], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.6e-182], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.5e+95], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.19999999999999977e248 or 7.5000000000000001e95 < (*.f64 a b)

   1. Initial program 85.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.4%

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

   if -4.19999999999999977e248 < (*.f64 a b) < -1.1499999999999999e47

   1. Initial program 96.8%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 88.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 88.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      3. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 72.9%

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

   if -1.1499999999999999e47 < (*.f64 a b) < -4.5999999999999998e-182

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.9%

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

   if -4.5999999999999998e-182 < (*.f64 a b) < 7.5000000000000001e95

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 68.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 68.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+248}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.6 \cdot 10^{-182}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+254}:\\ \;\;\;\;b \cdot \left(a + \frac{c \cdot i}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+165}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (+ (* x y) (* a b)))))
   (if (<= (* a b) -2e+254)
     (* b (+ a (/ (* c i) b)))
     (if (<= (* a b) -1e+47)
       t_1
       (if (<= (* a b) 2e+165) (+ (* c i) (+ (* x y) (* 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 = (z * t) + ((x * y) + (a * b));
	double tmp;
	if ((a * b) <= -2e+254) {
		tmp = b * (a + ((c * i) / b));
	} else if ((a * b) <= -1e+47) {
		tmp = t_1;
	} else if ((a * b) <= 2e+165) {
		tmp = (c * i) + ((x * y) + (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 = (z * t) + ((x * y) + (a * b))
    if ((a * b) <= (-2d+254)) then
        tmp = b * (a + ((c * i) / b))
    else if ((a * b) <= (-1d+47)) then
        tmp = t_1
    else if ((a * b) <= 2d+165) then
        tmp = (c * i) + ((x * y) + (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 = (z * t) + ((x * y) + (a * b));
	double tmp;
	if ((a * b) <= -2e+254) {
		tmp = b * (a + ((c * i) / b));
	} else if ((a * b) <= -1e+47) {
		tmp = t_1;
	} else if ((a * b) <= 2e+165) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + ((x * y) + (a * b))
	tmp = 0
	if (a * b) <= -2e+254:
		tmp = b * (a + ((c * i) / b))
	elif (a * b) <= -1e+47:
		tmp = t_1
	elif (a * b) <= 2e+165:
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(Float64(x * y) + Float64(a * b)))
	tmp = 0.0
	if (Float64(a * b) <= -2e+254)
		tmp = Float64(b * Float64(a + Float64(Float64(c * i) / b)));
	elseif (Float64(a * b) <= -1e+47)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e+165)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + 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 = (z * t) + ((x * y) + (a * b));
	tmp = 0.0;
	if ((a * b) <= -2e+254)
		tmp = b * (a + ((c * i) / b));
	elseif ((a * b) <= -1e+47)
		tmp = t_1;
	elseif ((a * b) <= 2e+165)
		tmp = (c * i) + ((x * y) + (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[(z * t), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+254], N[(b * N[(a + N[(N[(c * i), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e+47], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e+165], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e254

   1. Initial program 82.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 88.1%

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

   6. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{c \cdot i}{b}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{c \cdot i}{b}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(c \cdot i\right), \color{blue}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), b\right)\right)\right) \]

   8. Simplified 88.1%

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

   if -1.9999999999999999e254 < (*.f64 a b) < -1e47 or 1.9999999999999998e165 < (*.f64 a b)

   1. Initial program 88.6%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 86.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.2%

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

   if -1e47 < (*.f64 a b) < 1.9999999999999998e165

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z + x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot z\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      3. *-lowering-*.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   5. Simplified 93.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+254}:\\ \;\;\;\;b \cdot \left(a + \frac{c \cdot i}{b}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+47}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+165}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{-185}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.25 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.8e+93)
   (* c i)
   (if (<= (* c i) 1.7e-185)
     (* z t)
     (if (<= (* c i) 7.2e-13)
       (* a b)
       (if (<= (* c i) 2.25e+97) (* 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) <= -4.8e+93) {
		tmp = c * i;
	} else if ((c * i) <= 1.7e-185) {
		tmp = z * t;
	} else if ((c * i) <= 7.2e-13) {
		tmp = a * b;
	} else if ((c * i) <= 2.25e+97) {
		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) <= (-4.8d+93)) then
        tmp = c * i
    else if ((c * i) <= 1.7d-185) then
        tmp = z * t
    else if ((c * i) <= 7.2d-13) then
        tmp = a * b
    else if ((c * i) <= 2.25d+97) 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) <= -4.8e+93) {
		tmp = c * i;
	} else if ((c * i) <= 1.7e-185) {
		tmp = z * t;
	} else if ((c * i) <= 7.2e-13) {
		tmp = a * b;
	} else if ((c * i) <= 2.25e+97) {
		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) <= -4.8e+93:
		tmp = c * i
	elif (c * i) <= 1.7e-185:
		tmp = z * t
	elif (c * i) <= 7.2e-13:
		tmp = a * b
	elif (c * i) <= 2.25e+97:
		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) <= -4.8e+93)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.7e-185)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 7.2e-13)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.25e+97)
		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) <= -4.8e+93)
		tmp = c * i;
	elseif ((c * i) <= 1.7e-185)
		tmp = z * t;
	elseif ((c * i) <= 7.2e-13)
		tmp = a * b;
	elseif ((c * i) <= 2.25e+97)
		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], -4.8e+93], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.7e-185], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.2e-13], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.25e+97], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -4.80000000000000021e93 or 2.24999999999999988e97 < (*.f64 c i)

   1. Initial program 94.1%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.4%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 67.4%

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

   if -4.80000000000000021e93 < (*.f64 c i) < 1.6999999999999999e-185 or 7.1999999999999996e-13 < (*.f64 c i) < 2.24999999999999988e97

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 40.8%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 40.8%

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

   if 1.6999999999999999e-185 < (*.f64 c i) < 7.1999999999999996e-13

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 51.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{-185}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.2 \cdot 10^{-13}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.25 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{-67}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* a b) -5.8e+252)
     t_1
     (if (<= (* a b) -1.05e-67)
       (+ (* x y) (* a b))
       (if (<= (* a b) 1.9e+93) (+ (* 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -5.8e+252) {
		tmp = t_1;
	} else if ((a * b) <= -1.05e-67) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 1.9e+93) {
		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 = (a * b) + (c * i)
    if ((a * b) <= (-5.8d+252)) then
        tmp = t_1
    else if ((a * b) <= (-1.05d-67)) then
        tmp = (x * y) + (a * b)
    else if ((a * b) <= 1.9d+93) 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 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -5.8e+252) {
		tmp = t_1;
	} else if ((a * b) <= -1.05e-67) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 1.9e+93) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -5.8e+252:
		tmp = t_1
	elif (a * b) <= -1.05e-67:
		tmp = (x * y) + (a * b)
	elif (a * b) <= 1.9e+93:
		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(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5.8e+252)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.05e-67)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(a * b) <= 1.9e+93)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -5.8e+252)
		tmp = t_1;
	elseif ((a * b) <= -1.05e-67)
		tmp = (x * y) + (a * b);
	elseif ((a * b) <= 1.9e+93)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.8e+252], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.05e-67], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.9e+93], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.79999999999999992e252 or 1.8999999999999999e93 < (*.f64 a b)

   1. Initial program 85.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 77.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 77.4%

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

   if -5.79999999999999992e252 < (*.f64 a b) < -1.0500000000000001e-67

   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 c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 86.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      3. *-lowering-*.f64 68.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 68.2%

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

   if -1.0500000000000001e-67 < (*.f64 a b) < 1.8999999999999999e93

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 68.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 68.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+252}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{-67}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -3.8e+94)
     t_1
     (if (<= (* c i) 2.45e+97) (+ (* z t) (+ (* x y) (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.8e+94) {
		tmp = t_1;
	} else if ((c * i) <= 2.45e+97) {
		tmp = (z * t) + ((x * y) + (a * b));
	} 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 = (a * b) + (c * i)
    if ((c * i) <= (-3.8d+94)) then
        tmp = t_1
    else if ((c * i) <= 2.45d+97) then
        tmp = (z * t) + ((x * y) + (a * b))
    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 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.8e+94) {
		tmp = t_1;
	} else if ((c * i) <= 2.45e+97) {
		tmp = (z * t) + ((x * y) + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -3.8e+94:
		tmp = t_1
	elif (c * i) <= 2.45e+97:
		tmp = (z * t) + ((x * y) + (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -3.8e+94)
		tmp = t_1;
	elseif (Float64(c * i) <= 2.45e+97)
		tmp = Float64(Float64(z * t) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -3.8e+94)
		tmp = t_1;
	elseif ((c * i) <= 2.45e+97)
		tmp = (z * t) + ((x * y) + (a * b));
	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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.8e+94], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2.45e+97], N[(N[(z * t), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.7999999999999996e94 or 2.44999999999999982e97 < (*.f64 c i)

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 81.0%

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

   if -3.7999999999999996e94 < (*.f64 c i) < 2.44999999999999982e97

   1. Initial program 95.9%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 91.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+93}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -8.5e+32)
     t_1
     (if (<= (* c i) 2e+93) (+ (* x y) (* a b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+32) {
		tmp = t_1;
	} else if ((c * i) <= 2e+93) {
		tmp = (x * y) + (a * b);
	} 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 = (a * b) + (c * i)
    if ((c * i) <= (-8.5d+32)) then
        tmp = t_1
    else if ((c * i) <= 2d+93) then
        tmp = (x * y) + (a * b)
    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 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+32) {
		tmp = t_1;
	} else if ((c * i) <= 2e+93) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -8.5e+32:
		tmp = t_1
	elif (c * i) <= 2e+93:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -8.5e+32)
		tmp = t_1;
	elseif (Float64(c * i) <= 2e+93)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -8.5e+32)
		tmp = t_1;
	elseif ((c * i) <= 2e+93)
		tmp = (x * y) + (a * b);
	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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.5e+32], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2e+93], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -8.4999999999999998e32 or 2.00000000000000009e93 < (*.f64 c i)

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.6%

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

   if -8.4999999999999998e32 < (*.f64 c i) < 2.00000000000000009e93

   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 c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 93.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      3. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 61.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+93}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+208}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+32)
   (* x y)
   (if (<= (* x y) 5e+208) (+ (* 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) <= -4e+32) {
		tmp = x * y;
	} else if ((x * y) <= 5e+208) {
		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) <= (-4d+32)) then
        tmp = x * y
    else if ((x * y) <= 5d+208) 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) <= -4e+32) {
		tmp = x * y;
	} else if ((x * y) <= 5e+208) {
		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) <= -4e+32:
		tmp = x * y
	elif (x * y) <= 5e+208:
		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) <= -4e+32)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 5e+208)
		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) <= -4e+32)
		tmp = x * y;
	elseif ((x * y) <= 5e+208)
		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], -4e+32], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+208], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.00000000000000021e32 or 5.0000000000000004e208 < (*.f64 x y)

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 65.0%

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

   if -4.00000000000000021e32 < (*.f64 x y) < 5.0000000000000004e208

   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 a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 62.8%

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

Alternative 11: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{+79}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5e+79) (* c i) (if (<= (* c i) 3.8e+98) (* 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) <= -5e+79) {
		tmp = c * i;
	} else if ((c * i) <= 3.8e+98) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-5d+79)) then
        tmp = c * i
    else if ((c * i) <= 3.8d+98) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5e+79) {
		tmp = c * i;
	} else if ((c * i) <= 3.8e+98) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5e+79:
		tmp = c * i
	elif (c * i) <= 3.8e+98:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5e+79)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3.8e+98)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -5e+79)
		tmp = c * i;
	elseif ((c * i) <= 3.8e+98)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5e+79], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.8e+98], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5e79 or 3.7999999999999999e98 < (*.f64 c i)

   1. Initial program 94.4%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.9%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 65.9%

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

   if -5e79 < (*.f64 c i) < 3.7999999999999999e98

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 29.4%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 29.4%

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

Alternative 12: 26.4% 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 95.3%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 26.2%

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

5. Simplified 26.2%

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

Reproduce

herbie shell --seed 2024139 
(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)))