Linear.V3:$cdot from linear-1.19.1.3, B

Percentage Accurate: 97.9% → 98.9%

Time: 6.1s

Alternatives: 10

Speedup: 1.0×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * y) + (z * t)) + (a * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * y) + (z * t)) + (a * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-define 99.2%

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

   3. fma-define 99.2%

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

3. Simplified 99.2%

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

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 3: 52.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -4.8e+32)
   (* x y)
   (if (<= (* x y) -3.7e-171)
     (* z t)
     (if (<= (* x y) 2.85e-257)
       (* a b)
       (if (<= (* x y) 1.25e-122)
         (* z t)
         (if (<= (* x y) 2.8e-78) (* a b) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4.8e+32) {
		tmp = x * y;
	} else if ((x * y) <= -3.7e-171) {
		tmp = z * t;
	} else if ((x * y) <= 2.85e-257) {
		tmp = a * b;
	} else if ((x * y) <= 1.25e-122) {
		tmp = z * t;
	} else if ((x * y) <= 2.8e-78) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((x * y) <= (-4.8d+32)) then
        tmp = x * y
    else if ((x * y) <= (-3.7d-171)) then
        tmp = z * t
    else if ((x * y) <= 2.85d-257) then
        tmp = a * b
    else if ((x * y) <= 1.25d-122) then
        tmp = z * t
    else if ((x * y) <= 2.8d-78) then
        tmp = a * b
    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 tmp;
	if ((x * y) <= -4.8e+32) {
		tmp = x * y;
	} else if ((x * y) <= -3.7e-171) {
		tmp = z * t;
	} else if ((x * y) <= 2.85e-257) {
		tmp = a * b;
	} else if ((x * y) <= 1.25e-122) {
		tmp = z * t;
	} else if ((x * y) <= 2.8e-78) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -4.8e+32:
		tmp = x * y
	elif (x * y) <= -3.7e-171:
		tmp = z * t
	elif (x * y) <= 2.85e-257:
		tmp = a * b
	elif (x * y) <= 1.25e-122:
		tmp = z * t
	elif (x * y) <= 2.8e-78:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -4.8e+32)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.7e-171)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.85e-257)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.25e-122)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.8e-78)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -4.8e+32)
		tmp = x * y;
	elseif ((x * y) <= -3.7e-171)
		tmp = z * t;
	elseif ((x * y) <= 2.85e-257)
		tmp = a * b;
	elseif ((x * y) <= 1.25e-122)
		tmp = z * t;
	elseif ((x * y) <= 2.8e-78)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.8e+32], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.7e-171], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.85e-257], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.25e-122], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.8e-78], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.79999999999999983e32 or 2.80000000000000024e-78 < (*.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. +-commutative 78.3%

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

      2. associate-/l* 74.7%

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

      3. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around inf 65.8%

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

   if -4.79999999999999983e32 < (*.f64 x y) < -3.70000000000000012e-171 or 2.8499999999999999e-257 < (*.f64 x y) < 1.25e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 96.9%

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

      1. +-commutative 96.9%

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

      2. associate-/l* 89.3%

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

      3. associate-/l* 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in z around inf 58.0%

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

   if -3.70000000000000012e-171 < (*.f64 x y) < 2.8499999999999999e-257 or 1.25e-122 < (*.f64 x y) < 2.80000000000000024e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 66.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.85 \cdot 10^{-257}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+152} \lor \neg \left(t \leq 3.1 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= t -2.8e-27)
     t_1
     (if (<= t 2.75e+72)
       (+ (* a b) (* x y))
       (if (or (<= t 1.9e+152) (not (<= t 3.1e+169)))
         (+ (* x y) (* z t))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if (t <= -2.8e-27) {
		tmp = t_1;
	} else if (t <= 2.75e+72) {
		tmp = (a * b) + (x * y);
	} else if ((t <= 1.9e+152) || !(t <= 3.1e+169)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if (t <= (-2.8d-27)) then
        tmp = t_1
    else if (t <= 2.75d+72) then
        tmp = (a * b) + (x * y)
    else if ((t <= 1.9d+152) .or. (.not. (t <= 3.1d+169))) then
        tmp = (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 t_1 = (a * b) + (z * t);
	double tmp;
	if (t <= -2.8e-27) {
		tmp = t_1;
	} else if (t <= 2.75e+72) {
		tmp = (a * b) + (x * y);
	} else if ((t <= 1.9e+152) || !(t <= 3.1e+169)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if t <= -2.8e-27:
		tmp = t_1
	elif t <= 2.75e+72:
		tmp = (a * b) + (x * y)
	elif (t <= 1.9e+152) or not (t <= 3.1e+169):
		tmp = (x * y) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (t <= -2.8e-27)
		tmp = t_1;
	elseif (t <= 2.75e+72)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif ((t <= 1.9e+152) || !(t <= 3.1e+169))
		tmp = 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)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if (t <= -2.8e-27)
		tmp = t_1;
	elseif (t <= 2.75e+72)
		tmp = (a * b) + (x * y);
	elseif ((t <= 1.9e+152) || ~((t <= 3.1e+169)))
		tmp = (x * y) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-27], t$95$1, If[LessEqual[t, 2.75e+72], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.9e+152], N[Not[LessEqual[t, 3.1e+169]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e-27 or 1.9e152 < t < 3.1e169

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0 77.7%

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

   if -2.8e-27 < t < 2.75e72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 85.6%

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

   if 2.75e72 < t < 1.9e152 or 3.1e169 < t

   1. Initial program 94.6%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/l* 79.1%

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

      3. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in a around 0 89.7%

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

   7. Taylor expanded in z around 0 92.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+152} \lor \neg \left(t \leq 3.1 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ t (/ (* x y) z)))))
   (if (<= z -4.3e+161)
     t_1
     (if (<= z -8.5e+44)
       (+ (* a b) (* z t))
       (if (<= z 3.1e-60) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t + ((x * y) / z));
	double tmp;
	if (z <= -4.3e+161) {
		tmp = t_1;
	} else if (z <= -8.5e+44) {
		tmp = (a * b) + (z * t);
	} else if (z <= 3.1e-60) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = z * (t + ((x * y) / z))
    if (z <= (-4.3d+161)) then
        tmp = t_1
    else if (z <= (-8.5d+44)) then
        tmp = (a * b) + (z * t)
    else if (z <= 3.1d-60) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t + ((x * y) / z));
	double tmp;
	if (z <= -4.3e+161) {
		tmp = t_1;
	} else if (z <= -8.5e+44) {
		tmp = (a * b) + (z * t);
	} else if (z <= 3.1e-60) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t + ((x * y) / z))
	tmp = 0
	if z <= -4.3e+161:
		tmp = t_1
	elif z <= -8.5e+44:
		tmp = (a * b) + (z * t)
	elif z <= 3.1e-60:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t + Float64(Float64(x * y) / z)))
	tmp = 0.0
	if (z <= -4.3e+161)
		tmp = t_1;
	elseif (z <= -8.5e+44)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (z <= 3.1e-60)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t + ((x * y) / z));
	tmp = 0.0;
	if (z <= -4.3e+161)
		tmp = t_1;
	elseif (z <= -8.5e+44)
		tmp = (a * b) + (z * t);
	elseif (z <= 3.1e-60)
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+161], t$95$1, If[LessEqual[z, -8.5e+44], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-60], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e161 or 3.09999999999999988e-60 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 98.0%

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

      1. +-commutative 98.0%

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

      2. associate-/l* 97.9%

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

      3. associate-/l* 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in a around 0 78.8%

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

   if -4.3e161 < z < -8.5e44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.5%

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

   if -8.5e44 < z < 3.09999999999999988e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{-26} \lor \neg \left(x \cdot y \leq 3.3 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.85e-26) (not (<= (* x y) 3.3e-78)))
   (+ (* x y) (* z t))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.85e-26) || !((x * y) <= 3.3e-78)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (((x * y) <= (-1.85d-26)) .or. (.not. ((x * y) <= 3.3d-78))) then
        tmp = (x * y) + (z * t)
    else
        tmp = (a * b) + (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 tmp;
	if (((x * y) <= -1.85e-26) || !((x * y) <= 3.3e-78)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -1.85e-26) or not ((x * y) <= 3.3e-78):
		tmp = (x * y) + (z * t)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -1.85e-26) || !(Float64(x * y) <= 3.3e-78))
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -1.85e-26) || ~(((x * y) <= 3.3e-78)))
		tmp = (x * y) + (z * t);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.85e-26], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.3e-78]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.8499999999999999e-26 or 3.29999999999999982e-78 < (*.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. associate-/l* 74.3%

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

      3. associate-/l* 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in a around 0 69.9%

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

   7. Taylor expanded in z around 0 81.5%

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

   if -1.8499999999999999e-26 < (*.f64 x y) < 3.29999999999999982e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{-26} \lor \neg \left(x \cdot y \leq 3.3 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.9 \cdot 10^{+123} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4.9e+123) (not (<= (* x y) 5e+236)))
   (* x y)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -4.9e+123) || !((x * y) <= 5e+236)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (((x * y) <= (-4.9d+123)) .or. (.not. ((x * y) <= 5d+236))) then
        tmp = x * y
    else
        tmp = (a * b) + (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 tmp;
	if (((x * y) <= -4.9e+123) || !((x * y) <= 5e+236)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -4.9e+123) or not ((x * y) <= 5e+236):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -4.9e+123) || !(Float64(x * y) <= 5e+236))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -4.9e+123) || ~(((x * y) <= 5e+236)))
		tmp = x * y;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.9e+123], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+236]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.89999999999999976e123 or 4.9999999999999997e236 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. +-commutative 75.7%

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

      2. associate-/l* 74.2%

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

      3. associate-/l* 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in x around inf 90.0%

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

   if -4.89999999999999976e123 < (*.f64 x y) < 4.9999999999999997e236

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.9 \cdot 10^{+123} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+236}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4500000 \lor \neg \left(a \cdot b \leq 1.02 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -4500000.0) (not (<= (* a b) 1.02e+93))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -4500000.0) || !((a * b) <= 1.02e+93)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (((a * b) <= (-4500000.0d0)) .or. (.not. ((a * b) <= 1.02d+93))) then
        tmp = a * b
    else
        tmp = 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 tmp;
	if (((a * b) <= -4500000.0) || !((a * b) <= 1.02e+93)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -4500000.0) or not ((a * b) <= 1.02e+93):
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -4500000.0) || !(Float64(a * b) <= 1.02e+93))
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -4500000.0) || ~(((a * b) <= 1.02e+93)))
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -4500000.0], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.02e+93]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.5e6 or 1.0200000000000001e93 < (*.f64 a b)

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 61.2%

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

   if -4.5e6 < (*.f64 a b) < 1.0200000000000001e93

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-/l* 80.8%

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

      3. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in z around inf 44.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4500000 \lor \neg \left(a \cdot b \leq 1.02 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (a * b) + ((x * y) + (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

   \[\leadsto a \cdot b + \left(x \cdot y + z \cdot t\right) \]
4. Add Preprocessing

Alternative 10: 34.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = a * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in a around inf 31.1%

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

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))