Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.9% → 94.3%

Time: 14.0s

Alternatives: 13

Speedup: 0.7×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (fma(x, y, (z * t)) - ((a + (b * c)) * (c * i)));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

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

   1. fma-define 91.3%

      \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. associate-*l* 96.8%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

3. Simplified 96.8%

   \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -4.2 \cdot 10^{+70} \lor \neg \left(i \leq 5.8 \cdot 10^{-36}\right):\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -4.2e+70) (not (<= i 5.8e-36)))
     (* 2.0 (- t_1 (* i (* c (+ a (* b c))))))
     (* 2.0 (- t_1 (* c (+ (* a i) (* b (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -4.2e+70) || !(i <= 5.8e-36)) {
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	} else {
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((i <= (-4.2d+70)) .or. (.not. (i <= 5.8d-36))) then
        tmp = 2.0d0 * (t_1 - (i * (c * (a + (b * c)))))
    else
        tmp = 2.0d0 * (t_1 - (c * ((a * i) + (b * (c * i)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -4.2e+70) || !(i <= 5.8e-36)) {
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	} else {
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (i <= -4.2e+70) or not (i <= 5.8e-36):
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))))
	else:
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((i <= -4.2e+70) || !(i <= 5.8e-36))
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(a + Float64(b * c))))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(Float64(a * i) + Float64(b * Float64(c * i))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((i <= -4.2e+70) || ~((i <= 5.8e-36)))
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	else
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -4.2e+70], N[Not[LessEqual[i, 5.8e-36]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(N[(a * i), $MachinePrecision] + N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -4.20000000000000015e70 or 5.80000000000000026e-36 < i

   1. Initial program 96.0%

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

   if -4.20000000000000015e70 < i < 5.80000000000000026e-36

   1. Initial program 84.2%

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

   3. Taylor expanded in c around 0 96.8%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+70} \lor \neg \left(i \leq 5.8 \cdot 10^{-36}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{-220} \lor \neg \left(i \leq 5.2 \cdot 10^{-187}\right):\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -8.5e-220) (not (<= i 5.2e-187)))
     (* 2.0 (- t_1 (* i (* c (+ a (* b c))))))
     (* 2.0 (- t_1 (* c (* a i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -8.5e-220) || !(i <= 5.2e-187)) {
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	} else {
		tmp = 2.0 * (t_1 - (c * (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((i <= (-8.5d-220)) .or. (.not. (i <= 5.2d-187))) then
        tmp = 2.0d0 * (t_1 - (i * (c * (a + (b * c)))))
    else
        tmp = 2.0d0 * (t_1 - (c * (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -8.5e-220) || !(i <= 5.2e-187)) {
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	} else {
		tmp = 2.0 * (t_1 - (c * (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (i <= -8.5e-220) or not (i <= 5.2e-187):
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))))
	else:
		tmp = 2.0 * (t_1 - (c * (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((i <= -8.5e-220) || !(i <= 5.2e-187))
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(a + Float64(b * c))))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((i <= -8.5e-220) || ~((i <= 5.2e-187)))
		tmp = 2.0 * (t_1 - (i * (c * (a + (b * c)))));
	else
		tmp = 2.0 * (t_1 - (c * (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -8.5e-220], N[Not[LessEqual[i, 5.2e-187]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -8.4999999999999996e-220 or 5.1999999999999999e-187 < i

   1. Initial program 94.2%

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

   if -8.4999999999999996e-220 < i < 5.1999999999999999e-187

   1. Initial program 63.4%

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

   3. Taylor expanded in c around 0 100.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   4. Taylor expanded in a around inf 96.4%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{-220} \lor \neg \left(i \leq 5.2 \cdot 10^{-187}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 10^{-13}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+75) (not (<= (* x y) 1e-13)))
   (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+75) || !((x * y) <= 1e-13)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+75)) .or. (.not. ((x * y) <= 1d-13))) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+75) || !((x * y) <= 1e-13)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+75) or not ((x * y) <= 1e-13):
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+75) || !(Float64(x * y) <= 1e-13))
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+75) || ~(((x * y) <= 1e-13)))
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+75], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e-13]], $MachinePrecision]], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 1e-13 < (*.f64 x y)

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 84.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{a \cdot \left(c \cdot i\right)}\right) \]

   if -1.99999999999999985e75 < (*.f64 x y) < 1e-13

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 91.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 10^{-13}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(2 \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+205)
   (* y (* 2.0 x))
   (if (<= (* x y) 5e+176)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* t (* 2.0 (+ z (* x (/ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+205) {
		tmp = y * (2.0 * x);
	} else if ((x * y) <= 5e+176) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = t * (2.0 * (z + (x * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d+205)) then
        tmp = y * (2.0d0 * x)
    else if ((x * y) <= 5d+176) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = t * (2.0d0 * (z + (x * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+205) {
		tmp = y * (2.0 * x);
	} else if ((x * y) <= 5e+176) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = t * (2.0 * (z + (x * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+205:
		tmp = y * (2.0 * x)
	elif (x * y) <= 5e+176:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = t * (2.0 * (z + (x * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+205)
		tmp = Float64(y * Float64(2.0 * x));
	elseif (Float64(x * y) <= 5e+176)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(t * Float64(2.0 * Float64(z + Float64(x * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+205)
		tmp = y * (2.0 * x);
	elseif ((x * y) <= 5e+176)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = t * (2.0 * (z + (x * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+205], N[(y * N[(2.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+176], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(2.0 * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000002e205

   1. Initial program 79.4%

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

      1. associate--l+ 79.4%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 79.4%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 79.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 79.4%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 79.4%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 79.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 84.6%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 84.6%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 94.7%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 94.7%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 94.7%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.9%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 84.9%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 84.9%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

      4. *-commutative 84.9%

         \[\leadsto y \cdot \color{blue}{\left(2 \cdot x\right)} \]

   7. Simplified 84.9%

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot x\right)} \]

   if -1.00000000000000002e205 < (*.f64 x y) < 5e176

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 84.9%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if 5e176 < (*.f64 x y)

   1. Initial program 82.4%

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

   3. Taylor expanded in c around 0 89.6%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   4. Taylor expanded in t around inf 83.0%

      \[\leadsto \color{blue}{t \cdot \left(2 \cdot z + 2 \cdot \frac{x \cdot y}{t}\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out 83.0%

         \[\leadsto t \cdot \color{blue}{\left(2 \cdot \left(z + \frac{x \cdot y}{t}\right)\right)} \]

      2. associate-/l* 86.1%

         \[\leadsto t \cdot \left(2 \cdot \left(z + \color{blue}{x \cdot \frac{y}{t}}\right)\right) \]

   6. Simplified 86.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(2 \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+122} \lor \neg \left(a \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;2 \cdot \left(t\_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= a -4.1e+122) (not (<= a 1.85e+92)))
     (* 2.0 (- t_1 (* a (* c i))))
     (* 2.0 (- t_1 (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -4.1e+122) || !(a <= 1.85e+92)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a <= (-4.1d+122)) .or. (.not. (a <= 1.85d+92))) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -4.1e+122) || !(a <= 1.85e+92)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a <= -4.1e+122) or not (a <= 1.85e+92):
		tmp = 2.0 * (t_1 - (a * (c * i)))
	else:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((a <= -4.1e+122) || !(a <= 1.85e+92))
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a <= -4.1e+122) || ~((a <= 1.85e+92)))
		tmp = 2.0 * (t_1 - (a * (c * i)));
	else
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -4.1e+122], N[Not[LessEqual[a, 1.85e+92]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1000000000000002e122 or 1.84999999999999999e92 < a

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 89.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{a \cdot \left(c \cdot i\right)}\right) \]

   if -4.1000000000000002e122 < a < 1.84999999999999999e92

   1. Initial program 91.2%

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

   3. Taylor expanded in c around 0 94.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)}\right) \]

   4. Taylor expanded in a around 0 92.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+122} \lor \neg \left(a \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{-87} \lor \neg \left(c \leq 3.95 \cdot 10^{-22}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -9.6e-87) (not (<= c 3.95e-22)))
   (* (* c (* (+ a (* b c)) i)) -2.0)
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.6e-87) || !(c <= 3.95e-22)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-9.6d-87)) .or. (.not. (c <= 3.95d-22))) then
        tmp = (c * ((a + (b * c)) * i)) * (-2.0d0)
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.6e-87) || !(c <= 3.95e-22)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -9.6e-87) or not (c <= 3.95e-22):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -9.6e-87) || !(c <= 3.95e-22))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -9.6e-87) || ~((c <= 3.95e-22)))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -9.6e-87], N[Not[LessEqual[c, 3.95e-22]], $MachinePrecision]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.5999999999999998e-87 or 3.9499999999999999e-22 < c

   1. Initial program 85.1%

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

      1. associate--l+ 85.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 85.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 85.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 85.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 85.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 85.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 86.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 86.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 94.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 94.4%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 94.4%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 68.9%

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if -9.5999999999999998e-87 < c < 3.9499999999999999e-22

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 79.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{-87} \lor \neg \left(c \leq 3.95 \cdot 10^{-22}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot t\_1\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t\_1 \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -7.7e-87)
     (* 2.0 (* (* c t_1) (- i)))
     (if (<= c 5.6e-24)
       (* 2.0 (+ (* x y) (* z t)))
       (* (* c (* t_1 i)) -2.0)))))

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);
	double tmp;
	if (c <= -7.7e-87) {
		tmp = 2.0 * ((c * t_1) * -i);
	} else if (c <= 5.6e-24) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * (t_1 * i)) * -2.0;
	}
	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)
    if (c <= (-7.7d-87)) then
        tmp = 2.0d0 * ((c * t_1) * -i)
    else if (c <= 5.6d-24) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (c * (t_1 * i)) * (-2.0d0)
    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);
	double tmp;
	if (c <= -7.7e-87) {
		tmp = 2.0 * ((c * t_1) * -i);
	} else if (c <= 5.6e-24) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * (t_1 * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= -7.7e-87:
		tmp = 2.0 * ((c * t_1) * -i)
	elif c <= 5.6e-24:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (c * (t_1 * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (c <= -7.7e-87)
		tmp = Float64(2.0 * Float64(Float64(c * t_1) * Float64(-i)));
	elseif (c <= 5.6e-24)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * Float64(t_1 * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	tmp = 0.0;
	if (c <= -7.7e-87)
		tmp = 2.0 * ((c * t_1) * -i);
	elseif (c <= 5.6e-24)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (c * (t_1 * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.7e-87], N[(2.0 * N[(N[(c * t$95$1), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e-24], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.6999999999999998e-87

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 85.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in i around inf 81.6%

      \[\leadsto 2 \cdot \color{blue}{\left(i \cdot \left(\frac{t \cdot z}{i} - c \cdot \left(a + b \cdot c\right)\right)\right)} \]

   5. Taylor expanded in t around 0 71.6%

      \[\leadsto 2 \cdot \left(i \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)}\right) \]

   if -7.6999999999999998e-87 < c < 5.6000000000000003e-24

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 79.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 5.6000000000000003e-24 < c

   1. Initial program 77.8%

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

      1. associate--l+ 77.8%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 77.8%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 77.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 77.8%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 77.8%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 77.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 80.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 80.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 91.1%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 91.1%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 91.1%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 69.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.7 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-246}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -9.2e+14)
     t_1
     (if (<= z -2.85e-246)
       (* (* c i) (* a -2.0))
       (if (<= z 6.2e-100) (* y (* 2.0 x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -9.2e+14) {
		tmp = t_1;
	} else if (z <= -2.85e-246) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 6.2e-100) {
		tmp = y * (2.0 * x);
	} 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 = 2.0d0 * (z * t)
    if (z <= (-9.2d+14)) then
        tmp = t_1
    else if (z <= (-2.85d-246)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (z <= 6.2d-100) then
        tmp = y * (2.0d0 * x)
    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 = 2.0 * (z * t);
	double tmp;
	if (z <= -9.2e+14) {
		tmp = t_1;
	} else if (z <= -2.85e-246) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 6.2e-100) {
		tmp = y * (2.0 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -9.2e+14:
		tmp = t_1
	elif z <= -2.85e-246:
		tmp = (c * i) * (a * -2.0)
	elif z <= 6.2e-100:
		tmp = y * (2.0 * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -9.2e+14)
		tmp = t_1;
	elseif (z <= -2.85e-246)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (z <= 6.2e-100)
		tmp = Float64(y * Float64(2.0 * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -9.2e+14)
		tmp = t_1;
	elseif (z <= -2.85e-246)
		tmp = (c * i) * (a * -2.0);
	elseif (z <= 6.2e-100)
		tmp = y * (2.0 * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+14], t$95$1, If[LessEqual[z, -2.85e-246], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-100], N[(y * N[(2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2e14 or 6.1999999999999997e-100 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf 46.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -9.2e14 < z < -2.84999999999999994e-246

   1. Initial program 94.1%

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

      1. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 94.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 90.2%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 90.2%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 90.2%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 34.7%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(-2 \cdot a\right) \cdot \left(c \cdot i\right)} \]

   7. Simplified 34.7%

      \[\leadsto \color{blue}{\left(-2 \cdot a\right) \cdot \left(c \cdot i\right)} \]

   if -2.84999999999999994e-246 < z < 6.1999999999999997e-100

   1. Initial program 91.7%

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

      1. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 91.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 95.6%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 95.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 95.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 29.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 29.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

      4. *-commutative 29.4%

         \[\leadsto y \cdot \color{blue}{\left(2 \cdot x\right)} \]

   7. Simplified 29.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-246}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-248}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -2.8e+17)
     t_1
     (if (<= z -2.7e-248)
       (* -2.0 (* i (* a c)))
       (if (<= z 1.7e-94) (* y (* 2.0 x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -2.8e+17) {
		tmp = t_1;
	} else if (z <= -2.7e-248) {
		tmp = -2.0 * (i * (a * c));
	} else if (z <= 1.7e-94) {
		tmp = y * (2.0 * x);
	} 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 = 2.0d0 * (z * t)
    if (z <= (-2.8d+17)) then
        tmp = t_1
    else if (z <= (-2.7d-248)) then
        tmp = (-2.0d0) * (i * (a * c))
    else if (z <= 1.7d-94) then
        tmp = y * (2.0d0 * x)
    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 = 2.0 * (z * t);
	double tmp;
	if (z <= -2.8e+17) {
		tmp = t_1;
	} else if (z <= -2.7e-248) {
		tmp = -2.0 * (i * (a * c));
	} else if (z <= 1.7e-94) {
		tmp = y * (2.0 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -2.8e+17:
		tmp = t_1
	elif z <= -2.7e-248:
		tmp = -2.0 * (i * (a * c))
	elif z <= 1.7e-94:
		tmp = y * (2.0 * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -2.8e+17)
		tmp = t_1;
	elseif (z <= -2.7e-248)
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	elseif (z <= 1.7e-94)
		tmp = Float64(y * Float64(2.0 * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -2.8e+17)
		tmp = t_1;
	elseif (z <= -2.7e-248)
		tmp = -2.0 * (i * (a * c));
	elseif (z <= 1.7e-94)
		tmp = y * (2.0 * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+17], t$95$1, If[LessEqual[z, -2.7e-248], N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-94], N[(y * N[(2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e17 or 1.6999999999999999e-94 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf 46.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -2.8e17 < z < -2.7000000000000001e-248

   1. Initial program 94.1%

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

      1. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 94.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 94.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 94.1%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 90.2%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 90.2%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 90.2%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 34.7%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. *-commutative 34.7%

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      3. associate-*l* 31.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot a\right)\right)} \cdot -2 \]

      4. *-commutative 31.0%

         \[\leadsto \left(c \cdot \color{blue}{\left(a \cdot i\right)}\right) \cdot -2 \]

      5. associate-*r* 31.0%

         \[\leadsto \color{blue}{c \cdot \left(\left(a \cdot i\right) \cdot -2\right)} \]

      6. *-commutative 31.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot a\right)} \cdot -2\right) \]

      7. associate-*l* 31.0%

         \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(a \cdot -2\right)\right)} \]

   7. Simplified 31.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(a \cdot -2\right)\right)} \]

   8. Taylor expanded in c around 0 34.7%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto -2 \cdot \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \]

      2. associate-*r* 31.0%

         \[\leadsto -2 \cdot \color{blue}{\left(c \cdot \left(i \cdot a\right)\right)} \]

      3. *-commutative 31.0%

         \[\leadsto -2 \cdot \color{blue}{\left(\left(i \cdot a\right) \cdot c\right)} \]

      4. associate-*l* 34.7%

         \[\leadsto -2 \cdot \color{blue}{\left(i \cdot \left(a \cdot c\right)\right)} \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)} \]

   if -2.7000000000000001e-248 < z < 1.6999999999999999e-94

   1. Initial program 91.7%

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

      1. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 91.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 91.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 91.7%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 95.6%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 95.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 95.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 29.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 29.4%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 29.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

      4. *-commutative 29.4%

         \[\leadsto y \cdot \color{blue}{\left(2 \cdot x\right)} \]

   7. Simplified 29.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-248}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+248}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -4.2e+248)
   (* -2.0 (* i (* a c)))
   (if (<= a 6.8e+93) (* 2.0 (+ (* x y) (* z t))) (* (* c i) (* a -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -4.2e+248) {
		tmp = -2.0 * (i * (a * c));
	} else if (a <= 6.8e+93) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-4.2d+248)) then
        tmp = (-2.0d0) * (i * (a * c))
    else if (a <= 6.8d+93) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (c * i) * (a * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -4.2e+248) {
		tmp = -2.0 * (i * (a * c));
	} else if (a <= 6.8e+93) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -4.2e+248:
		tmp = -2.0 * (i * (a * c))
	elif a <= 6.8e+93:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (c * i) * (a * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -4.2e+248)
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	elseif (a <= 6.8e+93)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -4.2e+248)
		tmp = -2.0 * (i * (a * c));
	elseif (a <= 6.8e+93)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (c * i) * (a * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -4.2e+248], N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+93], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.19999999999999977e248

   1. Initial program 93.9%

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

      1. associate--l+ 93.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 93.9%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 93.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 93.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 93.9%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 93.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 99.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 99.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 89.1%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 89.1%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 89.1%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 65.3%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot i\right)\right) \cdot -2} \]

      2. *-commutative 65.3%

         \[\leadsto \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \cdot -2 \]

      3. associate-*l* 60.1%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot a\right)\right)} \cdot -2 \]

      4. *-commutative 60.1%

         \[\leadsto \left(c \cdot \color{blue}{\left(a \cdot i\right)}\right) \cdot -2 \]

      5. associate-*r* 60.1%

         \[\leadsto \color{blue}{c \cdot \left(\left(a \cdot i\right) \cdot -2\right)} \]

      6. *-commutative 60.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot a\right)} \cdot -2\right) \]

      7. associate-*l* 60.1%

         \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(a \cdot -2\right)\right)} \]

   7. Simplified 60.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(a \cdot -2\right)\right)} \]

   8. Taylor expanded in c around 0 65.3%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto -2 \cdot \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)} \]

      2. associate-*r* 60.1%

         \[\leadsto -2 \cdot \color{blue}{\left(c \cdot \left(i \cdot a\right)\right)} \]

      3. *-commutative 60.1%

         \[\leadsto -2 \cdot \color{blue}{\left(\left(i \cdot a\right) \cdot c\right)} \]

      4. associate-*l* 70.8%

         \[\leadsto -2 \cdot \color{blue}{\left(i \cdot \left(a \cdot c\right)\right)} \]

   10. Simplified 70.8%

       \[\leadsto \color{blue}{-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)} \]

   if -4.19999999999999977e248 < a < 6.8000000000000001e93

   1. Initial program 90.4%

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

   3. Taylor expanded in c around 0 60.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 6.8000000000000001e93 < a

   1. Initial program 87.6%

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

      1. associate--l+ 87.6%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 87.6%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 87.6%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 87.6%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 87.6%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 87.6%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 87.6%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 87.6%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 91.6%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 91.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 91.6%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 64.2%

      \[\leadsto \color{blue}{-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 64.2%

         \[\leadsto \color{blue}{\left(-2 \cdot a\right) \cdot \left(c \cdot i\right)} \]

   7. Simplified 64.2%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+248}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-49} \lor \neg \left(z \leq 3.7 \cdot 10^{-97}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -4.8e-49) (not (<= z 3.7e-97)))
   (* 2.0 (* z t))
   (* y (* 2.0 x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -4.8e-49) || !(z <= 3.7e-97)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = y * (2.0 * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-4.8d-49)) .or. (.not. (z <= 3.7d-97))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = y * (2.0d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -4.8e-49) || !(z <= 3.7e-97)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = y * (2.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -4.8e-49) or not (z <= 3.7e-97):
		tmp = 2.0 * (z * t)
	else:
		tmp = y * (2.0 * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -4.8e-49) || !(z <= 3.7e-97))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(y * Float64(2.0 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -4.8e-49) || ~((z <= 3.7e-97)))
		tmp = 2.0 * (z * t);
	else
		tmp = y * (2.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -4.8e-49], N[Not[LessEqual[z, 3.7e-97]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999985e-49 or 3.69999999999999976e-97 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in z around inf 45.4%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -4.79999999999999985e-49 < z < 3.69999999999999976e-97

   1. Initial program 91.9%

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

      1. associate--l+ 91.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. *-commutative 91.9%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{t \cdot z} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      3. associate--l+ 91.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + t \cdot z\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      4. associate--l+ 91.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(t \cdot z - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      5. *-commutative 91.9%

         \[\leadsto 2 \cdot \left(x \cdot y + \left(\color{blue}{z \cdot t} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right) \]

      6. associate--l+ 91.9%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} \]

      7. fma-define 91.9%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      8. *-commutative 91.9%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      9. associate-*l* 94.0%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

      10. +-commutative 94.0%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot i\right)\right) \]

      11. fma-define 94.0%

          \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot i\right)\right) \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 28.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 28.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 2} \]

      2. *-commutative 28.7%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 2 \]

      3. associate-*r* 28.7%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]

      4. *-commutative 28.7%

         \[\leadsto y \cdot \color{blue}{\left(2 \cdot x\right)} \]

   7. Simplified 28.7%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-49} \lor \neg \left(z \leq 3.7 \cdot 10^{-97}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

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 = 2.0d0 * (z * t)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (z * t)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(z * t))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (z * t);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

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

3. Taylor expanded in z around inf 33.7%

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

4. Final simplification 33.7%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
5. Add Preprocessing

Developer Target 1: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (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 = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (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 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024123 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))