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

Percentage Accurate: 89.7% → 93.8%

Time: 15.1s

Alternatives: 14

Speedup: 1.0×

• 48.4% 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: 89.7% 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: 93.8% 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]

Derivation

1. Initial program 90.9%

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

   1. associate-*l* 97.6%

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

4. Applied egg-rr 97.6%

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

Alternative 2: 93.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := c \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* c t_1)))
   (if (<= t_3 (- INFINITY))
     (* 2.0 (- (* x y) t_2))
     (if (<= t_3 5e+261)
       (* 2.0 (- (+ (* x y) (* z t)) (* i t_3)))
       (* 2.0 (- (* z t) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (t_3 <= 5e+261) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_3));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (t_3 <= 5e+261) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_3));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = c * t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 2.0 * ((x * y) - t_2)
	elif t_3 <= 5e+261:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_3))
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(c * t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	elseif (t_3 <= 5e+261)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * t_3)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	t_3 = c * t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 2.0 * ((x * y) - t_2);
	elseif (t_3 <= 5e+261)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_3));
	else
		tmp = 2.0 * ((z * t) - t_2);
	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]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+261], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -inf.0

   1. Initial program 68.3%

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

   3. Taylor expanded in z around 0 86.2%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 5.0000000000000001e261

   1. Initial program 99.9%

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

   if 5.0000000000000001e261 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 97.1%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 5 \cdot 10^{+261}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{if}\;c \leq -1.58 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 10^{-108}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))) (t_2 (* 2.0 (- (* z t) t_1))))
   (if (<= c -1.58e-86)
     t_2
     (if (<= c 1e-108)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 7.6e+61) (* 2.0 (- (* x y) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -1.58e-86) {
		tmp = t_2;
	} else if (c <= 1e-108) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 7.6e+61) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    if (c <= (-1.58d-86)) then
        tmp = t_2
    else if (c <= 1d-108) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 7.6d+61) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -1.58e-86) {
		tmp = t_2;
	} else if (c <= 1e-108) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 7.6e+61) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((z * t) - t_1)
	tmp = 0
	if c <= -1.58e-86:
		tmp = t_2
	elif c <= 1e-108:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 7.6e+61:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	tmp = 0.0
	if (c <= -1.58e-86)
		tmp = t_2;
	elseif (c <= 1e-108)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 7.6e+61)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = 2.0 * ((z * t) - t_1);
	tmp = 0.0;
	if (c <= -1.58e-86)
		tmp = t_2;
	elseif (c <= 1e-108)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 7.6e+61)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.58e-86], t$95$2, If[LessEqual[c, 1e-108], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+61], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.58000000000000007e-86 or 7.5999999999999999e61 < c

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 86.7%

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

   if -1.58000000000000007e-86 < c < 1.00000000000000004e-108

   1. Initial program 100.0%

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

   3. Taylor expanded in c around 0 91.6%

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

   if 1.00000000000000004e-108 < c < 7.5999999999999999e61

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 83.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.58 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 10^{-108}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-39}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6.7 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= (* x y) -1.6e+89)
     t_1
     (if (<= (* x y) -3.9e-39)
       (* -2.0 (* a (* c i)))
       (if (<= (* x y) 6.7e+16) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -1.6e+89) {
		tmp = t_1;
	} else if ((x * y) <= -3.9e-39) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 6.7e+16) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if ((x * y) <= (-1.6d+89)) then
        tmp = t_1
    else if ((x * y) <= (-3.9d-39)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if ((x * y) <= 6.7d+16) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -1.6e+89) {
		tmp = t_1;
	} else if ((x * y) <= -3.9e-39) {
		tmp = -2.0 * (a * (c * i));
	} else if ((x * y) <= 6.7e+16) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -1.6e+89:
		tmp = t_1
	elif (x * y) <= -3.9e-39:
		tmp = -2.0 * (a * (c * i))
	elif (x * y) <= 6.7e+16:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.6e+89)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.9e-39)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (Float64(x * y) <= 6.7e+16)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.6e+89)
		tmp = t_1;
	elseif ((x * y) <= -3.9e-39)
		tmp = -2.0 * (a * (c * i));
	elseif ((x * y) <= 6.7e+16)
		tmp = 2.0 * (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.6e+89], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.9e-39], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.7e+16], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.59999999999999994e89 or 6.7e16 < (*.f64 x y)

   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 x around inf 58.7%

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

   if -1.59999999999999994e89 < (*.f64 x y) < -3.9000000000000003e-39

   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 x around 0 73.7%

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

   4. Taylor expanded in a around inf 39.3%

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

      1. *-commutative 39.3%

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

   6. Simplified 39.3%

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

   if -3.9000000000000003e-39 < (*.f64 x y) < 6.7e16

   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 z around inf 44.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq -3.9 \cdot 10^{-39}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6.7 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{+15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= (* x y) -1.7e+70)
     t_1
     (if (<= (* x y) -4.2e-42)
       (* c (* -2.0 (* a i)))
       (if (<= (* x y) 1.15e+15) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -1.7e+70) {
		tmp = t_1;
	} else if ((x * y) <= -4.2e-42) {
		tmp = c * (-2.0 * (a * i));
	} else if ((x * y) <= 1.15e+15) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if ((x * y) <= (-1.7d+70)) then
        tmp = t_1
    else if ((x * y) <= (-4.2d-42)) then
        tmp = c * ((-2.0d0) * (a * i))
    else if ((x * y) <= 1.15d+15) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -1.7e+70) {
		tmp = t_1;
	} else if ((x * y) <= -4.2e-42) {
		tmp = c * (-2.0 * (a * i));
	} else if ((x * y) <= 1.15e+15) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -1.7e+70:
		tmp = t_1
	elif (x * y) <= -4.2e-42:
		tmp = c * (-2.0 * (a * i))
	elif (x * y) <= 1.15e+15:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.7e+70)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.2e-42)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	elseif (Float64(x * y) <= 1.15e+15)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.7e+70)
		tmp = t_1;
	elseif ((x * y) <= -4.2e-42)
		tmp = c * (-2.0 * (a * i));
	elseif ((x * y) <= 1.15e+15)
		tmp = 2.0 * (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.7e+70], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.2e-42], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.15e+15], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.7e70 or 1.15e15 < (*.f64 x y)

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 57.2%

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

   if -1.7e70 < (*.f64 x y) < -4.20000000000000013e-42

   1. Initial program 86.3%

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

   3. Taylor expanded in x around 0 81.9%

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

   4. Taylor expanded in t around 0 64.8%

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

   5. Taylor expanded in c around 0 39.4%

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

      1. *-commutative 39.4%

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

      2. associate-*r* 39.3%

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

      3. associate-*l* 39.3%

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

      4. *-commutative 39.3%

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

      5. associate-*r* 39.3%

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

      6. *-commutative 39.3%

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

   7. Simplified 39.3%

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

   if -4.20000000000000013e-42 < (*.f64 x y) < 1.15e15

   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 z around inf 44.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{+15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-86} \lor \neg \left(c \leq 5.4 \cdot 10^{+63}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.5e-86) (not (<= c 5.4e+63)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 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 <= -3.5e-86) || !(c <= 5.4e+63)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} 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 <= (-3.5d-86)) .or. (.not. (c <= 5.4d+63))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    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 <= -3.5e-86) || !(c <= 5.4e+63)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} 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 <= -3.5e-86) or not (c <= 5.4e+63):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	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 <= -3.5e-86) || !(c <= 5.4e+63))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	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 <= -3.5e-86) || ~((c <= 5.4e+63)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	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, -3.5e-86], N[Not[LessEqual[c, 5.4e+63]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 < -3.50000000000000021e-86 or 5.40000000000000035e63 < c

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 87.1%

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

   if -3.50000000000000021e-86 < c < 5.40000000000000035e63

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 83.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-86} \lor \neg \left(c \leq 5.4 \cdot 10^{+63}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+112}:\\ \;\;\;\;t\_1 \cdot -2\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -5e+112)
     (* t_1 -2.0)
     (if (<= c 2.25e+66)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5e+112) {
		tmp = t_1 * -2.0;
	} else if (c <= 2.25e+66) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - 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 = c * ((a + (b * c)) * i)
    if (c <= (-5d+112)) then
        tmp = t_1 * (-2.0d0)
    else if (c <= 2.25d+66) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5e+112) {
		tmp = t_1 * -2.0;
	} else if (c <= 2.25e+66) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -5e+112:
		tmp = t_1 * -2.0
	elif c <= 2.25e+66:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -5e+112)
		tmp = Float64(t_1 * -2.0);
	elseif (c <= 2.25e+66)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -5e+112)
		tmp = t_1 * -2.0;
	elseif (c <= 2.25e+66)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e+112], N[(t$95$1 * -2.0), $MachinePrecision], If[LessEqual[c, 2.25e+66], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5e112

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 94.6%

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

   4. Taylor expanded in t around 0 94.8%

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

   if -5e112 < c < 2.2499999999999999e66

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 91.6%

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

      1. *-commutative 91.6%

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

   5. Simplified 91.6%

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

   if 2.2499999999999999e66 < c

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0 92.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+112}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+66}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+181} \lor \neg \left(c \leq -1.15 \cdot 10^{+77}\right) \land c \leq 5 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.2e+181) (and (not (<= c -1.15e+77)) (<= c 5e+168)))
   (* 2.0 (+ (* x y) (* z t)))
   (* -2.0 (* a (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.2e+181) || (!(c <= -1.15e+77) && (c <= 5e+168))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (a * (c * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.2d+181)) .or. (.not. (c <= (-1.15d+77))) .and. (c <= 5d+168)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * (a * (c * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.2e+181) || (!(c <= -1.15e+77) && (c <= 5e+168))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * (a * (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.2e+181) or (not (c <= -1.15e+77) and (c <= 5e+168)):
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * (a * (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.2e+181) || (!(c <= -1.15e+77) && (c <= 5e+168)))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.2e+181) || (~((c <= -1.15e+77)) && (c <= 5e+168)))
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * (a * (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.2e+181], And[N[Not[LessEqual[c, -1.15e+77]], $MachinePrecision], LessEqual[c, 5e+168]]], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.2000000000000001e181 or -1.14999999999999997e77 < c < 4.99999999999999967e168

   1. Initial program 93.8%

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

   3. Taylor expanded in c around 0 68.4%

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

   if -2.2000000000000001e181 < c < -1.14999999999999997e77 or 4.99999999999999967e168 < c

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 93.5%

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

   4. Taylor expanded in a around inf 47.7%

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

      1. *-commutative 47.7%

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

   6. Simplified 47.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+181} \lor \neg \left(c \leq -1.15 \cdot 10^{+77}\right) \land c \leq 5 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;\left(c \cdot \left(t\_1 \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+79}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -1.8e+74)
     (* (* c (* t_1 i)) -2.0)
     (if (<= c 8.4e+79)
       (* 2.0 (+ (* x y) (* z t)))
       (* 2.0 (* t_1 (* c (- i))))))))

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 <= -1.8e+74) {
		tmp = (c * (t_1 * i)) * -2.0;
	} else if (c <= 8.4e+79) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * (t_1 * (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 = a + (b * c)
    if (c <= (-1.8d+74)) then
        tmp = (c * (t_1 * i)) * (-2.0d0)
    else if (c <= 8.4d+79) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * (t_1 * (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 = a + (b * c);
	double tmp;
	if (c <= -1.8e+74) {
		tmp = (c * (t_1 * i)) * -2.0;
	} else if (c <= 8.4e+79) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * (t_1 * (c * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= -1.8e+74:
		tmp = (c * (t_1 * i)) * -2.0
	elif c <= 8.4e+79:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * (t_1 * (c * -i))
	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 <= -1.8e+74)
		tmp = Float64(Float64(c * Float64(t_1 * i)) * -2.0);
	elseif (c <= 8.4e+79)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(t_1 * Float64(c * Float64(-i))));
	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 <= -1.8e+74)
		tmp = (c * (t_1 * i)) * -2.0;
	elseif (c <= 8.4e+79)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * (t_1 * (c * -i));
	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, -1.8e+74], N[(N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[c, 8.4e+79], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.79999999999999994e74

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0 92.7%

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

   4. Taylor expanded in t around 0 90.6%

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

   if -1.79999999999999994e74 < c < 8.40000000000000032e79

   1. Initial program 98.1%

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

   3. Taylor expanded in c around 0 78.1%

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

   if 8.40000000000000032e79 < c

   1. Initial program 77.3%

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

      1. associate-*l* 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in i around inf 79.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 79.2%

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

      2. associate-*r* 79.2%

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

      3. distribute-rgt-neg-in 79.2%

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

      4. sub0-neg 79.2%

         \[\leadsto 2 \cdot \left(\left(c \cdot i\right) \cdot \color{blue}{\left(0 - \left(a + b \cdot c\right)\right)}\right) \]

      5. associate--r+ 79.2%

         \[\leadsto 2 \cdot \left(\left(c \cdot i\right) \cdot \color{blue}{\left(\left(0 - a\right) - b \cdot c\right)}\right) \]

      6. neg-sub0 79.2%

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

   7. Simplified 79.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+74}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+79}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b \cdot c\right) \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+70} \lor \neg \left(c \leq 3.7 \cdot 10^{+79}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -7.2e+70) (not (<= c 3.7e+79)))
   (* (* 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 <= -7.2e+70) || !(c <= 3.7e+79)) {
		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 <= (-7.2d+70)) .or. (.not. (c <= 3.7d+79))) 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 <= -7.2e+70) || !(c <= 3.7e+79)) {
		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 <= -7.2e+70) or not (c <= 3.7e+79):
		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 <= -7.2e+70) || !(c <= 3.7e+79))
		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 <= -7.2e+70) || ~((c <= 3.7e+79)))
		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, -7.2e+70], N[Not[LessEqual[c, 3.7e+79]], $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 < -7.1999999999999999e70 or 3.70000000000000009e79 < c

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 92.5%

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

   4. Taylor expanded in t around 0 84.1%

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

   if -7.1999999999999999e70 < c < 3.70000000000000009e79

   1. Initial program 98.1%

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

   3. Taylor expanded in c around 0 78.1%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+70} \lor \neg \left(c \leq 3.7 \cdot 10^{+79}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+116} \lor \neg \left(c \leq 3.8 \cdot 10^{+103}\right):\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(c \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6.2e+116) (not (<= c 3.8e+103)))
   (* (* b -2.0) (* c (* c i)))
   (* 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 <= -6.2e+116) || !(c <= 3.8e+103)) {
		tmp = (b * -2.0) * (c * (c * i));
	} 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 <= (-6.2d+116)) .or. (.not. (c <= 3.8d+103))) then
        tmp = (b * (-2.0d0)) * (c * (c * i))
    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 <= -6.2e+116) || !(c <= 3.8e+103)) {
		tmp = (b * -2.0) * (c * (c * i));
	} 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 <= -6.2e+116) or not (c <= 3.8e+103):
		tmp = (b * -2.0) * (c * (c * i))
	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 <= -6.2e+116) || !(c <= 3.8e+103))
		tmp = Float64(Float64(b * -2.0) * Float64(c * Float64(c * i)));
	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 <= -6.2e+116) || ~((c <= 3.8e+103)))
		tmp = (b * -2.0) * (c * (c * i));
	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, -6.2e+116], N[Not[LessEqual[c, 3.8e+103]], $MachinePrecision]], N[(N[(b * -2.0), $MachinePrecision] * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $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 < -6.19999999999999992e116 or 3.7999999999999997e103 < c

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in c around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. unpow2 59.9%

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

      3. associate-*l* 62.9%

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

   6. Simplified 62.9%

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

   if -6.19999999999999992e116 < c < 3.7999999999999997e103

   1. Initial program 96.5%

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

   3. Taylor expanded in c around 0 76.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+116} \lor \neg \left(c \leq 3.8 \cdot 10^{+103}\right):\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(c \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+69} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -3.8e+69) (not (<= (* x y) 3.1e+14)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -3.8e+69) || !((x * y) <= 3.1e+14)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-3.8d+69)) .or. (.not. ((x * y) <= 3.1d+14))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -3.8e+69) || !((x * y) <= 3.1e+14)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -3.8e+69) or not ((x * y) <= 3.1e+14):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -3.8e+69) || !(Float64(x * y) <= 3.1e+14))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -3.8e+69) || ~(((x * y) <= 3.1e+14)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.8e+69], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.1e+14]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.80000000000000028e69 or 3.1e14 < (*.f64 x y)

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 56.8%

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

   if -3.80000000000000028e69 < (*.f64 x y) < 3.1e14

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf 40.0%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+69} \lor \neg \left(x \cdot y \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+115}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(c \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.6e+115)
   (* (* c i) (* c (* b -2.0)))
   (if (<= c 6.5e+103)
     (* 2.0 (+ (* x y) (* z t)))
     (* (* b -2.0) (* c (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.6e+115) {
		tmp = (c * i) * (c * (b * -2.0));
	} else if (c <= 6.5e+103) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (b * -2.0) * (c * (c * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.6d+115)) then
        tmp = (c * i) * (c * (b * (-2.0d0)))
    else if (c <= 6.5d+103) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (b * (-2.0d0)) * (c * (c * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.6e+115) {
		tmp = (c * i) * (c * (b * -2.0));
	} else if (c <= 6.5e+103) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (b * -2.0) * (c * (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.6e+115:
		tmp = (c * i) * (c * (b * -2.0))
	elif c <= 6.5e+103:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (b * -2.0) * (c * (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.6e+115)
		tmp = Float64(Float64(c * i) * Float64(c * Float64(b * -2.0)));
	elseif (c <= 6.5e+103)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(b * -2.0) * Float64(c * Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.6e+115)
		tmp = (c * i) * (c * (b * -2.0));
	elseif (c <= 6.5e+103)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (b * -2.0) * (c * (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.6e+115], N[(N[(c * i), $MachinePrecision] * N[(c * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+103], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * -2.0), $MachinePrecision] * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.6e115

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 94.6%

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

   4. Taylor expanded in c around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. unpow2 67.2%

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

      3. associate-*l* 69.6%

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

   6. Simplified 69.6%

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

      1. associate-*r* 81.6%

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

      2. *-commutative 81.6%

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

   8. Applied egg-rr 81.6%

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

   if -1.6e115 < c < 6.50000000000000001e103

   1. Initial program 96.5%

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

   3. Taylor expanded in c around 0 76.5%

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

   if 6.50000000000000001e103 < c

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 91.5%

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

   4. Taylor expanded in c around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. unpow2 54.2%

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

      3. associate-*l* 57.6%

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

   6. Simplified 57.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+115}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(c \cdot \left(b \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(c \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.3% 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 90.9%

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

3. Taylor expanded in z around inf 29.9%

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

4. Final simplification 29.9%

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

Developer target: 93.8% 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 2024097 
(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
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

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