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

Percentage Accurate: 89.5% → 96.0%

Time: 14.0s

Alternatives: 14

Speedup: 0.6×

• 47.5% 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: 89.5% 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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot t\_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - t\_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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

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 ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(a * Float64(i * Float64(c / x))))));
	end
	return 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[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * N[(y - N[(a * N[(i * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. fma-define 94.6%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 46.7%

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

      1. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in z around 0 53.5%

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

   7. Taylor expanded in x around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

      3. associate-/l* 53.5%

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

      4. *-commutative 53.5%

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

      5. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

4. Final simplification 96.5%

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

Alternative 2: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t\_1\right)\\ t_3 := \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1700000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (* b c) i)))
        (t_2 (* 2.0 (- (* z t) t_1)))
        (t_3 (* (* c (* (+ a (* b c)) i)) -2.0)))
   (if (<= c -5.6e+122)
     t_3
     (if (<= c -2e+51)
       (* 2.0 (- (* x y) (* a (* c i))))
       (if (<= c -1700000000000.0)
         t_2
         (if (<= c -9.2e-23)
           (* 2.0 (- (* x y) t_1))
           (if (<= c 1.75e-22)
             (* (+ (* x y) (* z t)) 2.0)
             (if (<= c 1.05e+64)
               t_2
               (if (<= c 6.2e+181)
                 (* 2.0 (* x (- y (* a (* i (/ c x))))))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((b * c) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -5.6e+122) {
		tmp = t_3;
	} else if (c <= -2e+51) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= -1700000000000.0) {
		tmp = t_2;
	} else if (c <= -9.2e-23) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.75e-22) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 1.05e+64) {
		tmp = t_2;
	} else if (c <= 6.2e+181) {
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))));
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c * ((b * c) * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    t_3 = (c * ((a + (b * c)) * i)) * (-2.0d0)
    if (c <= (-5.6d+122)) then
        tmp = t_3
    else if (c <= (-2d+51)) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if (c <= (-1700000000000.0d0)) then
        tmp = t_2
    else if (c <= (-9.2d-23)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 1.75d-22) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 1.05d+64) then
        tmp = t_2
    else if (c <= 6.2d+181) then
        tmp = 2.0d0 * (x * (y - (a * (i * (c / x)))))
    else
        tmp = t_3
    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 * ((b * c) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -5.6e+122) {
		tmp = t_3;
	} else if (c <= -2e+51) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= -1700000000000.0) {
		tmp = t_2;
	} else if (c <= -9.2e-23) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.75e-22) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 1.05e+64) {
		tmp = t_2;
	} else if (c <= 6.2e+181) {
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((b * c) * i)
	t_2 = 2.0 * ((z * t) - t_1)
	t_3 = (c * ((a + (b * c)) * i)) * -2.0
	tmp = 0
	if c <= -5.6e+122:
		tmp = t_3
	elif c <= -2e+51:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif c <= -1700000000000.0:
		tmp = t_2
	elif c <= -9.2e-23:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 1.75e-22:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 1.05e+64:
		tmp = t_2
	elif c <= 6.2e+181:
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(b * c) * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	t_3 = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0)
	tmp = 0.0
	if (c <= -5.6e+122)
		tmp = t_3;
	elseif (c <= -2e+51)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (c <= -1700000000000.0)
		tmp = t_2;
	elseif (c <= -9.2e-23)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 1.75e-22)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 1.05e+64)
		tmp = t_2;
	elseif (c <= 6.2e+181)
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(a * Float64(i * Float64(c / x))))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((b * c) * i);
	t_2 = 2.0 * ((z * t) - t_1);
	t_3 = (c * ((a + (b * c)) * i)) * -2.0;
	tmp = 0.0;
	if (c <= -5.6e+122)
		tmp = t_3;
	elseif (c <= -2e+51)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif (c <= -1700000000000.0)
		tmp = t_2;
	elseif (c <= -9.2e-23)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 1.75e-22)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 1.05e+64)
		tmp = t_2;
	elseif (c <= 6.2e+181)
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -5.6e+122], t$95$3, If[LessEqual[c, -2e+51], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1700000000000.0], t$95$2, If[LessEqual[c, -9.2e-23], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-22], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 1.05e+64], t$95$2, If[LessEqual[c, 6.2e+181], N[(2.0 * N[(x * N[(y - N[(a * N[(i * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.5999999999999999e122 or 6.19999999999999978e181 < c

   1. Initial program 78.3%

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

   3. Taylor expanded in i around inf 87.0%

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

   4. Taylor expanded in i around 0 87.0%

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

   if -5.5999999999999999e122 < c < -2e51

   1. Initial program 48.3%

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

   3. Taylor expanded in a around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in z around 0 74.8%

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

   if -2e51 < c < -1.7e12 or 1.75000000000000003e-22 < c < 1.05e64

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in a around 0 81.7%

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

   if -1.7e12 < c < -9.2000000000000004e-23

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 80.4%

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

   4. Taylor expanded in a around 0 80.4%

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

   if -9.2000000000000004e-23 < c < 1.75000000000000003e-22

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0 79.6%

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

   if 1.05e64 < c < 6.19999999999999978e181

   1. Initial program 96.2%

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

   3. Taylor expanded in a around inf 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around 0 71.8%

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

   7. Taylor expanded in x around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. associate-/l* 71.8%

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

      4. *-commutative 71.8%

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

      5. associate-/l* 63.8%

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

   9. Simplified 63.8%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1700000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-22}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a + b \cdot c\\ t_3 := c \cdot t\_2\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t\_2 \cdot i\right)\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;\left(t\_1 - t\_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(c \cdot \left(b \cdot i + \frac{a \cdot i}{c}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ a (* b c))) (t_3 (* c t_2)))
   (if (<= t_3 (- INFINITY))
     (* 2.0 (- (* x y) (* c (* t_2 i))))
     (if (<= t_3 2e+149)
       (* (- t_1 (* t_3 i)) 2.0)
       (* 2.0 (- t_1 (* c (* c (+ (* b i) (/ (* a i) c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = c * t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	} else if (t_3 <= 2e+149) {
		tmp = (t_1 - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * (c * ((b * i) + ((a * i) / c)))));
	}
	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 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = c * t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	} else if (t_3 <= 2e+149) {
		tmp = (t_1 - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * (c * ((b * i) + ((a * i) / c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = a + (b * c)
	t_3 = c * t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)))
	elif t_3 <= 2e+149:
		tmp = (t_1 - (t_3 * i)) * 2.0
	else:
		tmp = 2.0 * (t_1 - (c * (c * ((b * i) + ((a * i) / c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(a + Float64(b * c))
	t_3 = Float64(c * t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_2 * i))));
	elseif (t_3 <= 2e+149)
		tmp = Float64(Float64(t_1 - Float64(t_3 * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(Float64(b * i) + Float64(Float64(a * i) / c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = a + (b * c);
	t_3 = c * t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 2.0 * ((x * y) - (c * (t_2 * i)));
	elseif (t_3 <= 2e+149)
		tmp = (t_1 - (t_3 * i)) * 2.0;
	else
		tmp = 2.0 * (t_1 - (c * (c * ((b * i) + ((a * i) / c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+149], N[(N[(t$95$1 - N[(t$95$3 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(N[(b * i), $MachinePrecision] + N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 72.8%

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

   3. Taylor expanded in z around 0 90.8%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 2.0000000000000001e149

   1. Initial program 98.3%

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

   if 2.0000000000000001e149 < (*.f64 (+.f64 a (*.f64 b c)) c)

   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. Add Preprocessing

   3. Taylor expanded in c around 0 85.0%

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

   4. Taylor expanded in c around inf 91.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 2 \cdot 10^{+149}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(b \cdot i + \frac{a \cdot i}{c}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.01 \cdot 10^{-19}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (* (+ a (* b c)) i)) -2.0)))
   (if (<= c -4.4e+95)
     t_1
     (if (<= c 1.01e-19)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 2.5e+64)
         (* 2.0 (- (* z t) (* c (* (* b c) i))))
         (if (<= c 1.25e+182) (* 2.0 (* x (- y (* a (* i (/ c 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 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -4.4e+95) {
		tmp = t_1;
	} else if (c <= 1.01e-19) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.5e+64) {
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)));
	} else if (c <= 1.25e+182) {
		tmp = 2.0 * (x * (y - (a * (i * (c / 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 = (c * ((a + (b * c)) * i)) * (-2.0d0)
    if (c <= (-4.4d+95)) then
        tmp = t_1
    else if (c <= 1.01d-19) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 2.5d+64) then
        tmp = 2.0d0 * ((z * t) - (c * ((b * c) * i)))
    else if (c <= 1.25d+182) then
        tmp = 2.0d0 * (x * (y - (a * (i * (c / 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 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -4.4e+95) {
		tmp = t_1;
	} else if (c <= 1.01e-19) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.5e+64) {
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)));
	} else if (c <= 1.25e+182) {
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * ((a + (b * c)) * i)) * -2.0
	tmp = 0
	if c <= -4.4e+95:
		tmp = t_1
	elif c <= 1.01e-19:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 2.5e+64:
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)))
	elif c <= 1.25e+182:
		tmp = 2.0 * (x * (y - (a * (i * (c / x)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0)
	tmp = 0.0
	if (c <= -4.4e+95)
		tmp = t_1;
	elseif (c <= 1.01e-19)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 2.5e+64)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(b * c) * i))));
	elseif (c <= 1.25e+182)
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(a * Float64(i * Float64(c / x))))));
	else
		tmp = 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)) * -2.0;
	tmp = 0.0;
	if (c <= -4.4e+95)
		tmp = t_1;
	elseif (c <= 1.01e-19)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 2.5e+64)
		tmp = 2.0 * ((z * t) - (c * ((b * c) * i)));
	elseif (c <= 1.25e+182)
		tmp = 2.0 * (x * (y - (a * (i * (c / 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[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -4.4e+95], t$95$1, If[LessEqual[c, 1.01e-19], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 2.5e+64], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e+182], N[(2.0 * N[(x * N[(y - N[(a * N[(i * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.3999999999999998e95 or 1.24999999999999993e182 < c

   1. Initial program 74.1%

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

   3. Taylor expanded in i around inf 84.0%

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

   4. Taylor expanded in i around 0 84.0%

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

   if -4.3999999999999998e95 < c < 1.00999999999999995e-19

   1. Initial program 95.6%

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

   3. Taylor expanded in c around 0 77.3%

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

   if 1.00999999999999995e-19 < c < 2.5e64

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 89.1%

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

   4. Taylor expanded in a around 0 80.8%

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

   if 2.5e64 < c < 1.24999999999999993e182

   1. Initial program 96.2%

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

   3. Taylor expanded in a around inf 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around 0 71.8%

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

   7. Taylor expanded in x around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. associate-/l* 71.8%

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

      4. *-commutative 71.8%

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

      5. associate-/l* 63.8%

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

   9. Simplified 63.8%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{+95}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 1.01 \cdot 10^{-19}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - a \cdot \left(i \cdot \frac{c}{x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -8 \cdot 10^{-83} \lor \neg \left(i \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;\left(t\_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -8e-83) (not (<= i 1.4e-47)))
     (* (- t_1 (* (* c (+ a (* b c))) i)) 2.0)
     (* 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 <= -8e-83) || !(i <= 1.4e-47)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} 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 <= (-8d-83)) .or. (.not. (i <= 1.4d-47))) then
        tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0d0
    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 <= -8e-83) || !(i <= 1.4e-47)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} 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 <= -8e-83) or not (i <= 1.4e-47):
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0
	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 <= -8e-83) || !(i <= 1.4e-47))
		tmp = Float64(Float64(t_1 - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	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 <= -8e-83) || ~((i <= 1.4e-47)))
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	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, -8e-83], N[Not[LessEqual[i, 1.4e-47]], $MachinePrecision]], N[(N[(t$95$1 - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $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 < -8.0000000000000003e-83 or 1.39999999999999996e-47 < i

   1. Initial program 94.0%

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

   if -8.0000000000000003e-83 < i < 1.39999999999999996e-47

   1. Initial program 83.0%

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

   3. Taylor expanded in c around 0 95.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{-83} \lor \neg \left(i \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_1 \leq 10^{+290}:\\ \;\;\;\;\left(t\_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t + x \cdot \frac{y}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= t_1 1e+290)
     (* (- t_1 (* (* c (+ a (* b c))) i)) 2.0)
     (* 2.0 (* z (+ t (* x (/ y z))))))))

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 (t_1 <= 1e+290) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (z * (t + (x * (y / z))));
	}
	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 (t_1 <= 1d+290) then
        tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0d0
    else
        tmp = 2.0d0 * (z * (t + (x * (y / z))))
    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 (t_1 <= 1e+290) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (z * (t + (x * (y / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if t_1 <= 1e+290:
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0
	else:
		tmp = 2.0 * (z * (t + (x * (y / z))))
	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 (t_1 <= 1e+290)
		tmp = Float64(Float64(t_1 - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * Float64(t + Float64(x * Float64(y / z)))));
	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 (t_1 <= 1e+290)
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	else
		tmp = 2.0 * (z * (t + (x * (y / z))));
	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[LessEqual[t$95$1, 1e+290], N[(N[(t$95$1 - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < 1.00000000000000006e290

   1. Initial program 92.5%

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

   if 1.00000000000000006e290 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 72.1%

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

   3. Taylor expanded in c around 0 90.7%

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

   4. Taylor expanded in z around inf 90.7%

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

      1. associate-/l* 93.0%

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

   6. Simplified 93.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq 10^{+290}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t + x \cdot \frac{y}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+47)
   (* 2.0 (- (* x y) (* c (* (* b c) i))))
   (if (<= (* x y) 5e+128)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* (+ (* x y) (* z t)) 2.0))))

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+47) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= 5e+128) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((x * y) <= (-1d+47)) then
        tmp = 2.0d0 * ((x * y) - (c * ((b * c) * i)))
    else if ((x * y) <= 5d+128) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 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 ((x * y) <= -1e+47) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= 5e+128) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+47:
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)))
	elif (x * y) <= 5e+128:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+47)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(b * c) * i))));
	elseif (Float64(x * y) <= 5e+128)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+47)
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	elseif ((x * y) <= 5e+128)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+47], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+128], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e47

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.7%

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

   4. Taylor expanded in a around 0 83.5%

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

   if -1e47 < (*.f64 x y) < 5e128

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0 85.6%

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

   if 5e128 < (*.f64 x y)

   1. Initial program 82.8%

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

   3. Taylor expanded in c around 0 85.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -1e+47)
     (* 2.0 (- (* x y) t_1))
     (if (<= (* x y) 5e+128)
       (* 2.0 (- (* z t) t_1))
       (* (+ (* x y) (* z t)) 2.0)))))

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 ((x * y) <= -1e+47) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 5e+128) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = ((x * y) + (z * t)) * 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 = c * ((a + (b * c)) * i)
    if ((x * y) <= (-1d+47)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((x * y) <= 5d+128) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = ((x * y) + (z * t)) * 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 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -1e+47) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 5e+128) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if (x * y) <= -1e+47:
		tmp = 2.0 * ((x * y) - t_1)
	elif (x * y) <= 5e+128:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	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 (Float64(x * y) <= -1e+47)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (Float64(x * y) <= 5e+128)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	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 ((x * y) <= -1e+47)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((x * y) <= 5e+128)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	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[N[(x * y), $MachinePrecision], -1e+47], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+128], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e47

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 85.7%

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

   if -1e47 < (*.f64 x y) < 5e128

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0 85.6%

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

   if 5e128 < (*.f64 x y)

   1. Initial program 82.8%

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

   3. Taylor expanded in c around 0 85.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -6.6 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 1.18 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -6.6e+100)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 1.18e-19)
       (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
       (* 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 <= -6.6e+100) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.18e-19) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} 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 <= (-6.6d+100)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 1.18d-19) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    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 <= -6.6e+100) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.18e-19) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} 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 <= -6.6e+100:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 1.18e-19:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	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 <= -6.6e+100)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 1.18e-19)
		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) - 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 <= -6.6e+100)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 1.18e-19)
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	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, -6.6e+100], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.18e-19], 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] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.6000000000000002e100

   1. Initial program 73.9%

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

   3. Taylor expanded in z around 0 86.8%

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

   if -6.6000000000000002e100 < c < 1.17999999999999993e-19

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 92.5%

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

   if 1.17999999999999993e-19 < c

   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 x around 0 86.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.18 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+95} \lor \neg \left(c \leq 39000000\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.6e+95) (not (<= c 39000000.0)))
   (* (* c (* (+ a (* b c)) i)) -2.0)
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.6e+95) || !(c <= 39000000.0)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((c <= (-8.6d+95)) .or. (.not. (c <= 39000000.0d0))) then
        tmp = (c * ((a + (b * c)) * i)) * (-2.0d0)
    else
        tmp = ((x * y) + (z * t)) * 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 ((c <= -8.6e+95) || !(c <= 39000000.0)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.6e+95) or not (c <= 39000000.0):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.6e+95) || !(c <= 39000000.0))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0);
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8.6e+95) || ~((c <= 39000000.0)))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.6e+95], N[Not[LessEqual[c, 39000000.0]], $MachinePrecision]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.6e95 or 3.9e7 < c

   1. Initial program 80.8%

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

   3. Taylor expanded in i around inf 77.9%

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

   4. Taylor expanded in i around 0 77.9%

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

   if -8.6e95 < c < 3.9e7

   1. Initial program 95.6%

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

   3. Taylor expanded in c around 0 77.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+95} \lor \neg \left(c \leq 39000000\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-202}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -1.6e-63)
     t_1
     (if (<= t -6.6e-202)
       (* (* a (* c i)) -2.0)
       (if (<= t 4e+105) (* (* x y) 2.0) 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 (t <= -1.6e-63) {
		tmp = t_1;
	} else if (t <= -6.6e-202) {
		tmp = (a * (c * i)) * -2.0;
	} else if (t <= 4e+105) {
		tmp = (x * y) * 2.0;
	} 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 (t <= (-1.6d-63)) then
        tmp = t_1
    else if (t <= (-6.6d-202)) then
        tmp = (a * (c * i)) * (-2.0d0)
    else if (t <= 4d+105) then
        tmp = (x * y) * 2.0d0
    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 (t <= -1.6e-63) {
		tmp = t_1;
	} else if (t <= -6.6e-202) {
		tmp = (a * (c * i)) * -2.0;
	} else if (t <= 4e+105) {
		tmp = (x * y) * 2.0;
	} 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 t <= -1.6e-63:
		tmp = t_1
	elif t <= -6.6e-202:
		tmp = (a * (c * i)) * -2.0
	elif t <= 4e+105:
		tmp = (x * y) * 2.0
	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 (t <= -1.6e-63)
		tmp = t_1;
	elseif (t <= -6.6e-202)
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	elseif (t <= 4e+105)
		tmp = Float64(Float64(x * y) * 2.0);
	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 (t <= -1.6e-63)
		tmp = t_1;
	elseif (t <= -6.6e-202)
		tmp = (a * (c * i)) * -2.0;
	elseif (t <= 4e+105)
		tmp = (x * y) * 2.0;
	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[t, -1.6e-63], t$95$1, If[LessEqual[t, -6.6e-202], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, 4e+105], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999994e-63 or 3.9999999999999998e105 < t

   1. Initial program 84.8%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -1.59999999999999994e-63 < t < -6.59999999999999979e-202

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. associate-*l* 31.9%

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

      4. *-commutative 31.9%

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

      5. distribute-rgt-neg-in 31.9%

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

      6. *-commutative 31.9%

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

      7. distribute-rgt-neg-in 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in c around 0 39.6%

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

   if -6.59999999999999979e-202 < t < 3.9999999999999998e105

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf 38.3%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-202}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+224} \lor \neg \left(i \leq 3 \cdot 10^{+108}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -5.4e+224) (not (<= i 3e+108)))
   (* (* a (* c i)) -2.0)
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.4e+224) || !(i <= 3e+108)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((i <= (-5.4d+224)) .or. (.not. (i <= 3d+108))) then
        tmp = (a * (c * i)) * (-2.0d0)
    else
        tmp = ((x * y) + (z * t)) * 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 ((i <= -5.4e+224) || !(i <= 3e+108)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -5.4e+224) or not (i <= 3e+108):
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -5.4e+224) || !(i <= 3e+108))
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -5.4e+224) || ~((i <= 3e+108)))
		tmp = (a * (c * i)) * -2.0;
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -5.4e+224], N[Not[LessEqual[i, 3e+108]], $MachinePrecision]], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.3999999999999997e224 or 2.99999999999999984e108 < i

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*l* 41.3%

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

      4. *-commutative 41.3%

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

      5. distribute-rgt-neg-in 41.3%

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

      6. *-commutative 41.3%

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

      7. distribute-rgt-neg-in 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in c around 0 58.3%

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

   if -5.3999999999999997e224 < i < 2.99999999999999984e108

   1. Initial program 88.9%

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

   3. Taylor expanded in c around 0 66.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+224} \lor \neg \left(i \leq 3 \cdot 10^{+108}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-117} \lor \neg \left(t \leq 2.4 \cdot 10^{+105}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -1.18e-117) (not (<= t 2.4e+105)))
   (* 2.0 (* z t))
   (* (* x y) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -1.18e-117) || !(t <= 2.4e+105)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 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 ((t <= (-1.18d-117)) .or. (.not. (t <= 2.4d+105))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (x * y) * 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 ((t <= -1.18e-117) || !(t <= 2.4e+105)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -1.18e-117) or not (t <= 2.4e+105):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -1.18e-117) || !(t <= 2.4e+105))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -1.18e-117) || ~((t <= 2.4e+105)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -1.18e-117], N[Not[LessEqual[t, 2.4e+105]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18e-117 or 2.39999999999999975e105 < t

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 48.6%

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

   if -1.18e-117 < t < 2.39999999999999975e105

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 37.1%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{-117} \lor \neg \left(t \leq 2.4 \cdot 10^{+105}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.7% 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 89.1%

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

3. Taylor expanded in z around inf 30.7%

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

4. Final simplification 30.7%

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

Developer target: 93.9% 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 2024078 
(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))))