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

Percentage Accurate: 90.3% → 96.2%

Time: 13.6s

Alternatives: 11

Speedup: 0.6×

• 48.2% 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: 90.3% 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: 96.2% accurate, 0.1× speedup

Math

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

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 (* z (- t (* a (/ (* c i) z))))))))

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 * (z * (t - (a * ((c * i) / z))));
	}
	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(z * Float64(t - Float64(a * Float64(Float64(c * i) / z)))));
	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[(z * N[(t - N[(a * N[(N[(c * i), $MachinePrecision] / z), $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 95.0%

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

      1. fma-define 95.0%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   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 33.3%

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

      1. *-commutative 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in x around 0 34.4%

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

   7. Taylor expanded in z around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. associate-/l* 84.4%

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

   9. Simplified 84.4%

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

4. Final simplification 98.1%

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

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + z \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-40}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-24} \lor \neg \left(c \leq 1.45 \cdot 10^{+107}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(2 \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.15e+162)
     t_1
     (if (<= c -2.1e+138)
       (* y (* 2.0 (+ x (* z (/ t y)))))
       (if (<= c -4e-40)
         t_1
         (if (<= c 3.8e-40)
           (* (+ (* x y) (* z t)) 2.0)
           (if (or (<= c 2.45e-24) (not (<= c 1.45e+107)))
             t_1
             (* t (* 2.0 (+ z (* x (/ y t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.15e+162) {
		tmp = t_1;
	} else if (c <= -2.1e+138) {
		tmp = y * (2.0 * (x + (z * (t / y))));
	} else if (c <= -4e-40) {
		tmp = t_1;
	} else if (c <= 3.8e-40) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((c <= 2.45e-24) || !(c <= 1.45e+107)) {
		tmp = t_1;
	} else {
		tmp = t * (2.0 * (z + (x * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.15d+162)) then
        tmp = t_1
    else if (c <= (-2.1d+138)) then
        tmp = y * (2.0d0 * (x + (z * (t / y))))
    else if (c <= (-4d-40)) then
        tmp = t_1
    else if (c <= 3.8d-40) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((c <= 2.45d-24) .or. (.not. (c <= 1.45d+107))) then
        tmp = t_1
    else
        tmp = t * (2.0d0 * (z + (x * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.15e+162) {
		tmp = t_1;
	} else if (c <= -2.1e+138) {
		tmp = y * (2.0 * (x + (z * (t / y))));
	} else if (c <= -4e-40) {
		tmp = t_1;
	} else if (c <= 3.8e-40) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((c <= 2.45e-24) || !(c <= 1.45e+107)) {
		tmp = t_1;
	} else {
		tmp = t * (2.0 * (z + (x * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.15e+162:
		tmp = t_1
	elif c <= -2.1e+138:
		tmp = y * (2.0 * (x + (z * (t / y))))
	elif c <= -4e-40:
		tmp = t_1
	elif c <= 3.8e-40:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (c <= 2.45e-24) or not (c <= 1.45e+107):
		tmp = t_1
	else:
		tmp = t * (2.0 * (z + (x * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.15e+162)
		tmp = t_1;
	elseif (c <= -2.1e+138)
		tmp = Float64(y * Float64(2.0 * Float64(x + Float64(z * Float64(t / y)))));
	elseif (c <= -4e-40)
		tmp = t_1;
	elseif (c <= 3.8e-40)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif ((c <= 2.45e-24) || !(c <= 1.45e+107))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(2.0 * Float64(z + Float64(x * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.15e+162)
		tmp = t_1;
	elseif (c <= -2.1e+138)
		tmp = y * (2.0 * (x + (z * (t / y))));
	elseif (c <= -4e-40)
		tmp = t_1;
	elseif (c <= 3.8e-40)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((c <= 2.45e-24) || ~((c <= 1.45e+107)))
		tmp = t_1;
	else
		tmp = t * (2.0 * (z + (x * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+162], t$95$1, If[LessEqual[c, -2.1e+138], N[(y * N[(2.0 * N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-40], t$95$1, If[LessEqual[c, 3.8e-40], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[Or[LessEqual[c, 2.45e-24], N[Not[LessEqual[c, 1.45e+107]], $MachinePrecision]], t$95$1, N[(t * N[(2.0 * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.14999999999999997e162 or -2.10000000000000007e138 < c < -3.9999999999999997e-40 or 3.7999999999999999e-40 < c < 2.45e-24 or 1.44999999999999994e107 < c

   1. Initial program 87.4%

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

   3. Taylor expanded in c around 0 89.7%

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

   4. Taylor expanded in i around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-*r* 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. mul-1-neg 84.4%

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

      5. distribute-lft-out 84.4%

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

      6. associate-*r* 86.1%

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

      7. *-commutative 86.1%

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

      8. distribute-lft-out 86.1%

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

      9. mul-1-neg 86.1%

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

      10. distribute-lft-neg-in 86.1%

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

      11. distribute-rgt-neg-in 86.1%

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

      12. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   if -1.14999999999999997e162 < c < -2.10000000000000007e138

   1. Initial program 75.6%

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

   3. Taylor expanded in c around 0 75.6%

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

   4. Taylor expanded in y around inf 75.2%

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

      1. distribute-lft-out 75.2%

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

      2. associate-/l* 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in t around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-/l* 63.1%

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

   9. Simplified 63.1%

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

   if -3.9999999999999997e-40 < c < 3.7999999999999999e-40

   1. Initial program 99.0%

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

   3. Taylor expanded in c around 0 83.9%

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

   if 2.45e-24 < c < 1.44999999999999994e107

   1. Initial program 93.6%

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

   3. Taylor expanded in c around 0 71.3%

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

   4. Taylor expanded in t around inf 71.3%

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

      1. distribute-lft-out 71.3%

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

      2. associate-/l* 74.4%

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

   6. Simplified 74.4%

      \[\leadsto \color{blue}{t \cdot \left(2 \cdot \left(z + x \cdot \frac{y}{t}\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+162}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + z \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-40}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-24} \lor \neg \left(c \leq 1.45 \cdot 10^{+107}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(2 \cdot \left(z + x \cdot \frac{y}{t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + z \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{+94} \lor \neg \left(c \leq 5.8 \cdot 10^{+106}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.15e+162)
     t_1
     (if (<= c -2.1e+138)
       (* y (* 2.0 (+ x (* z (/ t y)))))
       (if (or (<= c -7e+94) (not (<= c 5.8e+106)))
         t_1
         (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.15e+162) {
		tmp = t_1;
	} else if (c <= -2.1e+138) {
		tmp = y * (2.0 * (x + (z * (t / y))));
	} else if ((c <= -7e+94) || !(c <= 5.8e+106)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	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 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.15d+162)) then
        tmp = t_1
    else if (c <= (-2.1d+138)) then
        tmp = y * (2.0d0 * (x + (z * (t / y))))
    else if ((c <= (-7d+94)) .or. (.not. (c <= 5.8d+106))) then
        tmp = t_1
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    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 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.15e+162) {
		tmp = t_1;
	} else if (c <= -2.1e+138) {
		tmp = y * (2.0 * (x + (z * (t / y))));
	} else if ((c <= -7e+94) || !(c <= 5.8e+106)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.15e+162:
		tmp = t_1
	elif c <= -2.1e+138:
		tmp = y * (2.0 * (x + (z * (t / y))))
	elif (c <= -7e+94) or not (c <= 5.8e+106):
		tmp = t_1
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.15e+162)
		tmp = t_1;
	elseif (c <= -2.1e+138)
		tmp = Float64(y * Float64(2.0 * Float64(x + Float64(z * Float64(t / y)))));
	elseif ((c <= -7e+94) || !(c <= 5.8e+106))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.15e+162)
		tmp = t_1;
	elseif (c <= -2.1e+138)
		tmp = y * (2.0 * (x + (z * (t / y))));
	elseif ((c <= -7e+94) || ~((c <= 5.8e+106)))
		tmp = t_1;
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+162], t$95$1, If[LessEqual[c, -2.1e+138], N[(y * N[(2.0 * N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -7e+94], N[Not[LessEqual[c, 5.8e+106]], $MachinePrecision]], t$95$1, N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.14999999999999997e162 or -2.10000000000000007e138 < c < -6.9999999999999994e94 or 5.8000000000000004e106 < c

   1. Initial program 84.6%

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

   3. Taylor expanded in c around 0 87.6%

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

   4. Taylor expanded in i around inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*r* 88.0%

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

      3. distribute-rgt-neg-in 88.0%

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

      4. mul-1-neg 88.0%

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

      5. distribute-lft-out 88.0%

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

      6. associate-*r* 90.3%

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

      7. *-commutative 90.3%

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

      8. distribute-lft-out 90.3%

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

      9. mul-1-neg 90.3%

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

      10. distribute-lft-neg-in 90.3%

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

      11. distribute-rgt-neg-in 90.3%

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

      12. *-commutative 90.3%

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

   6. Simplified 90.3%

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

   if -1.14999999999999997e162 < c < -2.10000000000000007e138

   1. Initial program 75.6%

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

   3. Taylor expanded in c around 0 75.6%

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

   4. Taylor expanded in y around inf 75.2%

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

      1. distribute-lft-out 75.2%

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

      2. associate-/l* 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in t around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-/l* 63.1%

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

   9. Simplified 63.1%

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

   if -6.9999999999999994e94 < c < 5.8000000000000004e106

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 91.2%

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

      1. *-commutative 91.2%

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

   5. Simplified 91.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+162}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(2 \cdot \left(x + z \cdot \frac{t}{y}\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{+94} \lor \neg \left(c \leq 5.8 \cdot 10^{+106}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+77} \lor \neg \left(i \leq 10^{+32}\right):\\ \;\;\;\;\left(t\_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -3.5e+77) (not (<= i 1e+32)))
     (* (- 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 <= -3.5e+77) || !(i <= 1e+32)) {
		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 <= (-3.5d+77)) .or. (.not. (i <= 1d+32))) 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 <= -3.5e+77) || !(i <= 1e+32)) {
		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 <= -3.5e+77) or not (i <= 1e+32):
		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 <= -3.5e+77) || !(i <= 1e+32))
		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 <= -3.5e+77) || ~((i <= 1e+32)))
		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, -3.5e+77], N[Not[LessEqual[i, 1e+32]], $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 < -3.5000000000000001e77 or 1.00000000000000005e32 < i

   1. Initial program 96.9%

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

   if -3.5000000000000001e77 < i < 1.00000000000000005e32

   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 c around 0 98.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+77} \lor \neg \left(i \leq 10^{+32}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot \left(a + b \cdot c\right)\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\left(t\_1 - t\_2 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (* c (+ a (* b c)))))
   (if (<= t_2 4e+305)
     (* (- t_1 (* t_2 i)) 2.0)
     (* 2.0 (- t_1 (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * (a + (b * c));
	double tmp;
	if (t_2 <= 4e+305) {
		tmp = (t_1 - (t_2 * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = c * (a + (b * c))
    if (t_2 <= 4d+305) then
        tmp = (t_1 - (t_2 * i)) * 2.0d0
    else
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * (a + (b * c));
	double tmp;
	if (t_2 <= 4e+305) {
		tmp = (t_1 - (t_2 * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = c * (a + (b * c))
	tmp = 0
	if t_2 <= 4e+305:
		tmp = (t_1 - (t_2 * i)) * 2.0
	else:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(c * Float64(a + Float64(b * c)))
	tmp = 0.0
	if (t_2 <= 4e+305)
		tmp = Float64(Float64(t_1 - Float64(t_2 * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = c * (a + (b * c));
	tmp = 0.0;
	if (t_2 <= 4e+305)
		tmp = (t_1 - (t_2 * i)) * 2.0;
	else
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e+305], N[(N[(t$95$1 - N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < 3.9999999999999998e305

   1. Initial program 97.1%

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

   if 3.9999999999999998e305 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 73.0%

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

   3. Taylor expanded in c around 0 86.9%

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

   4. Taylor expanded in a around 0 84.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= c -5.6e+98)
     (* 2.0 (- t_1 (* c (* b (* c i)))))
     (if (<= c 1.45e+107)
       (* 2.0 (- t_1 (* i (* a c))))
       (* 2.0 (* c (* (+ a (* b c)) (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -5.6e+98) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 1.45e+107) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-5.6d+98)) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else if (c <= 1.45d+107) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -5.6e+98) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 1.45e+107) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (c * ((a + (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 c <= -5.6e+98:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	elif c <= 1.45e+107:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * (c * ((a + (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 (c <= -5.6e+98)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 1.45e+107)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-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 (c <= -5.6e+98)
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	elseif (c <= 1.45e+107)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * (c * ((a + (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[LessEqual[c, -5.6e+98], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e+107], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.6000000000000001e98

   1. Initial program 84.5%

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

   3. Taylor expanded in c around 0 95.3%

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

   4. Taylor expanded in a around 0 95.3%

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

   if -5.6000000000000001e98 < c < 1.44999999999999994e107

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf 90.7%

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

      1. *-commutative 90.7%

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

   5. Simplified 90.7%

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

   if 1.44999999999999994e107 < c

   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 c around 0 82.1%

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

   4. Taylor expanded in i around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-*r* 86.7%

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

      3. distribute-rgt-neg-in 86.7%

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

      4. mul-1-neg 86.7%

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

      5. distribute-lft-out 86.7%

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

      6. associate-*r* 91.0%

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

      7. *-commutative 91.0%

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

      8. distribute-lft-out 91.0%

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

      9. mul-1-neg 91.0%

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

      10. distribute-lft-neg-in 91.0%

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

      11. distribute-rgt-neg-in 91.0%

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

      12. *-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+131} \lor \neg \left(c \leq -5 \cdot 10^{-51}\right) \land c \leq 1.05 \cdot 10^{+263}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.8e+131) (and (not (<= c -5e-51)) (<= c 1.05e+263)))
   (* (+ (* x y) (* z t)) 2.0)
   (* (* a (* c i)) -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 <= -3.8e+131) || (!(c <= -5e-51) && (c <= 1.05e+263))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.8d+131)) .or. (.not. (c <= (-5d-51))) .and. (c <= 1.05d+263)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (a * (c * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.8e+131) || (!(c <= -5e-51) && (c <= 1.05e+263))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.8e+131) or (not (c <= -5e-51) and (c <= 1.05e+263)):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (a * (c * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.8e+131) || (!(c <= -5e-51) && (c <= 1.05e+263)))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.8e+131) || (~((c <= -5e-51)) && (c <= 1.05e+263)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (a * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.8e+131], And[N[Not[LessEqual[c, -5e-51]], $MachinePrecision], LessEqual[c, 1.05e+263]]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.8000000000000004e131 or -5.00000000000000004e-51 < c < 1.0500000000000001e263

   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. Add Preprocessing

   3. Taylor expanded in c around 0 63.4%

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

   if -3.8000000000000004e131 < c < -5.00000000000000004e-51 or 1.0500000000000001e263 < c

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in c around 0 53.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+131} \lor \neg \left(c \leq -5 \cdot 10^{-51}\right) \land c \leq 1.05 \cdot 10^{+263}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+40} \lor \neg \left(z \leq 3.4 \cdot 10^{-129}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -4.4e+40) (not (<= z 3.4e-129)))
   (* (+ (* x y) (* z t)) 2.0)
   (* 2.0 (- (* x y) (* 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 ((z <= -4.4e+40) || !(z <= 3.4e-129)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - (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 ((z <= (-4.4d+40)) .or. (.not. (z <= 3.4d-129))) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((x * y) - (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 ((z <= -4.4e+40) || !(z <= 3.4e-129)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -4.4e+40) or not (z <= 3.4e-129):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -4.4e+40) || !(z <= 3.4e-129))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 ((z <= -4.4e+40) || ~((z <= 3.4e-129)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -4.4e+40], N[Not[LessEqual[z, 3.4e-129]], $MachinePrecision]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999998e40 or 3.40000000000000013e-129 < z

   1. Initial program 90.6%

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

   3. Taylor expanded in c around 0 67.6%

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

   if -4.3999999999999998e40 < z < 3.40000000000000013e-129

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around 0 58.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+40} \lor \neg \left(z \leq 3.4 \cdot 10^{-129}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-130} \lor \neg \left(y \leq 7.8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.62e-130) (not (<= y 7.8e-70)))
   (* (+ (* x y) (* z t)) 2.0)
   (* 2.0 (- (* z t) (* 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 ((y <= -1.62e-130) || !(y <= 7.8e-70)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (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 ((y <= (-1.62d-130)) .or. (.not. (y <= 7.8d-70))) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - (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 ((y <= -1.62e-130) || !(y <= 7.8e-70)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.62e-130) or not (y <= 7.8e-70):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.62e-130) || !(y <= 7.8e-70))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - 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 ((y <= -1.62e-130) || ~((y <= 7.8e-70)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.62e-130], N[Not[LessEqual[y, 7.8e-70]], $MachinePrecision]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.62e-130 or 7.80000000000000038e-70 < y

   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 c around 0 64.7%

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

   if -1.62e-130 < y < 7.80000000000000038e-70

   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 a around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around 0 61.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-130} \lor \neg \left(y \leq 7.8 \cdot 10^{-70}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+35} \lor \neg \left(t \leq 1.5 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -8e+35) (not (<= t 1.5e+129))) (* 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 <= -8e+35) || !(t <= 1.5e+129)) {
		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 <= (-8d+35)) .or. (.not. (t <= 1.5d+129))) 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 <= -8e+35) || !(t <= 1.5e+129)) {
		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 <= -8e+35) or not (t <= 1.5e+129):
		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 <= -8e+35) || !(t <= 1.5e+129))
		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 <= -8e+35) || ~((t <= 1.5e+129)))
		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, -8e+35], N[Not[LessEqual[t, 1.5e+129]], $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 < -7.9999999999999997e35 or 1.50000000000000015e129 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 51.9%

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

   if -7.9999999999999997e35 < t < 1.50000000000000015e129

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 37.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+35} \lor \neg \left(t \leq 1.5 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.2% 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 92.8%

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

3. Taylor expanded in z around inf 30.2%

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

4. Final simplification 30.2%

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

Developer target: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(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))))