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

Percentage Accurate: 90.3% → 95.2%

Time: 14.8s

Alternatives: 11

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 95.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * 2.0), $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 94.5%

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

      1. fma-def 94.5%

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

      2. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

      1. fma-def 98.0%

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

      2. +-commutative 98.0%

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

   6. Applied egg-rr 98.0%

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

   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 c around 0 53.3%

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

4. Final simplification 95.4%

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

Alternative 2: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.06 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-266}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -1.7e+185)
     t_2
     (if (<= (* x y) -1.06e+156)
       t_1
       (if (<= (* x y) -2.15e+25)
         t_2
         (if (<= (* x y) -1.75e-147)
           t_1
           (if (<= (* x y) -9e-266)
             (* (* c i) (* a -2.0))
             (if (<= (* x y) 8.2e-172)
               t_1
               (if (<= (* x y) 7.8e-122)
                 (* 2.0 (* a (* c i)))
                 (if (<= (* x y) 6e-32)
                   t_1
                   (if (<= (* x y) 3.5e+71)
                     (* c (* i (* a -2.0)))
                     t_2)))))))))))

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 t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.7e+185) {
		tmp = t_2;
	} else if ((x * y) <= -1.06e+156) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e+25) {
		tmp = t_2;
	} else if ((x * y) <= -1.75e-147) {
		tmp = t_1;
	} else if ((x * y) <= -9e-266) {
		tmp = (c * i) * (a * -2.0);
	} else if ((x * y) <= 8.2e-172) {
		tmp = t_1;
	} else if ((x * y) <= 7.8e-122) {
		tmp = 2.0 * (a * (c * i));
	} else if ((x * y) <= 6e-32) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+71) {
		tmp = c * (i * (a * -2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-1.7d+185)) then
        tmp = t_2
    else if ((x * y) <= (-1.06d+156)) then
        tmp = t_1
    else if ((x * y) <= (-2.15d+25)) then
        tmp = t_2
    else if ((x * y) <= (-1.75d-147)) then
        tmp = t_1
    else if ((x * y) <= (-9d-266)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if ((x * y) <= 8.2d-172) then
        tmp = t_1
    else if ((x * y) <= 7.8d-122) then
        tmp = 2.0d0 * (a * (c * i))
    else if ((x * y) <= 6d-32) then
        tmp = t_1
    else if ((x * y) <= 3.5d+71) then
        tmp = c * (i * (a * (-2.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1.7e+185) {
		tmp = t_2;
	} else if ((x * y) <= -1.06e+156) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e+25) {
		tmp = t_2;
	} else if ((x * y) <= -1.75e-147) {
		tmp = t_1;
	} else if ((x * y) <= -9e-266) {
		tmp = (c * i) * (a * -2.0);
	} else if ((x * y) <= 8.2e-172) {
		tmp = t_1;
	} else if ((x * y) <= 7.8e-122) {
		tmp = 2.0 * (a * (c * i));
	} else if ((x * y) <= 6e-32) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+71) {
		tmp = c * (i * (a * -2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1.7e+185:
		tmp = t_2
	elif (x * y) <= -1.06e+156:
		tmp = t_1
	elif (x * y) <= -2.15e+25:
		tmp = t_2
	elif (x * y) <= -1.75e-147:
		tmp = t_1
	elif (x * y) <= -9e-266:
		tmp = (c * i) * (a * -2.0)
	elif (x * y) <= 8.2e-172:
		tmp = t_1
	elif (x * y) <= 7.8e-122:
		tmp = 2.0 * (a * (c * i))
	elif (x * y) <= 6e-32:
		tmp = t_1
	elif (x * y) <= 3.5e+71:
		tmp = c * (i * (a * -2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1.7e+185)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.06e+156)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.15e+25)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.75e-147)
		tmp = t_1;
	elseif (Float64(x * y) <= -9e-266)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (Float64(x * y) <= 8.2e-172)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.8e-122)
		tmp = Float64(2.0 * Float64(a * Float64(c * i)));
	elseif (Float64(x * y) <= 6e-32)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e+71)
		tmp = Float64(c * Float64(i * Float64(a * -2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1.7e+185)
		tmp = t_2;
	elseif ((x * y) <= -1.06e+156)
		tmp = t_1;
	elseif ((x * y) <= -2.15e+25)
		tmp = t_2;
	elseif ((x * y) <= -1.75e-147)
		tmp = t_1;
	elseif ((x * y) <= -9e-266)
		tmp = (c * i) * (a * -2.0);
	elseif ((x * y) <= 8.2e-172)
		tmp = t_1;
	elseif ((x * y) <= 7.8e-122)
		tmp = 2.0 * (a * (c * i));
	elseif ((x * y) <= 6e-32)
		tmp = t_1;
	elseif ((x * y) <= 3.5e+71)
		tmp = c * (i * (a * -2.0));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.7e+185], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.06e+156], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.15e+25], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.75e-147], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -9e-266], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.2e-172], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.8e-122], N[(2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e-32], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+71], N[(c * N[(i * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.70000000000000009e185 or -1.05999999999999993e156 < (*.f64 x y) < -2.14999999999999999e25 or 3.4999999999999999e71 < (*.f64 x y)

   1. Initial program 81.1%

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

   3. Taylor expanded in x around inf 65.3%

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

   if -1.70000000000000009e185 < (*.f64 x y) < -1.05999999999999993e156 or -2.14999999999999999e25 < (*.f64 x y) < -1.75000000000000002e-147 or -9.0000000000000006e-266 < (*.f64 x y) < 8.2e-172 or 7.79999999999999979e-122 < (*.f64 x y) < 6.0000000000000001e-32

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 49.9%

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

   if -1.75000000000000002e-147 < (*.f64 x y) < -9.0000000000000006e-266

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 46.1%

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

      1. mul-1-neg 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l* 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in c around 0 46.1%

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

      1. *-commutative 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l* 46.1%

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

   8. Simplified 46.1%

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

   if 8.2e-172 < (*.f64 x y) < 7.79999999999999979e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 10.1%

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

      1. mul-1-neg 10.1%

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

      2. *-commutative 10.1%

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

      3. associate-*l* 10.2%

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

   5. Simplified 10.2%

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

      1. expm1-log1p-u 0.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(-c \cdot \left(i \cdot a\right)\right)\right)\right)} \]

      2. expm1-udef 0.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(-c \cdot \left(i \cdot a\right)\right)\right)} - 1} \]

   7. Applied egg-rr 26.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 26.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)\right)} \]

      2. expm1-log1p 51.7%

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

   9. Simplified 51.7%

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

   if 6.0000000000000001e-32 < (*.f64 x y) < 3.4999999999999999e71

   1. Initial program 87.2%

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

   3. Taylor expanded in i around inf 79.9%

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

   4. Taylor expanded in i around 0 79.9%

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

   5. Taylor expanded in c around 0 36.0%

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

      1. *-commutative 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*l* 36.0%

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

      4. *-commutative 36.0%

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

      5. associate-*l* 36.0%

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

      6. *-commutative 36.0%

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

      7. associate-*l* 36.0%

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

   7. Simplified 36.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(a \cdot -2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7 \cdot 10^{+185}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.06 \cdot 10^{+156}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -9 \cdot 10^{-266}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-32}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+258}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t\_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+258)))
     (* -2.0 (* c (* t_1 i)))
     (* (- (+ (* x y) (* z t)) t_2) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+258)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+258)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+258):
		tmp = -2.0 * (c * (t_1 * i))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+258))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+258)))
		tmp = -2.0 * (c * (t_1 * i));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+258]], $MachinePrecision]], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 73.5%

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

   3. Taylor expanded in i around inf 85.3%

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

   4. Taylor expanded in i around 0 85.3%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   1. Initial program 99.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-216}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 21500000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0))
        (t_2 (* -2.0 (* c (* b (* c i)))))
        (t_3 (* 2.0 (* z t))))
   (if (<= c -3.2e+71)
     t_2
     (if (<= c -2.2e-115)
       t_1
       (if (<= c -3.6e-216)
         t_3
         (if (<= c 1.4e-205) t_1 (if (<= c 21500000.0) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double t_2 = -2.0 * (c * (b * (c * i)));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -3.2e+71) {
		tmp = t_2;
	} else if (c <= -2.2e-115) {
		tmp = t_1;
	} else if (c <= -3.6e-216) {
		tmp = t_3;
	} else if (c <= 1.4e-205) {
		tmp = t_1;
	} else if (c <= 21500000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) * 2.0d0
    t_2 = (-2.0d0) * (c * (b * (c * i)))
    t_3 = 2.0d0 * (z * t)
    if (c <= (-3.2d+71)) then
        tmp = t_2
    else if (c <= (-2.2d-115)) then
        tmp = t_1
    else if (c <= (-3.6d-216)) then
        tmp = t_3
    else if (c <= 1.4d-205) then
        tmp = t_1
    else if (c <= 21500000.0d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double t_2 = -2.0 * (c * (b * (c * i)));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -3.2e+71) {
		tmp = t_2;
	} else if (c <= -2.2e-115) {
		tmp = t_1;
	} else if (c <= -3.6e-216) {
		tmp = t_3;
	} else if (c <= 1.4e-205) {
		tmp = t_1;
	} else if (c <= 21500000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	t_2 = -2.0 * (c * (b * (c * i)))
	t_3 = 2.0 * (z * t)
	tmp = 0
	if c <= -3.2e+71:
		tmp = t_2
	elif c <= -2.2e-115:
		tmp = t_1
	elif c <= -3.6e-216:
		tmp = t_3
	elif c <= 1.4e-205:
		tmp = t_1
	elif c <= 21500000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	t_2 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -3.2e+71)
		tmp = t_2;
	elseif (c <= -2.2e-115)
		tmp = t_1;
	elseif (c <= -3.6e-216)
		tmp = t_3;
	elseif (c <= 1.4e-205)
		tmp = t_1;
	elseif (c <= 21500000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) * 2.0;
	t_2 = -2.0 * (c * (b * (c * i)));
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -3.2e+71)
		tmp = t_2;
	elseif (c <= -2.2e-115)
		tmp = t_1;
	elseif (c <= -3.6e-216)
		tmp = t_3;
	elseif (c <= 1.4e-205)
		tmp = t_1;
	elseif (c <= 21500000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+71], t$95$2, If[LessEqual[c, -2.2e-115], t$95$1, If[LessEqual[c, -3.6e-216], t$95$3, If[LessEqual[c, 1.4e-205], t$95$1, If[LessEqual[c, 21500000.0], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.20000000000000023e71 or 2.15e7 < c

   1. Initial program 79.7%

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

   3. Taylor expanded in i around inf 74.0%

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

   4. Taylor expanded in i around 0 74.0%

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

   5. Taylor expanded in a around 0 67.4%

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

   if -3.20000000000000023e71 < c < -2.1999999999999999e-115 or -3.5999999999999999e-216 < c < 1.39999999999999996e-205

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 53.3%

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

   if -2.1999999999999999e-115 < c < -3.5999999999999999e-216 or 1.39999999999999996e-205 < c < 2.15e7

   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

   3. Taylor expanded in z around inf 57.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+71}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-115}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-216}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-205}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 21500000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+71} \lor \neg \left(c \leq 1.1 \cdot 10^{-79} \lor \neg \left(c \leq 9.2 \cdot 10^{+22}\right) \land c \leq 1.95 \cdot 10^{+52}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.3e+71)
         (not (or (<= c 1.1e-79) (and (not (<= c 9.2e+22)) (<= c 1.95e+52)))))
   (* -2.0 (* 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 ((c <= -3.3e+71) || !((c <= 1.1e-79) || (!(c <= 9.2e+22) && (c <= 1.95e+52)))) {
		tmp = -2.0 * (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 ((c <= (-3.3d+71)) .or. (.not. (c <= 1.1d-79) .or. (.not. (c <= 9.2d+22)) .and. (c <= 1.95d+52))) then
        tmp = (-2.0d0) * (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 ((c <= -3.3e+71) || !((c <= 1.1e-79) || (!(c <= 9.2e+22) && (c <= 1.95e+52)))) {
		tmp = -2.0 * (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 (c <= -3.3e+71) or not ((c <= 1.1e-79) or (not (c <= 9.2e+22) and (c <= 1.95e+52))):
		tmp = -2.0 * (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 ((c <= -3.3e+71) || !((c <= 1.1e-79) || (!(c <= 9.2e+22) && (c <= 1.95e+52))))
		tmp = Float64(-2.0 * 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 ((c <= -3.3e+71) || ~(((c <= 1.1e-79) || (~((c <= 9.2e+22)) && (c <= 1.95e+52)))))
		tmp = -2.0 * (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[Or[LessEqual[c, -3.3e+71], N[Not[Or[LessEqual[c, 1.1e-79], And[N[Not[LessEqual[c, 9.2e+22]], $MachinePrecision], LessEqual[c, 1.95e+52]]]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $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 < -3.2999999999999998e71 or 1.0999999999999999e-79 < c < 9.2000000000000008e22 or 1.95e52 < c

   1. Initial program 81.8%

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

   3. Taylor expanded in i around inf 78.5%

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

   4. Taylor expanded in i around 0 78.5%

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

   if -3.2999999999999998e71 < c < 1.0999999999999999e-79 or 9.2000000000000008e22 < c < 1.95e52

   1. Initial program 96.1%

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

   3. Taylor expanded in c around 0 82.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+71} \lor \neg \left(c \leq 1.1 \cdot 10^{-79} \lor \neg \left(c \leq 9.2 \cdot 10^{+22}\right) \land c \leq 1.95 \cdot 10^{+52}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot \left(c \cdot -2\right)\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-225}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{-23}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* a (* c -2.0))))
        (t_2 (* (* x y) 2.0))
        (t_3 (* 2.0 (* z t))))
   (if (<= x -8e+113)
     t_2
     (if (<= x -1.12e+83)
       t_1
       (if (<= x -4.7e-225)
         t_3
         (if (<= x 6.2e-204) t_1 (if (<= x 1e-23) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (a * (c * -2.0));
	double t_2 = (x * y) * 2.0;
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (x <= -8e+113) {
		tmp = t_2;
	} else if (x <= -1.12e+83) {
		tmp = t_1;
	} else if (x <= -4.7e-225) {
		tmp = t_3;
	} else if (x <= 6.2e-204) {
		tmp = t_1;
	} else if (x <= 1e-23) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (a * (c * (-2.0d0)))
    t_2 = (x * y) * 2.0d0
    t_3 = 2.0d0 * (z * t)
    if (x <= (-8d+113)) then
        tmp = t_2
    else if (x <= (-1.12d+83)) then
        tmp = t_1
    else if (x <= (-4.7d-225)) then
        tmp = t_3
    else if (x <= 6.2d-204) then
        tmp = t_1
    else if (x <= 1d-23) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (a * (c * -2.0));
	double t_2 = (x * y) * 2.0;
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (x <= -8e+113) {
		tmp = t_2;
	} else if (x <= -1.12e+83) {
		tmp = t_1;
	} else if (x <= -4.7e-225) {
		tmp = t_3;
	} else if (x <= 6.2e-204) {
		tmp = t_1;
	} else if (x <= 1e-23) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * (a * (c * -2.0))
	t_2 = (x * y) * 2.0
	t_3 = 2.0 * (z * t)
	tmp = 0
	if x <= -8e+113:
		tmp = t_2
	elif x <= -1.12e+83:
		tmp = t_1
	elif x <= -4.7e-225:
		tmp = t_3
	elif x <= 6.2e-204:
		tmp = t_1
	elif x <= 1e-23:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(a * Float64(c * -2.0)))
	t_2 = Float64(Float64(x * y) * 2.0)
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (x <= -8e+113)
		tmp = t_2;
	elseif (x <= -1.12e+83)
		tmp = t_1;
	elseif (x <= -4.7e-225)
		tmp = t_3;
	elseif (x <= 6.2e-204)
		tmp = t_1;
	elseif (x <= 1e-23)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i * (a * (c * -2.0));
	t_2 = (x * y) * 2.0;
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (x <= -8e+113)
		tmp = t_2;
	elseif (x <= -1.12e+83)
		tmp = t_1;
	elseif (x <= -4.7e-225)
		tmp = t_3;
	elseif (x <= 6.2e-204)
		tmp = t_1;
	elseif (x <= 1e-23)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(a * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+113], t$95$2, If[LessEqual[x, -1.12e+83], t$95$1, If[LessEqual[x, -4.7e-225], t$95$3, If[LessEqual[x, 6.2e-204], t$95$1, If[LessEqual[x, 1e-23], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8e113 or 9.9999999999999996e-24 < x

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 46.4%

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

   if -8e113 < x < -1.12e83 or -4.70000000000000014e-225 < x < 6.1999999999999998e-204

   1. Initial program 96.5%

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

   3. Taylor expanded in i around inf 64.1%

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

   4. Taylor expanded in i around 0 64.1%

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

   5. Taylor expanded in c around 0 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-*r* 38.9%

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

      3. associate-*l* 38.9%

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

      4. *-commutative 38.9%

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

      5. associate-*l* 42.4%

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

      6. *-commutative 42.4%

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

   7. Simplified 42.4%

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

   if -1.12e83 < x < -4.70000000000000014e-225 or 6.1999999999999998e-204 < x < 9.9999999999999996e-24

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf 33.5%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+113}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(a \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-225}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-204}:\\ \;\;\;\;i \cdot \left(a \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;x \leq 10^{-23}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-208}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= x -9.4e+76)
     t_2
     (if (<= x 2.7e-277)
       t_1
       (if (<= x 2.6e-208)
         (* c (* i (* a -2.0)))
         (if (<= x 4.2e-7) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (x <= -9.4e+76) {
		tmp = t_2;
	} else if (x <= 2.7e-277) {
		tmp = t_1;
	} else if (x <= 2.6e-208) {
		tmp = c * (i * (a * -2.0));
	} else if (x <= 4.2e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if (x <= (-9.4d+76)) then
        tmp = t_2
    else if (x <= 2.7d-277) then
        tmp = t_1
    else if (x <= 2.6d-208) then
        tmp = c * (i * (a * (-2.0d0)))
    else if (x <= 4.2d-7) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (x <= -9.4e+76) {
		tmp = t_2;
	} else if (x <= 2.7e-277) {
		tmp = t_1;
	} else if (x <= 2.6e-208) {
		tmp = c * (i * (a * -2.0));
	} else if (x <= 4.2e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if x <= -9.4e+76:
		tmp = t_2
	elif x <= 2.7e-277:
		tmp = t_1
	elif x <= 2.6e-208:
		tmp = c * (i * (a * -2.0))
	elif x <= 4.2e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (x <= -9.4e+76)
		tmp = t_2;
	elseif (x <= 2.7e-277)
		tmp = t_1;
	elseif (x <= 2.6e-208)
		tmp = Float64(c * Float64(i * Float64(a * -2.0)));
	elseif (x <= 4.2e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if (x <= -9.4e+76)
		tmp = t_2;
	elseif (x <= 2.7e-277)
		tmp = t_1;
	elseif (x <= 2.6e-208)
		tmp = c * (i * (a * -2.0));
	elseif (x <= 4.2e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[x, -9.4e+76], t$95$2, If[LessEqual[x, 2.7e-277], t$95$1, If[LessEqual[x, 2.6e-208], N[(c * N[(i * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4000000000000006e76 or 4.2e-7 < x

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 44.9%

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

   if -9.4000000000000006e76 < x < 2.69999999999999975e-277 or 2.60000000000000017e-208 < x < 4.2e-7

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 33.1%

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

   if 2.69999999999999975e-277 < x < 2.60000000000000017e-208

   1. Initial program 100.0%

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

   3. Taylor expanded in i around inf 73.9%

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

   4. Taylor expanded in i around 0 73.9%

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

   5. Taylor expanded in c around 0 54.3%

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

      1. *-commutative 54.3%

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

      2. *-commutative 54.3%

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

      3. associate-*l* 42.1%

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

      4. *-commutative 42.1%

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

      5. associate-*l* 42.1%

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

      6. *-commutative 42.1%

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

      7. associate-*l* 42.1%

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

   7. Simplified 42.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+76}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-208}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+76} \lor \neg \left(c \leq 3.3 \cdot 10^{+53}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e+76) (not (<= c 3.3e+53)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 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 tmp;
	if ((c <= -1.65e+76) || !(c <= 3.3e+53)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} 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) :: tmp
    if ((c <= (-1.65d+76)) .or. (.not. (c <= 3.3d+53))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    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 tmp;
	if ((c <= -1.65e+76) || !(c <= 3.3e+53)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.65e+76) or not (c <= 3.3e+53):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.65e+76) || !(c <= 3.3e+53))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	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)
	tmp = 0.0;
	if ((c <= -1.65e+76) || ~((c <= 3.3e+53)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	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_] := If[Or[LessEqual[c, -1.65e+76], N[Not[LessEqual[c, 3.3e+53]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 2 regimes

2. if c < -1.65e76 or 3.3000000000000002e53 < c

   1. Initial program 78.7%

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

   3. Taylor expanded in i around inf 80.3%

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

   4. Taylor expanded in i around 0 80.3%

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

   if -1.65e76 < c < 3.3000000000000002e53

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 88.5%

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

      1. *-commutative 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+76} \lor \neg \left(c \leq 3.3 \cdot 10^{+53}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.3e+80)
   (* -2.0 (* c (* b (* c i))))
   (if (<= c 8.5e+52)
     (* (+ (* x y) (* z t)) 2.0)
     (* -2.0 (* c (* c (* b i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.3e+80) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else if (c <= 8.5e+52) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = -2.0 * (c * (c * (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2.3d+80)) then
        tmp = (-2.0d0) * (c * (b * (c * i)))
    else if (c <= 8.5d+52) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (-2.0d0) * (c * (c * (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.3e+80) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else if (c <= 8.5e+52) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = -2.0 * (c * (c * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.3e+80:
		tmp = -2.0 * (c * (b * (c * i)))
	elif c <= 8.5e+52:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = -2.0 * (c * (c * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.3e+80)
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	elseif (c <= 8.5e+52)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.3e+80)
		tmp = -2.0 * (c * (b * (c * i)));
	elseif (c <= 8.5e+52)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = -2.0 * (c * (c * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.3e+80], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+52], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.30000000000000004e80

   1. Initial program 81.2%

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

   3. Taylor expanded in i around inf 86.4%

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

   4. Taylor expanded in i around 0 86.4%

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

   5. Taylor expanded in a around 0 79.0%

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

   if -2.30000000000000004e80 < c < 8.49999999999999994e52

   1. Initial program 96.0%

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

   3. Taylor expanded in c around 0 75.5%

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

   if 8.49999999999999994e52 < c

   1. Initial program 75.8%

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

   3. Taylor expanded in i around inf 73.3%

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

   4. Taylor expanded in i around 0 73.3%

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

   5. Taylor expanded in a around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*r* 65.4%

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

   7. Simplified 65.4%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+52}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+77} \lor \neg \left(x \leq 0.000225\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.12e+77) (not (<= x 0.000225)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.12e+77) || !(x <= 0.000225)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.12d+77)) .or. (.not. (x <= 0.000225d0))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.12e+77) || !(x <= 0.000225)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.12e+77) or not (x <= 0.000225):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.12e+77) || !(x <= 0.000225))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.12e+77) || ~((x <= 0.000225)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.12e+77], N[Not[LessEqual[x, 0.000225]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e77 or 2.2499999999999999e-4 < x

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 44.9%

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

   if -1.1199999999999999e77 < x < 2.2499999999999999e-4

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 32.7%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+77} \lor \neg \left(x \leq 0.000225\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.8% 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 89.0%

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

3. Taylor expanded in z around inf 28.2%

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

4. Final simplification 28.2%

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

Developer target: 94.2% 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 2024026 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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