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

Percentage Accurate: 90.2% → 95.6%

Time: 16.4s

Alternatives: 17

Speedup: 0.6×

• 47.0% 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: 90.2% 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: 95.6% accurate, 0.1× speedup

Math

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

FPCore

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

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 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * fma(x, y, (z * t));
	}
	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(i * Float64(c * t_1))) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * fma(x, y, Float64(z * t)));
	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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.8%

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

      1. fma-def 94.8%

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

      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
   5. Step-by-step derivation

      1. fma-def 98.4%

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

      2. +-commutative 98.4%

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

   6. Applied egg-rr 98.4%

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

   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. Step-by-step derivation

      1. fma-def 21.4%

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

      2. associate-*l* 42.9%

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

   3. Simplified 42.9%

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

      1. fma-def 21.4%

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

      2. +-commutative 21.4%

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

   6. Applied egg-rr 21.4%

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

   7. Taylor expanded in c around 0 35.7%

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

      1. *-commutative 35.7%

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

      2. +-commutative 35.7%

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

      3. fma-udef 57.1%

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

      4. *-commutative 57.1%

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

   9. Simplified 57.1%

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

4. Final simplification 96.1%

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

Alternative 2: 94.5% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.6%

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

   1. fma-def 90.8%

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

   2. associate-*l* 95.3%

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

3. Simplified 95.3%

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

5. Final simplification 95.3%

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

Alternative 3: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-8} \lor \neg \left(c \leq 5 \cdot 10^{-29}\right) \land \left(c \leq 1.8 \cdot 10^{+51} \lor \neg \left(c \leq 1.72 \cdot 10^{+71}\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (* (+ a (* b c)) i) (- c)))))
   (if (<= c -6.2e+100)
     t_1
     (if (<= c -5e+39)
       (* 2.0 (- (* z t) (* a (* c i))))
       (if (or (<= c -2.1e-8)
               (and (not (<= c 5e-29))
                    (or (<= c 1.8e+51) (not (<= c 1.72e+71)))))
         t_1
         (* 2.0 (+ (* x y) (* z t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= -5e+39) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((c <= -2.1e-8) || (!(c <= 5e-29) && ((c <= 1.8e+51) || !(c <= 1.72e+71)))) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (((a + (b * c)) * i) * -c)
    if (c <= (-6.2d+100)) then
        tmp = t_1
    else if (c <= (-5d+39)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if ((c <= (-2.1d-8)) .or. (.not. (c <= 5d-29)) .and. (c <= 1.8d+51) .or. (.not. (c <= 1.72d+71))) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= -5e+39) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((c <= -2.1e-8) || (!(c <= 5e-29) && ((c <= 1.8e+51) || !(c <= 1.72e+71)))) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (((a + (b * c)) * i) * -c)
	tmp = 0
	if c <= -6.2e+100:
		tmp = t_1
	elif c <= -5e+39:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif (c <= -2.1e-8) or (not (c <= 5e-29) and ((c <= 1.8e+51) or not (c <= 1.72e+71))):
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)))
	tmp = 0.0
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= -5e+39)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif ((c <= -2.1e-8) || (!(c <= 5e-29) && ((c <= 1.8e+51) || !(c <= 1.72e+71))))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	tmp = 0.0;
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= -5e+39)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif ((c <= -2.1e-8) || (~((c <= 5e-29)) && ((c <= 1.8e+51) || ~((c <= 1.72e+71)))))
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+100], t$95$1, If[LessEqual[c, -5e+39], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -2.1e-8], And[N[Not[LessEqual[c, 5e-29]], $MachinePrecision], Or[LessEqual[c, 1.8e+51], N[Not[LessEqual[c, 1.72e+71]], $MachinePrecision]]]], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.20000000000000014e100 or -5.00000000000000015e39 < c < -2.09999999999999994e-8 or 4.99999999999999986e-29 < c < 1.80000000000000005e51 or 1.72e71 < c

   1. Initial program 84.2%

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

   3. Taylor expanded in i around inf 76.8%

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

   if -6.20000000000000014e100 < c < -5.00000000000000015e39

   1. Initial program 64.3%

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

   3. Taylor expanded in a around inf 81.7%

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

   4. Taylor expanded in x around 0 82.1%

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

   if -2.09999999999999994e-8 < c < 4.99999999999999986e-29 or 1.80000000000000005e51 < c < 1.72e71

   1. Initial program 95.6%

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

   3. Taylor expanded in c around 0 81.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-8} \lor \neg \left(c \leq 5 \cdot 10^{-29}\right) \land \left(c \leq 1.8 \cdot 10^{+51} \lor \neg \left(c \leq 1.72 \cdot 10^{+71}\right)\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-29} \lor \neg \left(c \leq 1.1 \cdot 10^{+52}\right) \land c \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (* (+ a (* b c)) i) (- c)))))
   (if (<= c -6.2e+100)
     t_1
     (if (<= c -6.8e+64)
       (* 2.0 (- (* z t) (* a (* c i))))
       (if (<= c -9.5e-28)
         (* 2.0 (- (* x y) (* c (* b (* c i)))))
         (if (or (<= c 5e-29) (and (not (<= c 1.1e+52)) (<= c 1.65e+71)))
           (* 2.0 (+ (* x y) (* z t)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= -6.8e+64) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -9.5e-28) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else if ((c <= 5e-29) || (!(c <= 1.1e+52) && (c <= 1.65e+71))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (((a + (b * c)) * i) * -c)
    if (c <= (-6.2d+100)) then
        tmp = t_1
    else if (c <= (-6.8d+64)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= (-9.5d-28)) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    else if ((c <= 5d-29) .or. (.not. (c <= 1.1d+52)) .and. (c <= 1.65d+71)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = t_1;
	} else if (c <= -6.8e+64) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -9.5e-28) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else if ((c <= 5e-29) || (!(c <= 1.1e+52) && (c <= 1.65e+71))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (((a + (b * c)) * i) * -c)
	tmp = 0
	if c <= -6.2e+100:
		tmp = t_1
	elif c <= -6.8e+64:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= -9.5e-28:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	elif (c <= 5e-29) or (not (c <= 1.1e+52) and (c <= 1.65e+71)):
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)))
	tmp = 0.0
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= -6.8e+64)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= -9.5e-28)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	elseif ((c <= 5e-29) || (!(c <= 1.1e+52) && (c <= 1.65e+71)))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (((a + (b * c)) * i) * -c);
	tmp = 0.0;
	if (c <= -6.2e+100)
		tmp = t_1;
	elseif (c <= -6.8e+64)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= -9.5e-28)
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	elseif ((c <= 5e-29) || (~((c <= 1.1e+52)) && (c <= 1.65e+71)))
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+100], t$95$1, If[LessEqual[c, -6.8e+64], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.5e-28], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 5e-29], And[N[Not[LessEqual[c, 1.1e+52]], $MachinePrecision], LessEqual[c, 1.65e+71]]], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.20000000000000014e100 or 4.99999999999999986e-29 < c < 1.1e52 or 1.6499999999999999e71 < c

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf 78.0%

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

   if -6.20000000000000014e100 < c < -6.8000000000000003e64

   1. Initial program 58.1%

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

   3. Taylor expanded in a around inf 85.5%

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

   4. Taylor expanded in x around 0 99.8%

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

   if -6.8000000000000003e64 < c < -9.50000000000000001e-28

   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 z around 0 76.3%

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

   4. Taylor expanded in a around 0 70.4%

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

   if -9.50000000000000001e-28 < c < 4.99999999999999986e-29 or 1.1e52 < c < 1.6499999999999999e71

   1. Initial program 95.4%

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

   3. Taylor expanded in c around 0 82.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-29} \lor \neg \left(c \leq 1.1 \cdot 10^{+52}\right) \land c \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* i (* c t_1))) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 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 t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	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 - (i * (c * t_1))) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	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 - (i * (c * t_1))) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	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(i * Float64(c * t_1))) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	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)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   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. Step-by-step derivation

      1. fma-def 94.8%

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

      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
   5. Step-by-step derivation

      1. fma-def 98.4%

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

      2. +-commutative 98.4%

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

   6. Applied egg-rr 98.4%

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

   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 a around inf 35.7%

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

   4. Taylor expanded in x around 0 50.6%

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

4. Final simplification 95.8%

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

Alternative 6: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+86} \lor \neg \left(x \cdot y \leq -5000000\right) \land \left(x \cdot y \leq -6 \cdot 10^{-47} \lor \neg \left(x \cdot y \leq 1.5 \cdot 10^{+33}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1e+86)
         (and (not (<= (* x y) -5000000.0))
              (or (<= (* x y) -6e-47) (not (<= (* x y) 1.5e+33)))))
   (* 2.0 (+ (* x y) (* z t)))
   (* 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 (((x * y) <= -1e+86) || (!((x * y) <= -5000000.0) && (((x * y) <= -6e-47) || !((x * y) <= 1.5e+33)))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} 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 (((x * y) <= (-1d+86)) .or. (.not. ((x * y) <= (-5000000.0d0))) .and. ((x * y) <= (-6d-47)) .or. (.not. ((x * y) <= 1.5d+33))) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    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 (((x * y) <= -1e+86) || (!((x * y) <= -5000000.0) && (((x * y) <= -6e-47) || !((x * y) <= 1.5e+33)))) {
		tmp = 2.0 * ((x * y) + (z * t));
	} 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 ((x * y) <= -1e+86) or (not ((x * y) <= -5000000.0) and (((x * y) <= -6e-47) or not ((x * y) <= 1.5e+33))):
		tmp = 2.0 * ((x * y) + (z * t))
	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 ((Float64(x * y) <= -1e+86) || (!(Float64(x * y) <= -5000000.0) && ((Float64(x * y) <= -6e-47) || !(Float64(x * y) <= 1.5e+33))))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	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 (((x * y) <= -1e+86) || (~(((x * y) <= -5000000.0)) && (((x * y) <= -6e-47) || ~(((x * y) <= 1.5e+33)))))
		tmp = 2.0 * ((x * y) + (z * t));
	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[N[(x * y), $MachinePrecision], -1e+86], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -5000000.0]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -6e-47], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.5e+33]], $MachinePrecision]]]], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $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 (*.f64 x y) < -1e86 or -5e6 < (*.f64 x y) < -6.00000000000000033e-47 or 1.49999999999999992e33 < (*.f64 x y)

   1. Initial program 85.5%

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

   3. Taylor expanded in c around 0 80.1%

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

   if -1e86 < (*.f64 x y) < -5e6 or -6.00000000000000033e-47 < (*.f64 x y) < 1.49999999999999992e33

   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 a around inf 68.1%

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

   4. Taylor expanded in x around 0 60.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+86} \lor \neg \left(x \cdot y \leq -5000000\right) \land \left(x \cdot y \leq -6 \cdot 10^{-47} \lor \neg \left(x \cdot y \leq 1.5 \cdot 10^{+33}\right)\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+38} \lor \neg \left(c \leq -3.3 \cdot 10^{-16}\right) \land c \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -6.2e+100)
     (* 2.0 (- (* x y) t_1))
     (if (or (<= c -1.3e+38) (and (not (<= c -3.3e-16)) (<= c 1.7e-15)))
       (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((c <= -1.3e+38) || (!(c <= -3.3e-16) && (c <= 1.7e-15))) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-6.2d+100)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((c <= (-1.3d+38)) .or. (.not. (c <= (-3.3d-16))) .and. (c <= 1.7d-15)) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.2e+100) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((c <= -1.3e+38) || (!(c <= -3.3e-16) && (c <= 1.7e-15))) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -6.2e+100:
		tmp = 2.0 * ((x * y) - t_1)
	elif (c <= -1.3e+38) or (not (c <= -3.3e-16) and (c <= 1.7e-15)):
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -6.2e+100)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif ((c <= -1.3e+38) || (!(c <= -3.3e-16) && (c <= 1.7e-15)))
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -6.2e+100)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((c <= -1.3e+38) || (~((c <= -3.3e-16)) && (c <= 1.7e-15)))
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+100], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -1.3e+38], And[N[Not[LessEqual[c, -3.3e-16]], $MachinePrecision], LessEqual[c, 1.7e-15]]], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.20000000000000014e100

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 89.4%

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

   if -6.20000000000000014e100 < c < -1.3e38 or -3.29999999999999988e-16 < c < 1.7e-15

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf 92.5%

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

   if -1.3e38 < c < -3.29999999999999988e-16 or 1.7e-15 < c

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0 85.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+38} \lor \neg \left(c \leq -3.3 \cdot 10^{-16}\right) \land c \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= (* x y) -2e+149)
     t_2
     (if (<= (* x y) -2e-251)
       t_1
       (if (<= (* x y) 2e-187)
         (* 2.0 (* c (* a (- i))))
         (if (<= (* x y) 1e+99) 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 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -2e+149) {
		tmp = t_2;
	} else if ((x * y) <= -2e-251) {
		tmp = t_1;
	} else if ((x * y) <= 2e-187) {
		tmp = 2.0 * (c * (a * -i));
	} else if ((x * y) <= 1e+99) {
		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 = 2.0d0 * (x * y)
    if ((x * y) <= (-2d+149)) then
        tmp = t_2
    else if ((x * y) <= (-2d-251)) then
        tmp = t_1
    else if ((x * y) <= 2d-187) then
        tmp = 2.0d0 * (c * (a * -i))
    else if ((x * y) <= 1d+99) 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 = 2.0 * (x * y);
	double tmp;
	if ((x * y) <= -2e+149) {
		tmp = t_2;
	} else if ((x * y) <= -2e-251) {
		tmp = t_1;
	} else if ((x * y) <= 2e-187) {
		tmp = 2.0 * (c * (a * -i));
	} else if ((x * y) <= 1e+99) {
		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 = 2.0 * (x * y)
	tmp = 0
	if (x * y) <= -2e+149:
		tmp = t_2
	elif (x * y) <= -2e-251:
		tmp = t_1
	elif (x * y) <= 2e-187:
		tmp = 2.0 * (c * (a * -i))
	elif (x * y) <= 1e+99:
		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(2.0 * Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2e+149)
		tmp = t_2;
	elseif (Float64(x * y) <= -2e-251)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-187)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	elseif (Float64(x * y) <= 1e+99)
		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 = 2.0 * (x * y);
	tmp = 0.0;
	if ((x * y) <= -2e+149)
		tmp = t_2;
	elseif ((x * y) <= -2e-251)
		tmp = t_1;
	elseif ((x * y) <= 2e-187)
		tmp = 2.0 * (c * (a * -i));
	elseif ((x * y) <= 1e+99)
		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[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+149], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2e-251], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-187], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e149 or 9.9999999999999997e98 < (*.f64 x y)

   1. Initial program 82.1%

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

   3. Taylor expanded in x around inf 67.8%

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

   if -2.0000000000000001e149 < (*.f64 x y) < -2.00000000000000003e-251 or 2e-187 < (*.f64 x y) < 9.9999999999999997e98

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 40.8%

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

   if -2.00000000000000003e-251 < (*.f64 x y) < 2e-187

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. associate-*l* 43.2%

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

   5. Simplified 43.2%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+149}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-251}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+99}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.7% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))))
   (if (<= t_2 2e+305)
     (* 2.0 (- (+ (* x y) (* z t)) t_2))
     (* 2.0 (- (* x y) (* c (* t_1 i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= 2e+305) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) - (c * (t_1 * 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 = a + (b * c)
    t_2 = i * (c * t_1)
    if (t_2 <= 2d+305) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - t_2)
    else
        tmp = 2.0d0 * ((x * y) - (c * (t_1 * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if (t_2 <= 2e+305) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	tmp = 0
	if t_2 <= 2e+305:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_2 <= 2e+305)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= 2e+305)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e305

   1. Initial program 95.3%

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

   if 1.9999999999999999e305 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 55.9%

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

   3. Taylor expanded in z around 0 84.7%

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

4. Final simplification 93.8%

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

Alternative 10: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+84} \lor \neg \left(a \leq 0.25\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= a -1.5e+84) (not (<= a 0.25)))
   (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
   (* 2.0 (+ (* x y) (- (* z t) (* b (* c (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= -1.5e+84) || !(a <= 0.25)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (b * (c * (c * i)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a <= (-1.5d+84)) .or. (.not. (a <= 0.25d0))) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) + ((z * t) - (b * (c * (c * i)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= -1.5e+84) || !(a <= 0.25)) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (b * (c * (c * i)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a <= -1.5e+84) or not (a <= 0.25):
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * ((x * y) + ((z * t) - (b * (c * (c * i)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((a <= -1.5e+84) || !(a <= 0.25))
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(b * Float64(c * Float64(c * i))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a <= -1.5e+84) || ~((a <= 0.25)))
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * ((x * y) + ((z * t) - (b * (c * (c * i)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[a, -1.5e+84], N[Not[LessEqual[a, 0.25]], $MachinePrecision]], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.49999999999999998e84 or 0.25 < a

   1. Initial program 85.3%

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

   3. Taylor expanded in a around inf 89.1%

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

   if -1.49999999999999998e84 < a < 0.25

   1. Initial program 92.4%

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

      1. associate--l+ 92.4%

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

      2. *-commutative 92.4%

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

      3. fma-def 93.0%

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

      4. *-commutative 93.0%

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

      5. +-commutative 93.0%

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

      6. fma-udef 93.0%

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

      7. associate-*r* 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in b around inf 93.5%

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

      1. fma-udef 92.9%

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

      2. *-commutative 92.9%

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

      3. associate-*l* 89.3%

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

   7. Applied egg-rr 89.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+84} \lor \neg \left(a \leq 0.25\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -1.034 \cdot 10^{+19} \lor \neg \left(a \leq 0.25\right):\\ \;\;\;\;2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= a -1.034e+19) (not (<= a 0.25)))
     (* 2.0 (- t_1 (* a (* c i))))
     (* 2.0 (- t_1 (* i (* c (* b c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -1.034e+19) || !(a <= 0.25)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (i * (c * (b * 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 = (x * y) + (z * t)
    if ((a <= (-1.034d+19)) .or. (.not. (a <= 0.25d0))) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - (i * (c * (b * 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 = (x * y) + (z * t);
	double tmp;
	if ((a <= -1.034e+19) || !(a <= 0.25)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a <= -1.034e+19) or not (a <= 0.25):
		tmp = 2.0 * (t_1 - (a * (c * i)))
	else:
		tmp = 2.0 * (t_1 - (i * (c * (b * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((a <= -1.034e+19) || !(a <= 0.25))
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(b * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a <= -1.034e+19) || ~((a <= 0.25)))
		tmp = 2.0 * (t_1 - (a * (c * i)));
	else
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.034e+19], N[Not[LessEqual[a, 0.25]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.034e19 or 0.25 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 89.4%

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

   if -1.034e19 < a < 0.25

   1. Initial program 92.4%

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

   3. Taylor expanded in a around 0 91.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.034 \cdot 10^{+19} \lor \neg \left(a \leq 0.25\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+83} \lor \neg \left(a \leq 0.37\right):\\ \;\;\;\;2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= a -2.25e+83) (not (<= a 0.37)))
     (* 2.0 (- t_1 (* a (* c i))))
     (* 2.0 (- t_1 (* (* b c) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -2.25e+83) || !(a <= 0.37)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a <= (-2.25d+83)) .or. (.not. (a <= 0.37d0))) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a <= -2.25e+83) || !(a <= 0.37)) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a <= -2.25e+83) or not (a <= 0.37):
		tmp = 2.0 * (t_1 - (a * (c * i)))
	else:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((a <= -2.25e+83) || !(a <= 0.37))
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a <= -2.25e+83) || ~((a <= 0.37)))
		tmp = 2.0 * (t_1 - (a * (c * i)));
	else
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -2.25e+83], N[Not[LessEqual[a, 0.37]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e83 or 0.37 < a

   1. Initial program 85.3%

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

   3. Taylor expanded in a around inf 89.1%

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

   if -2.25e83 < a < 0.37

   1. Initial program 92.4%

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

      1. fma-def 93.0%

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

      2. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

      1. fma-def 95.4%

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

      2. +-commutative 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in a around 0 92.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+83} \lor \neg \left(a \leq 0.37\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-113}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))))
   (if (<= t -9.5e-118)
     t_1
     (if (<= t 7.5e-113)
       (* 2.0 (- (* x y) (* i (* a c))))
       (if (<= t 1.25e+188) t_1 (* 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 t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (t <= -9.5e-118) {
		tmp = t_1;
	} else if (t <= 7.5e-113) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} else if (t <= 1.25e+188) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    if (t <= (-9.5d-118)) then
        tmp = t_1
    else if (t <= 7.5d-113) then
        tmp = 2.0d0 * ((x * y) - (i * (a * c)))
    else if (t <= 1.25d+188) then
        tmp = t_1
    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 t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (t <= -9.5e-118) {
		tmp = t_1;
	} else if (t <= 7.5e-113) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} else if (t <= 1.25e+188) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	tmp = 0
	if t <= -9.5e-118:
		tmp = t_1
	elif t <= 7.5e-113:
		tmp = 2.0 * ((x * y) - (i * (a * c)))
	elif t <= 1.25e+188:
		tmp = t_1
	else:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (t <= -9.5e-118)
		tmp = t_1;
	elseif (t <= 7.5e-113)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))));
	elseif (t <= 1.25e+188)
		tmp = t_1;
	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)
	t_1 = 2.0 * ((x * y) + (z * t));
	tmp = 0.0;
	if (t <= -9.5e-118)
		tmp = t_1;
	elseif (t <= 7.5e-113)
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	elseif (t <= 1.25e+188)
		tmp = t_1;
	else
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-118], t$95$1, If[LessEqual[t, 7.5e-113], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+188], t$95$1, N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.49999999999999931e-118 or 7.5000000000000002e-113 < t < 1.25e188

   1. Initial program 91.7%

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

   3. Taylor expanded in c around 0 63.3%

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

   if -9.49999999999999931e-118 < t < 7.5000000000000002e-113

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 65.5%

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

      4. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   if 1.25e188 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in a around inf 75.3%

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

   4. Taylor expanded in x around 0 75.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-113}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+188}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+140} \lor \neg \left(z \leq -1.18 \cdot 10^{+107} \lor \neg \left(z \leq -2.2 \cdot 10^{+51}\right) \land z \leq 1.1 \cdot 10^{-172}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -1.6e+140)
         (not
          (or (<= z -1.18e+107) (and (not (<= z -2.2e+51)) (<= z 1.1e-172)))))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -1.6e+140) || !((z <= -1.18e+107) || (!(z <= -2.2e+51) && (z <= 1.1e-172)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	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 <= (-1.6d+140)) .or. (.not. (z <= (-1.18d+107)) .or. (.not. (z <= (-2.2d+51))) .and. (z <= 1.1d-172))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    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 <= -1.6e+140) || !((z <= -1.18e+107) || (!(z <= -2.2e+51) && (z <= 1.1e-172)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -1.6e+140) or not ((z <= -1.18e+107) or (not (z <= -2.2e+51) and (z <= 1.1e-172))):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -1.6e+140) || !((z <= -1.18e+107) || (!(z <= -2.2e+51) && (z <= 1.1e-172))))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -1.6e+140) || ~(((z <= -1.18e+107) || (~((z <= -2.2e+51)) && (z <= 1.1e-172)))))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -1.6e+140], N[Not[Or[LessEqual[z, -1.18e+107], And[N[Not[LessEqual[z, -2.2e+51]], $MachinePrecision], LessEqual[z, 1.1e-172]]]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000005e140 or -1.18000000000000005e107 < z < -2.19999999999999992e51 or 1.10000000000000004e-172 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf 46.2%

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

   if -1.60000000000000005e140 < z < -1.18000000000000005e107 or -2.19999999999999992e51 < z < 1.10000000000000004e-172

   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 x around inf 41.6%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+140} \lor \neg \left(z \leq -1.18 \cdot 10^{+107} \lor \neg \left(z \leq -2.2 \cdot 10^{+51}\right) \land z \leq 1.1 \cdot 10^{-172}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{-91} \lor \neg \left(c \leq 4.8 \cdot 10^{-44}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6.8e-91) (not (<= c 4.8e-44)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6.8e-91) || !(c <= 4.8e-44)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-6.8d-91)) .or. (.not. (c <= 4.8d-44))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6.8e-91) || !(c <= 4.8e-44)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -6.8e-91) or not (c <= 4.8e-44):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -6.8e-91) || !(c <= 4.8e-44))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -6.8e-91) || ~((c <= 4.8e-44)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -6.8e-91], N[Not[LessEqual[c, 4.8e-44]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.80000000000000053e-91 or 4.80000000000000017e-44 < c

   1. Initial program 83.8%

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

   3. Taylor expanded in x around 0 80.1%

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

   if -6.80000000000000053e-91 < c < 4.80000000000000017e-44

   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

   3. Taylor expanded in c around 0 85.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{-91} \lor \neg \left(c \leq 4.8 \cdot 10^{-44}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 9.5 \cdot 10^{+133}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c 9.5e+133) (* 2.0 (+ (* x y) (* z t))) (* (* c i) (* a -2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= 9.5e+133) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= 9.5d+133) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (c * i) * (a * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= 9.5e+133) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= 9.5e+133:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (c * i) * (a * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= 9.5e+133)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= 9.5e+133)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (c * i) * (a * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, 9.5e+133], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 9.49999999999999996e133

   1. Initial program 91.5%

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

   3. Taylor expanded in c around 0 63.6%

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

   if 9.49999999999999996e133 < c

   1. Initial program 70.4%

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

   3. Taylor expanded in a around inf 44.7%

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

   4. Taylor expanded in x around 0 44.6%

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

   5. Taylor expanded in t around 0 44.3%

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

      1. *-commutative 44.3%

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

      2. *-commutative 44.3%

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

      3. associate-*l* 44.3%

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

   7. Simplified 44.3%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 9.5 \cdot 10^{+133}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% 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 89.6%

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

3. Taylor expanded in z around inf 32.1%

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

4. Final simplification 32.1%

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

Developer target: 94.1% 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 2024021 
(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))))