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

Percentage Accurate: 89.9% → 95.5%

Time: 13.9s

Alternatives: 17

Speedup: 0.5×

• 47.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.9% 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: 95.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * z + N[(x * y), $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 96.7%

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

      1. associate-*l* 97.9%

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

      2. fma-def 97.9%

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

   3. Simplified 97.9%

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

   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. Taylor expanded in c around 0 41.2%

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

      1. fma-def 58.8%

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

   4. Simplified 58.8%

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

4. Final simplification 95.3%

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

Alternative 2: 92.1% accurate, 0.2× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 * 2.0), $MachinePrecision], N[(2.0 * N[(t * z + N[(x * y), $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 96.7%

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

   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. Taylor expanded in c around 0 41.2%

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

      1. fma-def 58.8%

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

   4. Simplified 58.8%

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

4. Final simplification 94.2%

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

Alternative 3: 91.3% accurate, 0.5× speedup

Math

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

FPCore

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

   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. Taylor expanded in x around inf 53.7%

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

4. Final simplification 93.9%

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

Alternative 4: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-57} \lor \neg \left(x \cdot y \leq 1.12 \cdot 10^{+98}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (* b c) i))))))
   (if (<= (* x y) -2.2e+95)
     t_1
     (if (<= (* x y) -1e+59)
       (* 2.0 (- (* z t) (* c (* a i))))
       (if (or (<= (* x y) -7.5e-57) (not (<= (* x y) 1.12e+98)))
         t_1
         (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)));
	double tmp;
	if ((x * y) <= -2.2e+95) {
		tmp = t_1;
	} else if ((x * y) <= -1e+59) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (((x * y) <= -7.5e-57) || !((x * y) <= 1.12e+98)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((b * c) * i)))
    if ((x * y) <= (-2.2d+95)) then
        tmp = t_1
    else if ((x * y) <= (-1d+59)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (((x * y) <= (-7.5d-57)) .or. (.not. ((x * y) <= 1.12d+98))) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)));
	double tmp;
	if ((x * y) <= -2.2e+95) {
		tmp = t_1;
	} else if ((x * y) <= -1e+59) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (((x * y) <= -7.5e-57) || !((x * y) <= 1.12e+98)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)))
	tmp = 0
	if (x * y) <= -2.2e+95:
		tmp = t_1
	elif (x * y) <= -1e+59:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif ((x * y) <= -7.5e-57) or not ((x * y) <= 1.12e+98):
		tmp = t_1
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * 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(c * Float64(Float64(b * c) * i))))
	tmp = 0.0
	if (Float64(x * y) <= -2.2e+95)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e+59)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif ((Float64(x * y) <= -7.5e-57) || !(Float64(x * y) <= 1.12e+98))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * 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) - (c * ((b * c) * i)));
	tmp = 0.0;
	if ((x * y) <= -2.2e+95)
		tmp = t_1;
	elseif ((x * y) <= -1e+59)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (((x * y) <= -7.5e-57) || ~(((x * y) <= 1.12e+98)))
		tmp = t_1;
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.2e+95], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e+59], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -7.5e-57], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.12e+98]], $MachinePrecision]], t$95$1, N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.1999999999999999e95 or -9.99999999999999972e58 < (*.f64 x y) < -7.49999999999999973e-57 or 1.12e98 < (*.f64 x y)

   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. Taylor expanded in z around 0 76.4%

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

   3. Taylor expanded in a around 0 76.4%

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

   if -2.1999999999999999e95 < (*.f64 x y) < -9.99999999999999972e58

   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. Taylor expanded in a around inf 87.0%

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

      1. *-commutative 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in x around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 85.5%

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

      3. *-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -7.49999999999999973e-57 < (*.f64 x y) < 1.12e98

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 85.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{-57} \lor \neg \left(x \cdot y \leq 1.12 \cdot 10^{+98}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 41.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-309}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* a (* c i))))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -7.5e-57)
     t_3
     (if (<= (* x y) -2e-309)
       t_1
       (if (<= (* x y) 1.5e-141)
         t_2
         (if (<= (* x y) 9e-82) t_1 (if (<= (* x y) 1e+83) t_2 t_3)))))))

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 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -7.5e-57) {
		tmp = t_3;
	} else if ((x * y) <= -2e-309) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-141) {
		tmp = t_2;
	} else if ((x * y) <= 9e-82) {
		tmp = t_1;
	} else if ((x * y) <= 1e+83) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-7.5d-57)) then
        tmp = t_3
    else if ((x * y) <= (-2d-309)) then
        tmp = t_1
    else if ((x * y) <= 1.5d-141) then
        tmp = t_2
    else if ((x * y) <= 9d-82) then
        tmp = t_1
    else if ((x * y) <= 1d+83) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -7.5e-57) {
		tmp = t_3;
	} else if ((x * y) <= -2e-309) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-141) {
		tmp = t_2;
	} else if ((x * y) <= 9e-82) {
		tmp = t_1;
	} else if ((x * y) <= 1e+83) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -7.5e-57:
		tmp = t_3
	elif (x * y) <= -2e-309:
		tmp = t_1
	elif (x * y) <= 1.5e-141:
		tmp = t_2
	elif (x * y) <= 9e-82:
		tmp = t_1
	elif (x * y) <= 1e+83:
		tmp = t_2
	else:
		tmp = t_3
	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(a * Float64(c * i)))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -7.5e-57)
		tmp = t_3;
	elseif (Float64(x * y) <= -2e-309)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.5e-141)
		tmp = t_2;
	elseif (Float64(x * y) <= 9e-82)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+83)
		tmp = t_2;
	else
		tmp = t_3;
	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 * (a * (c * i));
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -7.5e-57)
		tmp = t_3;
	elseif ((x * y) <= -2e-309)
		tmp = t_1;
	elseif ((x * y) <= 1.5e-141)
		tmp = t_2;
	elseif ((x * y) <= 9e-82)
		tmp = t_1;
	elseif ((x * y) <= 1e+83)
		tmp = t_2;
	else
		tmp = t_3;
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.5e-57], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2e-309], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.5e-141], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9e-82], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+83], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.49999999999999973e-57 or 1.00000000000000003e83 < (*.f64 x y)

   1. Initial program 86.4%

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

   2. Taylor expanded in x around inf 57.3%

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

   if -7.49999999999999973e-57 < (*.f64 x y) < -1.9999999999999988e-309 or 1.49999999999999992e-141 < (*.f64 x y) < 8.9999999999999997e-82

   1. Initial program 92.2%

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

   2. Taylor expanded in z around inf 53.3%

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

   if -1.9999999999999988e-309 < (*.f64 x y) < 1.49999999999999992e-141 or 8.9999999999999997e-82 < (*.f64 x y) < 1.00000000000000003e83

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf 43.6%

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

   3. Taylor expanded in a around 0 43.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-309}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{-141}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+83}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 6: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+292}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.8 \cdot 10^{-56} \lor \neg \left(x \cdot y \leq 8.6 \cdot 10^{+17}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -6.5e+292)
     (* (* x y) 2.0)
     (if (or (<= (* x y) -1.8e-56) (not (<= (* x y) 8.6e+17)))
       (* 2.0 (- (* x y) t_1))
       (* 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 ((x * y) <= -6.5e+292) {
		tmp = (x * y) * 2.0;
	} else if (((x * y) <= -1.8e-56) || !((x * y) <= 8.6e+17)) {
		tmp = 2.0 * ((x * y) - t_1);
	} 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 ((x * y) <= (-6.5d+292)) then
        tmp = (x * y) * 2.0d0
    else if (((x * y) <= (-1.8d-56)) .or. (.not. ((x * y) <= 8.6d+17))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    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 ((x * y) <= -6.5e+292) {
		tmp = (x * y) * 2.0;
	} else if (((x * y) <= -1.8e-56) || !((x * y) <= 8.6e+17)) {
		tmp = 2.0 * ((x * y) - t_1);
	} 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 (x * y) <= -6.5e+292:
		tmp = (x * y) * 2.0
	elif ((x * y) <= -1.8e-56) or not ((x * y) <= 8.6e+17):
		tmp = 2.0 * ((x * y) - t_1)
	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 (Float64(x * y) <= -6.5e+292)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif ((Float64(x * y) <= -1.8e-56) || !(Float64(x * y) <= 8.6e+17))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	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 ((x * y) <= -6.5e+292)
		tmp = (x * y) * 2.0;
	elseif (((x * y) <= -1.8e-56) || ~(((x * y) <= 8.6e+17)))
		tmp = 2.0 * ((x * y) - t_1);
	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[N[(x * y), $MachinePrecision], -6.5e+292], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.8e-56], N[Not[LessEqual[N[(x * y), $MachinePrecision], 8.6e+17]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.4999999999999999e292

   1. Initial program 71.4%

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

   2. Taylor expanded in x around inf 90.5%

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

   if -6.4999999999999999e292 < (*.f64 x y) < -1.79999999999999989e-56 or 8.6e17 < (*.f64 x y)

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 79.1%

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

   if -1.79999999999999989e-56 < (*.f64 x y) < 8.6e17

   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. Taylor expanded in x around 0 87.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.5 \cdot 10^{+292}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.8 \cdot 10^{-56} \lor \neg \left(x \cdot y \leq 8.6 \cdot 10^{+17}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 71.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-26} \lor \neg \left(c \leq 1.5 \cdot 10^{+84}\right) \land c \leq 1.35 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (* b c) i))))))
   (if (<= c -1.5e+60)
     t_1
     (if (<= c -9.5e+16)
       (* 2.0 (- (* z t) (* i (* c (* b c)))))
       (if (<= c -7.5e-107)
         t_1
         (if (or (<= c 4.3e-26) (and (not (<= c 1.5e+84)) (<= c 1.35e+119)))
           (* (+ (* x y) (* z t)) 2.0)
           (* 2.0 (* c (* (+ a (* b c)) (- i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)));
	double tmp;
	if (c <= -1.5e+60) {
		tmp = t_1;
	} else if (c <= -9.5e+16) {
		tmp = 2.0 * ((z * t) - (i * (c * (b * c))));
	} else if (c <= -7.5e-107) {
		tmp = t_1;
	} else if ((c <= 4.3e-26) || (!(c <= 1.5e+84) && (c <= 1.35e+119))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((b * c) * i)))
    if (c <= (-1.5d+60)) then
        tmp = t_1
    else if (c <= (-9.5d+16)) then
        tmp = 2.0d0 * ((z * t) - (i * (c * (b * c))))
    else if (c <= (-7.5d-107)) then
        tmp = t_1
    else if ((c <= 4.3d-26) .or. (.not. (c <= 1.5d+84)) .and. (c <= 1.35d+119)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)));
	double tmp;
	if (c <= -1.5e+60) {
		tmp = t_1;
	} else if (c <= -9.5e+16) {
		tmp = 2.0 * ((z * t) - (i * (c * (b * c))));
	} else if (c <= -7.5e-107) {
		tmp = t_1;
	} else if ((c <= 4.3e-26) || (!(c <= 1.5e+84) && (c <= 1.35e+119))) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)))
	tmp = 0
	if c <= -1.5e+60:
		tmp = t_1
	elif c <= -9.5e+16:
		tmp = 2.0 * ((z * t) - (i * (c * (b * c))))
	elif c <= -7.5e-107:
		tmp = t_1
	elif (c <= 4.3e-26) or (not (c <= 1.5e+84) and (c <= 1.35e+119)):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(b * c) * i))))
	tmp = 0.0
	if (c <= -1.5e+60)
		tmp = t_1;
	elseif (c <= -9.5e+16)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(c * Float64(b * c)))));
	elseif (c <= -7.5e-107)
		tmp = t_1;
	elseif ((c <= 4.3e-26) || (!(c <= 1.5e+84) && (c <= 1.35e+119)))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (c * ((b * c) * i)));
	tmp = 0.0;
	if (c <= -1.5e+60)
		tmp = t_1;
	elseif (c <= -9.5e+16)
		tmp = 2.0 * ((z * t) - (i * (c * (b * c))));
	elseif (c <= -7.5e-107)
		tmp = t_1;
	elseif ((c <= 4.3e-26) || (~((c <= 1.5e+84)) && (c <= 1.35e+119)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+60], t$95$1, If[LessEqual[c, -9.5e+16], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.5e-107], t$95$1, If[Or[LessEqual[c, 4.3e-26], And[N[Not[LessEqual[c, 1.5e+84]], $MachinePrecision], LessEqual[c, 1.35e+119]]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.4999999999999999e60 or -9.5e16 < c < -7.50000000000000047e-107

   1. Initial program 88.2%

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

   2. Taylor expanded in z around 0 87.1%

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

   3. Taylor expanded in a around 0 77.0%

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

   if -1.4999999999999999e60 < c < -9.5e16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 82.8%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. unpow2 91.1%

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

      4. associate-*r* 91.3%

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

   5. Simplified 91.3%

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

   if -7.50000000000000047e-107 < c < 4.29999999999999988e-26 or 1.49999999999999998e84 < c < 1.3499999999999999e119

   1. Initial program 94.4%

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

   2. Taylor expanded in c around 0 78.3%

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

   if 4.29999999999999988e-26 < c < 1.49999999999999998e84 or 1.3499999999999999e119 < c

   1. Initial program 84.3%

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

   2. Taylor expanded in i around inf 76.9%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-107}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-26} \lor \neg \left(c \leq 1.5 \cdot 10^{+84}\right) \land c \leq 1.35 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 8: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-i\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot t_1\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (- i))) (t_2 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= c -3.8e+37)
     (* 2.0 (* c (* b t_1)))
     (if (<= c 2.5e-27)
       t_2
       (if (<= c 8.5e+93)
         (* 2.0 (- (* z t) (* c (* a i))))
         (if (<= c 3.5e+121)
           t_2
           (if (<= c 5.8e+128)
             (* -2.0 (* a (* c i)))
             (* 2.0 (* b (* c 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 * -i;
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -3.8e+37) {
		tmp = 2.0 * (c * (b * t_1));
	} else if (c <= 2.5e-27) {
		tmp = t_2;
	} else if (c <= 8.5e+93) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 3.5e+121) {
		tmp = t_2;
	} else if (c <= 5.8e+128) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * (b * (c * 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) :: t_2
    real(8) :: tmp
    t_1 = c * -i
    t_2 = ((x * y) + (z * t)) * 2.0d0
    if (c <= (-3.8d+37)) then
        tmp = 2.0d0 * (c * (b * t_1))
    else if (c <= 2.5d-27) then
        tmp = t_2
    else if (c <= 8.5d+93) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (c <= 3.5d+121) then
        tmp = t_2
    else if (c <= 5.8d+128) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = 2.0d0 * (b * (c * 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 * -i;
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -3.8e+37) {
		tmp = 2.0 * (c * (b * t_1));
	} else if (c <= 2.5e-27) {
		tmp = t_2;
	} else if (c <= 8.5e+93) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 3.5e+121) {
		tmp = t_2;
	} else if (c <= 5.8e+128) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * (b * (c * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * -i
	t_2 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if c <= -3.8e+37:
		tmp = 2.0 * (c * (b * t_1))
	elif c <= 2.5e-27:
		tmp = t_2
	elif c <= 8.5e+93:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif c <= 3.5e+121:
		tmp = t_2
	elif c <= 5.8e+128:
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = 2.0 * (b * (c * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(-i))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	tmp = 0.0
	if (c <= -3.8e+37)
		tmp = Float64(2.0 * Float64(c * Float64(b * t_1)));
	elseif (c <= 2.5e-27)
		tmp = t_2;
	elseif (c <= 8.5e+93)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (c <= 3.5e+121)
		tmp = t_2;
	elseif (c <= 5.8e+128)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(2.0 * Float64(b * Float64(c * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * -i;
	t_2 = ((x * y) + (z * t)) * 2.0;
	tmp = 0.0;
	if (c <= -3.8e+37)
		tmp = 2.0 * (c * (b * t_1));
	elseif (c <= 2.5e-27)
		tmp = t_2;
	elseif (c <= 8.5e+93)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (c <= 3.5e+121)
		tmp = t_2;
	elseif (c <= 5.8e+128)
		tmp = -2.0 * (a * (c * i));
	else
		tmp = 2.0 * (b * (c * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * (-i)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -3.8e+37], N[(2.0 * N[(c * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e-27], t$95$2, If[LessEqual[c, 8.5e+93], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+121], t$95$2, If[LessEqual[c, 5.8e+128], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(b * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.7999999999999999e37

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 90.6%

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

   3. Taylor expanded in c around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

      6. unpow2 64.7%

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

      7. associate-*r* 66.6%

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

      8. *-commutative 66.6%

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

      9. associate-*l* 68.5%

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

      10. *-commutative 68.5%

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

      11. distribute-rgt-neg-in 68.5%

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

      12. associate-*r* 68.5%

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

      13. *-commutative 68.5%

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

      14. distribute-rgt-neg-in 68.5%

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

   5. Simplified 68.5%

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

   if -3.7999999999999999e37 < c < 2.5000000000000001e-27 or 8.5000000000000005e93 < c < 3.5e121

   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. Taylor expanded in c around 0 75.0%

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

   if 2.5000000000000001e-27 < c < 8.5000000000000005e93

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 62.2%

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

      1. *-commutative 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in x around 0 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*l* 57.2%

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

      3. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if 3.5e121 < c < 5.8000000000000001e128

   1. Initial program 68.0%

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

   2. Taylor expanded in a around inf 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   if 5.8000000000000001e128 < c

   1. Initial program 86.6%

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

   2. Taylor expanded in b around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. *-commutative 78.5%

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

      3. distribute-rgt-neg-in 78.5%

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

      4. unpow2 78.5%

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

      5. associate-*r* 76.0%

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

   4. Simplified 76.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-27}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+121}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+29} \lor \neg \left(c \leq 1.65 \cdot 10^{-29} \lor \neg \left(c \leq 1.9 \cdot 10^{+84}\right) \land c \leq 1.35 \cdot 10^{+119}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.7e+29)
         (not
          (or (<= c 1.65e-29) (and (not (<= c 1.9e+84)) (<= c 1.35e+119)))))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.7e+29) || !((c <= 1.65e-29) || (!(c <= 1.9e+84) && (c <= 1.35e+119)))) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.7d+29)) .or. (.not. (c <= 1.65d-29) .or. (.not. (c <= 1.9d+84)) .and. (c <= 1.35d+119))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.7e+29) || !((c <= 1.65e-29) || (!(c <= 1.9e+84) && (c <= 1.35e+119)))) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.7e+29) or not ((c <= 1.65e-29) or (not (c <= 1.9e+84) and (c <= 1.35e+119))):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.7e+29) || !((c <= 1.65e-29) || (!(c <= 1.9e+84) && (c <= 1.35e+119))))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.7e+29) || ~(((c <= 1.65e-29) || (~((c <= 1.9e+84)) && (c <= 1.35e+119)))))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.7e+29], N[Not[Or[LessEqual[c, 1.65e-29], And[N[Not[LessEqual[c, 1.9e+84]], $MachinePrecision], LessEqual[c, 1.35e+119]]]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.69999999999999974e29 or 1.65000000000000014e-29 < c < 1.9e84 or 1.3499999999999999e119 < c

   1. Initial program 86.5%

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

   2. Taylor expanded in i around inf 77.5%

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

   if -3.69999999999999974e29 < c < 1.65000000000000014e-29 or 1.9e84 < c < 1.3499999999999999e119

   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. Taylor expanded in c around 0 74.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+29} \lor \neg \left(c \leq 1.65 \cdot 10^{-29} \lor \neg \left(c \leq 1.9 \cdot 10^{+84}\right) \land c \leq 1.35 \cdot 10^{+119}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 10: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+38} \lor \neg \left(c \leq 2.3 \cdot 10^{-21}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.1e+38) (not (<= c 2.3e-21)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.1e+38) || !(c <= 2.3e-21)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.1d+38)) .or. (.not. (c <= 2.3d-21))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.1e+38) || !(c <= 2.3e-21)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.1e+38) or not (c <= 2.3e-21):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.1e+38) || !(c <= 2.3e-21))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.1e+38) || ~((c <= 2.3e-21)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.1e+38], N[Not[LessEqual[c, 2.3e-21]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.10000000000000003e38 or 2.29999999999999999e-21 < c

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0 87.0%

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

   if -1.10000000000000003e38 < c < 2.29999999999999999e-21

   1. Initial program 95.9%

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

   2. Taylor expanded in a around inf 89.2%

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

      1. *-commutative 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+38} \lor \neg \left(c \leq 2.3 \cdot 10^{-21}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 11: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-i\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -6 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot t_1\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (- i))) (t_2 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= c -6e+37)
     (* 2.0 (* c (* b t_1)))
     (if (<= c 9.2e-21)
       t_2
       (if (<= c 5e+44)
         (* c (* (* b c) (* i -2.0)))
         (if (<= c 6e+128) t_2 (* 2.0 (* b (* c 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 * -i;
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -6e+37) {
		tmp = 2.0 * (c * (b * t_1));
	} else if (c <= 9.2e-21) {
		tmp = t_2;
	} else if (c <= 5e+44) {
		tmp = c * ((b * c) * (i * -2.0));
	} else if (c <= 6e+128) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (b * (c * 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) :: t_2
    real(8) :: tmp
    t_1 = c * -i
    t_2 = ((x * y) + (z * t)) * 2.0d0
    if (c <= (-6d+37)) then
        tmp = 2.0d0 * (c * (b * t_1))
    else if (c <= 9.2d-21) then
        tmp = t_2
    else if (c <= 5d+44) then
        tmp = c * ((b * c) * (i * (-2.0d0)))
    else if (c <= 6d+128) then
        tmp = t_2
    else
        tmp = 2.0d0 * (b * (c * 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 * -i;
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -6e+37) {
		tmp = 2.0 * (c * (b * t_1));
	} else if (c <= 9.2e-21) {
		tmp = t_2;
	} else if (c <= 5e+44) {
		tmp = c * ((b * c) * (i * -2.0));
	} else if (c <= 6e+128) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (b * (c * t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * -i
	t_2 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if c <= -6e+37:
		tmp = 2.0 * (c * (b * t_1))
	elif c <= 9.2e-21:
		tmp = t_2
	elif c <= 5e+44:
		tmp = c * ((b * c) * (i * -2.0))
	elif c <= 6e+128:
		tmp = t_2
	else:
		tmp = 2.0 * (b * (c * t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(-i))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	tmp = 0.0
	if (c <= -6e+37)
		tmp = Float64(2.0 * Float64(c * Float64(b * t_1)));
	elseif (c <= 9.2e-21)
		tmp = t_2;
	elseif (c <= 5e+44)
		tmp = Float64(c * Float64(Float64(b * c) * Float64(i * -2.0)));
	elseif (c <= 6e+128)
		tmp = t_2;
	else
		tmp = Float64(2.0 * Float64(b * Float64(c * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * -i;
	t_2 = ((x * y) + (z * t)) * 2.0;
	tmp = 0.0;
	if (c <= -6e+37)
		tmp = 2.0 * (c * (b * t_1));
	elseif (c <= 9.2e-21)
		tmp = t_2;
	elseif (c <= 5e+44)
		tmp = c * ((b * c) * (i * -2.0));
	elseif (c <= 6e+128)
		tmp = t_2;
	else
		tmp = 2.0 * (b * (c * t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * (-i)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -6e+37], N[(2.0 * N[(c * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-21], t$95$2, If[LessEqual[c, 5e+44], N[(c * N[(N[(b * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e+128], t$95$2, N[(2.0 * N[(b * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.00000000000000043e37

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 90.6%

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

   3. Taylor expanded in c around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

      6. unpow2 64.7%

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

      7. associate-*r* 66.6%

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

      8. *-commutative 66.6%

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

      9. associate-*l* 68.5%

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

      10. *-commutative 68.5%

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

      11. distribute-rgt-neg-in 68.5%

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

      12. associate-*r* 68.5%

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

      13. *-commutative 68.5%

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

      14. distribute-rgt-neg-in 68.5%

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

   5. Simplified 68.5%

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

   if -6.00000000000000043e37 < c < 9.19999999999999998e-21 or 4.9999999999999996e44 < c < 5.9999999999999997e128

   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. Taylor expanded in c around 0 68.8%

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

   if 9.19999999999999998e-21 < c < 4.9999999999999996e44

   1. Initial program 90.2%

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

   2. Taylor expanded in i around inf 90.9%

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

   3. Taylor expanded in a around 0 62.5%

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

   4. Taylor expanded in c around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 62.5%

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

      3. associate-*l* 62.5%

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

      4. unpow2 62.5%

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

      5. associate-*r* 62.3%

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

      6. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in c around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. unpow2 62.5%

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

      5. associate-*r* 62.3%

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

      6. associate-*r* 62.3%

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

      7. associate-*l* 62.5%

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

   9. Simplified 62.5%

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

   if 5.9999999999999997e128 < c

   1. Initial program 86.6%

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

   2. Taylor expanded in b around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. *-commutative 78.5%

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

      3. distribute-rgt-neg-in 78.5%

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

      4. unpow2 78.5%

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

      5. associate-*r* 76.0%

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

   4. Simplified 76.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-21}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+128}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+38} \lor \neg \left(c \leq 7 \cdot 10^{-21} \lor \neg \left(c \leq 6.6 \cdot 10^{+44}\right) \land c \leq 5.8 \cdot 10^{+128}\right):\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.8e+38)
         (not (or (<= c 7e-21) (and (not (<= c 6.6e+44)) (<= c 5.8e+128)))))
   (* c (* (* b c) (* i -2.0)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.8e+38) || !((c <= 7e-21) || (!(c <= 6.6e+44) && (c <= 5.8e+128)))) {
		tmp = c * ((b * c) * (i * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.8d+38)) .or. (.not. (c <= 7d-21) .or. (.not. (c <= 6.6d+44)) .and. (c <= 5.8d+128))) then
        tmp = c * ((b * c) * (i * (-2.0d0)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.8e+38) || !((c <= 7e-21) || (!(c <= 6.6e+44) && (c <= 5.8e+128)))) {
		tmp = c * ((b * c) * (i * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.8e+38) or not ((c <= 7e-21) or (not (c <= 6.6e+44) and (c <= 5.8e+128))):
		tmp = c * ((b * c) * (i * -2.0))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.8e+38) || !((c <= 7e-21) || (!(c <= 6.6e+44) && (c <= 5.8e+128))))
		tmp = Float64(c * Float64(Float64(b * c) * Float64(i * -2.0)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.8e+38) || ~(((c <= 7e-21) || (~((c <= 6.6e+44)) && (c <= 5.8e+128)))))
		tmp = c * ((b * c) * (i * -2.0));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.8e+38], N[Not[Or[LessEqual[c, 7e-21], And[N[Not[LessEqual[c, 6.6e+44]], $MachinePrecision], LessEqual[c, 5.8e+128]]]], $MachinePrecision]], N[(c * N[(N[(b * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.8e38 or 7.0000000000000007e-21 < c < 6.60000000000000027e44 or 5.8000000000000001e128 < c

   1. Initial program 88.1%

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

   2. Taylor expanded in i around inf 81.5%

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

   3. Taylor expanded in a around 0 67.6%

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

   4. Taylor expanded in c around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*r* 67.7%

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

      3. associate-*l* 67.7%

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

      4. unpow2 67.7%

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

      5. associate-*r* 68.5%

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

      6. *-commutative 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in c around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*r* 67.7%

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

      3. *-commutative 67.7%

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

      4. unpow2 67.7%

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

      5. associate-*r* 68.5%

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

      6. associate-*r* 68.5%

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

      7. associate-*l* 67.6%

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

   9. Simplified 67.6%

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

   if -2.8e38 < c < 7.0000000000000007e-21 or 6.60000000000000027e44 < c < 5.8000000000000001e128

   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. Taylor expanded in c around 0 68.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+38} \lor \neg \left(c \leq 7 \cdot 10^{-21} \lor \neg \left(c \leq 6.6 \cdot 10^{+44}\right) \land c \leq 5.8 \cdot 10^{+128}\right):\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 13: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* c (* (* b c) (* i -2.0)))))
   (if (<= c -3.2e+37)
     t_2
     (if (<= c 8.5e-21)
       t_1
       (if (<= c 7.6e+44)
         t_2
         (if (<= c 5.8e+128) t_1 (* -2.0 (* i (* b (* c 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)) * 2.0;
	double t_2 = c * ((b * c) * (i * -2.0));
	double tmp;
	if (c <= -3.2e+37) {
		tmp = t_2;
	} else if (c <= 8.5e-21) {
		tmp = t_1;
	} else if (c <= 7.6e+44) {
		tmp = t_2;
	} else if (c <= 5.8e+128) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (b * (c * 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) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = c * ((b * c) * (i * (-2.0d0)))
    if (c <= (-3.2d+37)) then
        tmp = t_2
    else if (c <= 8.5d-21) then
        tmp = t_1
    else if (c <= 7.6d+44) then
        tmp = t_2
    else if (c <= 5.8d+128) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (i * (b * (c * 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)) * 2.0;
	double t_2 = c * ((b * c) * (i * -2.0));
	double tmp;
	if (c <= -3.2e+37) {
		tmp = t_2;
	} else if (c <= 8.5e-21) {
		tmp = t_1;
	} else if (c <= 7.6e+44) {
		tmp = t_2;
	} else if (c <= 5.8e+128) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (b * (c * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = c * ((b * c) * (i * -2.0))
	tmp = 0
	if c <= -3.2e+37:
		tmp = t_2
	elif c <= 8.5e-21:
		tmp = t_1
	elif c <= 7.6e+44:
		tmp = t_2
	elif c <= 5.8e+128:
		tmp = t_1
	else:
		tmp = -2.0 * (i * (b * (c * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(c * Float64(Float64(b * c) * Float64(i * -2.0)))
	tmp = 0.0
	if (c <= -3.2e+37)
		tmp = t_2;
	elseif (c <= 8.5e-21)
		tmp = t_1;
	elseif (c <= 7.6e+44)
		tmp = t_2;
	elseif (c <= 5.8e+128)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(i * Float64(b * Float64(c * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = c * ((b * c) * (i * -2.0));
	tmp = 0.0;
	if (c <= -3.2e+37)
		tmp = t_2;
	elseif (c <= 8.5e-21)
		tmp = t_1;
	elseif (c <= 7.6e+44)
		tmp = t_2;
	elseif (c <= 5.8e+128)
		tmp = t_1;
	else
		tmp = -2.0 * (i * (b * (c * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(b * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+37], t$95$2, If[LessEqual[c, 8.5e-21], t$95$1, If[LessEqual[c, 7.6e+44], t$95$2, If[LessEqual[c, 5.8e+128], t$95$1, N[(-2.0 * N[(i * N[(b * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.20000000000000014e37 or 8.4999999999999993e-21 < c < 7.6000000000000004e44

   1. Initial program 89.0%

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

   2. Taylor expanded in i around inf 81.2%

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

   3. Taylor expanded in a around 0 67.5%

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

   4. Taylor expanded in c around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 64.3%

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

      3. associate-*l* 64.3%

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

      4. unpow2 64.3%

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

      5. associate-*r* 65.9%

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

      6. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in c around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 64.3%

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

      3. *-commutative 64.3%

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

      4. unpow2 64.3%

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

      5. associate-*r* 65.9%

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

      6. associate-*r* 65.9%

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

      7. associate-*l* 67.5%

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

   9. Simplified 67.5%

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

   if -3.20000000000000014e37 < c < 8.4999999999999993e-21 or 7.6000000000000004e44 < c < 5.8000000000000001e128

   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. Taylor expanded in c around 0 68.8%

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

   if 5.8000000000000001e128 < c

   1. Initial program 86.6%

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

   2. Taylor expanded in i around inf 81.9%

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

   3. Taylor expanded in a around 0 67.7%

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

   4. Taylor expanded in c around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r* 73.4%

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

      3. unpow2 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 14: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= c -1.15e+38)
     (* 2.0 (* c (* b (* c (- i)))))
     (if (<= c 9.2e-21)
       t_1
       (if (<= c 3.8e+44)
         (* c (* (* b c) (* i -2.0)))
         (if (<= c 1.05e+129) t_1 (* -2.0 (* i (* b (* c 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)) * 2.0;
	double tmp;
	if (c <= -1.15e+38) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 9.2e-21) {
		tmp = t_1;
	} else if (c <= 3.8e+44) {
		tmp = c * ((b * c) * (i * -2.0));
	} else if (c <= 1.05e+129) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (b * (c * 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)) * 2.0d0
    if (c <= (-1.15d+38)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= 9.2d-21) then
        tmp = t_1
    else if (c <= 3.8d+44) then
        tmp = c * ((b * c) * (i * (-2.0d0)))
    else if (c <= 1.05d+129) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (i * (b * (c * 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)) * 2.0;
	double tmp;
	if (c <= -1.15e+38) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 9.2e-21) {
		tmp = t_1;
	} else if (c <= 3.8e+44) {
		tmp = c * ((b * c) * (i * -2.0));
	} else if (c <= 1.05e+129) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (b * (c * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if c <= -1.15e+38:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= 9.2e-21:
		tmp = t_1
	elif c <= 3.8e+44:
		tmp = c * ((b * c) * (i * -2.0))
	elif c <= 1.05e+129:
		tmp = t_1
	else:
		tmp = -2.0 * (i * (b * (c * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	tmp = 0.0
	if (c <= -1.15e+38)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= 9.2e-21)
		tmp = t_1;
	elseif (c <= 3.8e+44)
		tmp = Float64(c * Float64(Float64(b * c) * Float64(i * -2.0)));
	elseif (c <= 1.05e+129)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(i * Float64(b * Float64(c * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	tmp = 0.0;
	if (c <= -1.15e+38)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= 9.2e-21)
		tmp = t_1;
	elseif (c <= 3.8e+44)
		tmp = c * ((b * c) * (i * -2.0));
	elseif (c <= 1.05e+129)
		tmp = t_1;
	else
		tmp = -2.0 * (i * (b * (c * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -1.15e+38], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-21], t$95$1, If[LessEqual[c, 3.8e+44], N[(c * N[(N[(b * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+129], t$95$1, N[(-2.0 * N[(i * N[(b * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.1500000000000001e38

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 90.6%

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

   3. Taylor expanded in c around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

      6. unpow2 64.7%

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

      7. associate-*r* 66.6%

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

      8. *-commutative 66.6%

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

      9. associate-*l* 68.5%

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

      10. *-commutative 68.5%

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

      11. distribute-rgt-neg-in 68.5%

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

      12. associate-*r* 68.5%

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

      13. *-commutative 68.5%

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

      14. distribute-rgt-neg-in 68.5%

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

   5. Simplified 68.5%

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

   if -1.1500000000000001e38 < c < 9.19999999999999998e-21 or 3.8000000000000002e44 < c < 1.04999999999999998e129

   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. Taylor expanded in c around 0 68.8%

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

   if 9.19999999999999998e-21 < c < 3.8000000000000002e44

   1. Initial program 90.2%

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

   2. Taylor expanded in i around inf 90.9%

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

   3. Taylor expanded in a around 0 62.5%

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

   4. Taylor expanded in c around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 62.5%

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

      3. associate-*l* 62.5%

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

      4. unpow2 62.5%

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

      5. associate-*r* 62.3%

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

      6. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in c around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. unpow2 62.5%

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

      5. associate-*r* 62.3%

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

      6. associate-*r* 62.3%

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

      7. associate-*l* 62.5%

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

   9. Simplified 62.5%

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

   if 1.04999999999999998e129 < c

   1. Initial program 86.6%

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

   2. Taylor expanded in i around inf 81.9%

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

   3. Taylor expanded in a around 0 67.7%

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

   4. Taylor expanded in c around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r* 73.4%

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

      3. unpow2 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-21}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+129}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 15: 43.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.02 \cdot 10^{-59} \lor \neg \left(x \cdot y \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.02e-59) (not (<= (* x y) 1.92e+99)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.02e-59) || !((x * y) <= 1.92e+99)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.02d-59)) .or. (.not. ((x * y) <= 1.92d+99))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.02e-59) || !((x * y) <= 1.92e+99)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.02e-59) or not ((x * y) <= 1.92e+99):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.02e-59) || !(Float64(x * y) <= 1.92e+99))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.02e-59) || ~(((x * y) <= 1.92e+99)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.02e-59], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.92e+99]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.01999999999999996e-59 or 1.9199999999999999e99 < (*.f64 x y)

   1. Initial program 86.2%

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

   2. Taylor expanded in x around inf 58.3%

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

   if -1.01999999999999996e-59 < (*.f64 x y) < 1.9199999999999999e99

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 35.9%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.02 \cdot 10^{-59} \lor \neg \left(x \cdot y \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 57.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+176} \lor \neg \left(i \leq 5 \cdot 10^{+219}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.4e+176) (not (<= i 5e+219)))
   (* -2.0 (* a (* c i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.4e+176) || !(i <= 5e+219)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.4d+176)) .or. (.not. (i <= 5d+219))) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.4e+176) || !(i <= 5e+219)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.4e+176) or not (i <= 5e+219):
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.4e+176) || !(i <= 5e+219))
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.4e+176) || ~((i <= 5e+219)))
		tmp = -2.0 * (a * (c * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.4e+176], N[Not[LessEqual[i, 5e+219]], $MachinePrecision]], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.4000000000000001e176 or 5e219 < i

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 57.6%

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

   3. Taylor expanded in a around 0 57.6%

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

   if -1.4000000000000001e176 < i < 5e219

   1. Initial program 89.1%

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

   2. Taylor expanded in c around 0 62.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+176} \lor \neg \left(i \leq 5 \cdot 10^{+219}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 17: 29.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.3%

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

2. Taylor expanded in z around inf 28.0%

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

3. Final simplification 28.0%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]

Developer target: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(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))))