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

Percentage Accurate: 90.1% → 95.6%

Time: 22.9s

Alternatives: 19

Speedup: 0.5×

• 46.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 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 y x (* c (* a (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double 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(y, x, (c * (a * -i)));
	}
	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(y, x, Float64(c * Float64(a * Float64(-i)))));
	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[(y * x + N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.0%

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

      1. associate-*l* 97.6%

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

      2. fma-def 97.6%

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

   3. Simplified 97.6%

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

   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. Step-by-step derivation

      1. associate--l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. fma-def 18.8%

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

      4. *-commutative 18.8%

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

      5. +-commutative 18.8%

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

      6. fma-udef 18.8%

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

      7. associate-*r* 25.0%

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

   3. Applied egg-rr 25.0%

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

   4. Taylor expanded in a around inf 68.8%

      \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \color{blue}{-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 68.8%

         \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, -1 \cdot \color{blue}{\left(\left(c \cdot i\right) \cdot a\right)}\right) \]

      2. associate-*r* 68.8%

         \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \color{blue}{\left(-1 \cdot \left(c \cdot i\right)\right) \cdot a}\right) \]

      3. neg-mul-1 68.8%

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

      4. distribute-rgt-neg-in 68.8%

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

      5. associate-*l* 62.8%

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

   6. Simplified 62.8%

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

4. Final simplification 95.4%

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

Alternative 2: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{-107} \lor \neg \left(i \leq 6.2 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -3.3e-107) (not (<= i 6.2e-57)))
   (* (- (+ (* x y) (* z t)) (* (* c (+ a (* b c))) i)) 2.0)
   (* 2.0 (- (fma x y (* z t)) (* c (* b (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -3.3e-107) || !(i <= 6.2e-57)) {
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (fma(x, y, (z * t)) - (c * (b * (c * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -3.3e-107) || !(i <= 6.2e-57))
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -3.3e-107], N[Not[LessEqual[i, 6.2e-57]], $MachinePrecision]], N[(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] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.30000000000000004e-107 or 6.19999999999999952e-57 < i

   1. Initial program 91.9%

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

   if -3.30000000000000004e-107 < i < 6.19999999999999952e-57

   1. Initial program 78.6%

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

      1. fma-def 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*l* 92.8%

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

      4. +-commutative 92.8%

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

      5. fma-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in b around inf 94.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{-107} \lor \neg \left(i \leq 6.2 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 3: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{-104} \lor \neg \left(i \leq 8 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -5.2e-104) (not (<= i 8e-57)))
   (* (- (+ (* x y) (* z t)) (* (* c (+ a (* b c))) i)) 2.0)
   (* 2.0 (fma y x (- (* z t) (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.2e-104) || !(i <= 8e-57)) {
		tmp = (((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * fma(y, x, ((z * t) - (c * (b * (c * i)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -5.2e-104) || !(i <= 8e-57))
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -5.2e-104], N[Not[LessEqual[i, 8e-57]], $MachinePrecision]], N[(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] * 2.0), $MachinePrecision], N[(2.0 * N[(y * x + N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.20000000000000005e-104 or 7.99999999999999964e-57 < i

   1. Initial program 91.9%

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

   if -5.20000000000000005e-104 < i < 7.99999999999999964e-57

   1. Initial program 78.6%

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

      1. associate--l+ 78.6%

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

      2. *-commutative 78.6%

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

      3. fma-def 80.4%

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

      4. *-commutative 80.4%

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

      5. +-commutative 80.4%

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

      6. fma-udef 80.4%

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

      7. associate-*r* 92.8%

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

   3. Applied egg-rr 92.8%

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

   4. Taylor expanded in b around inf 94.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{-104} \lor \neg \left(i \leq 8 \cdot 10^{-57}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 4: 90.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.2%

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

   2. Taylor expanded in b around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-rgt-neg-in 78.8%

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

      3. unpow2 78.8%

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

      4. associate-*r* 82.3%

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

   4. Simplified 82.3%

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

   5. Taylor expanded in b around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. unpow2 78.8%

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

      3. associate-*l* 78.8%

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

      4. associate-*l* 82.3%

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

   7. Simplified 82.3%

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

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

   1. Initial program 90.7%

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

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

   1. Initial program 86.3%

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

   2. Taylor expanded in i around inf 48.8%

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

   3. Taylor expanded in i around 0 48.8%

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

4. Final simplification 89.2%

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

Alternative 5: 40.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-319}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* a i))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1e+103)
     t_3
     (if (<= (* x y) -20.0)
       t_1
       (if (<= (* x y) -5e-103)
         t_2
         (if (<= (* x y) -1e-319)
           t_1
           (if (<= (* x y) 3.2e-202) t_2 (if (<= (* x y) 1e+25) t_1 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 * (c * (a * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+103) {
		tmp = t_3;
	} else if ((x * y) <= -20.0) {
		tmp = t_1;
	} else if ((x * y) <= -5e-103) {
		tmp = t_2;
	} else if ((x * y) <= -1e-319) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = t_2;
	} else if ((x * y) <= 1e+25) {
		tmp = t_1;
	} 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) * (c * (a * i))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1d+103)) then
        tmp = t_3
    else if ((x * y) <= (-20.0d0)) then
        tmp = t_1
    else if ((x * y) <= (-5d-103)) then
        tmp = t_2
    else if ((x * y) <= (-1d-319)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-202) then
        tmp = t_2
    else if ((x * y) <= 1d+25) then
        tmp = t_1
    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 * (c * (a * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+103) {
		tmp = t_3;
	} else if ((x * y) <= -20.0) {
		tmp = t_1;
	} else if ((x * y) <= -5e-103) {
		tmp = t_2;
	} else if ((x * y) <= -1e-319) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = t_2;
	} else if ((x * y) <= 1e+25) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * (a * i))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1e+103:
		tmp = t_3
	elif (x * y) <= -20.0:
		tmp = t_1
	elif (x * y) <= -5e-103:
		tmp = t_2
	elif (x * y) <= -1e-319:
		tmp = t_1
	elif (x * y) <= 3.2e-202:
		tmp = t_2
	elif (x * y) <= 1e+25:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(a * i)))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1e+103)
		tmp = t_3;
	elseif (Float64(x * y) <= -20.0)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e-103)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e-319)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-202)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e+25)
		tmp = t_1;
	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 * (c * (a * i));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1e+103)
		tmp = t_3;
	elseif ((x * y) <= -20.0)
		tmp = t_1;
	elseif ((x * y) <= -5e-103)
		tmp = t_2;
	elseif ((x * y) <= -1e-319)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-202)
		tmp = t_2;
	elseif ((x * y) <= 1e+25)
		tmp = t_1;
	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[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+103], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -20.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e-103], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e-319], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-202], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e+25], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e103 or 1.00000000000000009e25 < (*.f64 x y)

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf 54.9%

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

   if -1e103 < (*.f64 x y) < -20 or -4.99999999999999966e-103 < (*.f64 x y) < -9.99989e-320 or 3.2000000000000001e-202 < (*.f64 x y) < 1.00000000000000009e25

   1. Initial program 90.5%

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

   2. Taylor expanded in i around inf 64.7%

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

   3. Taylor expanded in c around 0 39.3%

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

      1. *-commutative 39.3%

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

      2. associate-*l* 36.2%

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

   5. Simplified 36.2%

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

   if -20 < (*.f64 x y) < -4.99999999999999966e-103 or -9.99989e-320 < (*.f64 x y) < 3.2000000000000001e-202

   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 inf 42.5%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+25}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 6: 40.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-319}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* i (* a c))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1e+103)
     t_3
     (if (<= (* x y) -20.0)
       (* -2.0 (* c (* a i)))
       (if (<= (* x y) -5e-103)
         t_2
         (if (<= (* x y) -1e-319)
           t_1
           (if (<= (* x y) 3.2e-202) t_2 (if (<= (* x y) 5e+66) t_1 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 * (i * (a * c));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+103) {
		tmp = t_3;
	} else if ((x * y) <= -20.0) {
		tmp = -2.0 * (c * (a * i));
	} else if ((x * y) <= -5e-103) {
		tmp = t_2;
	} else if ((x * y) <= -1e-319) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = t_2;
	} else if ((x * y) <= 5e+66) {
		tmp = t_1;
	} 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) * (i * (a * c))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1d+103)) then
        tmp = t_3
    else if ((x * y) <= (-20.0d0)) then
        tmp = (-2.0d0) * (c * (a * i))
    else if ((x * y) <= (-5d-103)) then
        tmp = t_2
    else if ((x * y) <= (-1d-319)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-202) then
        tmp = t_2
    else if ((x * y) <= 5d+66) then
        tmp = t_1
    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 * (i * (a * c));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+103) {
		tmp = t_3;
	} else if ((x * y) <= -20.0) {
		tmp = -2.0 * (c * (a * i));
	} else if ((x * y) <= -5e-103) {
		tmp = t_2;
	} else if ((x * y) <= -1e-319) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = t_2;
	} else if ((x * y) <= 5e+66) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (i * (a * c))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1e+103:
		tmp = t_3
	elif (x * y) <= -20.0:
		tmp = -2.0 * (c * (a * i))
	elif (x * y) <= -5e-103:
		tmp = t_2
	elif (x * y) <= -1e-319:
		tmp = t_1
	elif (x * y) <= 3.2e-202:
		tmp = t_2
	elif (x * y) <= 5e+66:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(i * Float64(a * c)))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1e+103)
		tmp = t_3;
	elseif (Float64(x * y) <= -20.0)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	elseif (Float64(x * y) <= -5e-103)
		tmp = t_2;
	elseif (Float64(x * y) <= -1e-319)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-202)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e+66)
		tmp = t_1;
	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 * (i * (a * c));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1e+103)
		tmp = t_3;
	elseif ((x * y) <= -20.0)
		tmp = -2.0 * (c * (a * i));
	elseif ((x * y) <= -5e-103)
		tmp = t_2;
	elseif ((x * y) <= -1e-319)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-202)
		tmp = t_2;
	elseif ((x * y) <= 5e+66)
		tmp = t_1;
	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[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+103], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -20.0], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-103], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1e-319], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-202], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e+66], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1e103 or 4.99999999999999991e66 < (*.f64 x y)

   1. Initial program 82.5%

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

   2. Taylor expanded in x around inf 57.4%

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

   if -1e103 < (*.f64 x y) < -20

   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 i around inf 49.2%

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

   3. Taylor expanded in c around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-*l* 49.2%

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

   5. Simplified 49.2%

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

   if -20 < (*.f64 x y) < -4.99999999999999966e-103 or -9.99989e-320 < (*.f64 x y) < 3.2000000000000001e-202

   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 inf 42.5%

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

   if -4.99999999999999966e-103 < (*.f64 x y) < -9.99989e-320 or 3.2000000000000001e-202 < (*.f64 x y) < 4.99999999999999991e66

   1. Initial program 92.5%

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

   2. Taylor expanded in i around inf 65.8%

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

   3. Taylor expanded in c around 0 35.8%

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

      1. associate-*r* 32.2%

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

   5. Simplified 32.2%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+103}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 7: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* a (* c i))))))
   (if (<= (* x y) -5e+244)
     t_1
     (if (<= (* x y) -1e+181)
       (* 2.0 (- (* z t) (* c (* c (* b i)))))
       (if (<= (* x y) -5e+99)
         t_1
         (if (<= (* x y) 5e+31)
           (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
           (* (+ (* x y) (* z t)) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if ((x * y) <= -5e+244) {
		tmp = t_1;
	} else if ((x * y) <= -1e+181) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if ((x * y) <= -5e+99) {
		tmp = t_1;
	} else if ((x * y) <= 5e+31) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (a * (c * i)))
    if ((x * y) <= (-5d+244)) then
        tmp = t_1
    else if ((x * y) <= (-1d+181)) then
        tmp = 2.0d0 * ((z * t) - (c * (c * (b * i))))
    else if ((x * y) <= (-5d+99)) then
        tmp = t_1
    else if ((x * y) <= 5d+31) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if ((x * y) <= -5e+244) {
		tmp = t_1;
	} else if ((x * y) <= -1e+181) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if ((x * y) <= -5e+99) {
		tmp = t_1;
	} else if ((x * y) <= 5e+31) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (a * (c * i)))
	tmp = 0
	if (x * y) <= -5e+244:
		tmp = t_1
	elif (x * y) <= -1e+181:
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))))
	elif (x * y) <= -5e+99:
		tmp = t_1
	elif (x * y) <= 5e+31:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))))
	tmp = 0.0
	if (Float64(x * y) <= -5e+244)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e+181)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(c * Float64(b * i)))));
	elseif (Float64(x * y) <= -5e+99)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+31)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (a * (c * i)));
	tmp = 0.0;
	if ((x * y) <= -5e+244)
		tmp = t_1;
	elseif ((x * y) <= -1e+181)
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	elseif ((x * y) <= -5e+99)
		tmp = t_1;
	elseif ((x * y) <= 5e+31)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+244], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e+181], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+99], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+31], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000022e244 or -9.9999999999999992e180 < (*.f64 x y) < -5.00000000000000008e99

   1. Initial program 87.4%

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

   2. Taylor expanded in a around inf 90.7%

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

   3. Taylor expanded in z around 0 94.0%

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

   if -5.00000000000000022e244 < (*.f64 x y) < -9.9999999999999992e180

   1. Initial program 68.3%

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

   2. Taylor expanded in x around 0 68.3%

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

   3. Taylor expanded in a around 0 87.0%

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

      1. associate-*r* 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*r* 87.2%

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

   5. Simplified 87.2%

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

   if -5.00000000000000008e99 < (*.f64 x y) < 5.00000000000000027e31

   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 x around 0 85.3%

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

   if 5.00000000000000027e31 < (*.f64 x y)

   1. Initial program 82.6%

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

   2. Taylor expanded in c around 0 72.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+244}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 8: 44.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-209}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* (* b c) i)))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -5e+104)
     t_2
     (if (<= (* x y) -20.0)
       (* (* c i) (* a -2.0))
       (if (<= (* x y) -4e-283)
         t_1
         (if (<= (* x y) 1e-209)
           (* 2.0 (* z t))
           (if (<= (* x y) 5e+31) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * ((b * c) * i));
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5e+104) {
		tmp = t_2;
	} else if ((x * y) <= -20.0) {
		tmp = (c * i) * (a * -2.0);
	} else if ((x * y) <= -4e-283) {
		tmp = t_1;
	} else if ((x * y) <= 1e-209) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 5e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * ((b * c) * i))
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-5d+104)) then
        tmp = t_2
    else if ((x * y) <= (-20.0d0)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if ((x * y) <= (-4d-283)) then
        tmp = t_1
    else if ((x * y) <= 1d-209) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 5d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * ((b * c) * i));
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5e+104) {
		tmp = t_2;
	} else if ((x * y) <= -20.0) {
		tmp = (c * i) * (a * -2.0);
	} else if ((x * y) <= -4e-283) {
		tmp = t_1;
	} else if ((x * y) <= 1e-209) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 5e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * ((b * c) * i))
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -5e+104:
		tmp = t_2
	elif (x * y) <= -20.0:
		tmp = (c * i) * (a * -2.0)
	elif (x * y) <= -4e-283:
		tmp = t_1
	elif (x * y) <= 1e-209:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 5e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(Float64(b * c) * i)))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -5e+104)
		tmp = t_2;
	elseif (Float64(x * y) <= -20.0)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (Float64(x * y) <= -4e-283)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-209)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 5e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * ((b * c) * i));
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -5e+104)
		tmp = t_2;
	elseif ((x * y) <= -20.0)
		tmp = (c * i) * (a * -2.0);
	elseif ((x * y) <= -4e-283)
		tmp = t_1;
	elseif ((x * y) <= 1e-209)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 5e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+104], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -20.0], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-283], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-209], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+31], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.9999999999999997e104 or 5.00000000000000027e31 < (*.f64 x y)

   1. Initial program 83.3%

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

   2. Taylor expanded in x around inf 55.8%

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

   if -4.9999999999999997e104 < (*.f64 x y) < -20

   1. Initial program 86.8%

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

   2. Taylor expanded in a around inf 51.5%

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

   3. Taylor expanded in a around 0 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*l* 51.5%

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

   5. Simplified 51.5%

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

   if -20 < (*.f64 x y) < -3.99999999999999979e-283 or 1e-209 < (*.f64 x y) < 5.00000000000000027e31

   1. Initial program 93.0%

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

   2. Taylor expanded in i around inf 70.6%

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

   3. Taylor expanded in a around 0 54.8%

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

   4. Taylor expanded in c around 0 49.8%

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

      1. unpow2 49.8%

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

      2. associate-*r* 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

      5. associate-*l* 53.7%

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

   6. Simplified 53.7%

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

   if -3.99999999999999979e-283 < (*.f64 x y) < 1e-209

   1. Initial program 80.6%

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

   2. Taylor expanded in z around inf 46.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-283}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-209}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 9: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1000:\\ \;\;\;\;2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-96}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* x y) -1000.0)
     (* 2.0 (- t_1 (* a (* c i))))
     (if (<= (* x y) 1e-96)
       (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
       (* 2.0 (- t_1 (* b (* c (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -1000.0) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else if ((x * y) <= 1e-96) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (t_1 - (b * (c * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((x * y) <= (-1000.0d0)) then
        tmp = 2.0d0 * (t_1 - (a * (c * i)))
    else if ((x * y) <= 1d-96) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (t_1 - (b * (c * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -1000.0) {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	} else if ((x * y) <= 1e-96) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (t_1 - (b * (c * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -1000.0:
		tmp = 2.0 * (t_1 - (a * (c * i)))
	elif (x * y) <= 1e-96:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (t_1 - (b * (c * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1000.0)
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	elseif (Float64(x * y) <= 1e-96)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(b * Float64(c * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -1000.0)
		tmp = 2.0 * (t_1 - (a * (c * i)));
	elseif ((x * y) <= 1e-96)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (t_1 - (b * (c * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1000.0], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-96], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e3

   1. Initial program 85.1%

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

   2. Taylor expanded in a around inf 86.7%

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

   if -1e3 < (*.f64 x y) < 9.9999999999999991e-97

   1. Initial program 88.0%

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

   2. Taylor expanded in x around 0 88.3%

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

   if 9.9999999999999991e-97 < (*.f64 x y)

   1. Initial program 85.0%

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

   2. Taylor expanded in a around 0 76.3%

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

      1. unpow2 76.3%

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

      2. associate-*r* 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1000:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-96}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 10: 43.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* a -2.0))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -5e+104)
     t_2
     (if (<= (* x y) -20.0)
       t_1
       (if (<= (* x y) 3.2e-202)
         (* 2.0 (* z t))
         (if (<= (* x y) 5e+66) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5e+104) {
		tmp = t_2;
	} else if ((x * y) <= -20.0) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 5e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) * (a * (-2.0d0))
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-5d+104)) then
        tmp = t_2
    else if ((x * y) <= (-20.0d0)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-202) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 5d+66) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5e+104) {
		tmp = t_2;
	} else if ((x * y) <= -20.0) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-202) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 5e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (a * -2.0)
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -5e+104:
		tmp = t_2
	elif (x * y) <= -20.0:
		tmp = t_1
	elif (x * y) <= 3.2e-202:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 5e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -5e+104)
		tmp = t_2;
	elseif (Float64(x * y) <= -20.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-202)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 5e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (a * -2.0);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -5e+104)
		tmp = t_2;
	elseif ((x * y) <= -20.0)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-202)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 5e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+104], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -20.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-202], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+66], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999997e104 or 4.99999999999999991e66 < (*.f64 x y)

   1. Initial program 82.3%

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

   2. Taylor expanded in x around inf 57.9%

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

   if -4.9999999999999997e104 < (*.f64 x y) < -20 or 3.2000000000000001e-202 < (*.f64 x y) < 4.99999999999999991e66

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 42.6%

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

   3. Taylor expanded in a around 0 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

      3. associate-*l* 42.6%

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

   5. Simplified 42.6%

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

   if -20 < (*.f64 x y) < 3.2000000000000001e-202

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 37.8%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -20:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 11: 70.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+45}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-119}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i))) (t_2 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= c -1.1e+45)
     (* -2.0 (* c (* (+ a (* b c)) i)))
     (if (<= c -2.3e-12)
       t_2
       (if (<= c -1.08e-119)
         (* 2.0 (- (* x y) t_1))
         (if (<= c 2.55e-111)
           t_2
           (if (<= c 8.5e+123)
             (* 2.0 (- (* z t) t_1))
             (* 2.0 (* c (* b (* c (- i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -1.1e+45) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= -2.3e-12) {
		tmp = t_2;
	} else if (c <= -1.08e-119) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 2.55e-111) {
		tmp = t_2;
	} else if (c <= 8.5e+123) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * i)
    t_2 = ((x * y) + (z * t)) * 2.0d0
    if (c <= (-1.1d+45)) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else if (c <= (-2.3d-12)) then
        tmp = t_2
    else if (c <= (-1.08d-119)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 2.55d-111) then
        tmp = t_2
    else if (c <= 8.5d+123) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * (c * (b * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -1.1e+45) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= -2.3e-12) {
		tmp = t_2;
	} else if (c <= -1.08e-119) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 2.55e-111) {
		tmp = t_2;
	} else if (c <= 8.5e+123) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	t_2 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if c <= -1.1e+45:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	elif c <= -2.3e-12:
		tmp = t_2
	elif c <= -1.08e-119:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 2.55e-111:
		tmp = t_2
	elif c <= 8.5e+123:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * (c * (b * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	tmp = 0.0
	if (c <= -1.1e+45)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	elseif (c <= -2.3e-12)
		tmp = t_2;
	elseif (c <= -1.08e-119)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 2.55e-111)
		tmp = t_2;
	elseif (c <= 8.5e+123)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	t_2 = ((x * y) + (z * t)) * 2.0;
	tmp = 0.0;
	if (c <= -1.1e+45)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	elseif (c <= -2.3e-12)
		tmp = t_2;
	elseif (c <= -1.08e-119)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 2.55e-111)
		tmp = t_2;
	elseif (c <= 8.5e+123)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * (c * (b * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -1.1e+45], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-12], t$95$2, If[LessEqual[c, -1.08e-119], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.55e-111], t$95$2, If[LessEqual[c, 8.5e+123], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.1e45

   1. Initial program 77.5%

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

   2. Taylor expanded in i around inf 80.5%

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

   3. Taylor expanded in i around 0 80.5%

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

   if -1.1e45 < c < -2.29999999999999989e-12 or -1.0799999999999999e-119 < c < 2.55000000000000016e-111

   1. Initial program 96.6%

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

   2. Taylor expanded in c around 0 84.9%

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

   if -2.29999999999999989e-12 < c < -1.0799999999999999e-119

   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 a around inf 66.4%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 2.55000000000000016e-111 < c < 8.5e123

   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 x around 0 81.2%

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

   3. Taylor expanded in c around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. sub-neg 63.8%

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

   5. Simplified 63.8%

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

   if 8.5e123 < c

   1. Initial program 67.8%

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

   2. Taylor expanded in i around inf 75.9%

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

   3. Taylor expanded in a around 0 80.6%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right)\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+45}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{-119}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{-111}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-120}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i))))
   (if (<= c -6.5e+68)
     (* -2.0 (* c (* (+ a (* b c)) i)))
     (if (<= c -2.85e-11)
       (* 2.0 (- (* z t) (* c (* c (* b i)))))
       (if (<= c -8e-120)
         (* 2.0 (- (* x y) t_1))
         (if (<= c 2.5e-113)
           (* (+ (* x y) (* z t)) 2.0)
           (if (<= c 8e+124)
             (* 2.0 (- (* z t) t_1))
             (* 2.0 (* c (* b (* c (- i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double tmp;
	if (c <= -6.5e+68) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= -2.85e-11) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -8e-120) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 2.5e-113) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 8e+124) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * i)
    if (c <= (-6.5d+68)) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else if (c <= (-2.85d-11)) then
        tmp = 2.0d0 * ((z * t) - (c * (c * (b * i))))
    else if (c <= (-8d-120)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 2.5d-113) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 8d+124) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * (c * (b * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double tmp;
	if (c <= -6.5e+68) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= -2.85e-11) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -8e-120) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 2.5e-113) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 8e+124) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	tmp = 0
	if c <= -6.5e+68:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	elif c <= -2.85e-11:
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))))
	elif c <= -8e-120:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 2.5e-113:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 8e+124:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * (c * (b * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	tmp = 0.0
	if (c <= -6.5e+68)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	elseif (c <= -2.85e-11)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(c * Float64(b * i)))));
	elseif (c <= -8e-120)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 2.5e-113)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 8e+124)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	tmp = 0.0;
	if (c <= -6.5e+68)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	elseif (c <= -2.85e-11)
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	elseif (c <= -8e-120)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 2.5e-113)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 8e+124)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * (c * (b * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e+68], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.85e-11], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e-120], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e-113], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 8e+124], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.5000000000000005e68

   1. Initial program 80.2%

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

   2. Taylor expanded in i around inf 87.8%

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

   3. Taylor expanded in i around 0 87.8%

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

   if -6.5000000000000005e68 < c < -2.8499999999999999e-11

   1. Initial program 80.1%

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

   2. Taylor expanded in x around 0 76.1%

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

   3. Taylor expanded in a around 0 76.6%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*r* 76.7%

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

   5. Simplified 76.7%

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

   if -2.8499999999999999e-11 < c < -7.99999999999999983e-120

   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 a around inf 66.4%

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

   3. Taylor expanded in z around 0 70.8%

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

   if -7.99999999999999983e-120 < c < 2.4999999999999999e-113

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 87.0%

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

   if 2.4999999999999999e-113 < c < 7.99999999999999959e124

   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 x around 0 81.2%

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

   3. Taylor expanded in c around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. sub-neg 63.8%

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

   5. Simplified 63.8%

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

   if 7.99999999999999959e124 < c

   1. Initial program 67.8%

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

   2. Taylor expanded in i around inf 75.9%

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

   3. Taylor expanded in a around 0 80.6%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right)\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-120}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 13: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(c \cdot \left(c \cdot i\right)\right) \cdot -2\right)\\ t_2 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_3 := -2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.85 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (* (* c (* c i)) -2.0)))
        (t_2 (* (+ (* x y) (* z t)) 2.0))
        (t_3 (* -2.0 (* c (* (* b c) i)))))
   (if (<= c -7e+88)
     t_3
     (if (<= c 2.85e+85)
       t_2
       (if (<= c 6.6e+114)
         t_1
         (if (<= c 7.6e+127) t_2 (if (<= c 2.15e+156) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * ((c * (c * i)) * -2.0);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = -2.0 * (c * ((b * c) * i));
	double tmp;
	if (c <= -7e+88) {
		tmp = t_3;
	} else if (c <= 2.85e+85) {
		tmp = t_2;
	} else if (c <= 6.6e+114) {
		tmp = t_1;
	} else if (c <= 7.6e+127) {
		tmp = t_2;
	} else if (c <= 2.15e+156) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((c * (c * i)) * (-2.0d0))
    t_2 = ((x * y) + (z * t)) * 2.0d0
    t_3 = (-2.0d0) * (c * ((b * c) * i))
    if (c <= (-7d+88)) then
        tmp = t_3
    else if (c <= 2.85d+85) then
        tmp = t_2
    else if (c <= 6.6d+114) then
        tmp = t_1
    else if (c <= 7.6d+127) then
        tmp = t_2
    else if (c <= 2.15d+156) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * ((c * (c * i)) * -2.0);
	double t_2 = ((x * y) + (z * t)) * 2.0;
	double t_3 = -2.0 * (c * ((b * c) * i));
	double tmp;
	if (c <= -7e+88) {
		tmp = t_3;
	} else if (c <= 2.85e+85) {
		tmp = t_2;
	} else if (c <= 6.6e+114) {
		tmp = t_1;
	} else if (c <= 7.6e+127) {
		tmp = t_2;
	} else if (c <= 2.15e+156) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * ((c * (c * i)) * -2.0)
	t_2 = ((x * y) + (z * t)) * 2.0
	t_3 = -2.0 * (c * ((b * c) * i))
	tmp = 0
	if c <= -7e+88:
		tmp = t_3
	elif c <= 2.85e+85:
		tmp = t_2
	elif c <= 6.6e+114:
		tmp = t_1
	elif c <= 7.6e+127:
		tmp = t_2
	elif c <= 2.15e+156:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * Float64(Float64(c * Float64(c * i)) * -2.0))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(b * c) * i)))
	tmp = 0.0
	if (c <= -7e+88)
		tmp = t_3;
	elseif (c <= 2.85e+85)
		tmp = t_2;
	elseif (c <= 6.6e+114)
		tmp = t_1;
	elseif (c <= 7.6e+127)
		tmp = t_2;
	elseif (c <= 2.15e+156)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * ((c * (c * i)) * -2.0);
	t_2 = ((x * y) + (z * t)) * 2.0;
	t_3 = -2.0 * (c * ((b * c) * i));
	tmp = 0.0;
	if (c <= -7e+88)
		tmp = t_3;
	elseif (c <= 2.85e+85)
		tmp = t_2;
	elseif (c <= 6.6e+114)
		tmp = t_1;
	elseif (c <= 7.6e+127)
		tmp = t_2;
	elseif (c <= 2.15e+156)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[(N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+88], t$95$3, If[LessEqual[c, 2.85e+85], t$95$2, If[LessEqual[c, 6.6e+114], t$95$1, If[LessEqual[c, 7.6e+127], t$95$2, If[LessEqual[c, 2.15e+156], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.9999999999999995e88 or 7.59999999999999961e127 < c < 2.14999999999999993e156

   1. Initial program 79.1%

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

   2. Taylor expanded in i around inf 90.2%

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

   3. Taylor expanded in a around 0 74.8%

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

   4. Taylor expanded in c around 0 65.9%

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

      1. unpow2 65.9%

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

      2. associate-*r* 69.5%

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

      3. associate-*r* 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-*l* 74.8%

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

   6. Simplified 74.8%

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

   if -6.9999999999999995e88 < c < 2.8500000000000001e85 or 6.6000000000000001e114 < c < 7.59999999999999961e127

   1. Initial program 92.7%

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

   2. Taylor expanded in c around 0 68.2%

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

   if 2.8500000000000001e85 < c < 6.6000000000000001e114 or 2.14999999999999993e156 < c

   1. Initial program 70.0%

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

   2. Taylor expanded in b around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-rgt-neg-in 68.1%

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

      3. unpow2 68.1%

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

      4. associate-*r* 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in b around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. unpow2 68.1%

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

      3. associate-*l* 68.1%

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

      4. associate-*l* 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+88}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.85 \cdot 10^{+85}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(\left(c \cdot \left(c \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+127}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+156}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(c \cdot \left(c \cdot i\right)\right) \cdot -2\right)\\ \end{array} \]

Alternative 14: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+45} \lor \neg \left(c \leq 6.2 \cdot 10^{-60} \lor \neg \left(c \leq 0.0062\right) \land c \leq 9.4 \cdot 10^{+42}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e+45)
         (not (or (<= c 6.2e-60) (and (not (<= c 0.0062)) (<= c 9.4e+42)))))
   (* -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 <= -1.65e+45) || !((c <= 6.2e-60) || (!(c <= 0.0062) && (c <= 9.4e+42)))) {
		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 <= (-1.65d+45)) .or. (.not. (c <= 6.2d-60) .or. (.not. (c <= 0.0062d0)) .and. (c <= 9.4d+42))) 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 <= -1.65e+45) || !((c <= 6.2e-60) || (!(c <= 0.0062) && (c <= 9.4e+42)))) {
		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 <= -1.65e+45) or not ((c <= 6.2e-60) or (not (c <= 0.0062) and (c <= 9.4e+42))):
		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 <= -1.65e+45) || !((c <= 6.2e-60) || (!(c <= 0.0062) && (c <= 9.4e+42))))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.65e+45) || ~(((c <= 6.2e-60) || (~((c <= 0.0062)) && (c <= 9.4e+42)))))
		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, -1.65e+45], N[Not[Or[LessEqual[c, 6.2e-60], And[N[Not[LessEqual[c, 0.0062]], $MachinePrecision], LessEqual[c, 9.4e+42]]]], $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 < -1.65e45 or 6.19999999999999976e-60 < c < 0.00619999999999999978 or 9.39999999999999971e42 < c

   1. Initial program 77.4%

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

   2. Taylor expanded in i around inf 75.1%

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

   3. Taylor expanded in i around 0 75.1%

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

   if -1.65e45 < c < 6.19999999999999976e-60 or 0.00619999999999999978 < c < 9.39999999999999971e42

   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 c around 0 75.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+45} \lor \neg \left(c \leq 6.2 \cdot 10^{-60} \lor \neg \left(c \leq 0.0062\right) \land c \leq 9.4 \cdot 10^{+42}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 15: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2e-9)
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (if (<= c 3e+127)
     (* 2.0 (- (+ (* x y) (* z t)) (* a (* c i))))
     (* 2.0 (* c (* b (* c (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2e-9) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else if (c <= 3e+127) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2d-9)) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else if (c <= 3d+127) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (a * (c * i)))
    else
        tmp = 2.0d0 * (c * (b * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2e-9) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else if (c <= 3e+127) {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2e-9:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	elif c <= 3e+127:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	else:
		tmp = 2.0 * (c * (b * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2e-9)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	elseif (c <= 3e+127)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2e-9)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	elseif (c <= 3e+127)
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	else
		tmp = 2.0 * (c * (b * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2e-9], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+127], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.00000000000000012e-9

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0 81.0%

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

   if -2.00000000000000012e-9 < c < 3.0000000000000002e127

   1. Initial program 93.9%

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

   2. Taylor expanded in a around inf 86.0%

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

   if 3.0000000000000002e127 < c

   1. Initial program 67.8%

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

   2. Taylor expanded in i around inf 75.9%

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

   3. Taylor expanded in a around 0 80.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 16: 71.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-112}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+119}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -8e+44)
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (if (<= c 8e-112)
     (* (+ (* x y) (* z t)) 2.0)
     (if (<= c 9.5e+119)
       (* 2.0 (- (* z t) (* a (* c i))))
       (* 2.0 (* c (* b (* c (- i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -8e+44) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= 8e-112) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 9.5e+119) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-8d+44)) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else if (c <= 8d-112) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 9.5d+119) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = 2.0d0 * (c * (b * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -8e+44) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (c <= 8e-112) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 9.5e+119) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (c * (b * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -8e+44:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	elif c <= 8e-112:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 9.5e+119:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = 2.0 * (c * (b * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -8e+44)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	elseif (c <= 8e-112)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 9.5e+119)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -8e+44)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	elseif (c <= 8e-112)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 9.5e+119)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = 2.0 * (c * (b * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -8e+44], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e-112], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 9.5e+119], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.0000000000000007e44

   1. Initial program 77.5%

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

   2. Taylor expanded in i around inf 80.5%

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

   3. Taylor expanded in i around 0 80.5%

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

   if -8.0000000000000007e44 < c < 7.9999999999999996e-112

   1. Initial program 96.2%

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

   2. Taylor expanded in c around 0 77.1%

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

   if 7.9999999999999996e-112 < c < 9.4999999999999994e119

   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 x around 0 81.2%

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

   3. Taylor expanded in c around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. sub-neg 63.8%

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

   5. Simplified 63.8%

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

   if 9.4999999999999994e119 < c

   1. Initial program 67.8%

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

   2. Taylor expanded in i around inf 75.9%

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

   3. Taylor expanded in a around 0 80.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-112}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+119}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 17: 44.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+112} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+66}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+112) (not (<= (* x y) 5e+66)))
   (* (* 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) <= -5e+112) || !((x * y) <= 5e+66)) {
		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) <= (-5d+112)) .or. (.not. ((x * y) <= 5d+66))) 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) <= -5e+112) || !((x * y) <= 5e+66)) {
		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) <= -5e+112) or not ((x * y) <= 5e+66):
		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) <= -5e+112) || !(Float64(x * y) <= 5e+66))
		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) <= -5e+112) || ~(((x * y) <= 5e+66)))
		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], -5e+112], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+66]], $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) < -5e112 or 4.99999999999999991e66 < (*.f64 x y)

   1. Initial program 82.1%

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

   2. Taylor expanded in x around inf 58.5%

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

   if -5e112 < (*.f64 x y) < 4.99999999999999991e66

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 30.9%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+112} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+66}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 18: 68.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+83} \lor \neg \left(c \leq 7.2 \cdot 10^{+119}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -7.2e+83) (not (<= c 7.2e+119)))
   (* -2.0 (* c (* (* 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 <= -7.2e+83) || !(c <= 7.2e+119)) {
		tmp = -2.0 * (c * ((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 <= (-7.2d+83)) .or. (.not. (c <= 7.2d+119))) then
        tmp = (-2.0d0) * (c * ((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 <= -7.2e+83) || !(c <= 7.2e+119)) {
		tmp = -2.0 * (c * ((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 <= -7.2e+83) or not (c <= 7.2e+119):
		tmp = -2.0 * (c * ((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 <= -7.2e+83) || !(c <= 7.2e+119))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(b * c) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -7.2e+83) || ~((c <= 7.2e+119)))
		tmp = -2.0 * (c * ((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, -7.2e+83], N[Not[LessEqual[c, 7.2e+119]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(b * c), $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 < -7.1999999999999995e83 or 7.20000000000000003e119 < c

   1. Initial program 74.0%

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

   2. Taylor expanded in i around inf 83.3%

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

   3. Taylor expanded in a around 0 75.8%

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

   4. Taylor expanded in c around 0 67.3%

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

      1. unpow2 67.3%

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

      2. associate-*r* 71.5%

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

      3. associate-*r* 73.9%

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

      4. *-commutative 73.9%

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

      5. associate-*l* 72.7%

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

   6. Simplified 72.7%

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

   if -7.1999999999999995e83 < c < 7.20000000000000003e119

   1. Initial program 92.1%

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

   2. Taylor expanded in c around 0 65.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+83} \lor \neg \left(c \leq 7.2 \cdot 10^{+119}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 19: 29.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

2. Taylor expanded in z around inf 26.4%

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

3. Final simplification 26.4%

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

Developer target: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023282 
(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))))