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

Percentage Accurate: 89.9% → 97.3%

Time: 19.1s

Alternatives: 18

Speedup: 0.6×

• 46.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.1× speedup

Math

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

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 (* y (- x (* c (* i (/ (fma c b a) y)))))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.0%

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

      1. fma-define 95.0%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 38.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. associate-/l* 69.2%

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

      4. +-commutative 69.2%

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

      5. *-commutative 69.2%

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

      6. fma-undefine 69.2%

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

      7. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 96.9%

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

Alternative 2: 94.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a + b \cdot c\right)\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - c \cdot \left(i \cdot \frac{\mathsf{fma}\left(c, b, a\right)}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_1 \cdot i\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (+ a (* b c)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+302)))
     (* 2.0 (* y (- x (* c (* i (/ (fma c b a) y))))))
     (* (- (+ (* x y) (* z t)) (* t_1 i)) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a + (b * c));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+302)) {
		tmp = 2.0 * (y * (x - (c * (i * (fma(c, b, a) / y)))));
	} else {
		tmp = (((x * y) + (z * t)) - (t_1 * i)) * 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(a + Float64(b * c)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+302))
		tmp = Float64(2.0 * Float64(y * Float64(x - Float64(c * Float64(i * Float64(fma(c, b, a) / y))))));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_1 * i)) * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(2.0 * N[(y * N[(x - N[(c * N[(i * N[(N[(c * b + a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -inf.0 or 5e302 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 68.7%

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

   3. Taylor expanded in z around 0 86.1%

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

   4. Taylor expanded in y around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

      3. associate-/l* 90.4%

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

      4. +-commutative 90.4%

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

      5. *-commutative 90.4%

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

      6. fma-undefine 90.4%

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

      7. associate-/l* 90.4%

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

   6. Simplified 90.4%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 5e302

   1. Initial program 98.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty \lor \neg \left(c \cdot \left(a + b \cdot c\right) \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - c \cdot \left(i \cdot \frac{\mathsf{fma}\left(c, b, a\right)}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c t_1)))
   (if (<= t_2 (- INFINITY))
     (* (* c (+ (* b (* c i)) (* a i))) -2.0)
     (if (<= t_2 5e+258)
       (* (- (+ (* x y) (* z t)) (* t_2 i)) 2.0)
       (* 2.0 (- (* x y) (* c (* t_1 i))))))))

C

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

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (c * ((b * (c * i)) + (a * i))) * -2.0
	elif t_2 <= 5e+258:
		tmp = (((x * y) + (z * t)) - (t_2 * i)) * 2.0
	else:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(c * N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+258], 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[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.1%

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

   3. Taylor expanded in z around 0 81.5%

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

   4. Taylor expanded in x around 0 84.3%

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

      1. distribute-rgt-in 81.5%

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

      2. associate-*r* 86.4%

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

      3. +-commutative 86.4%

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

   6. Applied egg-rr 86.4%

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

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

   1. Initial program 98.4%

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

   if 5e258 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 78.0%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 95.7%

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

Alternative 4: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-261}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-45}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* i (* a c))))
        (t_3 (* (* x y) 2.0)))
   (if (<= a -1.06e+142)
     t_2
     (if (<= a -2.8e-182)
       t_1
       (if (<= a 1.9e-261)
         t_3
         (if (<= a 6.3e-86)
           t_1
           (if (<= a 5.4e-45) t_3 (if (<= a 4.3e+80) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (i * (a * c));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (a <= -1.06e+142) {
		tmp = t_2;
	} else if (a <= -2.8e-182) {
		tmp = t_1;
	} else if (a <= 1.9e-261) {
		tmp = t_3;
	} else if (a <= 6.3e-86) {
		tmp = t_1;
	} else if (a <= 5.4e-45) {
		tmp = t_3;
	} else if (a <= 4.3e+80) {
		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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (i * (a * c))
    t_3 = (x * y) * 2.0d0
    if (a <= (-1.06d+142)) then
        tmp = t_2
    else if (a <= (-2.8d-182)) then
        tmp = t_1
    else if (a <= 1.9d-261) then
        tmp = t_3
    else if (a <= 6.3d-86) then
        tmp = t_1
    else if (a <= 5.4d-45) then
        tmp = t_3
    else if (a <= 4.3d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (i * (a * c));
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (a <= -1.06e+142) {
		tmp = t_2;
	} else if (a <= -2.8e-182) {
		tmp = t_1;
	} else if (a <= 1.9e-261) {
		tmp = t_3;
	} else if (a <= 6.3e-86) {
		tmp = t_1;
	} else if (a <= 5.4e-45) {
		tmp = t_3;
	} else if (a <= 4.3e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (i * (a * c))
	t_3 = (x * y) * 2.0
	tmp = 0
	if a <= -1.06e+142:
		tmp = t_2
	elif a <= -2.8e-182:
		tmp = t_1
	elif a <= 1.9e-261:
		tmp = t_3
	elif a <= 6.3e-86:
		tmp = t_1
	elif a <= 5.4e-45:
		tmp = t_3
	elif a <= 4.3e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(i * Float64(a * c)))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (a <= -1.06e+142)
		tmp = t_2;
	elseif (a <= -2.8e-182)
		tmp = t_1;
	elseif (a <= 1.9e-261)
		tmp = t_3;
	elseif (a <= 6.3e-86)
		tmp = t_1;
	elseif (a <= 5.4e-45)
		tmp = t_3;
	elseif (a <= 4.3e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (i * (a * c));
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if (a <= -1.06e+142)
		tmp = t_2;
	elseif (a <= -2.8e-182)
		tmp = t_1;
	elseif (a <= 1.9e-261)
		tmp = t_3;
	elseif (a <= 6.3e-86)
		tmp = t_1;
	elseif (a <= 5.4e-45)
		tmp = t_3;
	elseif (a <= 4.3e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[a, -1.06e+142], t$95$2, If[LessEqual[a, -2.8e-182], t$95$1, If[LessEqual[a, 1.9e-261], t$95$3, If[LessEqual[a, 6.3e-86], t$95$1, If[LessEqual[a, 5.4e-45], t$95$3, If[LessEqual[a, 4.3e+80], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.06e142 or 4.30000000000000004e80 < a

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 74.4%

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

   4. Taylor expanded in x around 0 67.8%

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

   5. Taylor expanded in c around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. associate-*l* 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*r* 53.3%

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

      6. *-commutative 53.3%

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

      7. *-commutative 53.3%

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

      8. associate-*r* 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in c around 0 58.6%

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

      1. associate-*r* 59.7%

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

   10. Simplified 59.7%

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

   if -1.06e142 < a < -2.79999999999999993e-182 or 1.9e-261 < a < 6.2999999999999999e-86 or 5.3999999999999997e-45 < a < 4.30000000000000004e80

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -2.79999999999999993e-182 < a < 1.9e-261 or 6.2999999999999999e-86 < a < 5.3999999999999997e-45

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 44.7%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+142}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-182}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-261}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-45}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+80}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;a \leq -7 \cdot 10^{+139}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= a -7e+139)
     (* -2.0 (* a (* c i)))
     (if (<= a -3.5e-182)
       t_1
       (if (<= a 7.2e-264)
         t_2
         (if (<= a 8.2e-86)
           t_1
           (if (<= a 5.5e-49)
             t_2
             (if (<= a 1.2e+78) t_1 (* -2.0 (* i (* a c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (a <= -7e+139) {
		tmp = -2.0 * (a * (c * i));
	} else if (a <= -3.5e-182) {
		tmp = t_1;
	} else if (a <= 7.2e-264) {
		tmp = t_2;
	} else if (a <= 8.2e-86) {
		tmp = t_1;
	} else if (a <= 5.5e-49) {
		tmp = t_2;
	} else if (a <= 1.2e+78) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (a * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if (a <= (-7d+139)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (a <= (-3.5d-182)) then
        tmp = t_1
    else if (a <= 7.2d-264) then
        tmp = t_2
    else if (a <= 8.2d-86) then
        tmp = t_1
    else if (a <= 5.5d-49) then
        tmp = t_2
    else if (a <= 1.2d+78) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (i * (a * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (a <= -7e+139) {
		tmp = -2.0 * (a * (c * i));
	} else if (a <= -3.5e-182) {
		tmp = t_1;
	} else if (a <= 7.2e-264) {
		tmp = t_2;
	} else if (a <= 8.2e-86) {
		tmp = t_1;
	} else if (a <= 5.5e-49) {
		tmp = t_2;
	} else if (a <= 1.2e+78) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (i * (a * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if a <= -7e+139:
		tmp = -2.0 * (a * (c * i))
	elif a <= -3.5e-182:
		tmp = t_1
	elif a <= 7.2e-264:
		tmp = t_2
	elif a <= 8.2e-86:
		tmp = t_1
	elif a <= 5.5e-49:
		tmp = t_2
	elif a <= 1.2e+78:
		tmp = t_1
	else:
		tmp = -2.0 * (i * (a * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (a <= -7e+139)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (a <= -3.5e-182)
		tmp = t_1;
	elseif (a <= 7.2e-264)
		tmp = t_2;
	elseif (a <= 8.2e-86)
		tmp = t_1;
	elseif (a <= 5.5e-49)
		tmp = t_2;
	elseif (a <= 1.2e+78)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(i * Float64(a * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if (a <= -7e+139)
		tmp = -2.0 * (a * (c * i));
	elseif (a <= -3.5e-182)
		tmp = t_1;
	elseif (a <= 7.2e-264)
		tmp = t_2;
	elseif (a <= 8.2e-86)
		tmp = t_1;
	elseif (a <= 5.5e-49)
		tmp = t_2;
	elseif (a <= 1.2e+78)
		tmp = t_1;
	else
		tmp = -2.0 * (i * (a * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[a, -7e+139], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-182], t$95$1, If[LessEqual[a, 7.2e-264], t$95$2, If[LessEqual[a, 8.2e-86], t$95$1, If[LessEqual[a, 5.5e-49], t$95$2, If[LessEqual[a, 1.2e+78], t$95$1, N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.99999999999999957e139

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*l* 58.5%

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

      4. *-commutative 58.5%

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

      5. distribute-rgt-neg-in 58.5%

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

      6. *-commutative 58.5%

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

      7. distribute-rgt-neg-in 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in c around 0 63.2%

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

      1. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if -6.99999999999999957e139 < a < -3.49999999999999983e-182 or 7.2000000000000004e-264 < a < 8.19999999999999959e-86 or 5.50000000000000031e-49 < a < 1.1999999999999999e78

   1. Initial program 91.5%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -3.49999999999999983e-182 < a < 7.2000000000000004e-264 or 8.19999999999999959e-86 < a < 5.50000000000000031e-49

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 44.7%

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

   if 1.1999999999999999e78 < a

   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. Add Preprocessing

   3. Taylor expanded in z around 0 69.2%

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

   4. Taylor expanded in x around 0 63.2%

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

   5. Taylor expanded in c around 0 54.9%

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

      1. *-commutative 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*l* 49.2%

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

      4. *-commutative 49.2%

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

      5. associate-*r* 49.2%

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

      6. *-commutative 49.2%

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

      7. *-commutative 49.2%

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

      8. associate-*r* 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in c around 0 54.9%

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

      1. associate-*r* 58.8%

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

   10. Simplified 58.8%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+139}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-182}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-264}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot \left(t - \left(c \cdot i\right) \cdot \frac{a}{z}\right)\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-170}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 0.156:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* a (* c i)))))
        (t_2 (* 2.0 (* z (- t (* (* c i) (/ a z)))))))
   (if (<= z -6.5e+29)
     t_2
     (if (<= z -1.6e-272)
       t_1
       (if (<= z 7.8e-170)
         (* -2.0 (* c (* (+ a (* b c)) i)))
         (if (<= z 0.156) 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 * ((x * y) - (a * (c * i)));
	double t_2 = 2.0 * (z * (t - ((c * i) * (a / z))));
	double tmp;
	if (z <= -6.5e+29) {
		tmp = t_2;
	} else if (z <= -1.6e-272) {
		tmp = t_1;
	} else if (z <= 7.8e-170) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (z <= 0.156) {
		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 * ((x * y) - (a * (c * i)))
    t_2 = 2.0d0 * (z * (t - ((c * i) * (a / z))))
    if (z <= (-6.5d+29)) then
        tmp = t_2
    else if (z <= (-1.6d-272)) then
        tmp = t_1
    else if (z <= 7.8d-170) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else if (z <= 0.156d0) 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 * ((x * y) - (a * (c * i)));
	double t_2 = 2.0 * (z * (t - ((c * i) * (a / z))));
	double tmp;
	if (z <= -6.5e+29) {
		tmp = t_2;
	} else if (z <= -1.6e-272) {
		tmp = t_1;
	} else if (z <= 7.8e-170) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (z <= 0.156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (a * (c * i)))
	t_2 = 2.0 * (z * (t - ((c * i) * (a / z))))
	tmp = 0
	if z <= -6.5e+29:
		tmp = t_2
	elif z <= -1.6e-272:
		tmp = t_1
	elif z <= 7.8e-170:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	elif z <= 0.156:
		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(Float64(x * y) - Float64(a * Float64(c * i))))
	t_2 = Float64(2.0 * Float64(z * Float64(t - Float64(Float64(c * i) * Float64(a / z)))))
	tmp = 0.0
	if (z <= -6.5e+29)
		tmp = t_2;
	elseif (z <= -1.6e-272)
		tmp = t_1;
	elseif (z <= 7.8e-170)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	elseif (z <= 0.156)
		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 * ((x * y) - (a * (c * i)));
	t_2 = 2.0 * (z * (t - ((c * i) * (a / z))));
	tmp = 0.0;
	if (z <= -6.5e+29)
		tmp = t_2;
	elseif (z <= -1.6e-272)
		tmp = t_1;
	elseif (z <= 7.8e-170)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	elseif (z <= 0.156)
		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[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * N[(t - N[(N[(c * i), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+29], t$95$2, If[LessEqual[z, -1.6e-272], t$95$1, If[LessEqual[z, 7.8e-170], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.156], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.49999999999999971e29 or 0.156 < z

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 80.6%

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

   4. Taylor expanded in c around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. +-commutative 71.4%

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

      3. sub-neg 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-*l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-/l* 70.6%

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

   9. Simplified 70.6%

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

   if -6.49999999999999971e29 < z < -1.6e-272 or 7.80000000000000042e-170 < z < 0.156

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 81.7%

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

   4. Taylor expanded in c around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. +-commutative 65.4%

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

      3. sub-neg 65.4%

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

   6. Simplified 65.4%

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

   if -1.6e-272 < z < 7.80000000000000042e-170

   1. Initial program 79.1%

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

   3. Taylor expanded in z around 0 76.5%

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

   4. Taylor expanded in x around 0 59.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t - \left(c \cdot i\right) \cdot \frac{a}{z}\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-272}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-170}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 0.156:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t - \left(c \cdot i\right) \cdot \frac{a}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+240}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= (* x y) -4.3e+102)
     t_1
     (if (<= (* x y) 8.5e+51)
       (* 2.0 (- (* z t) (* c (* a i))))
       (if (<= (* x y) 2.4e+240) (* -2.0 (* c (* (+ a (* b c)) i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.3e+102) {
		tmp = t_1;
	} else if ((x * y) <= 8.5e+51) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((x * y) <= 2.4e+240) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) * 2.0d0
    if ((x * y) <= (-4.3d+102)) then
        tmp = t_1
    else if ((x * y) <= 8.5d+51) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if ((x * y) <= 2.4d+240) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    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 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.3e+102) {
		tmp = t_1;
	} else if ((x * y) <= 8.5e+51) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((x * y) <= 2.4e+240) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -4.3e+102:
		tmp = t_1
	elif (x * y) <= 8.5e+51:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif (x * y) <= 2.4e+240:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -4.3e+102)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.5e+51)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (Float64(x * y) <= 2.4e+240)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -4.3e+102)
		tmp = t_1;
	elseif ((x * y) <= 8.5e+51)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif ((x * y) <= 2.4e+240)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.3e+102], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.5e+51], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.4e+240], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.3000000000000001e102 or 2.3999999999999999e240 < (*.f64 x y)

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf 71.5%

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

   if -4.3000000000000001e102 < (*.f64 x y) < 8.4999999999999999e51

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 85.5%

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

   4. Taylor expanded in c around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. +-commutative 72.4%

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

      3. sub-neg 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-*l* 68.2%

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

   6. Simplified 68.2%

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

   if 8.4999999999999999e51 < (*.f64 x y) < 2.3999999999999999e240

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 85.5%

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

   4. Taylor expanded in x around 0 70.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+240}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-221}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -5.5e-19)
     t_2
     (if (<= c -9.5e-132)
       t_1
       (if (<= c -2.05e-221) (* (* x y) 2.0) (if (<= c 9.2e+107) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -5.5e-19) {
		tmp = t_2;
	} else if (c <= -9.5e-132) {
		tmp = t_1;
	} else if (c <= -2.05e-221) {
		tmp = (x * y) * 2.0;
	} else if (c <= 9.2e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-5.5d-19)) then
        tmp = t_2
    else if (c <= (-9.5d-132)) then
        tmp = t_1
    else if (c <= (-2.05d-221)) then
        tmp = (x * y) * 2.0d0
    else if (c <= 9.2d+107) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -5.5e-19) {
		tmp = t_2;
	} else if (c <= -9.5e-132) {
		tmp = t_1;
	} else if (c <= -2.05e-221) {
		tmp = (x * y) * 2.0;
	} else if (c <= 9.2e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -5.5e-19:
		tmp = t_2
	elif c <= -9.5e-132:
		tmp = t_1
	elif c <= -2.05e-221:
		tmp = (x * y) * 2.0
	elif c <= 9.2e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -5.5e-19)
		tmp = t_2;
	elseif (c <= -9.5e-132)
		tmp = t_1;
	elseif (c <= -2.05e-221)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (c <= 9.2e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -5.5e-19)
		tmp = t_2;
	elseif (c <= -9.5e-132)
		tmp = t_1;
	elseif (c <= -2.05e-221)
		tmp = (x * y) * 2.0;
	elseif (c <= 9.2e+107)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e-19], t$95$2, If[LessEqual[c, -9.5e-132], t$95$1, If[LessEqual[c, -2.05e-221], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 9.2e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.4999999999999996e-19 or 9.2000000000000001e107 < c

   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. Add Preprocessing

   3. Taylor expanded in z around 0 83.9%

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

   4. Taylor expanded in x around 0 76.2%

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

   if -5.4999999999999996e-19 < c < -9.49999999999999987e-132 or -2.04999999999999991e-221 < c < 9.2000000000000001e107

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 50.7%

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

   if -9.49999999999999987e-132 < c < -2.04999999999999991e-221

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 58.3%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-132}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-221}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 0.13:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* a (* c i)))))
        (t_2 (* 2.0 (- (* z t) (* c (* a i))))))
   (if (<= z -1.02e+76)
     t_2
     (if (<= z -4.8e-275)
       t_1
       (if (<= z 3.2e-172)
         (* -2.0 (* c (* (+ a (* b c)) i)))
         (if (<= z 0.13) 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 * ((x * y) - (a * (c * i)));
	double t_2 = 2.0 * ((z * t) - (c * (a * i)));
	double tmp;
	if (z <= -1.02e+76) {
		tmp = t_2;
	} else if (z <= -4.8e-275) {
		tmp = t_1;
	} else if (z <= 3.2e-172) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (z <= 0.13) {
		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 * ((x * y) - (a * (c * i)))
    t_2 = 2.0d0 * ((z * t) - (c * (a * i)))
    if (z <= (-1.02d+76)) then
        tmp = t_2
    else if (z <= (-4.8d-275)) then
        tmp = t_1
    else if (z <= 3.2d-172) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else if (z <= 0.13d0) 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 * ((x * y) - (a * (c * i)));
	double t_2 = 2.0 * ((z * t) - (c * (a * i)));
	double tmp;
	if (z <= -1.02e+76) {
		tmp = t_2;
	} else if (z <= -4.8e-275) {
		tmp = t_1;
	} else if (z <= 3.2e-172) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else if (z <= 0.13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (a * (c * i)))
	t_2 = 2.0 * ((z * t) - (c * (a * i)))
	tmp = 0
	if z <= -1.02e+76:
		tmp = t_2
	elif z <= -4.8e-275:
		tmp = t_1
	elif z <= 3.2e-172:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	elif z <= 0.13:
		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(Float64(x * y) - Float64(a * Float64(c * i))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))))
	tmp = 0.0
	if (z <= -1.02e+76)
		tmp = t_2;
	elseif (z <= -4.8e-275)
		tmp = t_1;
	elseif (z <= 3.2e-172)
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	elseif (z <= 0.13)
		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 * ((x * y) - (a * (c * i)));
	t_2 = 2.0 * ((z * t) - (c * (a * i)));
	tmp = 0.0;
	if (z <= -1.02e+76)
		tmp = t_2;
	elseif (z <= -4.8e-275)
		tmp = t_1;
	elseif (z <= 3.2e-172)
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	elseif (z <= 0.13)
		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[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+76], t$95$2, If[LessEqual[z, -4.8e-275], t$95$1, If[LessEqual[z, 3.2e-172], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.13], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02000000000000007e76 or 0.13 < z

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in c around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. +-commutative 73.3%

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

      3. sub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. associate-*l* 69.2%

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

   6. Simplified 69.2%

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

   if -1.02000000000000007e76 < z < -4.79999999999999981e-275 or 3.2000000000000001e-172 < z < 0.13

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 80.0%

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

   4. Taylor expanded in c around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. +-commutative 64.3%

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

      3. sub-neg 64.3%

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

   6. Simplified 64.3%

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

   if -4.79999999999999981e-275 < z < 3.2000000000000001e-172

   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. Add Preprocessing

   3. Taylor expanded in z around 0 78.3%

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

   4. Taylor expanded in x around 0 60.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-275}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-172}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 0.13:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -5 \cdot 10^{+70} \lor \neg \left(i \leq 2000000\right):\\ \;\;\;\;\left(t\_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right) + a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -5e+70) (not (<= i 2000000.0)))
     (* (- t_1 (* (* c (+ a (* b c))) i)) 2.0)
     (* 2.0 (- t_1 (* c (+ (* b (* c i)) (* a i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -5e+70) || !(i <= 2000000.0)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * ((b * (c * i)) + (a * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((i <= (-5d+70)) .or. (.not. (i <= 2000000.0d0))) then
        tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0d0
    else
        tmp = 2.0d0 * (t_1 - (c * ((b * (c * i)) + (a * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -5e+70) || !(i <= 2000000.0)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * ((b * (c * i)) + (a * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (i <= -5e+70) or not (i <= 2000000.0):
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0
	else:
		tmp = 2.0 * (t_1 - (c * ((b * (c * i)) + (a * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((i <= -5e+70) || !(i <= 2000000.0))
		tmp = Float64(Float64(t_1 - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(Float64(b * Float64(c * i)) + Float64(a * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((i <= -5e+70) || ~((i <= 2000000.0)))
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	else
		tmp = 2.0 * (t_1 - (c * ((b * (c * i)) + (a * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -5e+70], N[Not[LessEqual[i, 2000000.0]], $MachinePrecision]], N[(N[(t$95$1 - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -5.0000000000000002e70 or 2e6 < i

   1. Initial program 94.6%

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

   if -5.0000000000000002e70 < i < 2e6

   1. Initial program 87.0%

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

   3. Taylor expanded in c around 0 96.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+70} \lor \neg \left(i \leq 2000000\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right) + a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-221}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* -2.0 (* c (* (* b c) i)))))
   (if (<= c -3.2e-7)
     t_2
     (if (<= c -2.7e-131)
       t_1
       (if (<= c -1.8e-221) (* (* x y) 2.0) (if (<= c 1.35e+108) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * ((b * c) * i));
	double tmp;
	if (c <= -3.2e-7) {
		tmp = t_2;
	} else if (c <= -2.7e-131) {
		tmp = t_1;
	} else if (c <= -1.8e-221) {
		tmp = (x * y) * 2.0;
	} else if (c <= 1.35e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (c * ((b * c) * i))
    if (c <= (-3.2d-7)) then
        tmp = t_2
    else if (c <= (-2.7d-131)) then
        tmp = t_1
    else if (c <= (-1.8d-221)) then
        tmp = (x * y) * 2.0d0
    else if (c <= 1.35d+108) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * ((b * c) * i));
	double tmp;
	if (c <= -3.2e-7) {
		tmp = t_2;
	} else if (c <= -2.7e-131) {
		tmp = t_1;
	} else if (c <= -1.8e-221) {
		tmp = (x * y) * 2.0;
	} else if (c <= 1.35e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (c * ((b * c) * i))
	tmp = 0
	if c <= -3.2e-7:
		tmp = t_2
	elif c <= -2.7e-131:
		tmp = t_1
	elif c <= -1.8e-221:
		tmp = (x * y) * 2.0
	elif c <= 1.35e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(b * c) * i)))
	tmp = 0.0
	if (c <= -3.2e-7)
		tmp = t_2;
	elseif (c <= -2.7e-131)
		tmp = t_1;
	elseif (c <= -1.8e-221)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (c <= 1.35e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (c * ((b * c) * i));
	tmp = 0.0;
	if (c <= -3.2e-7)
		tmp = t_2;
	elseif (c <= -2.7e-131)
		tmp = t_1;
	elseif (c <= -1.8e-221)
		tmp = (x * y) * 2.0;
	elseif (c <= 1.35e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e-7], t$95$2, If[LessEqual[c, -2.7e-131], t$95$1, If[LessEqual[c, -1.8e-221], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 1.35e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.2000000000000001e-7 or 1.35e108 < c

   1. Initial program 78.1%

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

   3. Taylor expanded in z around 0 83.6%

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

   4. Taylor expanded in x around 0 75.7%

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

   5. Taylor expanded in a around 0 61.5%

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

   if -3.2000000000000001e-7 < c < -2.70000000000000021e-131 or -1.80000000000000006e-221 < c < 1.35e108

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -2.70000000000000021e-131 < c < -1.80000000000000006e-221

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 58.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-7}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-131}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-221}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 4.4 \cdot 10^{+181}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.7e+116) (not (<= (* x y) 4.4e+181)))
   (* 2.0 (- (* x y) (* a (* c i))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.7e+116) || !((x * y) <= 4.4e+181)) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2.7d+116)) .or. (.not. ((x * y) <= 4.4d+181))) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.7e+116) || !((x * y) <= 4.4e+181)) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.7e+116) or not ((x * y) <= 4.4e+181):
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.7e+116) || !(Float64(x * y) <= 4.4e+181))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2.7e+116) || ~(((x * y) <= 4.4e+181)))
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.7e+116], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.4e+181]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.7e116 or 4.4000000000000002e181 < (*.f64 x y)

   1. Initial program 80.8%

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

   3. Taylor expanded in z around 0 78.3%

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

   4. Taylor expanded in c around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. +-commutative 79.2%

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

      3. sub-neg 79.2%

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

   6. Simplified 79.2%

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

   if -2.7e116 < (*.f64 x y) < 4.4000000000000002e181

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 84.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 4.4 \cdot 10^{+181}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -4.8e+102)
     (* 2.0 (- (* x y) t_1))
     (if (<= (* x y) 2.25e+181)
       (* 2.0 (- (* z t) t_1))
       (* 2.0 (- (* x y) (* a (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -4.8e+102) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 2.25e+181) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if ((x * y) <= (-4.8d+102)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((x * y) <= 2.25d+181) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -4.8e+102) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 2.25e+181) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if (x * y) <= -4.8e+102:
		tmp = 2.0 * ((x * y) - t_1)
	elif (x * y) <= 2.25e+181:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (Float64(x * y) <= -4.8e+102)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (Float64(x * y) <= 2.25e+181)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if ((x * y) <= -4.8e+102)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((x * y) <= 2.25e+181)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.8e+102], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.25e+181], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.79999999999999989e102

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 80.6%

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

   if -4.79999999999999989e102 < (*.f64 x y) < 2.25e181

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 84.9%

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

   if 2.25e181 < (*.f64 x y)

   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. Add Preprocessing

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in c around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. +-commutative 90.0%

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

      3. sub-neg 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+181}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+166}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* a (* c i))))))
   (if (<= y -2.8e-60)
     t_1
     (if (<= y 2e-261)
       (* 2.0 (- (* z t) (* c (* a i))))
       (if (<= y 3.4e+166) (* 2.0 (- (* z t) (* c (* b (* c i))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if (y <= -2.8e-60) {
		tmp = t_1;
	} else if (y <= 2e-261) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (y <= 3.4e+166) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (a * (c * i)))
    if (y <= (-2.8d-60)) then
        tmp = t_1
    else if (y <= 2d-261) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (y <= 3.4d+166) then
        tmp = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (a * (c * i)));
	double tmp;
	if (y <= -2.8e-60) {
		tmp = t_1;
	} else if (y <= 2e-261) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (y <= 3.4e+166) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else {
		tmp = t_1;
	}
	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 y <= -2.8e-60:
		tmp = t_1
	elif y <= 2e-261:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif y <= 3.4e+166:
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))))
	else:
		tmp = t_1
	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 (y <= -2.8e-60)
		tmp = t_1;
	elseif (y <= 2e-261)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (y <= 3.4e+166)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (a * (c * i)));
	tmp = 0.0;
	if (y <= -2.8e-60)
		tmp = t_1;
	elseif (y <= 2e-261)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (y <= 3.4e+166)
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-60], t$95$1, If[LessEqual[y, 2e-261], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+166], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000002e-60 or 3.4e166 < y

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 75.5%

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

   4. Taylor expanded in c around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. +-commutative 68.1%

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

      3. sub-neg 68.1%

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

   6. Simplified 68.1%

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

   if -2.8000000000000002e-60 < y < 1.99999999999999997e-261

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 84.8%

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

   4. Taylor expanded in c around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. +-commutative 73.6%

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

      3. sub-neg 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-*l* 72.2%

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

   6. Simplified 72.2%

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

   if 1.99999999999999997e-261 < y < 3.4e166

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in a around 0 65.7%

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

   5. Taylor expanded in i around 0 66.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+166}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= a -4.7e+47)
     (* 2.0 (- t_1 (* i (* a c))))
     (if (<= a 1.7e+82)
       (* 2.0 (- t_1 (* c (* b (* c i)))))
       (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (a <= -4.7e+47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 1.7e+82) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (a <= (-4.7d+47)) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (a <= 1.7d+82) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (a <= -4.7e+47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 1.7e+82) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if a <= -4.7e+47:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif a <= 1.7e+82:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (a <= -4.7e+47)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (a <= 1.7e+82)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (a <= -4.7e+47)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (a <= 1.7e+82)
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+47], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+82], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.69999999999999964e47

   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. Add Preprocessing

   3. Taylor expanded in a around inf 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -4.69999999999999964e47 < a < 1.69999999999999997e82

   1. Initial program 88.6%

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

   3. Taylor expanded in c around 0 94.7%

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

   4. Taylor expanded in a around 0 93.4%

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

   if 1.69999999999999997e82 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 87.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 62:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -4.8e-18)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 62.0)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -4.8e-18) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 62.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-4.8d-18)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 62.0d0) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -4.8e-18) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 62.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -4.8e-18:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 62.0:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -4.8e-18)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 62.0)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -4.8e-18)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 62.0)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e-18], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 62.0], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.79999999999999988e-18

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0 84.9%

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

   if -4.79999999999999988e-18 < c < 62

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 95.5%

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

      1. *-commutative 95.5%

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

   5. Simplified 95.5%

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

   if 62 < c

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 85.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 62:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -3.4e+102) (not (<= (* x y) 7e+70)))
   (* (* 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) <= -3.4e+102) || !((x * y) <= 7e+70)) {
		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) <= (-3.4d+102)) .or. (.not. ((x * y) <= 7d+70))) 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) <= -3.4e+102) || !((x * y) <= 7e+70)) {
		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) <= -3.4e+102) or not ((x * y) <= 7e+70):
		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) <= -3.4e+102) || !(Float64(x * y) <= 7e+70))
		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) <= -3.4e+102) || ~(((x * y) <= 7e+70)))
		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], -3.4e+102], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7e+70]], $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) < -3.4e102 or 7.00000000000000005e70 < (*.f64 x y)

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 61.9%

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

   if -3.4e102 < (*.f64 x y) < 7.00000000000000005e70

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 43.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+70}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in z around inf 34.7%

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

4. Final simplification 34.7%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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