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

Percentage Accurate: 90.0% → 97.1%

Time: 16.6s

Alternatives: 15

Speedup: 0.5×

• 47.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% 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: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * N[(z - N[(c * N[(N[(i * N[(c * b + a), $MachinePrecision]), $MachinePrecision] / t), $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 94.3%

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

      1. fma-define 94.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 42.9%

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

   4. Taylor expanded in t around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

      3. associate-/l* 76.2%

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

      4. +-commutative 76.2%

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

      5. *-commutative 76.2%

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

      6. fma-define 76.2%

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

   6. Simplified 76.2%

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

4. Final simplification 96.4%

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

Alternative 2: 82.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ t_2 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_3 := 2 \cdot \left(x \cdot y - t\_2\right)\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* y (- x (/ (* c (* (* b c) i)) y)))))
        (t_2 (* c (* (+ a (* b c)) i)))
        (t_3 (* 2.0 (- (* x y) t_2))))
   (if (<= (* x y) (- INFINITY))
     t_1
     (if (<= (* x y) -1e+38)
       t_3
       (if (<= (* x y) -5e-5)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= (* x y) -1e-29)
           t_3
           (if (<= (* x y) 2e+91) (* 2.0 (- (* z t) t_2)) 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 * (y * (x - ((c * ((b * c) * i)) / y)));
	double t_2 = c * ((a + (b * c)) * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((x * y) <= -1e+38) {
		tmp = t_3;
	} else if ((x * y) <= -5e-5) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= -1e-29) {
		tmp = t_3;
	} else if ((x * y) <= 2e+91) {
		tmp = 2.0 * ((z * t) - t_2);
	} else {
		tmp = t_1;
	}
	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 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)));
	double t_2 = c * ((a + (b * c)) * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((x * y) <= -1e+38) {
		tmp = t_3;
	} else if ((x * y) <= -5e-5) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= -1e-29) {
		tmp = t_3;
	} else if ((x * y) <= 2e+91) {
		tmp = 2.0 * ((z * t) - t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)))
	t_2 = c * ((a + (b * c)) * i)
	t_3 = 2.0 * ((x * y) - t_2)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = t_1
	elif (x * y) <= -1e+38:
		tmp = t_3
	elif (x * y) <= -5e-5:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= -1e-29:
		tmp = t_3
	elif (x * y) <= 2e+91:
		tmp = 2.0 * ((z * t) - t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(y * Float64(x - Float64(Float64(c * Float64(Float64(b * c) * i)) / y))))
	t_2 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - t_2))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(x * y) <= -1e+38)
		tmp = t_3;
	elseif (Float64(x * y) <= -5e-5)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= -1e-29)
		tmp = t_3;
	elseif (Float64(x * y) <= 2e+91)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	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 * (y * (x - ((c * ((b * c) * i)) / y)));
	t_2 = c * ((a + (b * c)) * i);
	t_3 = 2.0 * ((x * y) - t_2);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = t_1;
	elseif ((x * y) <= -1e+38)
		tmp = t_3;
	elseif ((x * y) <= -5e-5)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= -1e-29)
		tmp = t_3;
	elseif ((x * y) <= 2e+91)
		tmp = 2.0 * ((z * t) - t_2);
	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[(y * N[(x - N[(N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e+38], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5e-5], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-29], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 2e+91], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -inf.0 or 2.00000000000000016e91 < (*.f64 x y)

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 88.6%

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

   4. Taylor expanded in t around 0 81.3%

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

   5. Taylor expanded in a around 0 84.6%

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

      1. associate-*r* 84.6%

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

      2. *-commutative 84.6%

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

      3. *-commutative 84.6%

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

   7. Simplified 84.6%

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

   if -inf.0 < (*.f64 x y) < -9.99999999999999977e37 or -5.00000000000000024e-5 < (*.f64 x y) < -9.99999999999999943e-30

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 82.4%

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

   if -9.99999999999999977e37 < (*.f64 x y) < -5.00000000000000024e-5

   1. Initial program 75.3%

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

   3. Taylor expanded in c around 0 91.7%

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

   if -9.99999999999999943e-30 < (*.f64 x y) < 2.00000000000000016e91

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 85.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(t\_1 \cdot i\right)}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (* c (* t_1 (- i))))
     (if (<= t_2 5e+268)
       (* (- (+ (* x y) (* z t)) t_2) 2.0)
       (* 2.0 (* y (- x (/ (* c (* t_1 i)) 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 t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 5e+268) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (y * (x - ((c * (t_1 * i)) / y)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 5e+268) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (y * (x - ((c * (t_1 * i)) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * (c * (t_1 * -i))
	elif t_2 <= 5e+268:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	else:
		tmp = 2.0 * (y * (x - ((c * (t_1 * i)) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	elseif (t_2 <= 5e+268)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	else
		tmp = Float64(2.0 * Float64(y * Float64(x - Float64(Float64(c * Float64(t_1 * i)) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * (c * (t_1 * -i));
	elseif (t_2 <= 5e+268)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	else
		tmp = 2.0 * (y * (x - ((c * (t_1 * i)) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+268], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(y * N[(x - N[(N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.9%

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

   3. Taylor expanded in i around inf 92.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000002e268

   1. Initial program 98.0%

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

   if 5.0000000000000002e268 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 80.7%

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

   4. Taylor expanded in t around 0 80.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := 2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -40000000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i)))))
        (t_2 (* 2.0 (* y (- x (/ (* c (* (* b c) i)) y))))))
   (if (<= (* x y) -5e+176)
     t_2
     (if (<= (* x y) -2e+60)
       t_1
       (if (<= (* x y) -40000000000000.0)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= (* x y) 2e+91) 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) - (c * ((a + (b * c)) * i)));
	double t_2 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)));
	double tmp;
	if ((x * y) <= -5e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2e+60) {
		tmp = t_1;
	} else if ((x * y) <= -40000000000000.0) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 2e+91) {
		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) - (c * ((a + (b * c)) * i)))
    t_2 = 2.0d0 * (y * (x - ((c * ((b * c) * i)) / y)))
    if ((x * y) <= (-5d+176)) then
        tmp = t_2
    else if ((x * y) <= (-2d+60)) then
        tmp = t_1
    else if ((x * y) <= (-40000000000000.0d0)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((x * y) <= 2d+91) 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) - (c * ((a + (b * c)) * i)));
	double t_2 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)));
	double tmp;
	if ((x * y) <= -5e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2e+60) {
		tmp = t_1;
	} else if ((x * y) <= -40000000000000.0) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 2e+91) {
		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) - (c * ((a + (b * c)) * i)))
	t_2 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)))
	tmp = 0
	if (x * y) <= -5e+176:
		tmp = t_2
	elif (x * y) <= -2e+60:
		tmp = t_1
	elif (x * y) <= -40000000000000.0:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= 2e+91:
		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(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	t_2 = Float64(2.0 * Float64(y * Float64(x - Float64(Float64(c * Float64(Float64(b * c) * i)) / y))))
	tmp = 0.0
	if (Float64(x * y) <= -5e+176)
		tmp = t_2;
	elseif (Float64(x * y) <= -2e+60)
		tmp = t_1;
	elseif (Float64(x * y) <= -40000000000000.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= 2e+91)
		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) - (c * ((a + (b * c)) * i)));
	t_2 = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)));
	tmp = 0.0;
	if ((x * y) <= -5e+176)
		tmp = t_2;
	elseif ((x * y) <= -2e+60)
		tmp = t_1;
	elseif ((x * y) <= -40000000000000.0)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= 2e+91)
		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[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(y * N[(x - N[(N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+176], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2e+60], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -40000000000000.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+91], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e176 or 2.00000000000000016e91 < (*.f64 x y)

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 90.5%

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

   4. Taylor expanded in t around 0 82.7%

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

   5. Taylor expanded in a around 0 82.9%

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

      1. associate-*r* 82.9%

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

      2. *-commutative 82.9%

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

      3. *-commutative 82.9%

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

   7. Simplified 82.9%

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

   if -5e176 < (*.f64 x y) < -1.9999999999999999e60 or -4e13 < (*.f64 x y) < 2.00000000000000016e91

   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 x around 0 83.7%

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

   if -1.9999999999999999e60 < (*.f64 x y) < -4e13

   1. Initial program 75.3%

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

   3. Taylor expanded in c around 0 83.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -40000000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - \frac{c \cdot \left(\left(b \cdot c\right) \cdot i\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-287}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -5.8e+167)
     t_2
     (if (<= (* x y) -3.3e+17)
       t_1
       (if (<= (* x y) -2.5e-35)
         t_2
         (if (<= (* x y) -1.2e-287)
           (* (* i (* a c)) -2.0)
           (if (<= (* x y) 3.2e+91) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5.8e+167) {
		tmp = t_2;
	} else if ((x * y) <= -3.3e+17) {
		tmp = t_1;
	} else if ((x * y) <= -2.5e-35) {
		tmp = t_2;
	} else if ((x * y) <= -1.2e-287) {
		tmp = (i * (a * c)) * -2.0;
	} else if ((x * y) <= 3.2e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-5.8d+167)) then
        tmp = t_2
    else if ((x * y) <= (-3.3d+17)) then
        tmp = t_1
    else if ((x * y) <= (-2.5d-35)) then
        tmp = t_2
    else if ((x * y) <= (-1.2d-287)) then
        tmp = (i * (a * c)) * (-2.0d0)
    else if ((x * y) <= 3.2d+91) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -5.8e+167) {
		tmp = t_2;
	} else if ((x * y) <= -3.3e+17) {
		tmp = t_1;
	} else if ((x * y) <= -2.5e-35) {
		tmp = t_2;
	} else if ((x * y) <= -1.2e-287) {
		tmp = (i * (a * c)) * -2.0;
	} else if ((x * y) <= 3.2e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -5.8e+167:
		tmp = t_2
	elif (x * y) <= -3.3e+17:
		tmp = t_1
	elif (x * y) <= -2.5e-35:
		tmp = t_2
	elif (x * y) <= -1.2e-287:
		tmp = (i * (a * c)) * -2.0
	elif (x * y) <= 3.2e+91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -5.8e+167)
		tmp = t_2;
	elseif (Float64(x * y) <= -3.3e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.5e-35)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.2e-287)
		tmp = Float64(Float64(i * Float64(a * c)) * -2.0);
	elseif (Float64(x * y) <= 3.2e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -5.8e+167)
		tmp = t_2;
	elseif ((x * y) <= -3.3e+17)
		tmp = t_1;
	elseif ((x * y) <= -2.5e-35)
		tmp = t_2;
	elseif ((x * y) <= -1.2e-287)
		tmp = (i * (a * c)) * -2.0;
	elseif ((x * y) <= 3.2e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5.8e+167], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -3.3e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.5e-35], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e-287], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+91], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.79999999999999949e167 or -3.3e17 < (*.f64 x y) < -2.49999999999999982e-35 or 3.19999999999999989e91 < (*.f64 x y)

   1. Initial program 81.3%

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

   3. Taylor expanded in x around inf 60.8%

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

   if -5.79999999999999949e167 < (*.f64 x y) < -3.3e17 or -1.2e-287 < (*.f64 x y) < 3.19999999999999989e91

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 38.4%

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

   if -2.49999999999999982e-35 < (*.f64 x y) < -1.2e-287

   1. Initial program 93.8%

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

      1. fma-define 93.8%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

      1. fma-define 97.9%

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

      2. +-commutative 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in a around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. associate-*r* 41.3%

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

      3. distribute-lft-neg-out 41.3%

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

      4. *-commutative 41.3%

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

      5. distribute-rgt-neg-in 41.3%

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

   9. Simplified 41.3%

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

   10. Taylor expanded in i around 0 47.3%

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

       1. *-commutative 47.3%

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

       2. associate-*r* 42.3%

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

       3. *-commutative 42.3%

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

       4. associate-*l* 41.3%

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

   12. Simplified 41.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+167}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{+17}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-287}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* y (- x (/ (* c (* (* b c) i)) 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 t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (y * (x - ((c * ((b * c) * i)) / y)));
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.3%

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

      1. fma-define 94.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 38.1%

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

   4. Taylor expanded in t around 0 47.6%

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

   5. Taylor expanded in a around 0 61.9%

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

      1. associate-*r* 61.9%

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

      2. *-commutative 61.9%

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

      3. *-commutative 61.9%

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

   7. Simplified 61.9%

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

4. Final simplification 95.3%

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

Alternative 7: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+107)
   (* 2.0 (* x (+ y (* t (/ z x)))))
   (if (<= (* x y) -1e+38)
     (* 2.0 (- (* x y) (* i (* a c))))
     (if (<= (* x y) -1e-29)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= (* x y) 4e+163)
         (* 2.0 (- (* z t) (* a (* c i))))
         (* 2.0 (* y (+ x (* t (/ z y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+107) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else if ((x * y) <= -1e+38) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} else if ((x * y) <= -1e-29) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 4e+163) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + (t * (z / y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d+107)) then
        tmp = 2.0d0 * (x * (y + (t * (z / x))))
    else if ((x * y) <= (-1d+38)) then
        tmp = 2.0d0 * ((x * y) - (i * (a * c)))
    else if ((x * y) <= (-1d-29)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((x * y) <= 4d+163) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = 2.0d0 * (y * (x + (t * (z / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+107) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else if ((x * y) <= -1e+38) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} else if ((x * y) <= -1e-29) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 4e+163) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + (t * (z / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+107:
		tmp = 2.0 * (x * (y + (t * (z / x))))
	elif (x * y) <= -1e+38:
		tmp = 2.0 * ((x * y) - (i * (a * c)))
	elif (x * y) <= -1e-29:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= 4e+163:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = 2.0 * (y * (x + (t * (z / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+107)
		tmp = Float64(2.0 * Float64(x * Float64(y + Float64(t * Float64(z / x)))));
	elseif (Float64(x * y) <= -1e+38)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))));
	elseif (Float64(x * y) <= -1e-29)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= 4e+163)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(y * Float64(x + Float64(t * Float64(z / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+107)
		tmp = 2.0 * (x * (y + (t * (z / x))));
	elseif ((x * y) <= -1e+38)
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	elseif ((x * y) <= -1e-29)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= 4e+163)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = 2.0 * (y * (x + (t * (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+107], N[(2.0 * N[(x * N[(y + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e+38], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-29], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+163], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.9999999999999997e106

   1. Initial program 72.7%

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

   3. Taylor expanded in a around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in z around inf 56.7%

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

      1. associate--l+ 56.7%

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

      2. div-sub 57.0%

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

      3. associate-*r* 57.0%

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

      4. *-commutative 57.0%

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

   8. Simplified 57.0%

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

   9. Taylor expanded in c around 0 59.2%

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

       1. associate-/l* 61.5%

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

   11. Simplified 61.5%

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

   12. Taylor expanded in x around inf 74.7%

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

       1. associate-/l* 77.0%

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

   14. Simplified 77.0%

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

   if -9.9999999999999997e106 < (*.f64 x y) < -9.99999999999999977e37

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in z around 0 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

   8. Simplified 64.3%

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

   if -9.99999999999999977e37 < (*.f64 x y) < -9.99999999999999943e-30

   1. Initial program 85.9%

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

   3. Taylor expanded in c around 0 73.3%

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

   if -9.99999999999999943e-30 < (*.f64 x y) < 3.9999999999999998e163

   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 a around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 67.9%

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

      3. associate-*r* 63.4%

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

      4. *-commutative 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in x around 0 61.3%

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

       1. associate-/l* 60.6%

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

       2. associate-/l* 56.1%

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

   11. Simplified 56.1%

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

   12. Taylor expanded in z around 0 67.0%

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

       1. +-commutative 67.0%

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

       2. mul-1-neg 67.0%

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

       3. sub-neg 67.0%

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

       4. *-commutative 67.0%

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

   14. Simplified 67.0%

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

   if 3.9999999999999998e163 < (*.f64 x y)

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. div-sub 75.1%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in c around 0 75.1%

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

       1. associate-/l* 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in y around inf 77.7%

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

       1. associate-/l* 80.5%

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

   14. Simplified 80.5%

       \[\leadsto 2 \cdot \color{blue}{\left(y \cdot \left(x + t \cdot \frac{z}{y}\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ t_2 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-189}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)) (t_2 (* (* c i) (* a -2.0))))
   (if (<= c -4.2e+30)
     t_2
     (if (<= c -6.8e-267)
       t_1
       (if (<= c 2.45e-189) (* 2.0 (* z t)) (if (<= c 4.2e-49) 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 = (x * y) * 2.0;
	double t_2 = (c * i) * (a * -2.0);
	double tmp;
	if (c <= -4.2e+30) {
		tmp = t_2;
	} else if (c <= -6.8e-267) {
		tmp = t_1;
	} else if (c <= 2.45e-189) {
		tmp = 2.0 * (z * t);
	} else if (c <= 4.2e-49) {
		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 = (x * y) * 2.0d0
    t_2 = (c * i) * (a * (-2.0d0))
    if (c <= (-4.2d+30)) then
        tmp = t_2
    else if (c <= (-6.8d-267)) then
        tmp = t_1
    else if (c <= 2.45d-189) then
        tmp = 2.0d0 * (z * t)
    else if (c <= 4.2d-49) 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 = (x * y) * 2.0;
	double t_2 = (c * i) * (a * -2.0);
	double tmp;
	if (c <= -4.2e+30) {
		tmp = t_2;
	} else if (c <= -6.8e-267) {
		tmp = t_1;
	} else if (c <= 2.45e-189) {
		tmp = 2.0 * (z * t);
	} else if (c <= 4.2e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	t_2 = (c * i) * (a * -2.0)
	tmp = 0
	if c <= -4.2e+30:
		tmp = t_2
	elif c <= -6.8e-267:
		tmp = t_1
	elif c <= 2.45e-189:
		tmp = 2.0 * (z * t)
	elif c <= 4.2e-49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	t_2 = Float64(Float64(c * i) * Float64(a * -2.0))
	tmp = 0.0
	if (c <= -4.2e+30)
		tmp = t_2;
	elseif (c <= -6.8e-267)
		tmp = t_1;
	elseif (c <= 2.45e-189)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (c <= 4.2e-49)
		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 = (x * y) * 2.0;
	t_2 = (c * i) * (a * -2.0);
	tmp = 0.0;
	if (c <= -4.2e+30)
		tmp = t_2;
	elseif (c <= -6.8e-267)
		tmp = t_1;
	elseif (c <= 2.45e-189)
		tmp = 2.0 * (z * t);
	elseif (c <= 4.2e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+30], t$95$2, If[LessEqual[c, -6.8e-267], t$95$1, If[LessEqual[c, 2.45e-189], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e-49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.2e30 or 4.1999999999999998e-49 < c

   1. Initial program 78.4%

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

      1. fma-define 78.4%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

      1. fma-define 87.0%

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

      2. +-commutative 87.0%

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in a around inf 45.5%

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

      1. mul-1-neg 45.5%

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

      2. associate-*r* 37.5%

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

      3. distribute-lft-neg-out 37.5%

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

      4. *-commutative 37.5%

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

      5. distribute-rgt-neg-in 37.5%

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

   9. Simplified 37.5%

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

   10. Taylor expanded in i around 0 45.5%

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

       1. associate-*r* 45.5%

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

   12. Simplified 45.5%

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

   if -4.2e30 < c < -6.80000000000000041e-267 or 2.4499999999999999e-189 < c < 4.1999999999999998e-49

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 49.8%

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

   if -6.80000000000000041e-267 < c < 2.4499999999999999e-189

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 72.9%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+30}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-267}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-189}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-147}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -4.6e+27)
     t_1
     (if (<= c 2.15e-147)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 2.9e+57) (* 2.0 (- (* x y) (* i (* a c)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -4.6e+27) {
		tmp = t_1;
	} else if (c <= 2.15e-147) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.9e+57) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} 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 * (c * ((a + (b * c)) * -i))
    if (c <= (-4.6d+27)) then
        tmp = t_1
    else if (c <= 2.15d-147) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 2.9d+57) then
        tmp = 2.0d0 * ((x * y) - (i * (a * c)))
    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 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -4.6e+27) {
		tmp = t_1;
	} else if (c <= 2.15e-147) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 2.9e+57) {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -4.6e+27:
		tmp = t_1
	elif c <= 2.15e-147:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 2.9e+57:
		tmp = 2.0 * ((x * y) - (i * (a * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -4.6e+27)
		tmp = t_1;
	elseif (c <= 2.15e-147)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 2.9e+57)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))));
	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 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -4.6e+27)
		tmp = t_1;
	elseif (c <= 2.15e-147)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 2.9e+57)
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	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[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.6e+27], t$95$1, If[LessEqual[c, 2.15e-147], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 2.9e+57], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.6000000000000001e27 or 2.9000000000000002e57 < c

   1. Initial program 74.5%

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

   3. Taylor expanded in i around inf 80.9%

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

   if -4.6000000000000001e27 < c < 2.1500000000000001e-147

   1. Initial program 95.1%

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

   3. Taylor expanded in c around 0 77.9%

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

   if 2.1500000000000001e-147 < c < 2.9000000000000002e57

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 93.0%

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

      1. *-commutative 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in z around 0 77.8%

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

      1. associate-*r* 77.8%

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

      2. *-commutative 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-147}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+57}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 10^{+113}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1e-29) (not (<= (* x y) 1e+113)))
   (* 2.0 (* x (+ y (* t (/ z x)))))
   (* 2.0 (- (* z t) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e-29) || !((x * y) <= 1e+113)) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1d-29)) .or. (.not. ((x * y) <= 1d+113))) then
        tmp = 2.0d0 * (x * (y + (t * (z / x))))
    else
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e-29) || !((x * y) <= 1e+113)) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1e-29) or not ((x * y) <= 1e+113):
		tmp = 2.0 * (x * (y + (t * (z / x))))
	else:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1e-29) || !(Float64(x * y) <= 1e+113))
		tmp = Float64(2.0 * Float64(x * Float64(y + Float64(t * Float64(z / x)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1e-29) || ~(((x * y) <= 1e+113)))
		tmp = 2.0 * (x * (y + (t * (z / x))));
	else
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e-29], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+113]], $MachinePrecision]], N[(2.0 * N[(x * N[(y + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999943e-30 or 1e113 < (*.f64 x y)

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in z around inf 66.2%

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

      1. associate--l+ 66.2%

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

      2. div-sub 68.7%

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

      3. associate-*r* 65.6%

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

      4. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in c around 0 60.8%

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

       1. associate-/l* 60.8%

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

   11. Simplified 60.8%

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

   12. Taylor expanded in x around inf 67.8%

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

       1. associate-/l* 69.0%

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

   14. Simplified 69.0%

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

   if -9.99999999999999943e-30 < (*.f64 x y) < 1e113

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in x around 0 67.2%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

   8. Simplified 63.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 10^{+113}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.66 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.66e+59)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 5.8e+69)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* x y) 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 <= -1.66e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 5.8e+69) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - 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 <= (-1.66d+59)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 5.8d+69) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - 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 <= -1.66e+59) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 5.8e+69) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - 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 <= -1.66e+59:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 5.8e+69:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - 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 <= -1.66e+59)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 5.8e+69)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 <= -1.66e+59)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 5.8e+69)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - 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, -1.66e+59], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+69], 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[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.6599999999999999e59

   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 x around 0 84.8%

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

   if -1.6599999999999999e59 < c < 5.7999999999999997e69

   1. Initial program 94.7%

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

   3. Taylor expanded in a around inf 88.7%

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

      1. *-commutative 88.7%

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

   5. Simplified 88.7%

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

   if 5.7999999999999997e69 < c

   1. Initial program 79.0%

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

   3. Taylor expanded in z around 0 90.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.66 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e-29)
   (* 2.0 (* x (+ y (* t (/ z x)))))
   (if (<= (* x y) 4e+163)
     (* 2.0 (- (* z t) (* a (* c i))))
     (* 2.0 (* y (+ x (* t (/ z y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e-29) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else if ((x * y) <= 4e+163) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + (t * (z / y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d-29)) then
        tmp = 2.0d0 * (x * (y + (t * (z / x))))
    else if ((x * y) <= 4d+163) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else
        tmp = 2.0d0 * (y * (x + (t * (z / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e-29) {
		tmp = 2.0 * (x * (y + (t * (z / x))));
	} else if ((x * y) <= 4e+163) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = 2.0 * (y * (x + (t * (z / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e-29:
		tmp = 2.0 * (x * (y + (t * (z / x))))
	elif (x * y) <= 4e+163:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	else:
		tmp = 2.0 * (y * (x + (t * (z / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e-29)
		tmp = Float64(2.0 * Float64(x * Float64(y + Float64(t * Float64(z / x)))));
	elseif (Float64(x * y) <= 4e+163)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(y * Float64(x + Float64(t * Float64(z / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e-29)
		tmp = 2.0 * (x * (y + (t * (z / x))));
	elseif ((x * y) <= 4e+163)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	else
		tmp = 2.0 * (y * (x + (t * (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-29], N[(2.0 * N[(x * N[(y + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+163], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999943e-30

   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 a around inf 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in z around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. div-sub 63.7%

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

      3. associate-*r* 62.4%

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

      4. *-commutative 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in c around 0 57.3%

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

       1. associate-/l* 54.6%

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

   11. Simplified 54.6%

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

   12. Taylor expanded in x around inf 66.2%

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

       1. associate-/l* 67.4%

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

   14. Simplified 67.4%

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

   if -9.99999999999999943e-30 < (*.f64 x y) < 3.9999999999999998e163

   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 a around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in z around inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 67.9%

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

      3. associate-*r* 63.4%

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

      4. *-commutative 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in x around 0 61.3%

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

       1. associate-/l* 60.6%

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

       2. associate-/l* 56.1%

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

   11. Simplified 56.1%

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

   12. Taylor expanded in z around 0 67.0%

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

       1. +-commutative 67.0%

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

       2. mul-1-neg 67.0%

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

       3. sub-neg 67.0%

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

       4. *-commutative 67.0%

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

   14. Simplified 67.0%

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

   if 3.9999999999999998e163 < (*.f64 x y)

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. div-sub 75.1%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in c around 0 75.1%

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

       1. associate-/l* 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in y around inf 77.7%

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

       1. associate-/l* 80.5%

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

   14. Simplified 80.5%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+163}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x + t \cdot \frac{z}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+28} \lor \neg \left(c \leq 1.26 \cdot 10^{+76}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.1e+28) (not (<= c 1.26e+76)))
   (* (* c i) (* a -2.0))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+28) || !(c <= 1.26e+76)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.1d+28)) .or. (.not. (c <= 1.26d+76))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+28) || !(c <= 1.26e+76)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.1e+28) or not (c <= 1.26e+76):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.1e+28) || !(c <= 1.26e+76))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.1e+28) || ~((c <= 1.26e+76)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.1e+28], N[Not[LessEqual[c, 1.26e+76]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.09999999999999989e28 or 1.26000000000000007e76 < c

   1. Initial program 75.5%

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

      1. fma-define 75.5%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

      1. fma-define 84.3%

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

      2. +-commutative 84.3%

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

   6. Applied egg-rr 84.3%

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

   7. Taylor expanded in a around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. associate-*r* 35.9%

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

      3. distribute-lft-neg-out 35.9%

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

      4. *-commutative 35.9%

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

      5. distribute-rgt-neg-in 35.9%

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

   9. Simplified 35.9%

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

   10. Taylor expanded in i around 0 45.6%

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

       1. associate-*r* 45.6%

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

   12. Simplified 45.6%

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

   if -2.09999999999999989e28 < c < 1.26000000000000007e76

   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

   3. Taylor expanded in c around 0 72.9%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+28} \lor \neg \left(c \leq 1.26 \cdot 10^{+76}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+168} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{+101}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.4e+168) (not (<= (* x y) 1.6e+101)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.4e+168) || !((x * y) <= 1.6e+101)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.4d+168)) .or. (.not. ((x * y) <= 1.6d+101))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.4e+168) || !((x * y) <= 1.6e+101)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.4e+168) or not ((x * y) <= 1.6e+101):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.4e+168) || !(Float64(x * y) <= 1.6e+101))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.4e+168) || ~(((x * y) <= 1.6e+101)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.4e+168], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.6e+101]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.39999999999999995e168 or 1.60000000000000003e101 < (*.f64 x y)

   1. Initial program 78.7%

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

   3. Taylor expanded in x around inf 64.2%

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

   if -1.39999999999999995e168 < (*.f64 x y) < 1.60000000000000003e101

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 33.5%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+168} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{+101}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in z around inf 26.9%

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

4. Final simplification 26.9%

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

Developer target: 93.9% 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 2024083 
(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))))