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

Percentage Accurate: 89.8% → 96.2%

Time: 14.8s

Alternatives: 17

Speedup: 0.5×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.8% 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: 96.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (z * t) + (x * y);
	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 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(z * t) + Float64(x * y))
	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(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.0%

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

      1. associate-*l* 98.3%

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

      2. fma-def 98.3%

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

   3. Simplified 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. Step-by-step derivation

      1. fma-def 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%

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

   5. 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. Taylor expanded in i around inf 70.3%

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

4. Final simplification 97.2%

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

Alternative 2: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* z t) (* c (* t_1 i))))
     (if (<= t_2 5e+296)
       (* (- (+ (* z t) (* x y)) t_2) 2.0)
       (* 2.0 (* c (* t_1 (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+296) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	} else if (t_2 <= 5e+296) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * (c * (t_1 * -i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	elif t_2 <= 5e+296:
		tmp = (((z * t) + (x * y)) - t_2) * 2.0
	else:
		tmp = 2.0 * (c * (t_1 * -i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	elseif (t_2 <= 5e+296)
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - t_2) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	elseif (t_2 <= 5e+296)
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	else
		tmp = 2.0 * (c * (t_1 * -i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+296], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 80.9%

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

   2. Taylor expanded in x around 0 92.1%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000001e296

   1. Initial program 97.9%

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

   if 5.0000000000000001e296 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   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. Taylor expanded in i around inf 91.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 3: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ t_2 := c \cdot \left(a \cdot i\right)\\ t_3 := 2 \cdot \left(z \cdot t - t_2\right)\\ t_4 := 2 \cdot \left(x \cdot y - t_2\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-69}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-275}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-220}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 10^{-11}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i)))))
        (t_2 (* c (* a i)))
        (t_3 (* 2.0 (- (* z t) t_2)))
        (t_4 (* 2.0 (- (* x y) t_2))))
   (if (<= c -2e+22)
     t_1
     (if (<= c -4.5e-69)
       t_4
       (if (<= c -1e-275)
         t_3
         (if (<= c 2.05e-220)
           t_4
           (if (<= c 4.6e-152) t_3 (if (<= c 1e-11) t_4 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 t_2 = c * (a * i);
	double t_3 = 2.0 * ((z * t) - t_2);
	double t_4 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -2e+22) {
		tmp = t_1;
	} else if (c <= -4.5e-69) {
		tmp = t_4;
	} else if (c <= -1e-275) {
		tmp = t_3;
	} else if (c <= 2.05e-220) {
		tmp = t_4;
	} else if (c <= 4.6e-152) {
		tmp = t_3;
	} else if (c <= 1e-11) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (b * c)) * -i))
    t_2 = c * (a * i)
    t_3 = 2.0d0 * ((z * t) - t_2)
    t_4 = 2.0d0 * ((x * y) - t_2)
    if (c <= (-2d+22)) then
        tmp = t_1
    else if (c <= (-4.5d-69)) then
        tmp = t_4
    else if (c <= (-1d-275)) then
        tmp = t_3
    else if (c <= 2.05d-220) then
        tmp = t_4
    else if (c <= 4.6d-152) then
        tmp = t_3
    else if (c <= 1d-11) then
        tmp = t_4
    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 t_2 = c * (a * i);
	double t_3 = 2.0 * ((z * t) - t_2);
	double t_4 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -2e+22) {
		tmp = t_1;
	} else if (c <= -4.5e-69) {
		tmp = t_4;
	} else if (c <= -1e-275) {
		tmp = t_3;
	} else if (c <= 2.05e-220) {
		tmp = t_4;
	} else if (c <= 4.6e-152) {
		tmp = t_3;
	} else if (c <= 1e-11) {
		tmp = t_4;
	} 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))
	t_2 = c * (a * i)
	t_3 = 2.0 * ((z * t) - t_2)
	t_4 = 2.0 * ((x * y) - t_2)
	tmp = 0
	if c <= -2e+22:
		tmp = t_1
	elif c <= -4.5e-69:
		tmp = t_4
	elif c <= -1e-275:
		tmp = t_3
	elif c <= 2.05e-220:
		tmp = t_4
	elif c <= 4.6e-152:
		tmp = t_3
	elif c <= 1e-11:
		tmp = t_4
	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))))
	t_2 = Float64(c * Float64(a * i))
	t_3 = Float64(2.0 * Float64(Float64(z * t) - t_2))
	t_4 = Float64(2.0 * Float64(Float64(x * y) - t_2))
	tmp = 0.0
	if (c <= -2e+22)
		tmp = t_1;
	elseif (c <= -4.5e-69)
		tmp = t_4;
	elseif (c <= -1e-275)
		tmp = t_3;
	elseif (c <= 2.05e-220)
		tmp = t_4;
	elseif (c <= 4.6e-152)
		tmp = t_3;
	elseif (c <= 1e-11)
		tmp = t_4;
	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));
	t_2 = c * (a * i);
	t_3 = 2.0 * ((z * t) - t_2);
	t_4 = 2.0 * ((x * y) - t_2);
	tmp = 0.0;
	if (c <= -2e+22)
		tmp = t_1;
	elseif (c <= -4.5e-69)
		tmp = t_4;
	elseif (c <= -1e-275)
		tmp = t_3;
	elseif (c <= 2.05e-220)
		tmp = t_4;
	elseif (c <= 4.6e-152)
		tmp = t_3;
	elseif (c <= 1e-11)
		tmp = t_4;
	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]}, Block[{t$95$2 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+22], t$95$1, If[LessEqual[c, -4.5e-69], t$95$4, If[LessEqual[c, -1e-275], t$95$3, If[LessEqual[c, 2.05e-220], t$95$4, If[LessEqual[c, 4.6e-152], t$95$3, If[LessEqual[c, 1e-11], t$95$4, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2e22 or 9.99999999999999939e-12 < c

   1. Initial program 81.2%

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

   2. Taylor expanded in i around inf 78.3%

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

   if -2e22 < c < -4.50000000000000009e-69 or -9.99999999999999934e-276 < c < 2.04999999999999995e-220 or 4.6000000000000003e-152 < c < 9.99999999999999939e-12

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 69.4%

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

   3. Taylor expanded in c around 0 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if -4.50000000000000009e-69 < c < -9.99999999999999934e-276 or 2.04999999999999995e-220 < c < 4.6000000000000003e-152

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 67.7%

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

   3. Taylor expanded in c around 0 67.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-275}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-152}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 4: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ t_3 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ t_4 := 2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{if}\;c \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-220}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-11}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* a i)))
        (t_2 (* 2.0 (- (* z t) t_1)))
        (t_3 (* 2.0 (* c (* (+ a (* b c)) (- i)))))
        (t_4 (* 2.0 (- (* x y) t_1))))
   (if (<= c -2.7e+72)
     t_3
     (if (<= c -1.15e-68)
       (* 2.0 (- (* x y) (* (* c c) (* b i))))
       (if (<= c -5.4e-276)
         t_2
         (if (<= c 2.5e-220)
           t_4
           (if (<= c 4.2e-149) t_2 (if (<= c 1.8e-11) t_4 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double t_4 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -2.7e+72) {
		tmp = t_3;
	} else if (c <= -1.15e-68) {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	} else if (c <= -5.4e-276) {
		tmp = t_2;
	} else if (c <= 2.5e-220) {
		tmp = t_4;
	} else if (c <= 4.2e-149) {
		tmp = t_2;
	} else if (c <= 1.8e-11) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c * (a * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    t_3 = 2.0d0 * (c * ((a + (b * c)) * -i))
    t_4 = 2.0d0 * ((x * y) - t_1)
    if (c <= (-2.7d+72)) then
        tmp = t_3
    else if (c <= (-1.15d-68)) then
        tmp = 2.0d0 * ((x * y) - ((c * c) * (b * i)))
    else if (c <= (-5.4d-276)) then
        tmp = t_2
    else if (c <= 2.5d-220) then
        tmp = t_4
    else if (c <= 4.2d-149) then
        tmp = t_2
    else if (c <= 1.8d-11) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double t_4 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -2.7e+72) {
		tmp = t_3;
	} else if (c <= -1.15e-68) {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	} else if (c <= -5.4e-276) {
		tmp = t_2;
	} else if (c <= 2.5e-220) {
		tmp = t_4;
	} else if (c <= 4.2e-149) {
		tmp = t_2;
	} else if (c <= 1.8e-11) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (a * i)
	t_2 = 2.0 * ((z * t) - t_1)
	t_3 = 2.0 * (c * ((a + (b * c)) * -i))
	t_4 = 2.0 * ((x * y) - t_1)
	tmp = 0
	if c <= -2.7e+72:
		tmp = t_3
	elif c <= -1.15e-68:
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)))
	elif c <= -5.4e-276:
		tmp = t_2
	elif c <= 2.5e-220:
		tmp = t_4
	elif c <= 4.2e-149:
		tmp = t_2
	elif c <= 1.8e-11:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(a * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	t_3 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	t_4 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	tmp = 0.0
	if (c <= -2.7e+72)
		tmp = t_3;
	elseif (c <= -1.15e-68)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * c) * Float64(b * i))));
	elseif (c <= -5.4e-276)
		tmp = t_2;
	elseif (c <= 2.5e-220)
		tmp = t_4;
	elseif (c <= 4.2e-149)
		tmp = t_2;
	elseif (c <= 1.8e-11)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (a * i);
	t_2 = 2.0 * ((z * t) - t_1);
	t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	t_4 = 2.0 * ((x * y) - t_1);
	tmp = 0.0;
	if (c <= -2.7e+72)
		tmp = t_3;
	elseif (c <= -1.15e-68)
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	elseif (c <= -5.4e-276)
		tmp = t_2;
	elseif (c <= 2.5e-220)
		tmp = t_4;
	elseif (c <= 4.2e-149)
		tmp = t_2;
	elseif (c <= 1.8e-11)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.7e+72], t$95$3, If[LessEqual[c, -1.15e-68], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.4e-276], t$95$2, If[LessEqual[c, 2.5e-220], t$95$4, If[LessEqual[c, 4.2e-149], t$95$2, If[LessEqual[c, 1.8e-11], t$95$4, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.7000000000000001e72 or 1.79999999999999992e-11 < c

   1. Initial program 80.4%

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

   2. Taylor expanded in i around inf 79.6%

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

   if -2.7000000000000001e72 < c < -1.14999999999999998e-68

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 67.1%

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

   3. Taylor expanded in a around 0 61.9%

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

      1. unpow2 61.9%

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

   5. Simplified 61.9%

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

   if -1.14999999999999998e-68 < c < -5.39999999999999971e-276 or 2.5000000000000001e-220 < c < 4.20000000000000022e-149

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 67.7%

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

   3. Taylor expanded in c around 0 67.7%

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

   if -5.39999999999999971e-276 < c < 2.5000000000000001e-220 or 4.20000000000000022e-149 < c < 1.79999999999999992e-11

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 69.7%

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

   3. Taylor expanded in c around 0 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-276}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 5: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (- (* z t) (* c (* a i))))))
   (if (<= c -2.1e+117)
     (* 2.0 (* c (* (* b c) (- i))))
     (if (<= c -1.75e-17)
       t_2
       (if (<= c -7.5e-69)
         t_1
         (if (<= c -5.8e-276)
           t_2
           (if (<= c 1e-267)
             t_1
             (if (<= c 7.5e-12) t_2 (* (* c (* c (* b i))) (- 2.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * ((z * t) - (c * (a * i)));
	double tmp;
	if (c <= -2.1e+117) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -1.75e-17) {
		tmp = t_2;
	} else if (c <= -7.5e-69) {
		tmp = t_1;
	} else if (c <= -5.8e-276) {
		tmp = t_2;
	} else if (c <= 1e-267) {
		tmp = t_1;
	} else if (c <= 7.5e-12) {
		tmp = t_2;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * ((z * t) - (c * (a * i)))
    if (c <= (-2.1d+117)) then
        tmp = 2.0d0 * (c * ((b * c) * -i))
    else if (c <= (-1.75d-17)) then
        tmp = t_2
    else if (c <= (-7.5d-69)) then
        tmp = t_1
    else if (c <= (-5.8d-276)) then
        tmp = t_2
    else if (c <= 1d-267) then
        tmp = t_1
    else if (c <= 7.5d-12) then
        tmp = t_2
    else
        tmp = (c * (c * (b * i))) * -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * ((z * t) - (c * (a * i)));
	double tmp;
	if (c <= -2.1e+117) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -1.75e-17) {
		tmp = t_2;
	} else if (c <= -7.5e-69) {
		tmp = t_1;
	} else if (c <= -5.8e-276) {
		tmp = t_2;
	} else if (c <= 1e-267) {
		tmp = t_1;
	} else if (c <= 7.5e-12) {
		tmp = t_2;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * ((z * t) - (c * (a * i)))
	tmp = 0
	if c <= -2.1e+117:
		tmp = 2.0 * (c * ((b * c) * -i))
	elif c <= -1.75e-17:
		tmp = t_2
	elif c <= -7.5e-69:
		tmp = t_1
	elif c <= -5.8e-276:
		tmp = t_2
	elif c <= 1e-267:
		tmp = t_1
	elif c <= 7.5e-12:
		tmp = t_2
	else:
		tmp = (c * (c * (b * i))) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))))
	tmp = 0.0
	if (c <= -2.1e+117)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(b * c) * Float64(-i))));
	elseif (c <= -1.75e-17)
		tmp = t_2;
	elseif (c <= -7.5e-69)
		tmp = t_1;
	elseif (c <= -5.8e-276)
		tmp = t_2;
	elseif (c <= 1e-267)
		tmp = t_1;
	elseif (c <= 7.5e-12)
		tmp = t_2;
	else
		tmp = Float64(Float64(c * Float64(c * Float64(b * i))) * Float64(-2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * ((z * t) - (c * (a * i)));
	tmp = 0.0;
	if (c <= -2.1e+117)
		tmp = 2.0 * (c * ((b * c) * -i));
	elseif (c <= -1.75e-17)
		tmp = t_2;
	elseif (c <= -7.5e-69)
		tmp = t_1;
	elseif (c <= -5.8e-276)
		tmp = t_2;
	elseif (c <= 1e-267)
		tmp = t_1;
	elseif (c <= 7.5e-12)
		tmp = t_2;
	else
		tmp = (c * (c * (b * i))) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.1e+117], N[(2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-17], t$95$2, If[LessEqual[c, -7.5e-69], t$95$1, If[LessEqual[c, -5.8e-276], t$95$2, If[LessEqual[c, 1e-267], t$95$1, If[LessEqual[c, 7.5e-12], t$95$2, N[(N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.1000000000000001e117

   1. Initial program 77.6%

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

   2. Taylor expanded in i around inf 79.6%

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

   3. Taylor expanded in c around inf 70.3%

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

   if -2.1000000000000001e117 < c < -1.7500000000000001e-17 or -7.5e-69 < c < -5.79999999999999975e-276 or 9.9999999999999998e-268 < c < 7.5e-12

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 65.9%

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

   3. Taylor expanded in c around 0 58.5%

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

   if -1.7500000000000001e-17 < c < -7.5e-69 or -5.79999999999999975e-276 < c < 9.9999999999999998e-268

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.7%

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

   if 7.5e-12 < c

   1. Initial program 81.8%

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

      1. associate-*l* 89.0%

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

      2. fma-def 89.0%

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

   3. Simplified 89.0%

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

      1. fma-def 89.0%

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

      2. +-commutative 89.0%

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

   5. Applied egg-rr 89.0%

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

   6. Taylor expanded in a around 0 79.0%

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

   7. Taylor expanded in c around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unpow2 64.6%

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

      3. associate-*r* 67.0%

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

      4. distribute-lft-neg-in 67.0%

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

      5. associate-*l* 72.8%

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

      6. distribute-lft-neg-in 72.8%

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

      7. associate-*r* 70.4%

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

      8. *-commutative 70.4%

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

      9. associate-*r* 70.4%

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

   9. Simplified 70.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-276}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 10^{-267}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \]

Alternative 6: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -1.36 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.12 \cdot 10^{-277}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 590:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* (* c (* c (* b i))) (- 2.0)))
        (t_3 (* 2.0 (* z t))))
   (if (<= c -1.36e+22)
     t_2
     (if (<= c -1.1e-68)
       t_1
       (if (<= c -2.12e-277)
         t_3
         (if (<= c 3.1e-201)
           t_1
           (if (<= c 2.9e-149) t_3 (if (<= c 590.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (c * (c * (b * i))) * -2.0;
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.36e+22) {
		tmp = t_2;
	} else if (c <= -1.1e-68) {
		tmp = t_1;
	} else if (c <= -2.12e-277) {
		tmp = t_3;
	} else if (c <= 3.1e-201) {
		tmp = t_1;
	} else if (c <= 2.9e-149) {
		tmp = t_3;
	} else if (c <= 590.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = (c * (c * (b * i))) * -2.0d0
    t_3 = 2.0d0 * (z * t)
    if (c <= (-1.36d+22)) then
        tmp = t_2
    else if (c <= (-1.1d-68)) then
        tmp = t_1
    else if (c <= (-2.12d-277)) then
        tmp = t_3
    else if (c <= 3.1d-201) then
        tmp = t_1
    else if (c <= 2.9d-149) then
        tmp = t_3
    else if (c <= 590.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (c * (c * (b * i))) * -2.0;
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.36e+22) {
		tmp = t_2;
	} else if (c <= -1.1e-68) {
		tmp = t_1;
	} else if (c <= -2.12e-277) {
		tmp = t_3;
	} else if (c <= 3.1e-201) {
		tmp = t_1;
	} else if (c <= 2.9e-149) {
		tmp = t_3;
	} else if (c <= 590.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = (c * (c * (b * i))) * -2.0
	t_3 = 2.0 * (z * t)
	tmp = 0
	if c <= -1.36e+22:
		tmp = t_2
	elif c <= -1.1e-68:
		tmp = t_1
	elif c <= -2.12e-277:
		tmp = t_3
	elif c <= 3.1e-201:
		tmp = t_1
	elif c <= 2.9e-149:
		tmp = t_3
	elif c <= 590.0:
		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(x * y))
	t_2 = Float64(Float64(c * Float64(c * Float64(b * i))) * Float64(-2.0))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -1.36e+22)
		tmp = t_2;
	elseif (c <= -1.1e-68)
		tmp = t_1;
	elseif (c <= -2.12e-277)
		tmp = t_3;
	elseif (c <= 3.1e-201)
		tmp = t_1;
	elseif (c <= 2.9e-149)
		tmp = t_3;
	elseif (c <= 590.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = (c * (c * (b * i))) * -2.0;
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -1.36e+22)
		tmp = t_2;
	elseif (c <= -1.1e-68)
		tmp = t_1;
	elseif (c <= -2.12e-277)
		tmp = t_3;
	elseif (c <= 3.1e-201)
		tmp = t_1;
	elseif (c <= 2.9e-149)
		tmp = t_3;
	elseif (c <= 590.0)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.36e+22], t$95$2, If[LessEqual[c, -1.1e-68], t$95$1, If[LessEqual[c, -2.12e-277], t$95$3, If[LessEqual[c, 3.1e-201], t$95$1, If[LessEqual[c, 2.9e-149], t$95$3, If[LessEqual[c, 590.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.36e22 or 590 < c

   1. Initial program 80.5%

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

      1. associate-*l* 91.8%

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

      2. fma-def 91.8%

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

   3. Simplified 91.8%

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

      1. fma-def 91.8%

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

      2. +-commutative 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in a around 0 80.8%

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

   7. Taylor expanded in c around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. unpow2 63.4%

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

      3. associate-*r* 64.3%

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

      4. distribute-lft-neg-in 64.3%

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

      5. associate-*l* 68.5%

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

      6. distribute-lft-neg-in 68.5%

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

      7. associate-*r* 67.7%

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

      8. *-commutative 67.7%

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

      9. associate-*r* 67.5%

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

   9. Simplified 67.5%

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

   if -1.36e22 < c < -1.10000000000000001e-68 or -2.12e-277 < c < 3.0999999999999999e-201 or 2.9e-149 < c < 590

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 47.9%

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

   if -1.10000000000000001e-68 < c < -2.12e-277 or 3.0999999999999999e-201 < c < 2.9e-149

   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. Taylor expanded in z around inf 61.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.36 \cdot 10^{+22}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.12 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 590:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \]

Alternative 7: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1300:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= c -1.3e+22)
     (* 2.0 (* c (* (* b c) (- i))))
     (if (<= c -4.2e-69)
       t_1
       (if (<= c -3.2e-277)
         t_2
         (if (<= c 4.8e-201)
           t_1
           (if (<= c 9.5e-153)
             t_2
             (if (<= c 1300.0) t_1 (* (* c (* c (* b i))) (- 2.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.3e+22) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -4.2e-69) {
		tmp = t_1;
	} else if (c <= -3.2e-277) {
		tmp = t_2;
	} else if (c <= 4.8e-201) {
		tmp = t_1;
	} else if (c <= 9.5e-153) {
		tmp = t_2;
	} else if (c <= 1300.0) {
		tmp = t_1;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (c <= (-1.3d+22)) then
        tmp = 2.0d0 * (c * ((b * c) * -i))
    else if (c <= (-4.2d-69)) then
        tmp = t_1
    else if (c <= (-3.2d-277)) then
        tmp = t_2
    else if (c <= 4.8d-201) then
        tmp = t_1
    else if (c <= 9.5d-153) then
        tmp = t_2
    else if (c <= 1300.0d0) then
        tmp = t_1
    else
        tmp = (c * (c * (b * i))) * -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.3e+22) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -4.2e-69) {
		tmp = t_1;
	} else if (c <= -3.2e-277) {
		tmp = t_2;
	} else if (c <= 4.8e-201) {
		tmp = t_1;
	} else if (c <= 9.5e-153) {
		tmp = t_2;
	} else if (c <= 1300.0) {
		tmp = t_1;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if c <= -1.3e+22:
		tmp = 2.0 * (c * ((b * c) * -i))
	elif c <= -4.2e-69:
		tmp = t_1
	elif c <= -3.2e-277:
		tmp = t_2
	elif c <= 4.8e-201:
		tmp = t_1
	elif c <= 9.5e-153:
		tmp = t_2
	elif c <= 1300.0:
		tmp = t_1
	else:
		tmp = (c * (c * (b * i))) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -1.3e+22)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(b * c) * Float64(-i))));
	elseif (c <= -4.2e-69)
		tmp = t_1;
	elseif (c <= -3.2e-277)
		tmp = t_2;
	elseif (c <= 4.8e-201)
		tmp = t_1;
	elseif (c <= 9.5e-153)
		tmp = t_2;
	elseif (c <= 1300.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * Float64(c * Float64(b * i))) * Float64(-2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -1.3e+22)
		tmp = 2.0 * (c * ((b * c) * -i));
	elseif (c <= -4.2e-69)
		tmp = t_1;
	elseif (c <= -3.2e-277)
		tmp = t_2;
	elseif (c <= 4.8e-201)
		tmp = t_1;
	elseif (c <= 9.5e-153)
		tmp = t_2;
	elseif (c <= 1300.0)
		tmp = t_1;
	else
		tmp = (c * (c * (b * i))) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e+22], N[(2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.2e-69], t$95$1, If[LessEqual[c, -3.2e-277], t$95$2, If[LessEqual[c, 4.8e-201], t$95$1, If[LessEqual[c, 9.5e-153], t$95$2, If[LessEqual[c, 1300.0], t$95$1, N[(N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.3e22

   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. Taylor expanded in i around inf 75.3%

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

   3. Taylor expanded in c around inf 61.7%

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

   if -1.3e22 < c < -4.1999999999999999e-69 or -3.1999999999999998e-277 < c < 4.80000000000000018e-201 or 9.50000000000000031e-153 < c < 1300

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 47.9%

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

   if -4.1999999999999999e-69 < c < -3.1999999999999998e-277 or 4.80000000000000018e-201 < c < 9.50000000000000031e-153

   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. Taylor expanded in z around inf 61.9%

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

   if 1300 < c

   1. Initial program 80.6%

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

      1. associate-*l* 88.2%

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

      2. fma-def 88.2%

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

   3. Simplified 88.2%

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

      1. fma-def 88.2%

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

      2. +-commutative 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in a around 0 78.9%

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

   7. Taylor expanded in c around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unpow2 67.4%

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

      3. associate-*r* 68.7%

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

      4. distribute-lft-neg-in 68.7%

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

      5. associate-*l* 74.9%

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

      6. distribute-lft-neg-in 74.9%

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

      7. associate-*r* 72.4%

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

      8. *-commutative 72.4%

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

      9. associate-*r* 73.5%

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

   9. Simplified 73.5%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-153}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1300:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \]

Alternative 8: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(\left(i \cdot \left(c \cdot c\right)\right) \cdot -2\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* b (* (* i (* c c)) -2.0)))
        (t_3 (* 2.0 (* z t))))
   (if (<= c -3e+22)
     t_2
     (if (<= c -1.15e-68)
       t_1
       (if (<= c -7.5e-277)
         t_3
         (if (<= c 2.8e-201)
           t_1
           (if (<= c 8.5e-152) t_3 (if (<= c 6.8e-13) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = b * ((i * (c * c)) * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -3e+22) {
		tmp = t_2;
	} else if (c <= -1.15e-68) {
		tmp = t_1;
	} else if (c <= -7.5e-277) {
		tmp = t_3;
	} else if (c <= 2.8e-201) {
		tmp = t_1;
	} else if (c <= 8.5e-152) {
		tmp = t_3;
	} else if (c <= 6.8e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = b * ((i * (c * c)) * (-2.0d0))
    t_3 = 2.0d0 * (z * t)
    if (c <= (-3d+22)) then
        tmp = t_2
    else if (c <= (-1.15d-68)) then
        tmp = t_1
    else if (c <= (-7.5d-277)) then
        tmp = t_3
    else if (c <= 2.8d-201) then
        tmp = t_1
    else if (c <= 8.5d-152) then
        tmp = t_3
    else if (c <= 6.8d-13) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = b * ((i * (c * c)) * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -3e+22) {
		tmp = t_2;
	} else if (c <= -1.15e-68) {
		tmp = t_1;
	} else if (c <= -7.5e-277) {
		tmp = t_3;
	} else if (c <= 2.8e-201) {
		tmp = t_1;
	} else if (c <= 8.5e-152) {
		tmp = t_3;
	} else if (c <= 6.8e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = b * ((i * (c * c)) * -2.0)
	t_3 = 2.0 * (z * t)
	tmp = 0
	if c <= -3e+22:
		tmp = t_2
	elif c <= -1.15e-68:
		tmp = t_1
	elif c <= -7.5e-277:
		tmp = t_3
	elif c <= 2.8e-201:
		tmp = t_1
	elif c <= 8.5e-152:
		tmp = t_3
	elif c <= 6.8e-13:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(i * Float64(c * c)) * -2.0))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -3e+22)
		tmp = t_2;
	elseif (c <= -1.15e-68)
		tmp = t_1;
	elseif (c <= -7.5e-277)
		tmp = t_3;
	elseif (c <= 2.8e-201)
		tmp = t_1;
	elseif (c <= 8.5e-152)
		tmp = t_3;
	elseif (c <= 6.8e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = b * ((i * (c * c)) * -2.0);
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -3e+22)
		tmp = t_2;
	elseif (c <= -1.15e-68)
		tmp = t_1;
	elseif (c <= -7.5e-277)
		tmp = t_3;
	elseif (c <= 2.8e-201)
		tmp = t_1;
	elseif (c <= 8.5e-152)
		tmp = t_3;
	elseif (c <= 6.8e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+22], t$95$2, If[LessEqual[c, -1.15e-68], t$95$1, If[LessEqual[c, -7.5e-277], t$95$3, If[LessEqual[c, 2.8e-201], t$95$1, If[LessEqual[c, 8.5e-152], t$95$3, If[LessEqual[c, 6.8e-13], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3e22 or 6.80000000000000031e-13 < c

   1. Initial program 81.2%

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

      1. associate-*l* 92.1%

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

      2. fma-def 92.1%

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

   3. Simplified 92.1%

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

      1. fma-def 92.1%

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

      2. +-commutative 92.1%

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

   5. Applied egg-rr 92.1%

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

   6. Taylor expanded in a around 0 80.7%

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

   7. Taylor expanded in c around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. unpow2 61.9%

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

      3. associate-*r* 63.5%

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

      4. *-commutative 63.5%

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

      5. associate-*l* 63.5%

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

      6. *-commutative 63.5%

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

   9. Simplified 63.5%

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

   if -3e22 < c < -1.14999999999999998e-68 or -7.49999999999999971e-277 < c < 2.7999999999999999e-201 or 8.5000000000000007e-152 < c < 6.80000000000000031e-13

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 48.5%

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

   if -1.14999999999999998e-68 < c < -7.49999999999999971e-277 or 2.7999999999999999e-201 < c < 8.5000000000000007e-152

   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. Taylor expanded in z around inf 61.9%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+22}:\\ \;\;\;\;b \cdot \left(\left(i \cdot \left(c \cdot c\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-152}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(i \cdot \left(c \cdot c\right)\right) \cdot -2\right)\\ \end{array} \]

Alternative 9: 55.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ t_3 := 2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2.16 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* a i)))
        (t_2 (* 2.0 (- (* x y) t_1)))
        (t_3 (* 2.0 (- (* z t) t_1))))
   (if (<= c -2.8e+117)
     (* 2.0 (* c (* (* b c) (- i))))
     (if (<= c -5.2e-276)
       t_3
       (if (<= c 2e-220)
         t_2
         (if (<= c 1.4e-151)
           t_3
           (if (<= c 2.16e+21) t_2 (* (* c (* c (* b i))) (- 2.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -2.8e+117) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -5.2e-276) {
		tmp = t_3;
	} else if (c <= 2e-220) {
		tmp = t_2;
	} else if (c <= 1.4e-151) {
		tmp = t_3;
	} else if (c <= 2.16e+21) {
		tmp = t_2;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (a * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    t_3 = 2.0d0 * ((z * t) - t_1)
    if (c <= (-2.8d+117)) then
        tmp = 2.0d0 * (c * ((b * c) * -i))
    else if (c <= (-5.2d-276)) then
        tmp = t_3
    else if (c <= 2d-220) then
        tmp = t_2
    else if (c <= 1.4d-151) then
        tmp = t_3
    else if (c <= 2.16d+21) then
        tmp = t_2
    else
        tmp = (c * (c * (b * i))) * -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (a * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -2.8e+117) {
		tmp = 2.0 * (c * ((b * c) * -i));
	} else if (c <= -5.2e-276) {
		tmp = t_3;
	} else if (c <= 2e-220) {
		tmp = t_2;
	} else if (c <= 1.4e-151) {
		tmp = t_3;
	} else if (c <= 2.16e+21) {
		tmp = t_2;
	} else {
		tmp = (c * (c * (b * i))) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (a * i)
	t_2 = 2.0 * ((x * y) - t_1)
	t_3 = 2.0 * ((z * t) - t_1)
	tmp = 0
	if c <= -2.8e+117:
		tmp = 2.0 * (c * ((b * c) * -i))
	elif c <= -5.2e-276:
		tmp = t_3
	elif c <= 2e-220:
		tmp = t_2
	elif c <= 1.4e-151:
		tmp = t_3
	elif c <= 2.16e+21:
		tmp = t_2
	else:
		tmp = (c * (c * (b * i))) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(a * i))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	t_3 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	tmp = 0.0
	if (c <= -2.8e+117)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(b * c) * Float64(-i))));
	elseif (c <= -5.2e-276)
		tmp = t_3;
	elseif (c <= 2e-220)
		tmp = t_2;
	elseif (c <= 1.4e-151)
		tmp = t_3;
	elseif (c <= 2.16e+21)
		tmp = t_2;
	else
		tmp = Float64(Float64(c * Float64(c * Float64(b * i))) * Float64(-2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (a * i);
	t_2 = 2.0 * ((x * y) - t_1);
	t_3 = 2.0 * ((z * t) - t_1);
	tmp = 0.0;
	if (c <= -2.8e+117)
		tmp = 2.0 * (c * ((b * c) * -i));
	elseif (c <= -5.2e-276)
		tmp = t_3;
	elseif (c <= 2e-220)
		tmp = t_2;
	elseif (c <= 1.4e-151)
		tmp = t_3;
	elseif (c <= 2.16e+21)
		tmp = t_2;
	else
		tmp = (c * (c * (b * i))) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+117], N[(2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.2e-276], t$95$3, If[LessEqual[c, 2e-220], t$95$2, If[LessEqual[c, 1.4e-151], t$95$3, If[LessEqual[c, 2.16e+21], t$95$2, N[(N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.79999999999999997e117

   1. Initial program 77.6%

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

   2. Taylor expanded in i around inf 79.6%

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

   3. Taylor expanded in c around inf 70.3%

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

   if -2.79999999999999997e117 < c < -5.19999999999999969e-276 or 1.99999999999999998e-220 < c < 1.4e-151

   1. Initial program 95.3%

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

   2. Taylor expanded in x around 0 66.6%

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

   3. Taylor expanded in c around 0 58.9%

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

   if -5.19999999999999969e-276 < c < 1.99999999999999998e-220 or 1.4e-151 < c < 2.16e21

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 72.3%

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

   3. Taylor expanded in c around 0 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 2.16e21 < c

   1. Initial program 80.6%

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

      1. associate-*l* 88.2%

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

      2. fma-def 88.2%

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

   3. Simplified 88.2%

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

      1. fma-def 88.2%

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

      2. +-commutative 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in a around 0 78.9%

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

   7. Taylor expanded in c around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unpow2 67.4%

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

      3. associate-*r* 68.7%

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

      4. distribute-lft-neg-in 68.7%

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

      5. associate-*l* 74.9%

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

      6. distribute-lft-neg-in 74.9%

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

      7. associate-*r* 72.4%

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

      8. *-commutative 72.4%

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

      9. associate-*r* 73.5%

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

   9. Simplified 73.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-276}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-151}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.16 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right) \cdot \left(-2\right)\\ \end{array} \]

Alternative 10: 36.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= z -1.9e+157)
     t_2
     (if (<= z -2.1e+135)
       t_1
       (if (<= z -7.4e+70)
         t_2
         (if (<= z -7e-11)
           (* 2.0 (* c (* a (- i))))
           (if (<= z -1.76e-280)
             t_1
             (if (<= z 3.2e-122) (* (* a (* c i)) (- 2.0)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.9e+157) {
		tmp = t_2;
	} else if (z <= -2.1e+135) {
		tmp = t_1;
	} else if (z <= -7.4e+70) {
		tmp = t_2;
	} else if (z <= -7e-11) {
		tmp = 2.0 * (c * (a * -i));
	} else if (z <= -1.76e-280) {
		tmp = t_1;
	} else if (z <= 3.2e-122) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (z <= (-1.9d+157)) then
        tmp = t_2
    else if (z <= (-2.1d+135)) then
        tmp = t_1
    else if (z <= (-7.4d+70)) then
        tmp = t_2
    else if (z <= (-7d-11)) then
        tmp = 2.0d0 * (c * (a * -i))
    else if (z <= (-1.76d-280)) then
        tmp = t_1
    else if (z <= 3.2d-122) then
        tmp = (a * (c * i)) * -2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.9e+157) {
		tmp = t_2;
	} else if (z <= -2.1e+135) {
		tmp = t_1;
	} else if (z <= -7.4e+70) {
		tmp = t_2;
	} else if (z <= -7e-11) {
		tmp = 2.0 * (c * (a * -i));
	} else if (z <= -1.76e-280) {
		tmp = t_1;
	} else if (z <= 3.2e-122) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if z <= -1.9e+157:
		tmp = t_2
	elif z <= -2.1e+135:
		tmp = t_1
	elif z <= -7.4e+70:
		tmp = t_2
	elif z <= -7e-11:
		tmp = 2.0 * (c * (a * -i))
	elif z <= -1.76e-280:
		tmp = t_1
	elif z <= 3.2e-122:
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -1.9e+157)
		tmp = t_2;
	elseif (z <= -2.1e+135)
		tmp = t_1;
	elseif (z <= -7.4e+70)
		tmp = t_2;
	elseif (z <= -7e-11)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	elseif (z <= -1.76e-280)
		tmp = t_1;
	elseif (z <= 3.2e-122)
		tmp = Float64(Float64(a * Float64(c * i)) * Float64(-2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -1.9e+157)
		tmp = t_2;
	elseif (z <= -2.1e+135)
		tmp = t_1;
	elseif (z <= -7.4e+70)
		tmp = t_2;
	elseif (z <= -7e-11)
		tmp = 2.0 * (c * (a * -i));
	elseif (z <= -1.76e-280)
		tmp = t_1;
	elseif (z <= 3.2e-122)
		tmp = (a * (c * i)) * -2.0;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+157], t$95$2, If[LessEqual[z, -2.1e+135], t$95$1, If[LessEqual[z, -7.4e+70], t$95$2, If[LessEqual[z, -7e-11], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e-280], t$95$1, If[LessEqual[z, 3.2e-122], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e157 or -2.1000000000000001e135 < z < -7.39999999999999977e70 or 3.2000000000000002e-122 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 42.1%

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

   if -1.9e157 < z < -2.1000000000000001e135 or -7.00000000000000038e-11 < z < -1.76000000000000003e-280

   1. Initial program 89.2%

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

   2. Taylor expanded in x around inf 45.6%

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

   if -7.39999999999999977e70 < z < -7.00000000000000038e-11

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

   4. Simplified 51.3%

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

   if -1.76000000000000003e-280 < z < 3.2000000000000002e-122

   1. Initial program 90.8%

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

      1. associate-*l* 96.7%

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

      2. fma-def 96.7%

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

   3. Simplified 96.7%

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

      1. fma-def 96.7%

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

      2. +-commutative 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in a around inf 34.5%

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

      1. associate-*r* 37.5%

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

      2. neg-mul-1 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

   8. Simplified 37.5%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+157}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 11: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-14} \lor \neg \left(z \leq -1.06 \cdot 10^{-277}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -3.1e-14) (not (<= z -1.06e-277)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (* x y) (* (* c c) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.1e-14) || !(z <= -1.06e-277)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-3.1d-14)) .or. (.not. (z <= (-1.06d-277)))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) - ((c * c) * (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.1e-14) || !(z <= -1.06e-277)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -3.1e-14) or not (z <= -1.06e-277):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -3.1e-14) || !(z <= -1.06e-277))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(c * c) * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -3.1e-14) || ~((z <= -1.06e-277)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) - ((c * c) * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -3.1e-14], N[Not[LessEqual[z, -1.06e-277]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000004e-14 or -1.06e-277 < z

   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. Taylor expanded in x around 0 77.8%

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

   if -3.10000000000000004e-14 < z < -1.06e-277

   1. Initial program 89.1%

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

   2. Taylor expanded in z around 0 79.3%

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

   3. Taylor expanded in a around 0 66.0%

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

      1. unpow2 66.0%

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

   5. Simplified 66.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-14} \lor \neg \left(z \leq -1.06 \cdot 10^{-277}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 12: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-176} \lor \neg \left(t \leq 8.6 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= t -2.9e-176) (not (<= t 8.6e+129)))
     (* 2.0 (- (* z t) t_1))
     (* 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 ((t <= -2.9e-176) || !(t <= 8.6e+129)) {
		tmp = 2.0 * ((z * t) - t_1);
	} 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 ((t <= (-2.9d-176)) .or. (.not. (t <= 8.6d+129))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    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 ((t <= -2.9e-176) || !(t <= 8.6e+129)) {
		tmp = 2.0 * ((z * t) - t_1);
	} 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 (t <= -2.9e-176) or not (t <= 8.6e+129):
		tmp = 2.0 * ((z * t) - t_1)
	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 ((t <= -2.9e-176) || !(t <= 8.6e+129))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	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 ((t <= -2.9e-176) || ~((t <= 8.6e+129)))
		tmp = 2.0 * ((z * t) - t_1);
	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[Or[LessEqual[t, -2.9e-176], N[Not[LessEqual[t, 8.6e+129]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000006e-176 or 8.60000000000000042e129 < t

   1. Initial program 88.2%

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

   2. Taylor expanded in x around 0 80.3%

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

   if -2.90000000000000006e-176 < t < 8.60000000000000042e129

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 77.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-176} \lor \neg \left(t \leq 8.6 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 13: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-55}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.3e+52)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 6.8e-55)
       (* 2.0 (- (+ (* z t) (* x y)) (* 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 <= -1.3e+52) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.8e-55) {
		tmp = 2.0 * (((z * t) + (x * y)) - (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 <= (-1.3d+52)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 6.8d-55) then
        tmp = 2.0d0 * (((z * t) + (x * y)) - (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 <= -1.3e+52) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.8e-55) {
		tmp = 2.0 * (((z * t) + (x * y)) - (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 <= -1.3e+52:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 6.8e-55:
		tmp = 2.0 * (((z * t) + (x * y)) - (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 <= -1.3e+52)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 6.8e-55)
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - 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 <= -1.3e+52)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 6.8e-55)
		tmp = 2.0 * (((z * t) + (x * y)) - (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, -1.3e+52], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-55], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $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 < -1.3e52

   1. Initial program 79.2%

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

   2. Taylor expanded in x around 0 92.9%

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

   if -1.3e52 < c < 6.79999999999999946e-55

   1. Initial program 96.6%

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

   2. Taylor expanded in a around inf 93.1%

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

   if 6.79999999999999946e-55 < c

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0 86.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-55}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 14: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.36 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* 2.0 (* i (* a (- c)))))
        (t_3 (* 2.0 (* z t))))
   (if (<= t -2.1e-40)
     t_3
     (if (<= t 2.36e-209)
       t_1
       (if (<= t 1.75e-158)
         t_2
         (if (<= t 4000000000000.0) t_1 (if (<= t 1.65e+128) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (i * (a * -c));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.1e-40) {
		tmp = t_3;
	} else if (t <= 2.36e-209) {
		tmp = t_1;
	} else if (t <= 1.75e-158) {
		tmp = t_2;
	} else if (t <= 4000000000000.0) {
		tmp = t_1;
	} else if (t <= 1.65e+128) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (i * (a * -c))
    t_3 = 2.0d0 * (z * t)
    if (t <= (-2.1d-40)) then
        tmp = t_3
    else if (t <= 2.36d-209) then
        tmp = t_1
    else if (t <= 1.75d-158) then
        tmp = t_2
    else if (t <= 4000000000000.0d0) then
        tmp = t_1
    else if (t <= 1.65d+128) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (i * (a * -c));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.1e-40) {
		tmp = t_3;
	} else if (t <= 2.36e-209) {
		tmp = t_1;
	} else if (t <= 1.75e-158) {
		tmp = t_2;
	} else if (t <= 4000000000000.0) {
		tmp = t_1;
	} else if (t <= 1.65e+128) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (i * (a * -c))
	t_3 = 2.0 * (z * t)
	tmp = 0
	if t <= -2.1e-40:
		tmp = t_3
	elif t <= 2.36e-209:
		tmp = t_1
	elif t <= 1.75e-158:
		tmp = t_2
	elif t <= 4000000000000.0:
		tmp = t_1
	elif t <= 1.65e+128:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(i * Float64(a * Float64(-c))))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -2.1e-40)
		tmp = t_3;
	elseif (t <= 2.36e-209)
		tmp = t_1;
	elseif (t <= 1.75e-158)
		tmp = t_2;
	elseif (t <= 4000000000000.0)
		tmp = t_1;
	elseif (t <= 1.65e+128)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (i * (a * -c));
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -2.1e-40)
		tmp = t_3;
	elseif (t <= 2.36e-209)
		tmp = t_1;
	elseif (t <= 1.75e-158)
		tmp = t_2;
	elseif (t <= 4000000000000.0)
		tmp = t_1;
	elseif (t <= 1.65e+128)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e-40], t$95$3, If[LessEqual[t, 2.36e-209], t$95$1, If[LessEqual[t, 1.75e-158], t$95$2, If[LessEqual[t, 4000000000000.0], t$95$1, If[LessEqual[t, 1.65e+128], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.10000000000000018e-40 or 1.65e128 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 45.0%

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

   if -2.10000000000000018e-40 < t < 2.3599999999999999e-209 or 1.75000000000000006e-158 < t < 4e12

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 36.0%

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

   if 2.3599999999999999e-209 < t < 1.75000000000000006e-158 or 4e12 < t < 1.65e128

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 69.4%

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

   3. Taylor expanded in a around inf 41.1%

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

      1. neg-mul-1 41.1%

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

      2. associate-*r* 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

      4. *-commutative 48.6%

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

      5. associate-*l* 43.7%

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

   5. Simplified 43.7%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 2.36 \cdot 10^{-209}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;t \leq 4000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.68 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;t \leq 14000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+126}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= t -1.2e-39)
     t_2
     (if (<= t 1.68e-208)
       t_1
       (if (<= t 1.1e-158)
         (* 2.0 (* i (* a (- c))))
         (if (<= t 14000000000000.0)
           t_1
           (if (<= t 2.8e+126) (* 2.0 (* c (* a (- i)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.2e-39) {
		tmp = t_2;
	} else if (t <= 1.68e-208) {
		tmp = t_1;
	} else if (t <= 1.1e-158) {
		tmp = 2.0 * (i * (a * -c));
	} else if (t <= 14000000000000.0) {
		tmp = t_1;
	} else if (t <= 2.8e+126) {
		tmp = 2.0 * (c * (a * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (t <= (-1.2d-39)) then
        tmp = t_2
    else if (t <= 1.68d-208) then
        tmp = t_1
    else if (t <= 1.1d-158) then
        tmp = 2.0d0 * (i * (a * -c))
    else if (t <= 14000000000000.0d0) then
        tmp = t_1
    else if (t <= 2.8d+126) then
        tmp = 2.0d0 * (c * (a * -i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.2e-39) {
		tmp = t_2;
	} else if (t <= 1.68e-208) {
		tmp = t_1;
	} else if (t <= 1.1e-158) {
		tmp = 2.0 * (i * (a * -c));
	} else if (t <= 14000000000000.0) {
		tmp = t_1;
	} else if (t <= 2.8e+126) {
		tmp = 2.0 * (c * (a * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.2e-39:
		tmp = t_2
	elif t <= 1.68e-208:
		tmp = t_1
	elif t <= 1.1e-158:
		tmp = 2.0 * (i * (a * -c))
	elif t <= 14000000000000.0:
		tmp = t_1
	elif t <= 2.8e+126:
		tmp = 2.0 * (c * (a * -i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1.2e-39)
		tmp = t_2;
	elseif (t <= 1.68e-208)
		tmp = t_1;
	elseif (t <= 1.1e-158)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	elseif (t <= 14000000000000.0)
		tmp = t_1;
	elseif (t <= 2.8e+126)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1.2e-39)
		tmp = t_2;
	elseif (t <= 1.68e-208)
		tmp = t_1;
	elseif (t <= 1.1e-158)
		tmp = 2.0 * (i * (a * -c));
	elseif (t <= 14000000000000.0)
		tmp = t_1;
	elseif (t <= 2.8e+126)
		tmp = 2.0 * (c * (a * -i));
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-39], t$95$2, If[LessEqual[t, 1.68e-208], t$95$1, If[LessEqual[t, 1.1e-158], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 14000000000000.0], t$95$1, If[LessEqual[t, 2.8e+126], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.20000000000000008e-39 or 2.80000000000000009e126 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 45.0%

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

   if -1.20000000000000008e-39 < t < 1.67999999999999997e-208 or 1.1000000000000001e-158 < t < 1.4e13

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 36.5%

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

   if 1.67999999999999997e-208 < t < 1.1000000000000001e-158

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 79.6%

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

   3. Taylor expanded in a around inf 58.9%

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

      1. neg-mul-1 58.9%

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

      2. associate-*r* 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-*l* 59.0%

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

   5. Simplified 59.0%

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

   if 1.4e13 < t < 2.80000000000000009e126

   1. Initial program 87.3%

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

   2. Taylor expanded in a around inf 31.8%

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

      1. associate-*r* 31.8%

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

      2. neg-mul-1 31.8%

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

   4. Simplified 31.8%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.68 \cdot 10^{-208}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;t \leq 14000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+126}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 39.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-39} \lor \neg \left(t \leq 8 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -5.2e-39) (not (<= t 8e+129))) (* 2.0 (* z t)) (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -5.2e-39) || !(t <= 8e+129)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-5.2d-39)) .or. (.not. (t <= 8d+129))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -5.2e-39) || !(t <= 8e+129)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -5.2e-39) or not (t <= 8e+129):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -5.2e-39) || !(t <= 8e+129))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -5.2e-39) || ~((t <= 8e+129)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -5.2e-39], N[Not[LessEqual[t, 8e+129]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e-39 or 8e129 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 45.0%

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

   if -5.2e-39 < t < 8e129

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 32.7%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-39} \lor \neg \left(t \leq 8 \cdot 10^{+129}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 29.4% 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 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. Taylor expanded in z around inf 28.6%

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

3. Final simplification 28.6%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023258 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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