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

Percentage Accurate: 90.4% → 96.4%

Time: 12.8s

Alternatives: 15

Speedup: 0.5×

• 46.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.4% 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: 96.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.6%

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

      1. associate-*l* 98.4%

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

      2. fma-def 98.4%

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

   3. Simplified 98.4%

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

   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 a around 0 28.6%

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

      1. unpow2 28.6%

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

   4. Simplified 28.6%

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

      1. associate--l+ 28.6%

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

      2. *-commutative 28.6%

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

      3. fma-def 42.9%

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

      4. associate-*l* 42.9%

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

   6. Applied egg-rr 42.9%

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

   7. Taylor expanded in z around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unpow2 85.7%

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

      3. *-commutative 85.7%

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

      4. *-commutative 85.7%

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

      5. distribute-rgt-neg-in 85.7%

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

      6. *-commutative 85.7%

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

      7. distribute-rgt-neg-in 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 98.0%

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

Alternative 2: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t_1 \cdot i\right)\\ t_3 := c \cdot t_1\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* c t_1)))
   (if (<= t_3 (- INFINITY))
     (* 2.0 (- (* z t) t_2))
     (if (<= t_3 5e+216)
       (* (- (+ (* z t) (* x y)) (* t_3 i)) 2.0)
       (* 2.0 (- (* x y) t_2))))))

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 t_3 = c * t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 5e+216) {
		tmp = (((z * t) + (x * y)) - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - t_2);
	}
	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 t_3 = c * t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 5e+216) {
		tmp = (((z * t) + (x * y)) - (t_3 * i)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = c * t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 2.0 * ((z * t) - t_2)
	elif t_3 <= 5e+216:
		tmp = (((z * t) + (x * y)) - (t_3 * i)) * 2.0
	else:
		tmp = 2.0 * ((x * y) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(c * t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	elseif (t_3 <= 5e+216)
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(t_3 * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	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);
	t_3 = c * t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 2.0 * ((z * t) - t_2);
	elseif (t_3 <= 5e+216)
		tmp = (((z * t) + (x * y)) - (t_3 * i)) * 2.0;
	else
		tmp = 2.0 * ((x * y) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+216], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.1%

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

   2. Taylor expanded in x around 0 94.9%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 4.9999999999999998e216

   1. Initial program 99.4%

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

   if 4.9999999999999998e216 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 95.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 5 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 3: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))
   (if (<= c -2.8e-66)
     t_1
     (if (<= c 1.45e-164)
       (* (+ (* z t) (* x y)) 2.0)
       (if (<= c 8.5e-48)
         t_1
         (if (<= c 1.2e-23)
           (* 2.0 (- (* x y) (* b (* i (* c c)))))
           (if (<= c 2.6e+123)
             t_1
             (* 2.0 (- (* x y) (* c (* b (* c i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (c <= -2.8e-66) {
		tmp = t_1;
	} else if (c <= 1.45e-164) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 8.5e-48) {
		tmp = t_1;
	} else if (c <= 1.2e-23) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if (c <= 2.6e+123) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    if (c <= (-2.8d-66)) then
        tmp = t_1
    else if (c <= 1.45d-164) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else if (c <= 8.5d-48) then
        tmp = t_1
    else if (c <= 1.2d-23) then
        tmp = 2.0d0 * ((x * y) - (b * (i * (c * c))))
    else if (c <= 2.6d+123) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (c <= -2.8e-66) {
		tmp = t_1;
	} else if (c <= 1.45e-164) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 8.5e-48) {
		tmp = t_1;
	} else if (c <= 1.2e-23) {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	} else if (c <= 2.6e+123) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	tmp = 0
	if c <= -2.8e-66:
		tmp = t_1
	elif c <= 1.45e-164:
		tmp = ((z * t) + (x * y)) * 2.0
	elif c <= 8.5e-48:
		tmp = t_1
	elif c <= 1.2e-23:
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))))
	elif c <= 2.6e+123:
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	tmp = 0.0
	if (c <= -2.8e-66)
		tmp = t_1;
	elseif (c <= 1.45e-164)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	elseif (c <= 8.5e-48)
		tmp = t_1;
	elseif (c <= 1.2e-23)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(b * Float64(i * Float64(c * c)))));
	elseif (c <= 2.6e+123)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	tmp = 0.0;
	if (c <= -2.8e-66)
		tmp = t_1;
	elseif (c <= 1.45e-164)
		tmp = ((z * t) + (x * y)) * 2.0;
	elseif (c <= 8.5e-48)
		tmp = t_1;
	elseif (c <= 1.2e-23)
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	elseif (c <= 2.6e+123)
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e-66], t$95$1, If[LessEqual[c, 1.45e-164], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 8.5e-48], t$95$1, If[LessEqual[c, 1.2e-23], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e+123], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.8e-66 or 1.45e-164 < c < 8.5000000000000004e-48 or 1.19999999999999998e-23 < c < 2.59999999999999985e123

   1. Initial program 91.0%

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

   2. Taylor expanded in x around 0 87.9%

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

   if -2.8e-66 < c < 1.45e-164

   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 c around 0 88.7%

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

   if 8.5000000000000004e-48 < c < 1.19999999999999998e-23

   1. Initial program 85.7%

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

   2. Taylor expanded in a around 0 99.8%

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

      1. unpow2 99.8%

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

   4. Simplified 99.8%

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

      1. associate--l+ 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. associate-*l* 86.8%

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

   6. Applied egg-rr 86.8%

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

   7. Taylor expanded in z around 0 86.8%

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

      1. unpow2 86.8%

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

      2. associate-*r* 99.8%

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

      3. associate-*r* 100.0%

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

      4. associate-*r* 86.8%

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

      5. *-commutative 86.8%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. associate-*r* 100.0%

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

      9. associate-*r* 99.8%

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

   9. Simplified 99.8%

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

   if 2.59999999999999985e123 < c

   1. Initial program 75.8%

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

   2. Taylor expanded in a around 0 69.4%

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

      1. unpow2 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. associate-*l* 86.6%

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

      4. associate-*l* 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*r* 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-48}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := z \cdot t + x \cdot y\\ t_3 := 2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -155000:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4400000000:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (+ (* z t) (* x y)))
        (t_3 (* 2.0 (- (* x y) t_1))))
   (if (<= c -4.5e+89)
     t_3
     (if (<= c -155000.0)
       (* 2.0 (- (* z t) t_1))
       (if (<= c 6.8e-162)
         (* 2.0 (- t_2 (* i (* a c))))
         (if (<= c 4400000000.0) (* 2.0 (- t_2 (* i (* c (* b c))))) 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 + (b * c)) * i);
	double t_2 = (z * t) + (x * y);
	double t_3 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -4.5e+89) {
		tmp = t_3;
	} else if (c <= -155000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.8e-162) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 4400000000.0) {
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	} 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 = c * ((a + (b * c)) * i)
    t_2 = (z * t) + (x * y)
    t_3 = 2.0d0 * ((x * y) - t_1)
    if (c <= (-4.5d+89)) then
        tmp = t_3
    else if (c <= (-155000.0d0)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 6.8d-162) then
        tmp = 2.0d0 * (t_2 - (i * (a * c)))
    else if (c <= 4400000000.0d0) then
        tmp = 2.0d0 * (t_2 - (i * (c * (b * c))))
    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 + (b * c)) * i);
	double t_2 = (z * t) + (x * y);
	double t_3 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -4.5e+89) {
		tmp = t_3;
	} else if (c <= -155000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.8e-162) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 4400000000.0) {
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = (z * t) + (x * y)
	t_3 = 2.0 * ((x * y) - t_1)
	tmp = 0
	if c <= -4.5e+89:
		tmp = t_3
	elif c <= -155000.0:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 6.8e-162:
		tmp = 2.0 * (t_2 - (i * (a * c)))
	elif c <= 4400000000.0:
		tmp = 2.0 * (t_2 - (i * (c * (b * c))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(Float64(z * t) + Float64(x * y))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	tmp = 0.0
	if (c <= -4.5e+89)
		tmp = t_3;
	elseif (c <= -155000.0)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 6.8e-162)
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(a * c))));
	elseif (c <= 4400000000.0)
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(c * Float64(b * c)))));
	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 + (b * c)) * i);
	t_2 = (z * t) + (x * y);
	t_3 = 2.0 * ((x * y) - t_1);
	tmp = 0.0;
	if (c <= -4.5e+89)
		tmp = t_3;
	elseif (c <= -155000.0)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 6.8e-162)
		tmp = 2.0 * (t_2 - (i * (a * c)));
	elseif (c <= 4400000000.0)
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	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[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e+89], t$95$3, If[LessEqual[c, -155000.0], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-162], N[(2.0 * N[(t$95$2 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4400000000.0], N[(2.0 * N[(t$95$2 - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.5e89 or 4.4e9 < c

   1. Initial program 82.3%

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

   2. Taylor expanded in z around 0 93.2%

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

   if -4.5e89 < c < -155000

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0 99.8%

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

   if -155000 < c < 6.8e-162

   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 a around inf 98.7%

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

   if 6.8e-162 < c < 4.4e9

   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 a around 0 91.0%

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

      1. unpow2 91.0%

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

      2. associate-*r* 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -155000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4400000000:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 86.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{if}\;c \leq -1.35 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -17000:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))) (t_2 (* 2.0 (- (* x y) t_1))))
   (if (<= c -1.35e+82)
     t_2
     (if (<= c -17000.0)
       (* 2.0 (- (* z t) t_1))
       (if (<= c 6.2e-65)
         (* 2.0 (- (+ (* z t) (* x y)) (* i (* a c))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -1.35e+82) {
		tmp = t_2;
	} else if (c <= -17000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.2e-65) {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    if (c <= (-1.35d+82)) then
        tmp = t_2
    else if (c <= (-17000.0d0)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 6.2d-65) then
        tmp = 2.0d0 * (((z * t) + (x * y)) - (i * (a * c)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if (c <= -1.35e+82) {
		tmp = t_2;
	} else if (c <= -17000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.2e-65) {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((x * y) - t_1)
	tmp = 0
	if c <= -1.35e+82:
		tmp = t_2
	elif c <= -17000.0:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 6.2e-65:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	tmp = 0.0
	if (c <= -1.35e+82)
		tmp = t_2;
	elseif (c <= -17000.0)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 6.2e-65)
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(i * Float64(a * c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = 2.0 * ((x * y) - t_1);
	tmp = 0.0;
	if (c <= -1.35e+82)
		tmp = t_2;
	elseif (c <= -17000.0)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 6.2e-65)
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.35e+82], t$95$2, If[LessEqual[c, -17000.0], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e-65], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.35e82 or 6.20000000000000032e-65 < c

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 90.9%

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

   if -1.35e82 < c < -17000

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0 99.8%

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

   if -17000 < c < 6.20000000000000032e-65

   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 a around inf 95.5%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -17000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ t_2 := 2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* a i)))))
        (t_2 (* 2.0 (* c (* i (* b (- c)))))))
   (if (<= c -1.45e+112)
     t_2
     (if (<= c -3.4e-65)
       t_1
       (if (<= c 1.95e+17)
         (* (+ (* z t) (* x y)) 2.0)
         (if (<= c 4.4e+125) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = 2.0 * (c * (i * (b * -c)));
	double tmp;
	if (c <= -1.45e+112) {
		tmp = t_2;
	} else if (c <= -3.4e-65) {
		tmp = t_1;
	} else if (c <= 1.95e+17) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 4.4e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (a * i)))
    t_2 = 2.0d0 * (c * (i * (b * -c)))
    if (c <= (-1.45d+112)) then
        tmp = t_2
    else if (c <= (-3.4d-65)) then
        tmp = t_1
    else if (c <= 1.95d+17) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else if (c <= 4.4d+125) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = 2.0 * (c * (i * (b * -c)));
	double tmp;
	if (c <= -1.45e+112) {
		tmp = t_2;
	} else if (c <= -3.4e-65) {
		tmp = t_1;
	} else if (c <= 1.95e+17) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 4.4e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (a * i)))
	t_2 = 2.0 * (c * (i * (b * -c)))
	tmp = 0
	if c <= -1.45e+112:
		tmp = t_2
	elif c <= -3.4e-65:
		tmp = t_1
	elif c <= 1.95e+17:
		tmp = ((z * t) + (x * y)) * 2.0
	elif c <= 4.4e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))))
	t_2 = Float64(2.0 * Float64(c * Float64(i * Float64(b * Float64(-c)))))
	tmp = 0.0
	if (c <= -1.45e+112)
		tmp = t_2;
	elseif (c <= -3.4e-65)
		tmp = t_1;
	elseif (c <= 1.95e+17)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	elseif (c <= 4.4e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (a * i)));
	t_2 = 2.0 * (c * (i * (b * -c)));
	tmp = 0.0;
	if (c <= -1.45e+112)
		tmp = t_2;
	elseif (c <= -3.4e-65)
		tmp = t_1;
	elseif (c <= 1.95e+17)
		tmp = ((z * t) + (x * y)) * 2.0;
	elseif (c <= 4.4e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(i * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e+112], t$95$2, If[LessEqual[c, -3.4e-65], t$95$1, If[LessEqual[c, 1.95e+17], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 4.4e+125], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4500000000000001e112 or 4.39999999999999982e125 < c

   1. Initial program 81.4%

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

   2. Taylor expanded in a around 0 72.5%

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

      1. unpow2 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in c around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. unpow2 70.0%

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

      4. associate-*l* 71.2%

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

      5. associate-*l* 75.3%

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

      6. *-commutative 75.3%

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

      7. distribute-rgt-neg-in 75.3%

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

      8. distribute-rgt-neg-in 75.3%

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

      9. *-commutative 75.3%

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

      10. distribute-rgt-neg-in 75.3%

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

   7. Simplified 75.3%

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

   if -1.4500000000000001e112 < c < -3.39999999999999987e-65 or 1.95e17 < c < 4.39999999999999982e125

   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 a around inf 71.6%

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

   3. Taylor expanded in x around 0 67.1%

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

   if -3.39999999999999987e-65 < c < 1.95e17

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 80.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+112}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+17}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+125}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6300000:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.6e-47)
     t_1
     (if (<= c 6300000.0)
       (* (+ (* z t) (* x y)) 2.0)
       (if (<= c 1.8e+120) t_1 (* 2.0 (- (* x y) (* c (* b (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.6e-47) {
		tmp = t_1;
	} else if (c <= 6300000.0) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 1.8e+120) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.6d-47)) then
        tmp = t_1
    else if (c <= 6300000.0d0) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else if (c <= 1.8d+120) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.6e-47) {
		tmp = t_1;
	} else if (c <= 6300000.0) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 1.8e+120) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.6e-47:
		tmp = t_1
	elif c <= 6300000.0:
		tmp = ((z * t) + (x * y)) * 2.0
	elif c <= 1.8e+120:
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.6e-47)
		tmp = t_1;
	elseif (c <= 6300000.0)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	elseif (c <= 1.8e+120)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.6e-47)
		tmp = t_1;
	elseif (c <= 6300000.0)
		tmp = ((z * t) + (x * y)) * 2.0;
	elseif (c <= 1.8e+120)
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.6e-47], t$95$1, If[LessEqual[c, 6300000.0], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 1.8e+120], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.6e-47 or 6.3e6 < c < 1.80000000000000008e120

   1. Initial program 88.0%

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

   2. Taylor expanded in i around inf 79.0%

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

   if -1.6e-47 < c < 6.3e6

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 81.0%

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

   if 1.80000000000000008e120 < c

   1. Initial program 75.8%

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

   2. Taylor expanded in a around 0 69.4%

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

      1. unpow2 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. associate-*l* 86.6%

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

      4. associate-*l* 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*r* 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 6300000:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+120}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 8: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= x -6.2e+139)
     (* 2.0 (- (* x y) t_1))
     (if (<= x 7.5e-35)
       (* 2.0 (- (* z t) t_1))
       (* 2.0 (- (* x y) (* b (* i (* c c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (x <= -6.2e+139) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (x <= 7.5e-35) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (x <= (-6.2d+139)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (x <= 7.5d-35) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * ((x * y) - (b * (i * (c * c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (x <= -6.2e+139) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (x <= 7.5e-35) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if x <= -6.2e+139:
		tmp = 2.0 * ((x * y) - t_1)
	elif x <= 7.5e-35:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))))
	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 (x <= -6.2e+139)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (x <= 7.5e-35)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(b * Float64(i * Float64(c * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (x <= -6.2e+139)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (x <= 7.5e-35)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * ((x * y) - (b * (i * (c * c))));
	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[x, -6.2e+139], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-35], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2e139

   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 76.7%

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

   if -6.2e139 < x < 7.5e-35

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 82.6%

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

   if 7.5e-35 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in a around 0 80.2%

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

      1. unpow2 80.2%

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

   4. Simplified 80.2%

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

      1. associate--l+ 80.2%

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

      2. *-commutative 80.2%

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

      3. fma-def 81.6%

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

      4. associate-*l* 84.0%

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

   6. Applied egg-rr 84.0%

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

   7. Taylor expanded in z around 0 69.6%

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

      1. unpow2 69.6%

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

      2. associate-*r* 72.3%

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

      3. associate-*r* 74.9%

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

      4. associate-*r* 73.6%

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

      5. *-commutative 73.6%

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

      6. associate-*l* 73.6%

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

      7. *-commutative 73.6%

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

      8. associate-*r* 74.9%

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

      9. associate-*r* 72.3%

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

   9. Simplified 72.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 9: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+121}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+142}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* i (* b (- c)))))))
   (if (<= c -1.65e+37)
     t_1
     (if (<= c 1.3e+16)
       (* (+ (* z t) (* x y)) 2.0)
       (if (<= c 7.6e+121)
         (* (* a i) (* c -2.0))
         (if (<= c 2.2e+142) (* 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 = 2.0 * (c * (i * (b * -c)));
	double tmp;
	if (c <= -1.65e+37) {
		tmp = t_1;
	} else if (c <= 1.3e+16) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 7.6e+121) {
		tmp = (a * i) * (c * -2.0);
	} else if (c <= 2.2e+142) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * (i * (b * -c)))
    if (c <= (-1.65d+37)) then
        tmp = t_1
    else if (c <= 1.3d+16) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else if (c <= 7.6d+121) then
        tmp = (a * i) * (c * (-2.0d0))
    else if (c <= 2.2d+142) then
        tmp = 2.0d0 * (x * y)
    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 * (i * (b * -c)));
	double tmp;
	if (c <= -1.65e+37) {
		tmp = t_1;
	} else if (c <= 1.3e+16) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else if (c <= 7.6e+121) {
		tmp = (a * i) * (c * -2.0);
	} else if (c <= 2.2e+142) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * (i * (b * -c)))
	tmp = 0
	if c <= -1.65e+37:
		tmp = t_1
	elif c <= 1.3e+16:
		tmp = ((z * t) + (x * y)) * 2.0
	elif c <= 7.6e+121:
		tmp = (a * i) * (c * -2.0)
	elif c <= 2.2e+142:
		tmp = 2.0 * (x * y)
	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(i * Float64(b * Float64(-c)))))
	tmp = 0.0
	if (c <= -1.65e+37)
		tmp = t_1;
	elseif (c <= 1.3e+16)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	elseif (c <= 7.6e+121)
		tmp = Float64(Float64(a * i) * Float64(c * -2.0));
	elseif (c <= 2.2e+142)
		tmp = Float64(2.0 * Float64(x * y));
	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 * (i * (b * -c)));
	tmp = 0.0;
	if (c <= -1.65e+37)
		tmp = t_1;
	elseif (c <= 1.3e+16)
		tmp = ((z * t) + (x * y)) * 2.0;
	elseif (c <= 7.6e+121)
		tmp = (a * i) * (c * -2.0);
	elseif (c <= 2.2e+142)
		tmp = 2.0 * (x * y);
	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[(i * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+37], t$95$1, If[LessEqual[c, 1.3e+16], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 7.6e+121], N[(N[(a * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+142], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.65e37 or 2.19999999999999987e142 < c

   1. Initial program 81.9%

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

   2. Taylor expanded in a around 0 73.2%

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

      1. unpow2 73.2%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in c around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-commutative 68.0%

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

      3. unpow2 68.0%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 72.6%

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

      6. *-commutative 72.6%

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

      7. distribute-rgt-neg-in 72.6%

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

      8. distribute-rgt-neg-in 72.6%

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

      9. *-commutative 72.6%

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

      10. distribute-rgt-neg-in 72.6%

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

   7. Simplified 72.6%

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

   if -1.65e37 < c < 1.3e16

   1. Initial program 98.6%

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

   2. Taylor expanded in c around 0 75.7%

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

   if 1.3e16 < c < 7.6e121

   1. Initial program 82.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-lft-in 81.1%

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

   3. Applied egg-rr 81.1%

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

   4. Taylor expanded in a around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. *-commutative 63.0%

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

      3. *-commutative 63.0%

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

      4. distribute-rgt-neg-in 63.0%

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

      5. associate-*l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in a around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

      3. associate-*l* 63.0%

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

   9. Simplified 63.0%

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

   if 7.6e121 < c < 2.19999999999999987e142

   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 100.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+121}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+142}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \end{array} \]

Alternative 10: 74.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-47} \lor \neg \left(c \leq 16000000\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.9e-47) (not (<= c 16000000.0)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.9e-47) || !(c <= 16000000.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.9d-47)) .or. (.not. (c <= 16000000.0d0))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.9e-47) || !(c <= 16000000.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.9e-47) or not (c <= 16000000.0):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.9e-47) || !(c <= 16000000.0))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.9e-47) || ~((c <= 16000000.0)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.9e-47], N[Not[LessEqual[c, 16000000.0]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.90000000000000007e-47 or 1.6e7 < c

   1. Initial program 84.1%

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

   2. Taylor expanded in i around inf 77.2%

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

   if -1.90000000000000007e-47 < c < 1.6e7

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 81.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-47} \lor \neg \left(c \leq 16000000\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 11: 39.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= y -1.12e-23)
     t_1
     (if (<= y -5.8e-217)
       (* 2.0 (* a (* c (- i))))
       (if (<= y 2.05e+48) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (y <= -1.12e-23) {
		tmp = t_1;
	} else if (y <= -5.8e-217) {
		tmp = 2.0 * (a * (c * -i));
	} else if (y <= 2.05e+48) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if (y <= (-1.12d-23)) then
        tmp = t_1
    else if (y <= (-5.8d-217)) then
        tmp = 2.0d0 * (a * (c * -i))
    else if (y <= 2.05d+48) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (y <= -1.12e-23) {
		tmp = t_1;
	} else if (y <= -5.8e-217) {
		tmp = 2.0 * (a * (c * -i));
	} else if (y <= 2.05e+48) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if y <= -1.12e-23:
		tmp = t_1
	elif y <= -5.8e-217:
		tmp = 2.0 * (a * (c * -i))
	elif y <= 2.05e+48:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -1.12e-23)
		tmp = t_1;
	elseif (y <= -5.8e-217)
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	elseif (y <= 2.05e+48)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -1.12e-23)
		tmp = t_1;
	elseif (y <= -5.8e-217)
		tmp = 2.0 * (a * (c * -i));
	elseif (y <= 2.05e+48)
		tmp = 2.0 * (z * t);
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e-23], t$95$1, If[LessEqual[y, -5.8e-217], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+48], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1200000000000001e-23 or 2.0500000000000001e48 < y

   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. Taylor expanded in x around inf 45.0%

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

   if -1.1200000000000001e-23 < y < -5.79999999999999963e-217

   1. Initial program 85.6%

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

      1. associate-*r* 96.8%

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

      2. *-commutative 96.8%

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

      3. +-commutative 96.8%

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

      4. distribute-lft-in 84.7%

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

   3. Applied egg-rr 84.7%

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

   4. Taylor expanded in a around inf 34.2%

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

      1. mul-1-neg 34.2%

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

      2. *-commutative 34.2%

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

      3. *-commutative 34.2%

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

      4. distribute-rgt-neg-in 34.2%

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

      5. associate-*l* 31.3%

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

   6. Simplified 31.3%

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

   if -5.79999999999999963e-217 < y < 2.0500000000000001e48

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 37.4%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 39.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-214}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= y -3.1e-118)
     t_1
     (if (<= y -3.2e-214)
       (* (* a i) (* c -2.0))
       (if (<= y 5.1e+52) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.1e-118) {
		tmp = t_1;
	} else if (y <= -3.2e-214) {
		tmp = (a * i) * (c * -2.0);
	} else if (y <= 5.1e+52) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    if (y <= (-3.1d-118)) then
        tmp = t_1
    else if (y <= (-3.2d-214)) then
        tmp = (a * i) * (c * (-2.0d0))
    else if (y <= 5.1d+52) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.1e-118) {
		tmp = t_1;
	} else if (y <= -3.2e-214) {
		tmp = (a * i) * (c * -2.0);
	} else if (y <= 5.1e+52) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if y <= -3.1e-118:
		tmp = t_1
	elif y <= -3.2e-214:
		tmp = (a * i) * (c * -2.0)
	elif y <= 5.1e+52:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -3.1e-118)
		tmp = t_1;
	elseif (y <= -3.2e-214)
		tmp = Float64(Float64(a * i) * Float64(c * -2.0));
	elseif (y <= 5.1e+52)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -3.1e-118)
		tmp = t_1;
	elseif (y <= -3.2e-214)
		tmp = (a * i) * (c * -2.0);
	elseif (y <= 5.1e+52)
		tmp = 2.0 * (z * t);
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-118], t$95$1, If[LessEqual[y, -3.2e-214], N[(N[(a * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e+52], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000001e-118 or 5.09999999999999997e52 < y

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 41.4%

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

   if -3.1000000000000001e-118 < y < -3.20000000000000013e-214

   1. Initial program 80.0%

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

      1. associate-*r* 94.6%

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

      2. *-commutative 94.6%

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

      3. +-commutative 94.6%

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

      4. distribute-lft-in 94.6%

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

   3. Applied egg-rr 94.6%

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

   4. Taylor expanded in a around inf 37.4%

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

      1. mul-1-neg 37.4%

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

      2. *-commutative 37.4%

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

      3. *-commutative 37.4%

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

      4. distribute-rgt-neg-in 37.4%

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

      5. associate-*l* 32.5%

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

   6. Simplified 32.5%

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

   7. Taylor expanded in a around 0 37.4%

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

      1. *-commutative 37.4%

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

      2. *-commutative 37.4%

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

      3. associate-*l* 37.4%

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

   9. Simplified 37.4%

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

   if -3.20000000000000013e-214 < y < 5.09999999999999997e52

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 37.4%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-214}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 54.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.6e+150) (* (+ (* z t) (* x y)) 2.0) (* (* a i) (* c -2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.6e+150) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = (a * i) * (c * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.6d+150) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = (a * i) * (c * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.6e+150) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = (a * i) * (c * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.6e+150:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = (a * i) * (c * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.6e+150)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(Float64(a * i) * Float64(c * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.6e+150)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = (a * i) * (c * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.6e+150], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(a * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.60000000000000002e150

   1. Initial program 91.6%

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

   2. Taylor expanded in c around 0 54.6%

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

   if 4.60000000000000002e150 < a

   1. Initial program 85.7%

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

      1. associate-*r* 96.4%

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

      2. *-commutative 96.4%

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

      3. +-commutative 96.4%

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

      4. distribute-lft-in 89.0%

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

   3. Applied egg-rr 89.0%

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

   4. Taylor expanded in a around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. *-commutative 62.0%

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

      4. distribute-rgt-neg-in 62.0%

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

      5. associate-*l* 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in a around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*l* 62.0%

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

   9. Simplified 62.0%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \end{array} \]

Alternative 14: 39.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-117} \lor \neg \left(y \leq 5.6 \cdot 10^{+50}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.08e-117) (not (<= y 5.6e+50)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.08e-117) || !(y <= 5.6e+50)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.08d-117)) .or. (.not. (y <= 5.6d+50))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.08e-117) || !(y <= 5.6e+50)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.08e-117) or not (y <= 5.6e+50):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.08e-117) || !(y <= 5.6e+50))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.08e-117) || ~((y <= 5.6e+50)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.08e-117], N[Not[LessEqual[y, 5.6e+50]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.07999999999999998e-117 or 5.5999999999999996e50 < y

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 41.4%

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

   if -1.07999999999999998e-117 < y < 5.5999999999999996e50

   1. Initial program 91.0%

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

   2. Taylor expanded in z around inf 37.6%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-117} \lor \neg \left(y \leq 5.6 \cdot 10^{+50}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 29.0% 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 91.0%

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

2. Taylor expanded in z around inf 27.4%

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

3. Final simplification 27.4%

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

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 2023257 
(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))))