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

Percentage Accurate: 89.8% → 96.0%

Time: 11.2s

Alternatives: 11

Speedup: 0.6×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

      1. fma-define 93.4%

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

      2. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. *-commutative 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 98.0%

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

Alternative 2: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + \frac{x \cdot y}{t}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))
   (if (<= (* x y) -1e+264)
     (* (* x y) 2.0)
     (if (<= (* x y) -2.5e+175)
       t_1
       (if (<= (* x y) -100000000000.0)
         (* 2.0 (* t (+ z (/ (* x y) t))))
         (if (<= (* x y) 4e-31) t_1 (* (+ (* x y) (* z t)) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if ((x * y) <= -1e+264) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= -2.5e+175) {
		tmp = t_1;
	} else if ((x * y) <= -100000000000.0) {
		tmp = 2.0 * (t * (z + ((x * y) / t)));
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    if ((x * y) <= (-1d+264)) then
        tmp = (x * y) * 2.0d0
    else if ((x * y) <= (-2.5d+175)) then
        tmp = t_1
    else if ((x * y) <= (-100000000000.0d0)) then
        tmp = 2.0d0 * (t * (z + ((x * y) / t)))
    else if ((x * y) <= 4d-31) then
        tmp = t_1
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if ((x * y) <= -1e+264) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= -2.5e+175) {
		tmp = t_1;
	} else if ((x * y) <= -100000000000.0) {
		tmp = 2.0 * (t * (z + ((x * y) / t)));
	} else if ((x * y) <= 4e-31) {
		tmp = t_1;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	tmp = 0
	if (x * y) <= -1e+264:
		tmp = (x * y) * 2.0
	elif (x * y) <= -2.5e+175:
		tmp = t_1
	elif (x * y) <= -100000000000.0:
		tmp = 2.0 * (t * (z + ((x * y) / t)))
	elif (x * y) <= 4e-31:
		tmp = t_1
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	tmp = 0.0
	if (Float64(x * y) <= -1e+264)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (Float64(x * y) <= -2.5e+175)
		tmp = t_1;
	elseif (Float64(x * y) <= -100000000000.0)
		tmp = Float64(2.0 * Float64(t * Float64(z + Float64(Float64(x * y) / t))));
	elseif (Float64(x * y) <= 4e-31)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	tmp = 0.0;
	if ((x * y) <= -1e+264)
		tmp = (x * y) * 2.0;
	elseif ((x * y) <= -2.5e+175)
		tmp = t_1;
	elseif ((x * y) <= -100000000000.0)
		tmp = 2.0 * (t * (z + ((x * y) / t)));
	elseif ((x * y) <= 4e-31)
		tmp = t_1;
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+264], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.5e+175], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -100000000000.0], N[(2.0 * N[(t * N[(z + N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-31], t$95$1, N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.00000000000000004e264

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf 85.2%

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

   if -1.00000000000000004e264 < (*.f64 x y) < -2.5e175 or -1e11 < (*.f64 x y) < 4e-31

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 87.1%

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

   if -2.5e175 < (*.f64 x y) < -1e11

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 71.5%

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

   4. Taylor expanded in c around 0 59.2%

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

   5. Taylor expanded in t around inf 76.2%

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

   if 4e-31 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in c around 0 73.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+264}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{+175}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -100000000000:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z + \frac{x \cdot y}{t}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := c \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_2\right)\\ \end{array} \end{array} \]

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 2e+277)
       (* (- (+ (* x y) (* z t)) (* 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 <= 2e+277) {
		tmp = (((x * y) + (z * t)) - (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 <= 2e+277) {
		tmp = (((x * y) + (z * t)) - (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 <= 2e+277:
		tmp = (((x * y) + (z * t)) - (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 <= 2e+277)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - 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 <= 2e+277)
		tmp = (((x * y) + (z * t)) - (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, 2e+277], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $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 66.7%

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

   3. Taylor expanded in x around 0 90.2%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 2.00000000000000001e277

   1. Initial program 98.8%

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

   if 2.00000000000000001e277 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 72.0%

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

   3. Taylor expanded in z around 0 90.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+82} \lor \neg \left(c \leq 7 \cdot 10^{+104}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -2.2e-67)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 1.9e-91)
       (* (+ (* x y) (* z t)) 2.0)
       (if (or (<= c 5.9e+82) (not (<= c 7e+104)))
         (* 2.0 (- (* z t) t_1))
         (* (* x y) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.2e-67) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.9e-91) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((c <= 5.9e+82) || !(c <= 7e+104)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-2.2d-67)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 1.9d-91) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((c <= 5.9d+82) .or. (.not. (c <= 7d+104))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = (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 t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.2e-67) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.9e-91) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((c <= 5.9e+82) || !(c <= 7e+104)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -2.2e-67:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 1.9e-91:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (c <= 5.9e+82) or not (c <= 7e+104):
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -2.2e-67)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 1.9e-91)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif ((c <= 5.9e+82) || !(c <= 7e+104))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -2.2e-67)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 1.9e-91)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((c <= 5.9e+82) || ~((c <= 7e+104)))
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e-67], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e-91], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[Or[LessEqual[c, 5.9e+82], N[Not[LessEqual[c, 7e+104]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.2000000000000001e-67

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 83.3%

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

   if -2.2000000000000001e-67 < c < 1.89999999999999989e-91

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 87.0%

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

   if 1.89999999999999989e-91 < c < 5.8999999999999997e82 or 7.0000000000000003e104 < c

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0 86.7%

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

   if 5.8999999999999997e82 < c < 7.0000000000000003e104

   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. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+82} \lor \neg \left(c \leq 7 \cdot 10^{+104}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;i \leq -100000 \lor \neg \left(i \leq 2.05 \cdot 10^{+115}\right):\\ \;\;\;\;\left(t\_1 - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= i -100000.0) (not (<= i 2.05e+115)))
     (* (- t_1 (* (* c (+ a (* b c))) i)) 2.0)
     (* 2.0 (- t_1 (* c (+ (* a i) (* b (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -100000.0) || !(i <= 2.05e+115)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((i <= (-100000.0d0)) .or. (.not. (i <= 2.05d+115))) then
        tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0d0
    else
        tmp = 2.0d0 * (t_1 - (c * ((a * i) + (b * (c * i)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((i <= -100000.0) || !(i <= 2.05e+115)) {
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	} else {
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (i <= -100000.0) or not (i <= 2.05e+115):
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0
	else:
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((i <= -100000.0) || !(i <= 2.05e+115))
		tmp = Float64(Float64(t_1 - Float64(Float64(c * Float64(a + Float64(b * c))) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(Float64(a * i) + Float64(b * Float64(c * i))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((i <= -100000.0) || ~((i <= 2.05e+115)))
		tmp = (t_1 - ((c * (a + (b * c))) * i)) * 2.0;
	else
		tmp = 2.0 * (t_1 - (c * ((a * i) + (b * (c * i)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -100000.0], N[Not[LessEqual[i, 2.05e+115]], $MachinePrecision]], N[(N[(t$95$1 - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(N[(a * i), $MachinePrecision] + N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -1e5 or 2.04999999999999981e115 < i

   1. Initial program 92.5%

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

   if -1e5 < i < 2.04999999999999981e115

   1. Initial program 87.1%

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

   3. Taylor expanded in c around 0 99.2%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -100000 \lor \neg \left(i \leq 2.05 \cdot 10^{+115}\right):\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i + b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t + \frac{x \cdot y}{z}\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -6.8e-65)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 7.2e+104)
       (* 2.0 (- (* z (+ t (/ (* x y) z))) (* a (* c i))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.8e-65) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 7.2e+104) {
		tmp = 2.0 * ((z * (t + ((x * y) / z))) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-6.8d-65)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 7.2d+104) then
        tmp = 2.0d0 * ((z * (t + ((x * y) / z))) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.8e-65) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 7.2e+104) {
		tmp = 2.0 * ((z * (t + ((x * y) / z))) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -6.8e-65:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 7.2e+104:
		tmp = 2.0 * ((z * (t + ((x * y) / z))) - (a * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -6.8e-65)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 7.2e+104)
		tmp = Float64(2.0 * Float64(Float64(z * Float64(t + Float64(Float64(x * y) / z))) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -6.8e-65)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 7.2e+104)
		tmp = 2.0 * ((z * (t + ((x * y) / z))) - (a * (c * i)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e-65], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.2e+104], N[(2.0 * N[(N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.79999999999999973e-65

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 83.3%

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

   if -6.79999999999999973e-65 < c < 7.20000000000000001e104

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 78.9%

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

   4. Taylor expanded in c around 0 83.5%

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

   if 7.20000000000000001e104 < c

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 93.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t + \frac{x \cdot y}{z}\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+147} \lor \neg \left(c \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6.2e+147) (not (<= c 2e+113)))
   (* (* c (* (+ a (* b c)) i)) -2.0)
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6.2e+147) || !(c <= 2e+113)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-6.2d+147)) .or. (.not. (c <= 2d+113))) then
        tmp = (c * ((a + (b * c)) * i)) * (-2.0d0)
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -6.2e+147) || !(c <= 2e+113)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -6.2e+147) or not (c <= 2e+113):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -6.2e+147) || !(c <= 2e+113))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0);
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -6.2e+147) || ~((c <= 2e+113)))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -6.2e+147], N[Not[LessEqual[c, 2e+113]], $MachinePrecision]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.2000000000000001e147 or 2e113 < c

   1. Initial program 76.2%

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

      1. associate--l+ 76.2%

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

      2. *-commutative 76.2%

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

      3. associate--l+ 76.2%

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

      4. associate--l+ 76.2%

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

      5. *-commutative 76.2%

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

      6. associate--l+ 76.2%

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

      7. fma-define 76.2%

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

      8. *-commutative 76.2%

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

      9. associate-*l* 90.8%

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

      10. +-commutative 90.8%

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

      11. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in i around inf 87.6%

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

   if -6.2000000000000001e147 < c < 2e113

   1. Initial program 95.0%

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

   3. Taylor expanded in c around 0 73.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+147} \lor \neg \left(c \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -2.2e-122)
     t_1
     (if (<= t 3.8e-241)
       (* (* c i) (* a -2.0))
       (if (<= t 3.4e+90) (* (* x y) 2.0) 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 * (z * t);
	double tmp;
	if (t <= -2.2e-122) {
		tmp = t_1;
	} else if (t <= 3.8e-241) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 3.4e+90) {
		tmp = (x * y) * 2.0;
	} 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 * (z * t)
    if (t <= (-2.2d-122)) then
        tmp = t_1
    else if (t <= 3.8d-241) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (t <= 3.4d+90) then
        tmp = (x * y) * 2.0d0
    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 * (z * t);
	double tmp;
	if (t <= -2.2e-122) {
		tmp = t_1;
	} else if (t <= 3.8e-241) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 3.4e+90) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -2.2e-122:
		tmp = t_1
	elif t <= 3.8e-241:
		tmp = (c * i) * (a * -2.0)
	elif t <= 3.4e+90:
		tmp = (x * y) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -2.2e-122)
		tmp = t_1;
	elseif (t <= 3.8e-241)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (t <= 3.4e+90)
		tmp = Float64(Float64(x * y) * 2.0);
	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 * (z * t);
	tmp = 0.0;
	if (t <= -2.2e-122)
		tmp = t_1;
	elseif (t <= 3.8e-241)
		tmp = (c * i) * (a * -2.0);
	elseif (t <= 3.4e+90)
		tmp = (x * y) * 2.0;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-122], t$95$1, If[LessEqual[t, 3.8e-241], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+90], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e-122 or 3.40000000000000018e90 < t

   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. Add Preprocessing

   3. Taylor expanded in z around inf 44.1%

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

   if -2.2e-122 < t < 3.7999999999999999e-241

   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. Step-by-step derivation

      1. associate--l+ 88.8%

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

      2. *-commutative 88.8%

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

      3. associate--l+ 88.8%

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

      4. associate--l+ 88.8%

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

      5. *-commutative 88.8%

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

      6. associate--l+ 88.8%

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

      7. fma-define 88.8%

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

      8. *-commutative 88.8%

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

      9. associate-*l* 91.1%

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

      10. +-commutative 91.1%

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

      11. fma-define 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 37.8%

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

      1. associate-*r* 37.8%

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

   7. Simplified 37.8%

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

   if 3.7999999999999999e-241 < t < 3.40000000000000018e90

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 45.8%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+212} \lor \neg \left(c \leq 5.1 \cdot 10^{+118}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.6e+212) (not (<= c 5.1e+118)))
   (* (* c i) (* a -2.0))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e+212) || !(c <= 5.1e+118)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.6d+212)) .or. (.not. (c <= 5.1d+118))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e+212) || !(c <= 5.1e+118)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.6e+212) or not (c <= 5.1e+118):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.6e+212) || !(c <= 5.1e+118))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.6e+212) || ~((c <= 5.1e+118)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.6e+212], N[Not[LessEqual[c, 5.1e+118]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.6e212 or 5.10000000000000002e118 < c

   1. Initial program 80.5%

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

      1. associate--l+ 80.5%

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

      2. *-commutative 80.5%

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

      3. associate--l+ 80.5%

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

      4. associate--l+ 80.5%

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

      5. *-commutative 80.5%

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

      6. associate--l+ 80.5%

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

      7. fma-define 80.5%

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

      8. *-commutative 80.5%

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

      9. associate-*l* 94.8%

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

      10. +-commutative 94.8%

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

      11. fma-define 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around inf 48.2%

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

      1. associate-*r* 48.2%

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

   7. Simplified 48.2%

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

   if -3.6e212 < c < 5.10000000000000002e118

   1. Initial program 92.0%

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

   3. Taylor expanded in c around 0 70.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+212} \lor \neg \left(c \leq 5.1 \cdot 10^{+118}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-72} \lor \neg \left(t \leq 5.9 \cdot 10^{+91}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -2.9e-72) (not (<= t 5.9e+91)))
   (* 2.0 (* 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 ((t <= -2.9e-72) || !(t <= 5.9e+91)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (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 ((t <= (-2.9d-72)) .or. (.not. (t <= 5.9d+91))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (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 ((t <= -2.9e-72) || !(t <= 5.9e+91)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -2.9e-72) or not (t <= 5.9e+91):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -2.9e-72) || !(t <= 5.9e+91))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(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 ((t <= -2.9e-72) || ~((t <= 5.9e+91)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -2.9e-72], N[Not[LessEqual[t, 5.9e+91]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999998e-72 or 5.9000000000000002e91 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 45.1%

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

   if -2.89999999999999998e-72 < t < 5.9000000000000002e91

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 44.9%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-72} \lor \neg \left(t \leq 5.9 \cdot 10^{+91}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.5% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

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

3. Taylor expanded in z around inf 30.7%

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

4. Final simplification 30.7%

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

Developer target: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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