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

Percentage Accurate: 89.7% → 96.7%

Time: 16.3s

Alternatives: 12

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.7% 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: 96.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.8%

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

      1. fma-define 94.8%

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

      2. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 41.2%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. unsub-neg 70.6%

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

      3. associate-/l* 70.6%

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

      4. +-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. fma-undefine 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 97.5%

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

Alternative 2: 96.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.8%

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

      1. fma-define 94.8%

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

      2. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

      1. fma-define 99.4%

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

      2. +-commutative 99.4%

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

   6. Applied egg-rr 99.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 41.2%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. unsub-neg 70.6%

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

      3. associate-/l* 70.6%

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

      4. +-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. fma-undefine 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 97.5%

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

Alternative 3: 79.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 10^{-14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+236}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -1e+220)
     (* 2.0 (- (* x y) (* c (* (* b c) i))))
     (if (<= (* x y) -5e+104)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= (* x y) 1e-14)
         (* 2.0 (- (* z t) t_1))
         (if (<= (* x y) 1e+236)
           (* 2.0 (- (* x y) t_1))
           (* x (* 2.0 (+ y (* t (/ z x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -1e+220) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= -5e+104) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 1e-14) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((x * y) <= 1e+236) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = x * (2.0 * (y + (t * (z / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if ((x * y) <= (-1d+220)) then
        tmp = 2.0d0 * ((x * y) - (c * ((b * c) * i)))
    else if ((x * y) <= (-5d+104)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((x * y) <= 1d-14) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if ((x * y) <= 1d+236) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = x * (2.0d0 * (y + (t * (z / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -1e+220) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= -5e+104) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 1e-14) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((x * y) <= 1e+236) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = x * (2.0 * (y + (t * (z / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if (x * y) <= -1e+220:
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)))
	elif (x * y) <= -5e+104:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= 1e-14:
		tmp = 2.0 * ((z * t) - t_1)
	elif (x * y) <= 1e+236:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = x * (2.0 * (y + (t * (z / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (Float64(x * y) <= -1e+220)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(b * c) * i))));
	elseif (Float64(x * y) <= -5e+104)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= 1e-14)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (Float64(x * y) <= 1e+236)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(x * Float64(2.0 * Float64(y + Float64(t * Float64(z / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if ((x * y) <= -1e+220)
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	elseif ((x * y) <= -5e+104)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= 1e-14)
		tmp = 2.0 * ((z * t) - t_1);
	elseif ((x * y) <= 1e+236)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = x * (2.0 * (y + (t * (z / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+220], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+104], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-14], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+236], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 * N[(y + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1e220

   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. Add Preprocessing

   3. Taylor expanded in z around 0 85.7%

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

   4. Taylor expanded in a around 0 89.3%

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

      1. *-commutative 89.3%

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

   6. Simplified 89.3%

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

   if -1e220 < (*.f64 x y) < -4.9999999999999997e104

   1. Initial program 86.4%

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

   3. Taylor expanded in c around 0 86.9%

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

   if -4.9999999999999997e104 < (*.f64 x y) < 9.99999999999999999e-15

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 86.9%

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

   if 9.99999999999999999e-15 < (*.f64 x y) < 1.00000000000000005e236

   1. Initial program 79.2%

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

   3. Taylor expanded in z around 0 84.8%

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

   if 1.00000000000000005e236 < (*.f64 x y)

   1. Initial program 84.2%

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

   3. Taylor expanded in c around 0 89.5%

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

   4. Taylor expanded in x around inf 92.1%

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

      1. distribute-lft-out 92.1%

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

      2. associate-/l* 94.7%

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

   6. Simplified 94.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 10^{-14}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+236}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := c \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t\_2\\ \end{array} \end{array} \]

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 4e+306)
       (* (- (+ (* x y) (* z t)) (* t_3 i)) 2.0)
       (* -2.0 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 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 <= 4e+306) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = -2.0 * 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 <= 4e+306) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = -2.0 * 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 <= 4e+306:
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0
	else:
		tmp = -2.0 * 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 <= 4e+306)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_3 * i)) * 2.0);
	else
		tmp = Float64(-2.0 * 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 <= 4e+306)
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	else
		tmp = -2.0 * 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, 4e+306], 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 * t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 97.1%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 4.00000000000000007e306

   1. Initial program 97.2%

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

   if 4.00000000000000007e306 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 52.6%

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

      1. fma-define 52.6%

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

      2. associate-*l* 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in i around inf 89.3%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 4 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.8%

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

      1. fma-define 94.8%

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

      2. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

      1. fma-define 99.4%

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

      2. +-commutative 99.4%

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

   6. Applied egg-rr 99.4%

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

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

   1. Initial program 0.0%

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

      1. fma-define 5.9%

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

      2. associate-*l* 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in i around inf 53.0%

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

4. Final simplification 96.3%

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

Alternative 6: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+178}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+220)
   (* 2.0 (- (* x y) (* c (* (* b c) i))))
   (if (<= (* x y) -5e+104)
     (* (+ (* x y) (* z t)) 2.0)
     (if (<= (* x y) 2e+178)
       (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
       (* x (* 2.0 (+ y (* t (/ z x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+220) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= -5e+104) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 2e+178) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = x * (2.0 * (y + (t * (z / x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d+220)) then
        tmp = 2.0d0 * ((x * y) - (c * ((b * c) * i)))
    else if ((x * y) <= (-5d+104)) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((x * y) <= 2d+178) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = x * (2.0d0 * (y + (t * (z / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+220) {
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	} else if ((x * y) <= -5e+104) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 2e+178) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = x * (2.0 * (y + (t * (z / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+220:
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)))
	elif (x * y) <= -5e+104:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= 2e+178:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = x * (2.0 * (y + (t * (z / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+220)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(b * c) * i))));
	elseif (Float64(x * y) <= -5e+104)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= 2e+178)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(x * Float64(2.0 * Float64(y + Float64(t * Float64(z / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+220)
		tmp = 2.0 * ((x * y) - (c * ((b * c) * i)));
	elseif ((x * y) <= -5e+104)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= 2e+178)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = x * (2.0 * (y + (t * (z / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+220], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(b * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+104], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+178], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 * N[(y + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1e220

   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. Add Preprocessing

   3. Taylor expanded in z around 0 85.7%

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

   4. Taylor expanded in a around 0 89.3%

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

      1. *-commutative 89.3%

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

   6. Simplified 89.3%

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

   if -1e220 < (*.f64 x y) < -4.9999999999999997e104

   1. Initial program 86.4%

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

   3. Taylor expanded in c around 0 86.9%

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

   if -4.9999999999999997e104 < (*.f64 x y) < 2.0000000000000001e178

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0 83.1%

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

   if 2.0000000000000001e178 < (*.f64 x y)

   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 c around 0 86.1%

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

   4. Taylor expanded in x around inf 88.4%

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

      1. distribute-lft-out 88.4%

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

      2. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+220}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+178}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + t \cdot \frac{z}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+52} \lor \neg \left(c \leq 1.3 \cdot 10^{+84}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.05e+52) (not (<= c 1.3e+84)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.05e+52) || !(c <= 1.3e+84)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.05d+52)) .or. (.not. (c <= 1.3d+84))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.05e+52) || !(c <= 1.3e+84)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.05e+52) or not (c <= 1.3e+84):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.05e+52) || !(c <= 1.3e+84))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.05e+52) || ~((c <= 1.3e+84)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.05e+52], N[Not[LessEqual[c, 1.3e+84]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.05e52 or 1.3000000000000001e84 < c

   1. Initial program 75.7%

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

   3. Taylor expanded in z around 0 88.6%

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

   if -2.05e52 < c < 1.3000000000000001e84

   1. Initial program 97.3%

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

   3. Taylor expanded in a around inf 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+52} \lor \neg \left(c \leq 1.3 \cdot 10^{+84}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+83} \lor \neg \left(c \leq 5.8 \cdot 10^{+105}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.2e+83) (not (<= c 5.8e+105)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* 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 <= -8.2e+83) || !(c <= 5.8e+105)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} 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 <= (-8.2d+83)) .or. (.not. (c <= 5.8d+105))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    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 <= -8.2e+83) || !(c <= 5.8e+105)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} 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 <= -8.2e+83) or not (c <= 5.8e+105):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	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 <= -8.2e+83) || !(c <= 5.8e+105))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	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 <= -8.2e+83) || ~((c <= 5.8e+105)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	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, -8.2e+83], N[Not[LessEqual[c, 5.8e+105]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $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 < -8.2000000000000002e83 or 5.8000000000000002e105 < c

   1. Initial program 76.7%

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

      1. fma-define 76.7%

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

      2. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in i around inf 81.6%

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

   if -8.2000000000000002e83 < c < 5.8000000000000002e105

   1. Initial program 95.6%

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

   3. Taylor expanded in c around 0 78.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+83} \lor \neg \left(c \leq 5.8 \cdot 10^{+105}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 2\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6800000000:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* z (* t 2.0))))
   (if (<= z -2.3e+83)
     t_1
     (if (<= z -6800000000.0)
       (* (* c i) (* a -2.0))
       (if (<= z 6.6e-74) (* y (* x 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 = z * (t * 2.0);
	double tmp;
	if (z <= -2.3e+83) {
		tmp = t_1;
	} else if (z <= -6800000000.0) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 6.6e-74) {
		tmp = y * (x * 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 = z * (t * 2.0d0)
    if (z <= (-2.3d+83)) then
        tmp = t_1
    else if (z <= (-6800000000.0d0)) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (z <= 6.6d-74) then
        tmp = y * (x * 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 = z * (t * 2.0);
	double tmp;
	if (z <= -2.3e+83) {
		tmp = t_1;
	} else if (z <= -6800000000.0) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 6.6e-74) {
		tmp = y * (x * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z * (t * 2.0)
	tmp = 0
	if z <= -2.3e+83:
		tmp = t_1
	elif z <= -6800000000.0:
		tmp = (c * i) * (a * -2.0)
	elif z <= 6.6e-74:
		tmp = y * (x * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z * Float64(t * 2.0))
	tmp = 0.0
	if (z <= -2.3e+83)
		tmp = t_1;
	elseif (z <= -6800000000.0)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (z <= 6.6e-74)
		tmp = Float64(y * Float64(x * 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 = z * (t * 2.0);
	tmp = 0.0;
	if (z <= -2.3e+83)
		tmp = t_1;
	elseif (z <= -6800000000.0)
		tmp = (c * i) * (a * -2.0);
	elseif (z <= 6.6e-74)
		tmp = y * (x * 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[(z * N[(t * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+83], t$95$1, If[LessEqual[z, -6800000000.0], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-74], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999995e83 or 6.59999999999999992e-74 < z

   1. Initial program 87.5%

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

      1. fma-define 88.3%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf 44.3%

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

      1. associate-*r* 44.3%

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

   7. Simplified 44.3%

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

   if -2.29999999999999995e83 < z < -6.8e9

   1. Initial program 80.4%

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

      1. fma-define 80.4%

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

      2. associate-*l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in a around inf 38.8%

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

      1. associate-*r* 38.8%

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

   7. Simplified 38.8%

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

   if -6.8e9 < z < 6.59999999999999992e-74

   1. Initial program 90.6%

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

      1. fma-define 90.6%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 41.6%

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

      1. *-commutative 41.6%

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

      2. *-commutative 41.6%

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

      3. associate-*r* 41.6%

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

      4. *-commutative 41.6%

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

   7. Simplified 41.6%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(t \cdot 2\right)\\ \mathbf{elif}\;z \leq -6800000000:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{+202} \lor \neg \left(c \leq 8.2 \cdot 10^{+124}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -7.6e+202) (not (<= c 8.2e+124)))
   (* (* 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 <= -7.6e+202) || !(c <= 8.2e+124)) {
		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 <= (-7.6d+202)) .or. (.not. (c <= 8.2d+124))) 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 <= -7.6e+202) || !(c <= 8.2e+124)) {
		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 <= -7.6e+202) or not (c <= 8.2e+124):
		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 <= -7.6e+202) || !(c <= 8.2e+124))
		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 <= -7.6e+202) || ~((c <= 8.2e+124)))
		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, -7.6e+202], N[Not[LessEqual[c, 8.2e+124]], $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 < -7.6000000000000001e202 or 8.20000000000000002e124 < c

   1. Initial program 74.1%

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

      1. fma-define 74.1%

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

      2. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in a around inf 45.9%

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

      1. associate-*r* 45.9%

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

   7. Simplified 45.9%

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

   if -7.6000000000000001e202 < c < 8.20000000000000002e124

   1. Initial program 93.3%

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

   3. Taylor expanded in c around 0 73.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{+202} \lor \neg \left(c \leq 8.2 \cdot 10^{+124}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+64} \lor \neg \left(z \leq 1.55 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(t \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -5e+64) (not (<= z 1.55e-76))) (* z (* t 2.0)) (* y (* x 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -5e+64) || !(z <= 1.55e-76)) {
		tmp = z * (t * 2.0);
	} else {
		tmp = y * (x * 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 ((z <= (-5d+64)) .or. (.not. (z <= 1.55d-76))) then
        tmp = z * (t * 2.0d0)
    else
        tmp = y * (x * 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 ((z <= -5e+64) || !(z <= 1.55e-76)) {
		tmp = z * (t * 2.0);
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -5e+64) or not (z <= 1.55e-76):
		tmp = z * (t * 2.0)
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -5e+64) || !(z <= 1.55e-76))
		tmp = Float64(z * Float64(t * 2.0));
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -5e+64) || ~((z <= 1.55e-76)))
		tmp = z * (t * 2.0);
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -5e+64], N[Not[LessEqual[z, 1.55e-76]], $MachinePrecision]], N[(z * N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e64 or 1.54999999999999985e-76 < z

   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. Step-by-step derivation

      1. fma-define 87.9%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around inf 44.0%

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

      1. associate-*r* 44.0%

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

   7. Simplified 44.0%

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

   if -5e64 < z < 1.54999999999999985e-76

   1. Initial program 89.9%

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

      1. fma-define 89.9%

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

      2. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-*r* 41.0%

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

      4. *-commutative 41.0%

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

   7. Simplified 41.0%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+64} \lor \neg \left(z \leq 1.55 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(t \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 2\right) \end{array} \]

FPCore

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

C

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

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 = y * (x * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. fma-define 88.9%

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

   2. associate-*l* 94.3%

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

3. Simplified 94.3%

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

5. Taylor expanded in x around inf 35.1%

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

   1. *-commutative 35.1%

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

   2. *-commutative 35.1%

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

   3. associate-*r* 35.1%

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

   4. *-commutative 35.1%

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

7. Simplified 35.1%

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

8. Final simplification 35.1%

   \[\leadsto y \cdot \left(x \cdot 2\right) \]
9. Add Preprocessing

Developer Target 1: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024128 
(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
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

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