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

Percentage Accurate: 89.6% → 95.3%

Time: 25.9s

Alternatives: 16

Speedup: 0.5×

• 46.9% 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: 89.6% 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: 95.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \mathsf{fma}\left(b, c, a\right) \cdot \left(-i\right), x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -9e+23)
   (* 2.0 (fma z t (fma c (* (fma b c a) (- i)) (* x y))))
   (* 2.0 (- (fma x y (* z t)) (* (+ a (* c b)) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -9e+23) {
		tmp = 2.0 * fma(z, t, fma(c, (fma(b, c, a) * -i), (x * y)));
	} else {
		tmp = 2.0 * (fma(x, y, (z * t)) - ((a + (c * b)) * (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -9e+23)
		tmp = Float64(2.0 * fma(z, t, fma(c, Float64(fma(b, c, a) * Float64(-i)), Float64(x * y))));
	else
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(Float64(a + Float64(c * b)) * Float64(c * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -9e+23], N[(2.0 * N[(z * t + N[(c * N[(N[(b * c + a), $MachinePrecision] * (-i)), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.99999999999999958e23

   1. Initial program 83.0%

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

      1. associate--l+ 83.0%

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

      2. +-commutative 83.0%

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

      3. associate-+l- 83.0%

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

      4. fma-neg 86.5%

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

      5. neg-sub0 86.5%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{0 - \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - x \cdot y\right)}\right) \]

      6. associate-+l- 86.5%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(0 - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y}\right) \]

      7. neg-sub0 86.5%

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

      8. distribute-rgt-neg-in 86.5%

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

      9. *-commutative 86.5%

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

      10. associate-*l* 99.8%

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

      11. fma-def 99.8%

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

      12. +-commutative 99.8%

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

      13. fma-def 99.8%

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

   3. Simplified 99.8%

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

   if -8.99999999999999958e23 < c

   1. Initial program 94.7%

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

      1. associate-*l* 96.0%

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

      2. fma-def 97.0%

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

   3. Simplified 97.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \mathsf{fma}\left(b, c, a\right) \cdot \left(-i\right), x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 2: 94.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. associate-*l* 95.0%

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

   2. fma-def 95.8%

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

3. Simplified 95.8%

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

4. Final simplification 95.8%

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

Alternative 3: 95.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $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[(N[(x * y), $MachinePrecision] - N[(c * N[(i * t$95$1), $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 96.2%

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

      1. associate-*l* 98.0%

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

      2. fma-def 98.0%

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

   3. Simplified 98.0%

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

      1. fma-def 98.0%

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

      2. +-commutative 98.0%

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

   5. Applied egg-rr 98.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around 0 63.7%

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

4. Final simplification 96.6%

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

Alternative 4: 93.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + c \cdot b\\ t_2 := c \cdot t_1\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+169} \lor \neg \left(t_2 \leq 10^{+275}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))) (t_2 (* c t_1)))
   (if (or (<= t_2 -4e+169) (not (<= t_2 1e+275)))
     (* 2.0 (- (* x y) (* c (* i t_1))))
     (* 2.0 (- (+ (* x y) (* z t)) (* i t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = c * t_1;
	double tmp;
	if ((t_2 <= -4e+169) || !(t_2 <= 1e+275)) {
		tmp = 2.0 * ((x * y) - (c * (i * t_1)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (c * b)
    t_2 = c * t_1
    if ((t_2 <= (-4d+169)) .or. (.not. (t_2 <= 1d+275))) then
        tmp = 2.0d0 * ((x * y) - (c * (i * t_1)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * t_2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double t_2 = c * t_1;
	double tmp;
	if ((t_2 <= -4e+169) || !(t_2 <= 1e+275)) {
		tmp = 2.0 * ((x * y) - (c * (i * t_1)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (c * b)
	t_2 = c * t_1
	tmp = 0
	if (t_2 <= -4e+169) or not (t_2 <= 1e+275):
		tmp = 2.0 * ((x * y) - (c * (i * t_1)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	t_2 = Float64(c * t_1)
	tmp = 0.0
	if ((t_2 <= -4e+169) || !(t_2 <= 1e+275))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(i * t_1))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (c * b);
	t_2 = c * t_1;
	tmp = 0.0;
	if ((t_2 <= -4e+169) || ~((t_2 <= 1e+275)))
		tmp = 2.0 * ((x * y) - (c * (i * t_1)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -4e+169], N[Not[LessEqual[t$95$2, 1e+275]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -3.99999999999999974e169 or 9.9999999999999996e274 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 80.3%

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

   2. Taylor expanded in z around 0 96.4%

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

   if -3.99999999999999974e169 < (*.f64 (+.f64 a (*.f64 b c)) c) < 9.9999999999999996e274

   1. Initial program 97.9%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + c \cdot b\right) \leq -4 \cdot 10^{+169} \lor \neg \left(c \cdot \left(a + c \cdot b\right) \leq 10^{+275}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 5: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+23} \lor \neg \left(c \leq 7200000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.25e+23) (not (<= c 7200000.0)))
   (* 2.0 (- (* x y) (* c (* i (+ a (* c b))))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.25e+23) || !(c <= 7200000.0)) {
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.25d+23)) .or. (.not. (c <= 7200000.0d0))) then
        tmp = 2.0d0 * ((x * y) - (c * (i * (a + (c * b)))))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.25e+23) || !(c <= 7200000.0)) {
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.25e+23) or not (c <= 7200000.0):
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.25e+23) || !(c <= 7200000.0))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.25e+23) || ~((c <= 7200000.0)))
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.25e+23], N[Not[LessEqual[c, 7200000.0]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.2499999999999999e23 or 7.2e6 < c

   1. Initial program 85.6%

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

   2. Taylor expanded in z around 0 90.6%

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

   if -2.2499999999999999e23 < c < 7.2e6

   1. Initial program 97.5%

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

   2. Taylor expanded in c around 0 79.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+23} \lor \neg \left(c \leq 7200000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 6: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+65} \lor \neg \left(c \leq 1.5 \cdot 10^{+22}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -9.2e+65) (not (<= c 1.5e+22)))
   (* 2.0 (- (* x y) (* c (* i (+ a (* c b))))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.2e+65) || !(c <= 1.5e+22)) {
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	}
	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 <= (-9.2d+65)) .or. (.not. (c <= 1.5d+22))) then
        tmp = 2.0d0 * ((x * y) - (c * (i * (a + (c * b)))))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    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 <= -9.2e+65) || !(c <= 1.5e+22)) {
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -9.2e+65) or not (c <= 1.5e+22):
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -9.2e+65) || !(c <= 1.5e+22))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -9.2e+65) || ~((c <= 1.5e+22)))
		tmp = 2.0 * ((x * y) - (c * (i * (a + (c * b)))));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -9.2e+65], N[Not[LessEqual[c, 1.5e+22]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.2e65 or 1.5e22 < c

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0 93.1%

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

   if -9.2e65 < c < 1.5e22

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 89.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+65} \lor \neg \left(c \leq 1.5 \cdot 10^{+22}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]

Alternative 7: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-145}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.15e+138)
   (* 2.0 (+ (* x y) (* z t)))
   (if (<= x 1.45e-145)
     (* 2.0 (- (* z t) (* c (* i (+ a (* c b))))))
     (* 2.0 (- (* x y) (* i (* c a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.15e+138) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (x <= 1.45e-145) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) - (i * (c * a)));
	}
	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 <= (-1.15d+138)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (x <= 1.45d-145) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (c * b)))))
    else
        tmp = 2.0d0 * ((x * y) - (i * (c * a)))
    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 <= -1.15e+138) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (x <= 1.45e-145) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * ((x * y) - (i * (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.15e+138:
		tmp = 2.0 * ((x * y) + (z * t))
	elif x <= 1.45e-145:
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))))
	else:
		tmp = 2.0 * ((x * y) - (i * (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.15e+138)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (x <= 1.45e-145)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(c * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.15e+138)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (x <= 1.45e-145)
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	else
		tmp = 2.0 * ((x * y) - (i * (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.15e+138], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-145], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000004e138

   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. Taylor expanded in c around 0 68.2%

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

   if -1.15000000000000004e138 < x < 1.44999999999999992e-145

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0 79.4%

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

   if 1.44999999999999992e-145 < x

   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. Taylor expanded in a around inf 75.5%

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

   3. Taylor expanded in z around 0 58.3%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

   5. Simplified 60.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-145}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]

Alternative 8: 75.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+64} \lor \neg \left(c \leq 112000000\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.4e+64) (not (<= c 112000000.0)))
   (* (* c (* i (+ a (* c b)))) -2.0)
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.4e+64) || !(c <= 112000000.0)) {
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.4d+64)) .or. (.not. (c <= 112000000.0d0))) then
        tmp = (c * (i * (a + (c * b)))) * (-2.0d0)
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.4e+64) || !(c <= 112000000.0)) {
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.4e+64) or not (c <= 112000000.0):
		tmp = (c * (i * (a + (c * b)))) * -2.0
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.4e+64) || !(c <= 112000000.0))
		tmp = Float64(Float64(c * Float64(i * Float64(a + Float64(c * b)))) * -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.4e+64) || ~((c <= 112000000.0)))
		tmp = (c * (i * (a + (c * b)))) * -2.0;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.4e+64], N[Not[LessEqual[c, 112000000.0]], $MachinePrecision]], N[(N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.4000000000000002e64 or 1.12e8 < c

   1. Initial program 85.7%

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

   2. Taylor expanded in i around inf 78.3%

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

   3. Taylor expanded in i around 0 78.3%

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

   if -3.4000000000000002e64 < c < 1.12e8

   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. Taylor expanded in c around 0 78.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+64} \lor \neg \left(c \leq 112000000\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 9: 37.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= y -9e-127)
     t_1
     (if (<= y 9.6e-14)
       (* 2.0 (* z t))
       (if (<= y 1.38e+164) (* (* a (* c i)) (- 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 * (x * y);
	double tmp;
	if (y <= -9e-127) {
		tmp = t_1;
	} else if (y <= 9.6e-14) {
		tmp = 2.0 * (z * t);
	} else if (y <= 1.38e+164) {
		tmp = (a * (c * i)) * -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 * (x * y)
    if (y <= (-9d-127)) then
        tmp = t_1
    else if (y <= 9.6d-14) then
        tmp = 2.0d0 * (z * t)
    else if (y <= 1.38d+164) then
        tmp = (a * (c * i)) * -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 * (x * y);
	double tmp;
	if (y <= -9e-127) {
		tmp = t_1;
	} else if (y <= 9.6e-14) {
		tmp = 2.0 * (z * t);
	} else if (y <= 1.38e+164) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if y <= -9e-127:
		tmp = t_1
	elif y <= 9.6e-14:
		tmp = 2.0 * (z * t)
	elif y <= 1.38e+164:
		tmp = (a * (c * i)) * -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(x * y))
	tmp = 0.0
	if (y <= -9e-127)
		tmp = t_1;
	elseif (y <= 9.6e-14)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (y <= 1.38e+164)
		tmp = Float64(Float64(a * Float64(c * i)) * Float64(-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 * (x * y);
	tmp = 0.0;
	if (y <= -9e-127)
		tmp = t_1;
	elseif (y <= 9.6e-14)
		tmp = 2.0 * (z * t);
	elseif (y <= 1.38e+164)
		tmp = (a * (c * i)) * -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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-127], t$95$1, If[LessEqual[y, 9.6e-14], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.38e+164], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999998e-127 or 1.3800000000000001e164 < y

   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. Taylor expanded in x around inf 48.1%

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

   if -8.9999999999999998e-127 < y < 9.599999999999999e-14

   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. Taylor expanded in z around inf 34.3%

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

   if 9.599999999999999e-14 < y < 1.3800000000000001e164

   1. Initial program 97.0%

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

      1. associate-*l* 94.6%

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

      2. fma-def 94.6%

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

   3. Simplified 94.6%

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

      1. add-cube-cbrt 94.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right) \]

      2. pow3 94.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{a + b \cdot c}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

      3. +-commutative 94.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{b \cdot c + a}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

      4. fma-udef 94.3%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(b, c, a\right)}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 94.3%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. *-commutative 36.8%

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

      3. *-commutative 36.8%

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

      4. associate-*l* 39.4%

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

      5. *-commutative 39.4%

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

      6. distribute-rgt-neg-in 39.4%

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

      7. distribute-rgt-neg-in 39.4%

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

   8. Simplified 39.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-127}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 10: 37.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-242}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= t -1.6e-114)
     t_2
     (if (<= t 3.1e-261)
       t_1
       (if (<= t 2.55e-242)
         (* (* c -2.0) (* a i))
         (if (<= t 1.2e+177) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.6e-114) {
		tmp = t_2;
	} else if (t <= 3.1e-261) {
		tmp = t_1;
	} else if (t <= 2.55e-242) {
		tmp = (c * -2.0) * (a * i);
	} else if (t <= 1.2e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (t <= (-1.6d-114)) then
        tmp = t_2
    else if (t <= 3.1d-261) then
        tmp = t_1
    else if (t <= 2.55d-242) then
        tmp = (c * (-2.0d0)) * (a * i)
    else if (t <= 1.2d+177) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.6e-114) {
		tmp = t_2;
	} else if (t <= 3.1e-261) {
		tmp = t_1;
	} else if (t <= 2.55e-242) {
		tmp = (c * -2.0) * (a * i);
	} else if (t <= 1.2e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.6e-114:
		tmp = t_2
	elif t <= 3.1e-261:
		tmp = t_1
	elif t <= 2.55e-242:
		tmp = (c * -2.0) * (a * i)
	elif t <= 1.2e+177:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1.6e-114)
		tmp = t_2;
	elseif (t <= 3.1e-261)
		tmp = t_1;
	elseif (t <= 2.55e-242)
		tmp = Float64(Float64(c * -2.0) * Float64(a * i));
	elseif (t <= 1.2e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1.6e-114)
		tmp = t_2;
	elseif (t <= 3.1e-261)
		tmp = t_1;
	elseif (t <= 2.55e-242)
		tmp = (c * -2.0) * (a * i);
	elseif (t <= 1.2e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-114], t$95$2, If[LessEqual[t, 3.1e-261], t$95$1, If[LessEqual[t, 2.55e-242], N[(N[(c * -2.0), $MachinePrecision] * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+177], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e-114 or 1.2e177 < t

   1. Initial program 88.8%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -1.6000000000000001e-114 < t < 3.0999999999999998e-261 or 2.54999999999999984e-242 < t < 1.2e177

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 43.2%

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

   if 3.0999999999999998e-261 < t < 2.54999999999999984e-242

   1. Initial program 99.6%

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

      1. associate-*l* 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 98.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right) \]

      2. pow3 98.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{a + b \cdot c}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

      3. +-commutative 98.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{b \cdot c + a}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

      4. fma-udef 98.8%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(b, c, a\right)}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 98.8%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. *-commutative 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*l* 75.9%

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

      5. *-commutative 75.9%

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

      6. distribute-rgt-neg-in 75.9%

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

      7. distribute-rgt-neg-in 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in a around 0 75.5%

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

       1. associate-*r* 75.5%

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

   11. Simplified 75.5%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-114}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-242}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+177}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 11: 69.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+100} \lor \neg \left(c \leq 2.35 \cdot 10^{+54}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.9e+100) (not (<= c 2.35e+54)))
   (* -2.0 (* c (* c (* b i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.9e+100) || !(c <= 2.35e+54)) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.9d+100)) .or. (.not. (c <= 2.35d+54))) then
        tmp = (-2.0d0) * (c * (c * (b * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.9e+100) || !(c <= 2.35e+54)) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.9e+100) or not (c <= 2.35e+54):
		tmp = -2.0 * (c * (c * (b * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.9e+100) || !(c <= 2.35e+54))
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.9e+100) || ~((c <= 2.35e+54)))
		tmp = -2.0 * (c * (c * (b * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.9e+100], N[Not[LessEqual[c, 2.35e+54]], $MachinePrecision]], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.9e100 or 2.34999999999999996e54 < c

   1. Initial program 87.0%

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

   2. Taylor expanded in b around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. *-commutative 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. unpow2 66.6%

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

      5. distribute-rgt-neg-in 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in i around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. unpow2 66.6%

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

      3. *-commutative 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in c around 0 66.6%

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

      1. unpow2 66.6%

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

      2. associate-*r* 64.6%

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

   10. Simplified 64.6%

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

   if -2.9e100 < c < 2.34999999999999996e54

   1. Initial program 94.9%

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

   2. Taylor expanded in c around 0 74.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+100} \lor \neg \left(c \leq 2.35 \cdot 10^{+54}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 12: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{+242}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+171}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot \left(i \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -3.95e+242)
   (* (* a (* c i)) (- 2.0))
   (if (<= a 8e+171) (* 2.0 (+ (* x y) (* z t))) (* (* c a) (* i -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.95e+242) {
		tmp = (a * (c * i)) * -2.0;
	} else if (a <= 8e+171) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * a) * (i * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-3.95d+242)) then
        tmp = (a * (c * i)) * -2.0d0
    else if (a <= 8d+171) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (c * a) * (i * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -3.95e+242) {
		tmp = (a * (c * i)) * -2.0;
	} else if (a <= 8e+171) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = (c * a) * (i * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -3.95e+242:
		tmp = (a * (c * i)) * -2.0
	elif a <= 8e+171:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = (c * a) * (i * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -3.95e+242)
		tmp = Float64(Float64(a * Float64(c * i)) * Float64(-2.0));
	elseif (a <= 8e+171)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * a) * Float64(i * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -3.95e+242)
		tmp = (a * (c * i)) * -2.0;
	elseif (a <= 8e+171)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = (c * a) * (i * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -3.95e+242], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[a, 8e+171], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * a), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.94999999999999993e242

   1. Initial program 85.5%

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

      1. associate-*l* 96.2%

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

      2. fma-def 96.2%

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

   3. Simplified 96.2%

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

      1. add-cube-cbrt 96.0%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right) \]

      2. pow3 96.0%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{a + b \cdot c}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

      3. +-commutative 96.0%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{b \cdot c + a}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

      4. fma-udef 96.0%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(b, c, a\right)}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 96.0%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. *-commutative 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*l* 67.1%

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

      5. *-commutative 67.1%

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

      6. distribute-rgt-neg-in 67.1%

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

      7. distribute-rgt-neg-in 67.1%

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

   8. Simplified 67.1%

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

   if -3.94999999999999993e242 < a < 7.99999999999999963e171

   1. Initial program 93.2%

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

   2. Taylor expanded in c around 0 60.6%

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

   if 7.99999999999999963e171 < a

   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. Step-by-step derivation

      1. associate-*l* 89.4%

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

      2. fma-def 94.7%

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

   3. Simplified 94.7%

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

      1. add-cube-cbrt 94.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right) \]

      2. pow3 94.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{a + b \cdot c}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

      3. +-commutative 94.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{b \cdot c + a}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

      4. fma-udef 94.4%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(b, c, a\right)}}\right)}^{3} \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 94.4%

      \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. *-commutative 54.4%

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

      3. *-commutative 54.4%

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

      4. associate-*l* 59.4%

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

      5. *-commutative 59.4%

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

      6. distribute-rgt-neg-in 59.4%

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

      7. distribute-rgt-neg-in 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in a around 0 54.4%

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

       1. *-commutative 54.4%

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

       2. *-commutative 54.4%

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

       3. associate-*r* 64.4%

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

       4. associate-*l* 64.4%

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

   11. Simplified 64.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.95 \cdot 10^{+242}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+171}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot a\right) \cdot \left(i \cdot -2\right)\\ \end{array} \]

Alternative 13: 69.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.5e+100)
   (* -2.0 (* c (* c (* b i))))
   (if (<= c 2.9e+56)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* (* c c) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.5e+100) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else if (c <= 2.9e+56) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2.5d+100)) then
        tmp = (-2.0d0) * (c * (c * (b * i)))
    else if (c <= 2.9d+56) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * ((c * c) * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.5e+100) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else if (c <= 2.9e+56) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.5e+100:
		tmp = -2.0 * (c * (c * (b * i)))
	elif c <= 2.9e+56:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * ((c * c) * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.5e+100)
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	elseif (c <= 2.9e+56)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.5e+100)
		tmp = -2.0 * (c * (c * (b * i)));
	elseif (c <= 2.9e+56)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * ((c * c) * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.5e+100], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e+56], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.4999999999999999e100

   1. Initial program 86.4%

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

   2. Taylor expanded in b around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. distribute-rgt-neg-in 63.5%

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

      4. unpow2 63.5%

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

      5. distribute-rgt-neg-in 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in i around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. unpow2 63.5%

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

      3. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in c around 0 63.5%

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

      1. unpow2 63.5%

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

      2. associate-*r* 63.6%

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

   10. Simplified 63.6%

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

   if -2.4999999999999999e100 < c < 2.90000000000000007e56

   1. Initial program 94.9%

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

   2. Taylor expanded in c around 0 74.3%

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

   if 2.90000000000000007e56 < c

   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. Taylor expanded in b around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. unpow2 69.3%

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

      5. distribute-rgt-neg-in 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in i around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. unpow2 69.3%

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

      3. *-commutative 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 14: 69.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+115}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -4.7e+115)
   (* -2.0 (* (* c i) (* c b)))
   (if (<= c 6.5e+56)
     (* 2.0 (+ (* x y) (* z t)))
     (* -2.0 (* (* c c) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.7e+115) {
		tmp = -2.0 * ((c * i) * (c * b));
	} else if (c <= 6.5e+56) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-4.7d+115)) then
        tmp = (-2.0d0) * ((c * i) * (c * b))
    else if (c <= 6.5d+56) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = (-2.0d0) * ((c * c) * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.7e+115) {
		tmp = -2.0 * ((c * i) * (c * b));
	} else if (c <= 6.5e+56) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -4.7e+115:
		tmp = -2.0 * ((c * i) * (c * b))
	elif c <= 6.5e+56:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = -2.0 * ((c * c) * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -4.7e+115)
		tmp = Float64(-2.0 * Float64(Float64(c * i) * Float64(c * b)));
	elseif (c <= 6.5e+56)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -4.7e+115)
		tmp = -2.0 * ((c * i) * (c * b));
	elseif (c <= 6.5e+56)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = -2.0 * ((c * c) * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -4.7e+115], N[(-2.0 * N[(N[(c * i), $MachinePrecision] * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+56], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.6999999999999996e115

   1. Initial program 85.1%

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

   2. Taylor expanded in b around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. *-commutative 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

      4. unpow2 64.9%

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

      5. distribute-rgt-neg-in 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in i around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. unpow2 64.9%

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

      3. *-commutative 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in c around 0 64.9%

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

      1. unpow2 64.9%

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

      2. associate-*r* 65.0%

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

      3. *-commutative 65.0%

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

      4. associate-*r* 67.6%

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

      5. associate-*l* 67.7%

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

      6. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   if -4.6999999999999996e115 < c < 6.5000000000000001e56

   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. Taylor expanded in c around 0 73.2%

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

   if 6.5000000000000001e56 < c

   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. Taylor expanded in b around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. unpow2 69.3%

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

      5. distribute-rgt-neg-in 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in i around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. unpow2 69.3%

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

      3. *-commutative 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+115}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot i\right) \cdot \left(c \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 15: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-110} \lor \neg \left(t \leq 8.8 \cdot 10^{+176}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -3.7e-110) (not (<= t 8.8e+176)))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -3.7e-110) || !(t <= 8.8e+176)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-3.7d-110)) .or. (.not. (t <= 8.8d+176))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -3.7e-110) || !(t <= 8.8e+176)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -3.7e-110) or not (t <= 8.8e+176):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -3.7e-110) || !(t <= 8.8e+176))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -3.7e-110) || ~((t <= 8.8e+176)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -3.7e-110], N[Not[LessEqual[t, 8.8e+176]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.70000000000000016e-110 or 8.80000000000000029e176 < t

   1. Initial program 88.8%

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

   2. Taylor expanded in z around inf 47.9%

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

   if -3.70000000000000016e-110 < t < 8.80000000000000029e176

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 42.3%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-110} \lor \neg \left(t \leq 8.8 \cdot 10^{+176}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 29.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

2. Taylor expanded in z around inf 28.7%

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

3. Final simplification 28.7%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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