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

Percentage Accurate: 90.0% → 95.3%

Time: 17.6s

Alternatives: 16

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot t\_1\right) \leq 2 \cdot 10^{+295}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(c \cdot i\right) \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(i \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* y x) (* z t)) (* i (* c t_1))) 2e+295)
     (* 2.0 (- (fma x y (* z t)) (* (* c i) t_1)))
     (* 2.0 (fma y x (- (* z t) (* 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 + (b * c);
	double tmp;
	if ((((y * x) + (z * t)) - (i * (c * t_1))) <= 2e+295) {
		tmp = 2.0 * (fma(x, y, (z * t)) - ((c * i) * t_1));
	} else {
		tmp = 2.0 * fma(y, x, ((z * t) - (c * (i * t_1))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (Float64(Float64(Float64(y * x) + Float64(z * t)) - Float64(i * Float64(c * t_1))) <= 2e+295)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(Float64(c * i) * t_1)));
	else
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(z * t) - Float64(c * Float64(i * t_1)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+295], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * i), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x + N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < 2e295

   1. Initial program 95.3%

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

      1. fma-define 95.3%

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

      2. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   if 2e295 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 72.8%

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

      1. associate--l+ 72.8%

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

      2. fma-neg 72.8%

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

      3. *-commutative 72.8%

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

      4. +-commutative 72.8%

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

      5. fma-undefine 72.8%

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

      6. associate-*r* 87.5%

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

      7. *-commutative 87.5%

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

      8. *-commutative 87.5%

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

      9. fma-define 98.7%

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

      10. *-commutative 98.7%

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

      11. associate-*r* 84.1%

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

      12. fma-undefine 84.1%

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

      13. +-commutative 84.1%

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

      14. *-commutative 84.1%

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

      15. associate-*r* 98.7%

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

      16. distribute-rgt-neg-in 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in z around 0 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 2 \cdot 10^{+295}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(c \cdot i\right) \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. associate--l+ 89.0%

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

   2. fma-neg 89.0%

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

   3. *-commutative 89.0%

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

   4. +-commutative 89.0%

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

   5. fma-undefine 89.0%

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

   6. associate-*r* 89.8%

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

   7. *-commutative 89.8%

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

   8. *-commutative 89.8%

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

   9. fma-define 92.9%

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

   10. *-commutative 92.9%

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

   11. associate-*r* 92.2%

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

   12. fma-undefine 92.2%

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

   13. +-commutative 92.2%

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

   14. *-commutative 92.2%

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

   15. associate-*r* 98.8%

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

   16. distribute-rgt-neg-in 98.8%

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

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 95.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

      1. fma-define 92.7%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 90.0%

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

   4. Taylor expanded in a around 0 90.1%

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

4. Final simplification 98.4%

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

Alternative 4: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t\_1\right)\\ t_3 := c \cdot \left(i \cdot t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(y \cdot x - t\_3\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+282}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))) (t_3 (* c (* i t_1))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* y x) t_3))
     (if (<= t_2 1e+282)
       (* 2.0 (- (+ (* y x) (* z t)) t_2))
       (* 2.0 (- (* z t) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (i * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((y * x) - t_3);
	} else if (t_2 <= 1e+282) {
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((z * t) - t_3);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (i * t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((y * x) - t_3);
	} else if (t_2 <= 1e+282) {
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((z * t) - t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	t_3 = c * (i * t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((y * x) - t_3)
	elif t_2 <= 1e+282:
		tmp = 2.0 * (((y * x) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((z * t) - t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	t_3 = Float64(c * Float64(i * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(y * x) - t_3));
	elseif (t_2 <= 1e+282)
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	t_3 = c * (i * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((y * x) - t_3);
	elseif (t_2 <= 1e+282)
		tmp = 2.0 * (((y * x) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((z * t) - t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+282], N[(2.0 * N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 76.0%

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

   3. Taylor expanded in z around 0 97.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.00000000000000003e282

   1. Initial program 99.9%

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

   if 1.00000000000000003e282 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 69.4%

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

   3. Taylor expanded in x around 0 94.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 10^{+282}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ t_3 := 2 \cdot \left(y \cdot x - t\_1\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-81}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+140}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* b (* c i))))
        (t_2 (* (* c (* i (+ a (* b c)))) -2.0))
        (t_3 (* 2.0 (- (* y x) t_1))))
   (if (<= c -8.5e+222)
     t_3
     (if (<= c -8e+183)
       t_2
       (if (<= c -1.45e+45)
         (* 2.0 (- (* z t) t_1))
         (if (<= c 7e-81)
           (* 2.0 (+ (* y x) (* z t)))
           (if (<= c 1.2e+29)
             (* 2.0 (- (* y x) (* i (* c a))))
             (if (<= c 1.6e+140) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (b * (c * i));
	double t_2 = (c * (i * (a + (b * c)))) * -2.0;
	double t_3 = 2.0 * ((y * x) - t_1);
	double tmp;
	if (c <= -8.5e+222) {
		tmp = t_3;
	} else if (c <= -8e+183) {
		tmp = t_2;
	} else if (c <= -1.45e+45) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-81) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 1.2e+29) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else if (c <= 1.6e+140) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (b * (c * i))
    t_2 = (c * (i * (a + (b * c)))) * (-2.0d0)
    t_3 = 2.0d0 * ((y * x) - t_1)
    if (c <= (-8.5d+222)) then
        tmp = t_3
    else if (c <= (-8d+183)) then
        tmp = t_2
    else if (c <= (-1.45d+45)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 7d-81) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if (c <= 1.2d+29) then
        tmp = 2.0d0 * ((y * x) - (i * (c * a)))
    else if (c <= 1.6d+140) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (b * (c * i));
	double t_2 = (c * (i * (a + (b * c)))) * -2.0;
	double t_3 = 2.0 * ((y * x) - t_1);
	double tmp;
	if (c <= -8.5e+222) {
		tmp = t_3;
	} else if (c <= -8e+183) {
		tmp = t_2;
	} else if (c <= -1.45e+45) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-81) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 1.2e+29) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else if (c <= 1.6e+140) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (b * (c * i))
	t_2 = (c * (i * (a + (b * c)))) * -2.0
	t_3 = 2.0 * ((y * x) - t_1)
	tmp = 0
	if c <= -8.5e+222:
		tmp = t_3
	elif c <= -8e+183:
		tmp = t_2
	elif c <= -1.45e+45:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 7e-81:
		tmp = 2.0 * ((y * x) + (z * t))
	elif c <= 1.2e+29:
		tmp = 2.0 * ((y * x) - (i * (c * a)))
	elif c <= 1.6e+140:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(b * Float64(c * i)))
	t_2 = Float64(Float64(c * Float64(i * Float64(a + Float64(b * c)))) * -2.0)
	t_3 = Float64(2.0 * Float64(Float64(y * x) - t_1))
	tmp = 0.0
	if (c <= -8.5e+222)
		tmp = t_3;
	elseif (c <= -8e+183)
		tmp = t_2;
	elseif (c <= -1.45e+45)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 7e-81)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif (c <= 1.2e+29)
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(i * Float64(c * a))));
	elseif (c <= 1.6e+140)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (b * (c * i));
	t_2 = (c * (i * (a + (b * c)))) * -2.0;
	t_3 = 2.0 * ((y * x) - t_1);
	tmp = 0.0;
	if (c <= -8.5e+222)
		tmp = t_3;
	elseif (c <= -8e+183)
		tmp = t_2;
	elseif (c <= -1.45e+45)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 7e-81)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif (c <= 1.2e+29)
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	elseif (c <= 1.6e+140)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+222], t$95$3, If[LessEqual[c, -8e+183], t$95$2, If[LessEqual[c, -1.45e+45], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-81], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.2e+29], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+140], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8.4999999999999994e222 or 1.2e29 < c < 1.60000000000000005e140

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 79.6%

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

   4. Taylor expanded in a around 0 84.5%

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

   if -8.4999999999999994e222 < c < -7.99999999999999957e183 or 1.60000000000000005e140 < c

   1. Initial program 70.4%

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

   3. Taylor expanded in i around inf 94.3%

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

   4. Taylor expanded in i around 0 94.3%

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

   if -7.99999999999999957e183 < c < -1.4499999999999999e45

   1. Initial program 79.4%

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

   3. Taylor expanded in x around 0 89.6%

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

   4. Taylor expanded in a around 0 83.0%

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

   if -1.4499999999999999e45 < c < 6.99999999999999973e-81

   1. Initial program 99.0%

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

   3. Taylor expanded in c around 0 77.6%

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

   if 6.99999999999999973e-81 < c < 1.2e29

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 87.3%

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

      1. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-*l* 82.3%

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

      4. *-commutative 82.3%

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

   8. Simplified 82.3%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - i \cdot \left(a \cdot c\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+222}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+183}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-81}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+140}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

      1. fma-define 92.7%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

      1. fma-define 98.8%

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

      2. +-commutative 98.8%

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

   6. Applied egg-rr 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 90.0%

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

   4. Taylor expanded in a around 0 90.1%

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

4. Final simplification 98.4%

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

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+56} \lor \neg \left(c \leq 5.2 \cdot 10^{-80} \lor \neg \left(c \leq 7.8 \cdot 10^{-7}\right) \land c \leq 3.8 \cdot 10^{+19}\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.6e+56)
         (not (or (<= c 5.2e-80) (and (not (<= c 7.8e-7)) (<= c 3.8e+19)))))
   (* (* c (* i (+ a (* b c)))) -2.0)
   (* 2.0 (+ (* y x) (* 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 <= -8.6e+56) || !((c <= 5.2e-80) || (!(c <= 7.8e-7) && (c <= 3.8e+19)))) {
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	} else {
		tmp = 2.0 * ((y * x) + (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 <= (-8.6d+56)) .or. (.not. (c <= 5.2d-80) .or. (.not. (c <= 7.8d-7)) .and. (c <= 3.8d+19))) then
        tmp = (c * (i * (a + (b * c)))) * (-2.0d0)
    else
        tmp = 2.0d0 * ((y * x) + (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 <= -8.6e+56) || !((c <= 5.2e-80) || (!(c <= 7.8e-7) && (c <= 3.8e+19)))) {
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.6e+56) or not ((c <= 5.2e-80) or (not (c <= 7.8e-7) and (c <= 3.8e+19))):
		tmp = (c * (i * (a + (b * c)))) * -2.0
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.6e+56) || !((c <= 5.2e-80) || (!(c <= 7.8e-7) && (c <= 3.8e+19))))
		tmp = Float64(Float64(c * Float64(i * Float64(a + Float64(b * c)))) * -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + 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 <= -8.6e+56) || ~(((c <= 5.2e-80) || (~((c <= 7.8e-7)) && (c <= 3.8e+19)))))
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.6e+56], N[Not[Or[LessEqual[c, 5.2e-80], And[N[Not[LessEqual[c, 7.8e-7]], $MachinePrecision], LessEqual[c, 3.8e+19]]]], $MachinePrecision]], N[(N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.6000000000000007e56 or 5.2000000000000002e-80 < c < 7.80000000000000049e-7 or 3.8e19 < c

   1. Initial program 78.8%

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

   3. Taylor expanded in i around inf 79.5%

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

   4. Taylor expanded in i around 0 79.5%

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

   if -8.6000000000000007e56 < c < 5.2000000000000002e-80 or 7.80000000000000049e-7 < c < 3.8e19

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 77.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+56} \lor \neg \left(c \leq 5.2 \cdot 10^{-80} \lor \neg \left(c \leq 7.8 \cdot 10^{-7}\right) \land c \leq 3.8 \cdot 10^{+19}\right):\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* i (+ a (* b c))))))))
   (if (<= c -3.5e-48)
     t_1
     (if (<= c 2.9e-87)
       (* 2.0 (+ (* y x) (* z t)))
       (if (<= c 9.2e+18) (* 2.0 (- (* y x) (* i (* c a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	double tmp;
	if (c <= -3.5e-48) {
		tmp = t_1;
	} else if (c <= 2.9e-87) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 9.2e+18) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (i * (a + (b * c)))))
    if (c <= (-3.5d-48)) then
        tmp = t_1
    else if (c <= 2.9d-87) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if (c <= 9.2d+18) then
        tmp = 2.0d0 * ((y * x) - (i * (c * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	double tmp;
	if (c <= -3.5e-48) {
		tmp = t_1;
	} else if (c <= 2.9e-87) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 9.2e+18) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (i * (a + (b * c)))))
	tmp = 0
	if c <= -3.5e-48:
		tmp = t_1
	elif c <= 2.9e-87:
		tmp = 2.0 * ((y * x) + (z * t))
	elif c <= 9.2e+18:
		tmp = 2.0 * ((y * x) - (i * (c * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(b * c))))))
	tmp = 0.0
	if (c <= -3.5e-48)
		tmp = t_1;
	elseif (c <= 2.9e-87)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif (c <= 9.2e+18)
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(i * Float64(c * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	tmp = 0.0;
	if (c <= -3.5e-48)
		tmp = t_1;
	elseif (c <= 2.9e-87)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif (c <= 9.2e+18)
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	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[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e-48], t$95$1, If[LessEqual[c, 2.9e-87], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+18], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.49999999999999991e-48 or 9.2e18 < c

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0 86.5%

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

   if -3.49999999999999991e-48 < c < 2.8999999999999999e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0 79.5%

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

   if 2.8999999999999999e-87 < c < 9.2e18

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*l* 80.2%

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

      4. *-commutative 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+18}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (+ a (* b c))))) (t_2 (* 2.0 (- (* z t) t_1))))
   (if (<= c -3.8e-48)
     t_2
     (if (<= c 5e-82)
       (* 2.0 (+ (* y x) (* z t)))
       (if (<= c 2.3e+128) (* 2.0 (- (* y x) 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 = c * (i * (a + (b * c)));
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -3.8e-48) {
		tmp = t_2;
	} else if (c <= 5e-82) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 2.3e+128) {
		tmp = 2.0 * ((y * x) - 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 = c * (i * (a + (b * c)))
    t_2 = 2.0d0 * ((z * t) - t_1)
    if (c <= (-3.8d-48)) then
        tmp = t_2
    else if (c <= 5d-82) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if (c <= 2.3d+128) then
        tmp = 2.0d0 * ((y * x) - 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 = c * (i * (a + (b * c)));
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -3.8e-48) {
		tmp = t_2;
	} else if (c <= 5e-82) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 2.3e+128) {
		tmp = 2.0 * ((y * x) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * (a + (b * c)))
	t_2 = 2.0 * ((z * t) - t_1)
	tmp = 0
	if c <= -3.8e-48:
		tmp = t_2
	elif c <= 5e-82:
		tmp = 2.0 * ((y * x) + (z * t))
	elif c <= 2.3e+128:
		tmp = 2.0 * ((y * x) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(a + Float64(b * c))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	tmp = 0.0
	if (c <= -3.8e-48)
		tmp = t_2;
	elseif (c <= 5e-82)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif (c <= 2.3e+128)
		tmp = Float64(2.0 * Float64(Float64(y * x) - 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 = c * (i * (a + (b * c)));
	t_2 = 2.0 * ((z * t) - t_1);
	tmp = 0.0;
	if (c <= -3.8e-48)
		tmp = t_2;
	elseif (c <= 5e-82)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif (c <= 2.3e+128)
		tmp = 2.0 * ((y * x) - 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[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e-48], t$95$2, If[LessEqual[c, 5e-82], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e+128], N[(2.0 * N[(N[(y * x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.80000000000000002e-48 or 2.29999999999999998e128 < c

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 87.9%

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

   if -3.80000000000000002e-48 < c < 4.9999999999999998e-82

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0 79.5%

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

   if 4.9999999999999998e-82 < c < 2.29999999999999998e128

   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. Add Preprocessing

   3. Taylor expanded in z around 0 86.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-48}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-84}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (* i (+ a (* b c)))) -2.0)))
   (if (<= c -1.95e+57)
     t_1
     (if (<= c 4.1e-84)
       (* 2.0 (+ (* y x) (* z t)))
       (if (<= c 8.5e+19) (* 2.0 (- (* y x) (* i (* c a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (i * (a + (b * c)))) * -2.0;
	double tmp;
	if (c <= -1.95e+57) {
		tmp = t_1;
	} else if (c <= 4.1e-84) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 8.5e+19) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} 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 = (c * (i * (a + (b * c)))) * (-2.0d0)
    if (c <= (-1.95d+57)) then
        tmp = t_1
    else if (c <= 4.1d-84) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if (c <= 8.5d+19) then
        tmp = 2.0d0 * ((y * x) - (i * (c * a)))
    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 = (c * (i * (a + (b * c)))) * -2.0;
	double tmp;
	if (c <= -1.95e+57) {
		tmp = t_1;
	} else if (c <= 4.1e-84) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 8.5e+19) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (i * (a + (b * c)))) * -2.0
	tmp = 0
	if c <= -1.95e+57:
		tmp = t_1
	elif c <= 4.1e-84:
		tmp = 2.0 * ((y * x) + (z * t))
	elif c <= 8.5e+19:
		tmp = 2.0 * ((y * x) - (i * (c * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(i * Float64(a + Float64(b * c)))) * -2.0)
	tmp = 0.0
	if (c <= -1.95e+57)
		tmp = t_1;
	elseif (c <= 4.1e-84)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif (c <= 8.5e+19)
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(i * Float64(c * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (i * (a + (b * c)))) * -2.0;
	tmp = 0.0;
	if (c <= -1.95e+57)
		tmp = t_1;
	elseif (c <= 4.1e-84)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif (c <= 8.5e+19)
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -1.95e+57], t$95$1, If[LessEqual[c, 4.1e-84], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+19], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.94999999999999984e57 or 8.5e19 < c

   1. Initial program 76.7%

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

   3. Taylor expanded in i around inf 80.7%

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

   4. Taylor expanded in i around 0 80.7%

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

   if -1.94999999999999984e57 < c < 4.10000000000000005e-84

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 76.8%

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

   if 4.10000000000000005e-84 < c < 8.5e19

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*l* 80.2%

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

      4. *-commutative 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-84}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -3.8e+42)
   (* 2.0 (- (* z t) (* c (* b (* c i)))))
   (if (<= c 5.4e-80)
     (* 2.0 (+ (* y x) (* z t)))
     (if (<= c 3.2e+19)
       (* 2.0 (- (* y x) (* i (* c a))))
       (* (* c (* i (+ a (* b c)))) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.8e+42) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 5.4e-80) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 3.2e+19) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else {
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-3.8d+42)) then
        tmp = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    else if (c <= 5.4d-80) then
        tmp = 2.0d0 * ((y * x) + (z * t))
    else if (c <= 3.2d+19) then
        tmp = 2.0d0 * ((y * x) - (i * (c * a)))
    else
        tmp = (c * (i * (a + (b * c)))) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.8e+42) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 5.4e-80) {
		tmp = 2.0 * ((y * x) + (z * t));
	} else if (c <= 3.2e+19) {
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	} else {
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -3.8e+42:
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))))
	elif c <= 5.4e-80:
		tmp = 2.0 * ((y * x) + (z * t))
	elif c <= 3.2e+19:
		tmp = 2.0 * ((y * x) - (i * (c * a)))
	else:
		tmp = (c * (i * (a + (b * c)))) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -3.8e+42)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 5.4e-80)
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	elseif (c <= 3.2e+19)
		tmp = Float64(2.0 * Float64(Float64(y * x) - Float64(i * Float64(c * a))));
	else
		tmp = Float64(Float64(c * Float64(i * Float64(a + Float64(b * c)))) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -3.8e+42)
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	elseif (c <= 5.4e-80)
		tmp = 2.0 * ((y * x) + (z * t));
	elseif (c <= 3.2e+19)
		tmp = 2.0 * ((y * x) - (i * (c * a)));
	else
		tmp = (c * (i * (a + (b * c)))) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -3.8e+42], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-80], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+19], N[(2.0 * N[(N[(y * x), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.7999999999999998e42

   1. Initial program 76.2%

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

   3. Taylor expanded in x around 0 86.5%

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

   4. Taylor expanded in a around 0 79.3%

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

   if -3.7999999999999998e42 < c < 5.4000000000000004e-80

   1. Initial program 99.0%

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

   3. Taylor expanded in c around 0 77.6%

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

   if 5.4000000000000004e-80 < c < 3.2e19

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in z around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*l* 80.2%

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

      4. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   if 3.2e19 < c

   1. Initial program 78.6%

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

   3. Taylor expanded in i around inf 82.9%

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

   4. Taylor expanded in i around 0 82.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-80}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(y \cdot x - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+42} \lor \neg \left(c \leq 9 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e+42) (not (<= c 9e+19)))
   (* 2.0 (- (* z t) (* c (* i (+ a (* b c))))))
   (* 2.0 (- (+ (* y x) (* 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 <= -1.65e+42) || !(c <= 9e+19)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * (((y * x) + (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 <= (-1.65d+42)) .or. (.not. (c <= 9d+19))) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (b * c)))))
    else
        tmp = 2.0d0 * (((y * x) + (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 <= -1.65e+42) || !(c <= 9e+19)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.65e+42) or not (c <= 9e+19):
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))))
	else:
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.65e+42) || !(c <= 9e+19))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(b * c))))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(y * x) + 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 <= -1.65e+42) || ~((c <= 9e+19)))
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	else
		tmp = 2.0 * (((y * x) + (z * t)) - (i * (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.65e+42], N[Not[LessEqual[c, 9e+19]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(y * x), $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 < -1.6499999999999999e42 or 9e19 < c

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 88.7%

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

   if -1.6499999999999999e42 < c < 9e19

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 93.2%

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

      1. *-commutative 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+42} \lor \neg \left(c \leq 9 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(y \cdot x + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-45}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -7.8e+130)
     t_1
     (if (<= z -1.22e-45)
       (* -2.0 (* a (* c i)))
       (if (<= z 1.06e-175) (* 2.0 (* y x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -7.8e+130) {
		tmp = t_1;
	} else if (z <= -1.22e-45) {
		tmp = -2.0 * (a * (c * i));
	} else if (z <= 1.06e-175) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (z <= (-7.8d+130)) then
        tmp = t_1
    else if (z <= (-1.22d-45)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (z <= 1.06d-175) then
        tmp = 2.0d0 * (y * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (z <= -7.8e+130) {
		tmp = t_1;
	} else if (z <= -1.22e-45) {
		tmp = -2.0 * (a * (c * i));
	} else if (z <= 1.06e-175) {
		tmp = 2.0 * (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -7.8e+130:
		tmp = t_1
	elif z <= -1.22e-45:
		tmp = -2.0 * (a * (c * i))
	elif z <= 1.06e-175:
		tmp = 2.0 * (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -7.8e+130)
		tmp = t_1;
	elseif (z <= -1.22e-45)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (z <= 1.06e-175)
		tmp = Float64(2.0 * Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -7.8e+130)
		tmp = t_1;
	elseif (z <= -1.22e-45)
		tmp = -2.0 * (a * (c * i));
	elseif (z <= 1.06e-175)
		tmp = 2.0 * (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+130], t$95$1, If[LessEqual[z, -1.22e-45], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-175], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000004e130 or 1.06000000000000002e-175 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 41.6%

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

   if -7.8000000000000004e130 < z < -1.22000000000000007e-45

   1. Initial program 85.9%

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

      1. fma-define 86.0%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

      1. fma-define 96.3%

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

      2. +-commutative 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in a around inf 29.3%

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

      1. mul-1-neg 29.3%

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

      2. *-commutative 29.3%

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

      3. associate-*r* 25.8%

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

      4. distribute-rgt-neg-in 25.8%

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

      5. distribute-rgt-neg-in 25.8%

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

   9. Simplified 25.8%

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

   10. Taylor expanded in c around 0 29.3%

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

   if -1.22000000000000007e-45 < z < 1.06000000000000002e-175

   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. Add Preprocessing

   3. Taylor expanded in x around inf 28.8%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+130}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-45}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+107} \lor \neg \left(z \leq 1.06 \cdot 10^{-175}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -1.2e+107) (not (<= z 1.06e-175)))
   (* 2.0 (* z t))
   (* 2.0 (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -1.2e+107) || !(z <= 1.06e-175)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-1.2d+107)) .or. (.not. (z <= 1.06d-175))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -1.2e+107) || !(z <= 1.06e-175)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -1.2e+107) or not (z <= 1.06e-175):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (y * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -1.2e+107) || !(z <= 1.06e-175))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -1.2e+107) || ~((z <= 1.06e-175)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -1.2e+107], N[Not[LessEqual[z, 1.06e-175]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e107 or 1.06000000000000002e-175 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf 42.0%

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

   if -1.2e107 < z < 1.06000000000000002e-175

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 26.2%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+107} \lor \neg \left(z \leq 1.06 \cdot 10^{-175}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+205}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -2.4e+205) (* -2.0 (* a (* c i))) (* 2.0 (+ (* y x) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -2.4e+205) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((y * x) + (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 (i <= (-2.4d+205)) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = 2.0d0 * ((y * x) + (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 (i <= -2.4e+205) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((y * x) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -2.4e+205:
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = 2.0 * ((y * x) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -2.4e+205)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(y * x) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -2.4e+205)
		tmp = -2.0 * (a * (c * i));
	else
		tmp = 2.0 * ((y * x) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -2.4e+205], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.39999999999999986e205

   1. Initial program 95.1%

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

      1. fma-define 95.1%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

      1. fma-define 95.3%

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

      2. +-commutative 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in a around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. *-commutative 71.4%

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

      3. associate-*r* 43.3%

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

      4. distribute-rgt-neg-in 43.3%

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

      5. distribute-rgt-neg-in 43.3%

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

   9. Simplified 43.3%

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

   10. Taylor expanded in c around 0 71.4%

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

   if -2.39999999999999986e205 < i

   1. Initial program 88.5%

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

   3. Taylor expanded in c around 0 55.3%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+205}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

3. Taylor expanded in z around inf 29.2%

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

4. Final simplification 29.2%

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

Developer target: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(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))))