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

Percentage Accurate: 90.1% → 96.7%

Time: 15.6s

Alternatives: 15

Speedup: 0.5×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (fma t z (* (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) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * fma(t, z, (fma(b, c, a) * (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(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * fma(t, z, Float64(fma(b, c, a) * Float64(c * Float64(-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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * z + N[(N[(b * c + a), $MachinePrecision] * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.8%

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

      1. associate--l+ 96.8%

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

      2. *-commutative 96.8%

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

      3. associate--l+ 96.8%

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

      4. associate--l+ 96.8%

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

      5. *-commutative 96.8%

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

      6. associate--l+ 96.8%

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

      7. fma-def 96.8%

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

      8. 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-def 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. Step-by-step derivation

      1. associate--l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate--l+ 0.0%

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

      4. associate--l+ 0.0%

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

      5. *-commutative 0.0%

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

      6. associate--l+ 0.0%

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

      7. fma-def 8.3%

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

      8. associate-*l* 25.0%

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

   3. Simplified 25.0%

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

      1. fma-def 16.7%

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

      2. +-commutative 16.7%

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

   6. Applied egg-rr 16.7%

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

   7. Taylor expanded in x around 0 50.0%

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

      1. associate-*r* 50.0%

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

      2. +-commutative 50.0%

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

      3. fma-udef 50.0%

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

      4. *-commutative 50.0%

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

      5. fma-neg 83.4%

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

      6. distribute-rgt-neg-in 83.4%

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

      7. distribute-rgt-neg-in 83.4%

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

   9. Simplified 83.4%

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

4. Final simplification 98.0%

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

Alternative 2: 96.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (fma 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 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * fma(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(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * fma(z, t, Float64(c * Float64(b * Float64(c * Float64(-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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t + 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 96.8%

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

      1. associate--l+ 96.8%

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

      2. *-commutative 96.8%

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

      3. associate--l+ 96.8%

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

      4. associate--l+ 96.8%

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

      5. *-commutative 96.8%

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

      6. associate--l+ 96.8%

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

      7. fma-def 96.8%

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

      8. 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-def 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 50.0%

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

      1. cancel-sign-sub-inv 50.0%

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

      2. *-commutative 50.0%

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

      3. fma-def 83.4%

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

      4. +-commutative 83.4%

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

      5. fma-def 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in b around inf 75.1%

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

4. Final simplification 97.6%

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

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ t_3 := c \cdot \left(t_1 \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_3\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)) (t_3 (* c (* t_1 i))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* x y) t_3))
     (if (<= t_2 5e+306)
       (* (- (+ (* x y) (* z t)) t_2) 2.0)
       (* 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 = (c * t_1) * i;
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 5e+306) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} 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 = (c * t_1) * i;
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 5e+306) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} 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 = (c * t_1) * i
	t_3 = c * (t_1 * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) - t_3)
	elif t_2 <= 5e+306:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	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(Float64(c * t_1) * i)
	t_3 = Float64(c * Float64(t_1 * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_3));
	elseif (t_2 <= 5e+306)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	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 = (c * t_1) * i;
	t_3 = c * (t_1 * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) - t_3);
	elseif (t_2 <= 5e+306)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	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[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $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 82.0%

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

   3. Taylor expanded in z around 0 94.6%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.99999999999999993e306

   1. Initial program 99.2%

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

   if 4.99999999999999993e306 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 93.8%

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

4. Final simplification 97.4%

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

Alternative 4: 96.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.8%

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

      1. associate--l+ 96.8%

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

      2. *-commutative 96.8%

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

      3. associate--l+ 96.8%

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

      4. associate--l+ 96.8%

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

      5. *-commutative 96.8%

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

      6. associate--l+ 96.8%

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

      7. fma-def 96.8%

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

      8. 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-def 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 i around inf 67.0%

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

4. Final simplification 97.3%

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

Alternative 5: 42.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -5000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-313}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-93}:\\ \;\;\;\;\left(c \cdot \left(a \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* a -2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -1e+61)
     t_3
     (if (<= (* x y) -5000000000000.0)
       t_1
       (if (<= (* x y) 2e-313)
         t_2
         (if (<= (* x y) 5e-93)
           (* (* c (* a i)) -2.0)
           (if (<= (* x y) 4e-7) t_2 (if (<= (* x y) 4e+77) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+61) {
		tmp = t_3;
	} else if ((x * y) <= -5000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-313) {
		tmp = t_2;
	} else if ((x * y) <= 5e-93) {
		tmp = (c * (a * i)) * -2.0;
	} else if ((x * y) <= 4e-7) {
		tmp = t_2;
	} else if ((x * y) <= 4e+77) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * i) * (a * (-2.0d0))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-1d+61)) then
        tmp = t_3
    else if ((x * y) <= (-5000000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 2d-313) then
        tmp = t_2
    else if ((x * y) <= 5d-93) then
        tmp = (c * (a * i)) * (-2.0d0)
    else if ((x * y) <= 4d-7) then
        tmp = t_2
    else if ((x * y) <= 4d+77) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -1e+61) {
		tmp = t_3;
	} else if ((x * y) <= -5000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e-313) {
		tmp = t_2;
	} else if ((x * y) <= 5e-93) {
		tmp = (c * (a * i)) * -2.0;
	} else if ((x * y) <= 4e-7) {
		tmp = t_2;
	} else if ((x * y) <= 4e+77) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (a * -2.0)
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -1e+61:
		tmp = t_3
	elif (x * y) <= -5000000000000.0:
		tmp = t_1
	elif (x * y) <= 2e-313:
		tmp = t_2
	elif (x * y) <= 5e-93:
		tmp = (c * (a * i)) * -2.0
	elif (x * y) <= 4e-7:
		tmp = t_2
	elif (x * y) <= 4e+77:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -1e+61)
		tmp = t_3;
	elseif (Float64(x * y) <= -5000000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-313)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-93)
		tmp = Float64(Float64(c * Float64(a * i)) * -2.0);
	elseif (Float64(x * y) <= 4e-7)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e+77)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (a * -2.0);
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -1e+61)
		tmp = t_3;
	elseif ((x * y) <= -5000000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 2e-313)
		tmp = t_2;
	elseif ((x * y) <= 5e-93)
		tmp = (c * (a * i)) * -2.0;
	elseif ((x * y) <= 4e-7)
		tmp = t_2;
	elseif ((x * y) <= 4e+77)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+61], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5000000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-313], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-93], N[(N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-7], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e+77], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999949e60 or 3.99999999999999993e77 < (*.f64 x y)

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 63.7%

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

   if -9.99999999999999949e60 < (*.f64 x y) < -5e12 or 3.9999999999999998e-7 < (*.f64 x y) < 3.99999999999999993e77

   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 a around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. *-commutative 51.8%

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

      3. distribute-rgt-neg-in 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in c around 0 51.8%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   if -5e12 < (*.f64 x y) < 1.99999999998e-313 or 4.99999999999999994e-93 < (*.f64 x y) < 3.9999999999999998e-7

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 48.9%

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

   if 1.99999999998e-313 < (*.f64 x y) < 4.99999999999999994e-93

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 37.5%

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

      1. mul-1-neg 37.5%

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

      2. *-commutative 37.5%

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

      3. distribute-rgt-neg-in 37.5%

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

   5. Simplified 37.5%

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

   6. Taylor expanded in c around 0 37.5%

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

      1. *-commutative 37.5%

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

      2. associate-*r* 45.5%

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

   8. Simplified 45.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+61}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -5000000000000:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-313}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-93}:\\ \;\;\;\;\left(c \cdot \left(a \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(c \cdot \left(a \cdot i\right)\right) \cdot -2\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-313}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* (* c (* a i)) -2.0))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -2e+32)
     t_3
     (if (<= (* x y) 2e-313)
       t_1
       (if (<= (* x y) 5e-93)
         t_2
         (if (<= (* x y) 4e-7) t_1 (if (<= (* x y) 4e+77) t_2 t_3)))))))

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 t_2 = (c * (a * i)) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+32) {
		tmp = t_3;
	} else if ((x * y) <= 2e-313) {
		tmp = t_1;
	} else if ((x * y) <= 5e-93) {
		tmp = t_2;
	} else if ((x * y) <= 4e-7) {
		tmp = t_1;
	} else if ((x * y) <= 4e+77) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (c * (a * i)) * (-2.0d0)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-2d+32)) then
        tmp = t_3
    else if ((x * y) <= 2d-313) then
        tmp = t_1
    else if ((x * y) <= 5d-93) then
        tmp = t_2
    else if ((x * y) <= 4d-7) then
        tmp = t_1
    else if ((x * y) <= 4d+77) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (c * (a * i)) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+32) {
		tmp = t_3;
	} else if ((x * y) <= 2e-313) {
		tmp = t_1;
	} else if ((x * y) <= 5e-93) {
		tmp = t_2;
	} else if ((x * y) <= 4e-7) {
		tmp = t_1;
	} else if ((x * y) <= 4e+77) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (c * (a * i)) * -2.0
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2e+32:
		tmp = t_3
	elif (x * y) <= 2e-313:
		tmp = t_1
	elif (x * y) <= 5e-93:
		tmp = t_2
	elif (x * y) <= 4e-7:
		tmp = t_1
	elif (x * y) <= 4e+77:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(c * Float64(a * i)) * -2.0)
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2e+32)
		tmp = t_3;
	elseif (Float64(x * y) <= 2e-313)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-93)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e-7)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+77)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (c * (a * i)) * -2.0;
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2e+32)
		tmp = t_3;
	elseif ((x * y) <= 2e-313)
		tmp = t_1;
	elseif ((x * y) <= 5e-93)
		tmp = t_2;
	elseif ((x * y) <= 4e-7)
		tmp = t_1;
	elseif ((x * y) <= 4e+77)
		tmp = t_2;
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+32], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 2e-313], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-93], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e-7], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+77], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000011e32 or 3.99999999999999993e77 < (*.f64 x y)

   1. Initial program 88.1%

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

   3. Taylor expanded in x around inf 60.4%

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

   if -2.00000000000000011e32 < (*.f64 x y) < 1.99999999998e-313 or 4.99999999999999994e-93 < (*.f64 x y) < 3.9999999999999998e-7

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 47.8%

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

   if 1.99999999998e-313 < (*.f64 x y) < 4.99999999999999994e-93 or 3.9999999999999998e-7 < (*.f64 x y) < 3.99999999999999993e77

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. *-commutative 42.5%

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

      3. distribute-rgt-neg-in 42.5%

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

   5. Simplified 42.5%

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

   6. Taylor expanded in c around 0 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-*r* 42.5%

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

   8. Simplified 42.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-313}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-93}:\\ \;\;\;\;\left(c \cdot \left(a \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;\left(c \cdot \left(a \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+91)
   (* 2.0 (- (* x y) (* c (* a i))))
   (if (<= (* x y) 1e+80)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* (+ (* x y) (* z t)) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+91) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if ((x * y) <= 1e+80) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-2d+91)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if ((x * y) <= 1d+80) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -2e+91) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if ((x * y) <= 1e+80) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+91:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif (x * y) <= 1e+80:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+91)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (Float64(x * y) <= 1e+80)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+91)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif ((x * y) <= 1e+80)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+91], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+80], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000016e91

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 88.3%

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

      1. *-commutative 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around 0 90.4%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

   8. Simplified 77.1%

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

   if -2.00000000000000016e91 < (*.f64 x y) < 1e80

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 85.2%

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

   if 1e80 < (*.f64 x y)

   1. Initial program 80.7%

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

   3. Taylor expanded in c around 0 73.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -5000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -5000000000000.0)
     (* 2.0 (- (* x y) t_1))
     (if (<= (* x y) 1e+80)
       (* 2.0 (- (* z t) t_1))
       (* (+ (* x y) (* z t)) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -5000000000000.0) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 1e+80) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if ((x * y) <= (-5000000000000.0d0)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((x * y) <= 1d+80) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -5000000000000.0) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 1e+80) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if (x * y) <= -5000000000000.0:
		tmp = 2.0 * ((x * y) - t_1)
	elif (x * y) <= 1e+80:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (Float64(x * y) <= -5000000000000.0)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (Float64(x * y) <= 1e+80)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if ((x * y) <= -5000000000000.0)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((x * y) <= 1e+80)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5000000000000.0], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+80], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e12

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 84.1%

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

   if -5e12 < (*.f64 x y) < 1e80

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 87.5%

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

   if 1e80 < (*.f64 x y)

   1. Initial program 80.7%

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

   3. Taylor expanded in c around 0 73.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+80}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(-c\right) \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.18 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-127}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (- c) (* (+ a (* b c)) i)))))
   (if (<= c -1.18e+97)
     t_1
     (if (<= c -1.25e-86)
       (* 2.0 (- (* x y) (* c (* a i))))
       (if (<= c -2.6e-127)
         (* 2.0 (- (* z t) (* i (* a c))))
         (if (<= c 3.7e+25) (* (+ (* x y) (* z t)) 2.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (-c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.18e+97) {
		tmp = t_1;
	} else if (c <= -1.25e-86) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= -2.6e-127) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 3.7e+25) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (-c * ((a + (b * c)) * i))
    if (c <= (-1.18d+97)) then
        tmp = t_1
    else if (c <= (-1.25d-86)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if (c <= (-2.6d-127)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= 3.7d+25) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (-c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.18e+97) {
		tmp = t_1;
	} else if (c <= -1.25e-86) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (c <= -2.6e-127) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 3.7e+25) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (-c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.18e+97:
		tmp = t_1
	elif c <= -1.25e-86:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif c <= -2.6e-127:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= 3.7e+25:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(-c) * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.18e+97)
		tmp = t_1;
	elseif (c <= -1.25e-86)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (c <= -2.6e-127)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= 3.7e+25)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (-c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.18e+97)
		tmp = t_1;
	elseif (c <= -1.25e-86)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif (c <= -2.6e-127)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= 3.7e+25)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[((-c) * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.18e+97], t$95$1, If[LessEqual[c, -1.25e-86], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-127], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+25], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.18000000000000006e97 or 3.6999999999999999e25 < c

   1. Initial program 83.2%

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

   3. Taylor expanded in i around inf 81.2%

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

   if -1.18000000000000006e97 < c < -1.25e-86

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 85.3%

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

      1. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in z around 0 71.3%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*r* 68.8%

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

      4. *-commutative 68.8%

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

   8. Simplified 68.8%

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

   if -1.25e-86 < c < -2.59999999999999991e-127

   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 93.3%

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

      1. *-commutative 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in x around 0 87.3%

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

      1. associate-*r* 87.1%

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

      2. *-commutative 87.1%

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

      3. *-commutative 87.1%

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

   8. Simplified 87.1%

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

   if -2.59999999999999991e-127 < c < 3.6999999999999999e25

   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 83.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.18 \cdot 10^{+97}:\\ \;\;\;\;2 \cdot \left(\left(-c\right) \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-127}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(-c\right) \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1e+43) (not (<= (* x y) 4e+77)))
   (* (+ (* x y) (* z t)) 2.0)
   (* 2.0 (- (* z t) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e+43) || !((x * y) <= 4e+77)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1d+43)) .or. (.not. ((x * y) <= 4d+77))) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1e+43) || !((x * y) <= 4e+77)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1e+43) or not ((x * y) <= 4e+77):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+43) || !(Float64(x * y) <= 4e+77))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1e+43) || ~(((x * y) <= 4e+77)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+43], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+77]], $MachinePrecision]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000001e43 or 3.99999999999999993e77 < (*.f64 x y)

   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 c around 0 68.8%

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

   if -1.00000000000000001e43 < (*.f64 x y) < 3.99999999999999993e77

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in x around 0 64.6%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. *-commutative 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+77}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+100} \lor \neg \left(c \leq 1.06 \cdot 10^{+27}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.8e+100) (not (<= c 1.06e+27)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e+100) || !(c <= 1.06e+27)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.8d+100)) .or. (.not. (c <= 1.06d+27))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e+100) || !(c <= 1.06e+27)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.8e+100) or not (c <= 1.06e+27):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.8e+100) || !(c <= 1.06e+27))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.8e+100) || ~((c <= 1.06e+27)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.8e+100], N[Not[LessEqual[c, 1.06e+27]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8e100 or 1.05999999999999994e27 < c

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 89.1%

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

   if -1.8e100 < c < 1.05999999999999994e27

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 93.8%

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

      1. *-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+100} \lor \neg \left(c \leq 1.06 \cdot 10^{+27}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+14)
   (* 2.0 (- (* x y) (* c (* a i))))
   (if (<= (* x y) 4e+77)
     (* 2.0 (- (* z t) (* i (* a c))))
     (* (+ (* x y) (* z t)) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+14) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if ((x * y) <= 4e+77) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-5d+14)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if ((x * y) <= 4d+77) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -5e+14) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if ((x * y) <= 4e+77) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+14:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif (x * y) <= 4e+77:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+14)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (Float64(x * y) <= 4e+77)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -5e+14)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif ((x * y) <= 4e+77)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+14], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+77], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e14

   1. Initial program 94.7%

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

   3. Taylor expanded in a around inf 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in z around 0 82.8%

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

      1. associate-*r* 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r* 70.9%

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

      4. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -5e14 < (*.f64 x y) < 3.99999999999999993e77

   1. Initial program 94.8%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around 0 64.8%

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

      1. associate-*r* 63.5%

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

      2. *-commutative 63.5%

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

      3. *-commutative 63.5%

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

   8. Simplified 63.5%

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

   if 3.99999999999999993e77 < (*.f64 x y)

   1. Initial program 81.1%

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

   3. Taylor expanded in c around 0 72.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+77}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32} \lor \neg \left(x \cdot y \leq 50\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+32) (not (<= (* x y) 50.0)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+32) || !((x * y) <= 50.0)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+32)) .or. (.not. ((x * y) <= 50.0d0))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+32) || !((x * y) <= 50.0)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+32) or not ((x * y) <= 50.0):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+32) || !(Float64(x * y) <= 50.0))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+32) || ~(((x * y) <= 50.0)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+32], N[Not[LessEqual[N[(x * y), $MachinePrecision], 50.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000011e32 or 50 < (*.f64 x y)

   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 x around inf 53.5%

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

   if -2.00000000000000011e32 < (*.f64 x y) < 50

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 42.9%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32} \lor \neg \left(x \cdot y \leq 50\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+93} \lor \neg \left(i \leq 1.45 \cdot 10^{+74}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.8e+93) (not (<= i 1.45e+74)))
   (* (* c i) (* a -2.0))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.8e+93) || !(i <= 1.45e+74)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.8d+93)) .or. (.not. (i <= 1.45d+74))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.8e+93) || !(i <= 1.45e+74)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.8e+93) or not (i <= 1.45e+74):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.8e+93) || !(i <= 1.45e+74))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.8e+93) || ~((i <= 1.45e+74)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.8e+93], N[Not[LessEqual[i, 1.45e+74]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.8e93 or 1.4500000000000001e74 < i

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. *-commutative 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in c around 0 51.1%

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

      1. associate-*r* 51.1%

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

      2. *-commutative 51.1%

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

      3. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -1.8e93 < i < 1.4500000000000001e74

   1. Initial program 91.8%

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

   3. Taylor expanded in c around 0 67.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+93} \lor \neg \left(i \leq 1.45 \cdot 10^{+74}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.8% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.3%

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

3. Taylor expanded in z around inf 28.1%

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

4. Final simplification 28.1%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(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))))