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

Percentage Accurate: 89.7% → 96.3%

Time: 14.7s

Alternatives: 17

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.1× speedup

Math

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

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 y x (* (- c) (* i (* b c))))))))

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(y, x, (-c * (i * (b * c))));
	}
	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(y, x, Float64(Float64(-c) * Float64(i * Float64(b * c)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x + N[((-c) * N[(i * N[(b * c), $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 93.6%

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

      1. associate-*l* 99.5%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. fma-def 99.5%

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

      2. +-commutative 99.5%

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

   5. Applied egg-rr 99.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0 20.0%

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

      1. unpow2 20.0%

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

      2. associate-*r* 33.3%

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

   4. Simplified 33.3%

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

   5. Taylor expanded in z around 0 33.8%

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

      1. unpow2 33.8%

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

      2. *-commutative 33.8%

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

      3. associate-*r* 53.8%

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

      4. associate-*r* 47.2%

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

      5. *-commutative 47.2%

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

      6. *-commutative 47.2%

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

      7. *-commutative 47.2%

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

   7. Simplified 47.2%

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

      1. cancel-sign-sub-inv 47.2%

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

      2. fma-def 67.2%

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

   9. Applied egg-rr 67.2%

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

4. Final simplification 97.6%

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

Alternative 2: 95.6% accurate, 0.5× speedup

Math

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

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 (* b (* i (* c c)))))))

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 * (b * (i * (c * c)));
	}
	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 * (b * (i * (c * c)));
	}
	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 * (b * (i * (c * c)))
	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(b * Float64(i * Float64(c * c))));
	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 * (b * (i * (c * c)));
	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[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.6%

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

      1. associate-*l* 99.5%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. fma-def 99.5%

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

      2. +-commutative 99.5%

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

   5. Applied egg-rr 99.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in b around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. distribute-rgt-neg-in 47.2%

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

      3. unpow2 47.2%

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

   4. Simplified 47.2%

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

   5. Taylor expanded in c around 0 47.2%

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

      1. associate-*r* 66.8%

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

      2. unpow2 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 97.6%

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

Alternative 3: 46.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -9500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+211}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* c (* c (* b i)))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -9500.0)
     t_2
     (if (<= c -2.8e-147)
       t_1
       (if (<= c -5.6e-193)
         t_3
         (if (<= c -3.1e-261)
           t_1
           (if (<= c 1.4e-82)
             t_3
             (if (<= c 1.2e+20)
               t_1
               (if (<= c 9e+68)
                 t_3
                 (if (<= c 1.35e+211) (* 2.0 (* a (* c (- i)))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * (c * (b * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -9500.0) {
		tmp = t_2;
	} else if (c <= -2.8e-147) {
		tmp = t_1;
	} else if (c <= -5.6e-193) {
		tmp = t_3;
	} else if (c <= -3.1e-261) {
		tmp = t_1;
	} else if (c <= 1.4e-82) {
		tmp = t_3;
	} else if (c <= 1.2e+20) {
		tmp = t_1;
	} else if (c <= 9e+68) {
		tmp = t_3;
	} else if (c <= 1.35e+211) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (c * (c * (b * i)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-9500.0d0)) then
        tmp = t_2
    else if (c <= (-2.8d-147)) then
        tmp = t_1
    else if (c <= (-5.6d-193)) then
        tmp = t_3
    else if (c <= (-3.1d-261)) then
        tmp = t_1
    else if (c <= 1.4d-82) then
        tmp = t_3
    else if (c <= 1.2d+20) then
        tmp = t_1
    else if (c <= 9d+68) then
        tmp = t_3
    else if (c <= 1.35d+211) then
        tmp = 2.0d0 * (a * (c * -i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (c * (c * (b * i)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -9500.0) {
		tmp = t_2;
	} else if (c <= -2.8e-147) {
		tmp = t_1;
	} else if (c <= -5.6e-193) {
		tmp = t_3;
	} else if (c <= -3.1e-261) {
		tmp = t_1;
	} else if (c <= 1.4e-82) {
		tmp = t_3;
	} else if (c <= 1.2e+20) {
		tmp = t_1;
	} else if (c <= 9e+68) {
		tmp = t_3;
	} else if (c <= 1.35e+211) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (c * (c * (b * i)))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -9500.0:
		tmp = t_2
	elif c <= -2.8e-147:
		tmp = t_1
	elif c <= -5.6e-193:
		tmp = t_3
	elif c <= -3.1e-261:
		tmp = t_1
	elif c <= 1.4e-82:
		tmp = t_3
	elif c <= 1.2e+20:
		tmp = t_1
	elif c <= 9e+68:
		tmp = t_3
	elif c <= 1.35e+211:
		tmp = 2.0 * (a * (c * -i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -9500.0)
		tmp = t_2;
	elseif (c <= -2.8e-147)
		tmp = t_1;
	elseif (c <= -5.6e-193)
		tmp = t_3;
	elseif (c <= -3.1e-261)
		tmp = t_1;
	elseif (c <= 1.4e-82)
		tmp = t_3;
	elseif (c <= 1.2e+20)
		tmp = t_1;
	elseif (c <= 9e+68)
		tmp = t_3;
	elseif (c <= 1.35e+211)
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (c * (c * (b * i)));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -9500.0)
		tmp = t_2;
	elseif (c <= -2.8e-147)
		tmp = t_1;
	elseif (c <= -5.6e-193)
		tmp = t_3;
	elseif (c <= -3.1e-261)
		tmp = t_1;
	elseif (c <= 1.4e-82)
		tmp = t_3;
	elseif (c <= 1.2e+20)
		tmp = t_1;
	elseif (c <= 9e+68)
		tmp = t_3;
	elseif (c <= 1.35e+211)
		tmp = 2.0 * (a * (c * -i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9500.0], t$95$2, If[LessEqual[c, -2.8e-147], t$95$1, If[LessEqual[c, -5.6e-193], t$95$3, If[LessEqual[c, -3.1e-261], t$95$1, If[LessEqual[c, 1.4e-82], t$95$3, If[LessEqual[c, 1.2e+20], t$95$1, If[LessEqual[c, 9e+68], t$95$3, If[LessEqual[c, 1.35e+211], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9500 or 1.35e211 < c

   1. Initial program 72.0%

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

   2. Taylor expanded in b around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-rgt-neg-in 64.5%

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

      3. unpow2 64.5%

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

   4. Simplified 64.5%

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

   5. Taylor expanded in c around 0 64.5%

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

      1. unpow2 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 63.4%

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

      4. associate-*r* 66.1%

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

      5. *-commutative 66.1%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-*r* 63.4%

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

   7. Simplified 63.4%

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

   if -9500 < c < -2.8e-147 or -5.6000000000000005e-193 < c < -3.0999999999999998e-261 or 1.40000000000000012e-82 < c < 1.2e20

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -2.8e-147 < c < -5.6000000000000005e-193 or -3.0999999999999998e-261 < c < 1.40000000000000012e-82 or 1.2e20 < c < 9.0000000000000007e68

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 59.1%

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

   if 9.0000000000000007e68 < c < 1.35e211

   1. Initial program 79.3%

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

      1. associate-*l* 91.5%

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

      2. fma-def 91.5%

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

   3. Simplified 91.5%

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

      1. fma-def 91.5%

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

      2. +-commutative 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in a around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. associate-*r* 57.4%

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

      3. distribute-lft-neg-in 57.4%

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

      4. distribute-rgt-neg-in 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9500:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-193}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+211}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 4: 46.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -75000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* (* c c) (* b i))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -75000.0)
     t_2
     (if (<= c -9.2e-147)
       t_1
       (if (<= c -6e-194)
         t_3
         (if (<= c -4.5e-261)
           t_1
           (if (<= c 2.6e-87)
             t_3
             (if (<= c 8.5e+20)
               t_1
               (if (<= c 1.65e+69)
                 t_3
                 (if (<= c 1.46e+168) (* 2.0 (* a (* c (- i)))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * ((c * c) * (b * i));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -75000.0) {
		tmp = t_2;
	} else if (c <= -9.2e-147) {
		tmp = t_1;
	} else if (c <= -6e-194) {
		tmp = t_3;
	} else if (c <= -4.5e-261) {
		tmp = t_1;
	} else if (c <= 2.6e-87) {
		tmp = t_3;
	} else if (c <= 8.5e+20) {
		tmp = t_1;
	} else if (c <= 1.65e+69) {
		tmp = t_3;
	} else if (c <= 1.46e+168) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * ((c * c) * (b * i))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-75000.0d0)) then
        tmp = t_2
    else if (c <= (-9.2d-147)) then
        tmp = t_1
    else if (c <= (-6d-194)) then
        tmp = t_3
    else if (c <= (-4.5d-261)) then
        tmp = t_1
    else if (c <= 2.6d-87) then
        tmp = t_3
    else if (c <= 8.5d+20) then
        tmp = t_1
    else if (c <= 1.65d+69) then
        tmp = t_3
    else if (c <= 1.46d+168) then
        tmp = 2.0d0 * (a * (c * -i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * ((c * c) * (b * i));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -75000.0) {
		tmp = t_2;
	} else if (c <= -9.2e-147) {
		tmp = t_1;
	} else if (c <= -6e-194) {
		tmp = t_3;
	} else if (c <= -4.5e-261) {
		tmp = t_1;
	} else if (c <= 2.6e-87) {
		tmp = t_3;
	} else if (c <= 8.5e+20) {
		tmp = t_1;
	} else if (c <= 1.65e+69) {
		tmp = t_3;
	} else if (c <= 1.46e+168) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * ((c * c) * (b * i))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -75000.0:
		tmp = t_2
	elif c <= -9.2e-147:
		tmp = t_1
	elif c <= -6e-194:
		tmp = t_3
	elif c <= -4.5e-261:
		tmp = t_1
	elif c <= 2.6e-87:
		tmp = t_3
	elif c <= 8.5e+20:
		tmp = t_1
	elif c <= 1.65e+69:
		tmp = t_3
	elif c <= 1.46e+168:
		tmp = 2.0 * (a * (c * -i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -75000.0)
		tmp = t_2;
	elseif (c <= -9.2e-147)
		tmp = t_1;
	elseif (c <= -6e-194)
		tmp = t_3;
	elseif (c <= -4.5e-261)
		tmp = t_1;
	elseif (c <= 2.6e-87)
		tmp = t_3;
	elseif (c <= 8.5e+20)
		tmp = t_1;
	elseif (c <= 1.65e+69)
		tmp = t_3;
	elseif (c <= 1.46e+168)
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * ((c * c) * (b * i));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -75000.0)
		tmp = t_2;
	elseif (c <= -9.2e-147)
		tmp = t_1;
	elseif (c <= -6e-194)
		tmp = t_3;
	elseif (c <= -4.5e-261)
		tmp = t_1;
	elseif (c <= 2.6e-87)
		tmp = t_3;
	elseif (c <= 8.5e+20)
		tmp = t_1;
	elseif (c <= 1.65e+69)
		tmp = t_3;
	elseif (c <= 1.46e+168)
		tmp = 2.0 * (a * (c * -i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -75000.0], t$95$2, If[LessEqual[c, -9.2e-147], t$95$1, If[LessEqual[c, -6e-194], t$95$3, If[LessEqual[c, -4.5e-261], t$95$1, If[LessEqual[c, 2.6e-87], t$95$3, If[LessEqual[c, 8.5e+20], t$95$1, If[LessEqual[c, 1.65e+69], t$95$3, If[LessEqual[c, 1.46e+168], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -75000 or 1.45999999999999996e168 < c

   1. Initial program 73.2%

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

   2. Taylor expanded in b around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-rgt-neg-in 64.0%

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

      3. unpow2 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in c around 0 64.0%

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

      1. unpow2 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-*r* 60.9%

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

      4. associate-*r* 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-*r* 66.6%

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

      7. *-commutative 66.6%

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

      8. associate-*r* 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in c around 0 64.0%

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

      1. unpow2 64.0%

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

      2. *-commutative 64.0%

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

   10. Simplified 64.0%

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

   if -75000 < c < -9.19999999999999962e-147 or -6e-194 < c < -4.5000000000000001e-261 or 2.60000000000000002e-87 < c < 8.5e20

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -9.19999999999999962e-147 < c < -6e-194 or -4.5000000000000001e-261 < c < 2.60000000000000002e-87 or 8.5e20 < c < 1.6499999999999999e69

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 59.1%

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

   if 1.6499999999999999e69 < c < 1.45999999999999996e168

   1. Initial program 76.2%

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

      1. associate-*l* 87.7%

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

      2. fma-def 87.7%

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

   3. Simplified 87.7%

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

      1. fma-def 87.7%

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

      2. +-commutative 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. associate-*r* 57.4%

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

      3. distribute-lft-neg-in 57.4%

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

      4. distribute-rgt-neg-in 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -75000:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-194}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-87}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 47.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -90000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* b (* i (* c c)))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -90000.0)
     t_2
     (if (<= c -2.8e-147)
       t_1
       (if (<= c -1.25e-193)
         t_3
         (if (<= c -3.3e-261)
           t_1
           (if (<= c 4e-81)
             t_3
             (if (<= c 1.05e+20)
               t_1
               (if (<= c 1.8e+68)
                 t_3
                 (if (<= c 4.7e+167) (* 2.0 (* a (* c (- i)))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (b * (i * (c * c)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -90000.0) {
		tmp = t_2;
	} else if (c <= -2.8e-147) {
		tmp = t_1;
	} else if (c <= -1.25e-193) {
		tmp = t_3;
	} else if (c <= -3.3e-261) {
		tmp = t_1;
	} else if (c <= 4e-81) {
		tmp = t_3;
	} else if (c <= 1.05e+20) {
		tmp = t_1;
	} else if (c <= 1.8e+68) {
		tmp = t_3;
	} else if (c <= 4.7e+167) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (b * (i * (c * c)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-90000.0d0)) then
        tmp = t_2
    else if (c <= (-2.8d-147)) then
        tmp = t_1
    else if (c <= (-1.25d-193)) then
        tmp = t_3
    else if (c <= (-3.3d-261)) then
        tmp = t_1
    else if (c <= 4d-81) then
        tmp = t_3
    else if (c <= 1.05d+20) then
        tmp = t_1
    else if (c <= 1.8d+68) then
        tmp = t_3
    else if (c <= 4.7d+167) then
        tmp = 2.0d0 * (a * (c * -i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (b * (i * (c * c)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -90000.0) {
		tmp = t_2;
	} else if (c <= -2.8e-147) {
		tmp = t_1;
	} else if (c <= -1.25e-193) {
		tmp = t_3;
	} else if (c <= -3.3e-261) {
		tmp = t_1;
	} else if (c <= 4e-81) {
		tmp = t_3;
	} else if (c <= 1.05e+20) {
		tmp = t_1;
	} else if (c <= 1.8e+68) {
		tmp = t_3;
	} else if (c <= 4.7e+167) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (b * (i * (c * c)))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -90000.0:
		tmp = t_2
	elif c <= -2.8e-147:
		tmp = t_1
	elif c <= -1.25e-193:
		tmp = t_3
	elif c <= -3.3e-261:
		tmp = t_1
	elif c <= 4e-81:
		tmp = t_3
	elif c <= 1.05e+20:
		tmp = t_1
	elif c <= 1.8e+68:
		tmp = t_3
	elif c <= 4.7e+167:
		tmp = 2.0 * (a * (c * -i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -90000.0)
		tmp = t_2;
	elseif (c <= -2.8e-147)
		tmp = t_1;
	elseif (c <= -1.25e-193)
		tmp = t_3;
	elseif (c <= -3.3e-261)
		tmp = t_1;
	elseif (c <= 4e-81)
		tmp = t_3;
	elseif (c <= 1.05e+20)
		tmp = t_1;
	elseif (c <= 1.8e+68)
		tmp = t_3;
	elseif (c <= 4.7e+167)
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (b * (i * (c * c)));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -90000.0)
		tmp = t_2;
	elseif (c <= -2.8e-147)
		tmp = t_1;
	elseif (c <= -1.25e-193)
		tmp = t_3;
	elseif (c <= -3.3e-261)
		tmp = t_1;
	elseif (c <= 4e-81)
		tmp = t_3;
	elseif (c <= 1.05e+20)
		tmp = t_1;
	elseif (c <= 1.8e+68)
		tmp = t_3;
	elseif (c <= 4.7e+167)
		tmp = 2.0 * (a * (c * -i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -90000.0], t$95$2, If[LessEqual[c, -2.8e-147], t$95$1, If[LessEqual[c, -1.25e-193], t$95$3, If[LessEqual[c, -3.3e-261], t$95$1, If[LessEqual[c, 4e-81], t$95$3, If[LessEqual[c, 1.05e+20], t$95$1, If[LessEqual[c, 1.8e+68], t$95$3, If[LessEqual[c, 4.7e+167], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9e4 or 4.70000000000000013e167 < c

   1. Initial program 73.2%

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

   2. Taylor expanded in b around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-rgt-neg-in 64.0%

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

      3. unpow2 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in c around 0 64.0%

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

      1. associate-*r* 70.0%

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

      2. unpow2 70.0%

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

   7. Simplified 70.0%

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

   if -9e4 < c < -2.8e-147 or -1.2500000000000001e-193 < c < -3.2999999999999998e-261 or 3.9999999999999998e-81 < c < 1.05e20

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -2.8e-147 < c < -1.2500000000000001e-193 or -3.2999999999999998e-261 < c < 3.9999999999999998e-81 or 1.05e20 < c < 1.7999999999999999e68

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 59.1%

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

   if 1.7999999999999999e68 < c < 4.70000000000000013e167

   1. Initial program 76.2%

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

      1. associate-*l* 87.7%

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

      2. fma-def 87.7%

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

   3. Simplified 87.7%

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

      1. fma-def 87.7%

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

      2. +-commutative 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in a around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. associate-*r* 57.4%

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

      3. distribute-lft-neg-in 57.4%

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

      4. distribute-rgt-neg-in 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -90000:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-193}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-81}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 6: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t_1 \cdot i\right)\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_2\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+127}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot t_1\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))))
   (if (<= c -3.3e+21)
     (* 2.0 (- (* x y) t_2))
     (if (<= c 5.5e+127)
       (* (- (+ (* x y) (* z t)) (* (* c t_1) i)) 2.0)
       (* 2.0 (- (* z t) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double tmp;
	if (c <= -3.3e+21) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (c <= 5.5e+127) {
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = c * (t_1 * i)
    if (c <= (-3.3d+21)) then
        tmp = 2.0d0 * ((x * y) - t_2)
    else if (c <= 5.5d+127) then
        tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double tmp;
	if (c <= -3.3e+21) {
		tmp = 2.0 * ((x * y) - t_2);
	} else if (c <= 5.5e+127) {
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	tmp = 0
	if c <= -3.3e+21:
		tmp = 2.0 * ((x * y) - t_2)
	elif c <= 5.5e+127:
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	tmp = 0.0
	if (c <= -3.3e+21)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	elseif (c <= 5.5e+127)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	tmp = 0.0;
	if (c <= -3.3e+21)
		tmp = 2.0 * ((x * y) - t_2);
	elseif (c <= 5.5e+127)
		tmp = (((x * y) + (z * t)) - ((c * t_1) * i)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.3e+21], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e+127], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.3e21

   1. Initial program 71.3%

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

   2. Taylor expanded in z around 0 89.7%

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

   if -3.3e21 < c < 5.50000000000000041e127

   1. Initial program 97.5%

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

   if 5.50000000000000041e127 < c

   1. Initial program 72.7%

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

   2. Taylor expanded in x around 0 91.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+127}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= c -2e+22)
     (* 2.0 (* c (* t_1 (- i))))
     (if (<= c 7.2e-96)
       (* 2.0 (+ (* x y) (* z t)))
       (* 2.0 (- (* z t) (* 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 tmp;
	if (c <= -2e+22) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (c <= 7.2e-96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (b * c)
    if (c <= (-2d+22)) then
        tmp = 2.0d0 * (c * (t_1 * -i))
    else if (c <= 7.2d-96) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((z * t) - (c * (t_1 * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double tmp;
	if (c <= -2e+22) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (c <= 7.2e-96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	tmp = 0
	if c <= -2e+22:
		tmp = 2.0 * (c * (t_1 * -i))
	elif c <= 7.2e-96:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	tmp = 0.0
	if (c <= -2e+22)
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	elseif (c <= 7.2e-96)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - 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);
	tmp = 0.0;
	if (c <= -2e+22)
		tmp = 2.0 * (c * (t_1 * -i));
	elseif (c <= 7.2e-96)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((z * t) - (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]}, If[LessEqual[c, -2e+22], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.2e-96], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2e22

   1. Initial program 71.3%

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

   2. Taylor expanded in i around inf 79.7%

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

   if -2e22 < c < 7.20000000000000016e-96

   1. Initial program 98.2%

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

   2. Taylor expanded in c around 0 84.1%

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

   if 7.20000000000000016e-96 < c

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0 82.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -19000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -19000000000000.0)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 3.2e-96) (* 2.0 (+ (* x y) (* z t))) (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -19000000000000.0) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.2e-96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-19000000000000.0d0)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 3.2d-96) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -19000000000000.0) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.2e-96) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -19000000000000.0:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 3.2e-96:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -19000000000000.0)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 3.2e-96)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -19000000000000.0)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 3.2e-96)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -19000000000000.0], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-96], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.9e13

   1. Initial program 71.3%

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

   2. Taylor expanded in z around 0 89.7%

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

   if -1.9e13 < c < 3.20000000000000012e-96

   1. Initial program 98.2%

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

   2. Taylor expanded in c around 0 84.1%

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

   if 3.20000000000000012e-96 < c

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0 82.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -19000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -2.06 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+116}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -2.06e+71)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 1.45e+116)
       (* 2.0 (- (+ (* x y) (* z t)) (* c (* a i))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.06e+71) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.45e+116) {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-2.06d+71)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 1.45d+116) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (c * (a * i)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.06e+71) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.45e+116) {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -2.06e+71:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 1.45e+116:
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -2.06e+71)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 1.45e+116)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(c * Float64(a * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -2.06e+71)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 1.45e+116)
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.06e+71], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e+116], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.0599999999999999e71

   1. Initial program 68.0%

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

   2. Taylor expanded in z around 0 88.6%

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

   if -2.0599999999999999e71 < c < 1.4500000000000001e116

   1. Initial program 97.6%

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

      1. associate-*l* 98.2%

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

      2. fma-def 98.2%

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

   3. Simplified 98.2%

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

      1. fma-def 98.2%

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

      2. +-commutative 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in a around inf 86.8%

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

      1. *-commutative 86.8%

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

   8. Simplified 86.8%

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

   if 1.4500000000000001e116 < c

   1. Initial program 72.7%

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

   2. Taylor expanded in x around 0 91.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.06 \cdot 10^{+71}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+116}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-93}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* b (* i (* c c))))))
   (if (<= c -1.65e+65)
     t_1
     (if (<= c 8e-93)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 5.6e+207) (* 2.0 (- (* z t) (* c (* a i)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (b * (i * (c * c)));
	double tmp;
	if (c <= -1.65e+65) {
		tmp = t_1;
	} else if (c <= 8e-93) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.6e+207) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} 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) * (b * (i * (c * c)))
    if (c <= (-1.65d+65)) then
        tmp = t_1
    else if (c <= 8d-93) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 5.6d+207) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    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 * (b * (i * (c * c)));
	double tmp;
	if (c <= -1.65e+65) {
		tmp = t_1;
	} else if (c <= 8e-93) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.6e+207) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (b * (i * (c * c)))
	tmp = 0
	if c <= -1.65e+65:
		tmp = t_1
	elif c <= 8e-93:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 5.6e+207:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))))
	tmp = 0.0
	if (c <= -1.65e+65)
		tmp = t_1;
	elseif (c <= 8e-93)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 5.6e+207)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	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 * (b * (i * (c * c)));
	tmp = 0.0;
	if (c <= -1.65e+65)
		tmp = t_1;
	elseif (c <= 8e-93)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 5.6e+207)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	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[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+65], t$95$1, If[LessEqual[c, 8e-93], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e+207], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.65000000000000012e65 or 5.60000000000000022e207 < c

   1. Initial program 69.8%

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

   2. Taylor expanded in b around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-in 69.4%

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

      3. unpow2 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in c around 0 69.4%

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

      1. associate-*r* 76.5%

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

      2. unpow2 76.5%

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

   7. Simplified 76.5%

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

   if -1.65000000000000012e65 < c < 7.9999999999999992e-93

   1. Initial program 98.3%

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

   2. Taylor expanded in c around 0 81.8%

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

   if 7.9999999999999992e-93 < c < 5.60000000000000022e207

   1. Initial program 89.8%

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

      1. associate-*l* 94.7%

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

      2. fma-def 94.7%

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

   3. Simplified 94.7%

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

      1. fma-def 94.7%

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

      2. +-commutative 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in a around inf 76.7%

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

      1. *-commutative 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in x around 0 63.1%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-93}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 11: 74.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+21} \lor \neg \left(c \leq 1.05 \cdot 10^{+81}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.6e+21) (not (<= c 1.05e+81)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.6e+21) || !(c <= 1.05e+81)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.6d+21)) .or. (.not. (c <= 1.05d+81))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.6e+21) || !(c <= 1.05e+81)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.6e+21) or not (c <= 1.05e+81):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.6e+21) || !(c <= 1.05e+81))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.6e+21) || ~((c <= 1.05e+81)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.6e+21], N[Not[LessEqual[c, 1.05e+81]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6e21 or 1.0499999999999999e81 < c

   1. Initial program 72.8%

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

   2. Taylor expanded in i around inf 79.4%

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

   if -1.6e21 < c < 1.0499999999999999e81

   1. Initial program 98.0%

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

   2. Taylor expanded in c around 0 78.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+21} \lor \neg \left(c \leq 1.05 \cdot 10^{+81}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 12: 36.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-265}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= x -3.8e+115)
     t_2
     (if (<= x -1.42e-64)
       t_1
       (if (<= x -4.9e-265)
         (* 2.0 (* i (* a (- c))))
         (if (<= x 1.42e-126) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -3.8e+115) {
		tmp = t_2;
	} else if (x <= -1.42e-64) {
		tmp = t_1;
	} else if (x <= -4.9e-265) {
		tmp = 2.0 * (i * (a * -c));
	} else if (x <= 1.42e-126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (x <= (-3.8d+115)) then
        tmp = t_2
    else if (x <= (-1.42d-64)) then
        tmp = t_1
    else if (x <= (-4.9d-265)) then
        tmp = 2.0d0 * (i * (a * -c))
    else if (x <= 1.42d-126) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -3.8e+115) {
		tmp = t_2;
	} else if (x <= -1.42e-64) {
		tmp = t_1;
	} else if (x <= -4.9e-265) {
		tmp = 2.0 * (i * (a * -c));
	} else if (x <= 1.42e-126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if x <= -3.8e+115:
		tmp = t_2
	elif x <= -1.42e-64:
		tmp = t_1
	elif x <= -4.9e-265:
		tmp = 2.0 * (i * (a * -c))
	elif x <= 1.42e-126:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (x <= -3.8e+115)
		tmp = t_2;
	elseif (x <= -1.42e-64)
		tmp = t_1;
	elseif (x <= -4.9e-265)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	elseif (x <= 1.42e-126)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (x <= -3.8e+115)
		tmp = t_2;
	elseif (x <= -1.42e-64)
		tmp = t_1;
	elseif (x <= -4.9e-265)
		tmp = 2.0 * (i * (a * -c));
	elseif (x <= 1.42e-126)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+115], t$95$2, If[LessEqual[x, -1.42e-64], t$95$1, If[LessEqual[x, -4.9e-265], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.42e-126], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.8000000000000001e115 or 1.42e-126 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 46.6%

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

   if -3.8000000000000001e115 < x < -1.42000000000000006e-64 or -4.89999999999999999e-265 < x < 1.42e-126

   1. Initial program 87.0%

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

   2. Taylor expanded in z around inf 36.9%

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

   if -1.42000000000000006e-64 < x < -4.89999999999999999e-265

   1. Initial program 93.6%

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

   2. Taylor expanded in a around inf 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. associate-*r* 39.7%

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

      4. distribute-lft-neg-in 39.7%

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

   4. Simplified 39.7%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-265}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-126}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-265}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= x -7.2e+111)
     t_2
     (if (<= x -9.5e-65)
       t_1
       (if (<= x -1.12e-265)
         (* 2.0 (* a (* c (- i))))
         (if (<= x 1.8e-128) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -7.2e+111) {
		tmp = t_2;
	} else if (x <= -9.5e-65) {
		tmp = t_1;
	} else if (x <= -1.12e-265) {
		tmp = 2.0 * (a * (c * -i));
	} else if (x <= 1.8e-128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (x <= (-7.2d+111)) then
        tmp = t_2
    else if (x <= (-9.5d-65)) then
        tmp = t_1
    else if (x <= (-1.12d-265)) then
        tmp = 2.0d0 * (a * (c * -i))
    else if (x <= 1.8d-128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (x <= -7.2e+111) {
		tmp = t_2;
	} else if (x <= -9.5e-65) {
		tmp = t_1;
	} else if (x <= -1.12e-265) {
		tmp = 2.0 * (a * (c * -i));
	} else if (x <= 1.8e-128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if x <= -7.2e+111:
		tmp = t_2
	elif x <= -9.5e-65:
		tmp = t_1
	elif x <= -1.12e-265:
		tmp = 2.0 * (a * (c * -i))
	elif x <= 1.8e-128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (x <= -7.2e+111)
		tmp = t_2;
	elseif (x <= -9.5e-65)
		tmp = t_1;
	elseif (x <= -1.12e-265)
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	elseif (x <= 1.8e-128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (x <= -7.2e+111)
		tmp = t_2;
	elseif (x <= -9.5e-65)
		tmp = t_1;
	elseif (x <= -1.12e-265)
		tmp = 2.0 * (a * (c * -i));
	elseif (x <= 1.8e-128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+111], t$95$2, If[LessEqual[x, -9.5e-65], t$95$1, If[LessEqual[x, -1.12e-265], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000004e111 or 1.80000000000000012e-128 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 46.6%

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

   if -7.2000000000000004e111 < x < -9.5000000000000004e-65 or -1.12e-265 < x < 1.80000000000000012e-128

   1. Initial program 87.0%

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

   2. Taylor expanded in z around inf 36.9%

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

   if -9.5000000000000004e-65 < x < -1.12e-265

   1. Initial program 93.6%

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

      1. associate-*l* 97.8%

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

      2. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-def 97.8%

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

      2. +-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

   6. Taylor expanded in a around inf 35.5%

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

      1. mul-1-neg 35.5%

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

      2. associate-*r* 43.9%

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

      3. distribute-lft-neg-in 43.9%

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

      4. distribute-rgt-neg-in 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-265}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-128}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+72}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+126}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(c \cdot i\right) \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.75e+72)
   (* -2.0 (* b (* i (* c c))))
   (if (<= c 9.5e+126)
     (* 2.0 (+ (* x y) (* z t)))
     (* 2.0 (* c (* (* c i) (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.75e+72) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else if (c <= 9.5e+126) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * (c * ((c * i) * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-2.75d+72)) then
        tmp = (-2.0d0) * (b * (i * (c * c)))
    else if (c <= 9.5d+126) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * (c * ((c * i) * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.75e+72) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else if (c <= 9.5e+126) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * (c * ((c * i) * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.75e+72:
		tmp = -2.0 * (b * (i * (c * c)))
	elif c <= 9.5e+126:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * (c * ((c * i) * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.75e+72)
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	elseif (c <= 9.5e+126)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(c * Float64(Float64(c * i) * Float64(-b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.75e+72)
		tmp = -2.0 * (b * (i * (c * c)));
	elseif (c <= 9.5e+126)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * (c * ((c * i) * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.75e+72], N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e+126], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(N[(c * i), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.75e72

   1. Initial program 68.0%

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

   2. Taylor expanded in b around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-rgt-neg-in 71.5%

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

      3. unpow2 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in c around 0 71.5%

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

      1. associate-*r* 79.3%

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

      2. unpow2 79.3%

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

   7. Simplified 79.3%

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

   if -2.75e72 < c < 9.49999999999999951e126

   1. Initial program 97.6%

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

   2. Taylor expanded in c around 0 74.8%

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

   if 9.49999999999999951e126 < c

   1. Initial program 72.7%

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

      1. associate-*l* 88.5%

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

      2. fma-def 88.5%

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

   3. Simplified 88.5%

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

      1. fma-def 88.5%

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

      2. +-commutative 88.5%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in b around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unpow2 58.2%

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

      3. *-commutative 58.2%

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

      4. associate-*r* 55.5%

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

      5. distribute-rgt-neg-in 55.5%

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

      6. associate-*r* 58.8%

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

      7. *-commutative 58.8%

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

      8. associate-*l* 64.1%

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

   8. Simplified 64.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+72}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+126}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(c \cdot i\right) \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 15: 68.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+70} \lor \neg \left(c \leq 5.5 \cdot 10^{+118}\right):\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -7.5e+70) (not (<= c 5.5e+118)))
   (* -2.0 (* b (* i (* c c))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -7.5e+70) || !(c <= 5.5e+118)) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-7.5d+70)) .or. (.not. (c <= 5.5d+118))) then
        tmp = (-2.0d0) * (b * (i * (c * c)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -7.5e+70) || !(c <= 5.5e+118)) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -7.5e+70) or not (c <= 5.5e+118):
		tmp = -2.0 * (b * (i * (c * c)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -7.5e+70) || !(c <= 5.5e+118))
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -7.5e+70) || ~((c <= 5.5e+118)))
		tmp = -2.0 * (b * (i * (c * c)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -7.5e+70], N[Not[LessEqual[c, 5.5e+118]], $MachinePrecision]], N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.50000000000000031e70 or 5.5000000000000003e118 < c

   1. Initial program 69.9%

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

   2. Taylor expanded in b around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. distribute-rgt-neg-in 66.2%

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

      3. unpow2 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in c around 0 66.2%

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

      1. associate-*r* 72.2%

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

      2. unpow2 72.2%

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

   7. Simplified 72.2%

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

   if -7.50000000000000031e70 < c < 5.5000000000000003e118

   1. Initial program 97.6%

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

   2. Taylor expanded in c around 0 74.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+70} \lor \neg \left(c \leq 5.5 \cdot 10^{+118}\right):\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 16: 37.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+111} \lor \neg \left(x \leq 1.42 \cdot 10^{-126}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.8e+111) (not (<= x 1.42e-126)))
   (* 2.0 (* x y))
   (* 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 <= -8.8e+111) || !(x <= 1.42e-126)) {
		tmp = 2.0 * (x * y);
	} 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 <= (-8.8d+111)) .or. (.not. (x <= 1.42d-126))) then
        tmp = 2.0d0 * (x * y)
    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 <= -8.8e+111) || !(x <= 1.42e-126)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.8e+111) or not (x <= 1.42e-126):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.8e+111) || !(x <= 1.42e-126))
		tmp = Float64(2.0 * Float64(x * y));
	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 <= -8.8e+111) || ~((x <= 1.42e-126)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.8e+111], N[Not[LessEqual[x, 1.42e-126]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999994e111 or 1.42e-126 < x

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 46.6%

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

   if -8.79999999999999994e111 < x < 1.42e-126

   1. Initial program 89.5%

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

   2. Taylor expanded in z around inf 35.0%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+111} \lor \neg \left(x \leq 1.42 \cdot 10^{-126}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 17: 28.3% 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 88.2%

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

2. Taylor expanded in z around inf 28.7%

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

3. Final simplification 28.7%

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

Developer target: 93.7% 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 2023266 
(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))))