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

Percentage Accurate: 89.5% → 96.7%

Time: 15.9s

Alternatives: 20

Speedup: 1.0×

• 47.2% 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: 89.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.0%

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

      1. associate--l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-+l- 0.0%

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

      4. fma-neg 33.3%

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

      5. neg-sub0 33.3%

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

      6. associate-+l- 33.3%

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

      7. neg-sub0 33.3%

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

      8. distribute-rgt-neg-in 33.3%

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

      9. *-commutative 33.3%

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

      10. associate-*l* 50.0%

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

      11. fma-def 50.0%

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

      12. +-commutative 50.0%

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

      13. fma-def 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in i around 0 50.0%

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

   5. Taylor expanded in c around inf 83.3%

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 83.3%

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

      2. unpow2 83.3%

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

   7. Simplified 83.3%

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

4. Final simplification 99.1%

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

Alternative 2: 94.4% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (fma 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 * (fma(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(fma(x, y, Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. associate-*l* 97.6%

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

   2. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 92.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (* c (* t_1 (- i))))
     (* 2.0 (- (+ (* z t) (* x y)) 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 = i * (c * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - t_2);
	}
	return tmp;
}

Java

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

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * (c * (t_1 * -i))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - 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(i * Float64(c * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - 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 = i * (c * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * (c * (t_1 * -i));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - 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[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 77.2%

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

   2. Taylor expanded in i around inf 93.6%

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

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

   1. Initial program 96.2%

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

4. Final simplification 95.7%

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

Alternative 4: 44.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5600000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* (* c c) (* b i)) -2.0)))
   (if (<= c -3.4e+134)
     t_3
     (if (<= c -2.1e+78)
       t_2
       (if (<= c -5600000000000.0)
         t_3
         (if (<= c -8e-92)
           t_1
           (if (<= c -6.2e-288)
             t_2
             (if (<= c 2e-201)
               t_1
               (if (<= c 1.25e-141)
                 t_2
                 (if (<= c 1.15e+43) (* 2.0 (* i (* a (- c)))) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double t_3 = ((c * c) * (b * i)) * -2.0;
	double tmp;
	if (c <= -3.4e+134) {
		tmp = t_3;
	} else if (c <= -2.1e+78) {
		tmp = t_2;
	} else if (c <= -5600000000000.0) {
		tmp = t_3;
	} else if (c <= -8e-92) {
		tmp = t_1;
	} else if (c <= -6.2e-288) {
		tmp = t_2;
	} else if (c <= 2e-201) {
		tmp = t_1;
	} else if (c <= 1.25e-141) {
		tmp = t_2;
	} else if (c <= 1.15e+43) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    t_3 = ((c * c) * (b * i)) * (-2.0d0)
    if (c <= (-3.4d+134)) then
        tmp = t_3
    else if (c <= (-2.1d+78)) then
        tmp = t_2
    else if (c <= (-5600000000000.0d0)) then
        tmp = t_3
    else if (c <= (-8d-92)) then
        tmp = t_1
    else if (c <= (-6.2d-288)) then
        tmp = t_2
    else if (c <= 2d-201) then
        tmp = t_1
    else if (c <= 1.25d-141) then
        tmp = t_2
    else if (c <= 1.15d+43) then
        tmp = 2.0d0 * (i * (a * -c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double t_3 = ((c * c) * (b * i)) * -2.0;
	double tmp;
	if (c <= -3.4e+134) {
		tmp = t_3;
	} else if (c <= -2.1e+78) {
		tmp = t_2;
	} else if (c <= -5600000000000.0) {
		tmp = t_3;
	} else if (c <= -8e-92) {
		tmp = t_1;
	} else if (c <= -6.2e-288) {
		tmp = t_2;
	} else if (c <= 2e-201) {
		tmp = t_1;
	} else if (c <= 1.25e-141) {
		tmp = t_2;
	} else if (c <= 1.15e+43) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	t_3 = ((c * c) * (b * i)) * -2.0
	tmp = 0
	if c <= -3.4e+134:
		tmp = t_3
	elif c <= -2.1e+78:
		tmp = t_2
	elif c <= -5600000000000.0:
		tmp = t_3
	elif c <= -8e-92:
		tmp = t_1
	elif c <= -6.2e-288:
		tmp = t_2
	elif c <= 2e-201:
		tmp = t_1
	elif c <= 1.25e-141:
		tmp = t_2
	elif c <= 1.15e+43:
		tmp = 2.0 * (i * (a * -c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(Float64(c * c) * Float64(b * i)) * -2.0)
	tmp = 0.0
	if (c <= -3.4e+134)
		tmp = t_3;
	elseif (c <= -2.1e+78)
		tmp = t_2;
	elseif (c <= -5600000000000.0)
		tmp = t_3;
	elseif (c <= -8e-92)
		tmp = t_1;
	elseif (c <= -6.2e-288)
		tmp = t_2;
	elseif (c <= 2e-201)
		tmp = t_1;
	elseif (c <= 1.25e-141)
		tmp = t_2;
	elseif (c <= 1.15e+43)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	t_3 = ((c * c) * (b * i)) * -2.0;
	tmp = 0.0;
	if (c <= -3.4e+134)
		tmp = t_3;
	elseif (c <= -2.1e+78)
		tmp = t_2;
	elseif (c <= -5600000000000.0)
		tmp = t_3;
	elseif (c <= -8e-92)
		tmp = t_1;
	elseif (c <= -6.2e-288)
		tmp = t_2;
	elseif (c <= 2e-201)
		tmp = t_1;
	elseif (c <= 1.25e-141)
		tmp = t_2;
	elseif (c <= 1.15e+43)
		tmp = 2.0 * (i * (a * -c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -3.4e+134], t$95$3, If[LessEqual[c, -2.1e+78], t$95$2, If[LessEqual[c, -5600000000000.0], t$95$3, If[LessEqual[c, -8e-92], t$95$1, If[LessEqual[c, -6.2e-288], t$95$2, If[LessEqual[c, 2e-201], t$95$1, If[LessEqual[c, 1.25e-141], t$95$2, If[LessEqual[c, 1.15e+43], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.40000000000000018e134 or -2.1000000000000001e78 < c < -5.6e12 or 1.1500000000000001e43 < c

   1. Initial program 85.0%

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

   2. Taylor expanded in b around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-rgt-neg-in 61.3%

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

      3. unpow2 61.3%

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

   4. Simplified 61.3%

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

   5. Taylor expanded in c around 0 61.3%

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

      1. unpow2 61.3%

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

   7. Simplified 61.3%

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

   if -3.40000000000000018e134 < c < -2.1000000000000001e78 or -7.9999999999999999e-92 < c < -6.19999999999999967e-288 or 1.99999999999999989e-201 < c < 1.25e-141

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 60.2%

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

   if -5.6e12 < c < -7.9999999999999999e-92 or -6.19999999999999967e-288 < c < 1.99999999999999989e-201

   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 x around inf 60.2%

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

   if 1.25e-141 < c < 1.1500000000000001e43

   1. Initial program 93.8%

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

      1. associate-*l* 96.8%

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

      2. fma-def 96.8%

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

   3. Simplified 96.8%

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

      1. fma-def 96.8%

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

      2. +-commutative 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in a around inf 90.8%

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

   7. Taylor expanded in a around inf 41.0%

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

      1. mul-1-neg 41.0%

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

      2. associate-*r* 43.7%

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

      3. *-commutative 43.7%

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

      4. associate-*r* 43.7%

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

      5. distribute-rgt-neg-in 43.7%

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

      6. *-commutative 43.7%

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

   9. Simplified 43.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+134}:\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -5600000000000:\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-92}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 5: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* i (* a c)))))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.2e+161)
     t_2
     (if (<= c -1.45e+79)
       (* 2.0 (- (* z t) (* a (* c i))))
       (if (<= c -1.75e-16)
         t_1
         (if (<= c 1.2e-141)
           (* 2.0 (+ (* z t) (* x y)))
           (if (<= c 2.5e+14)
             t_1
             (if (<= c 5.8e+40)
               (* 2.0 (- (* z t) (* b (* c (* 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 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+161) {
		tmp = t_2;
	} else if (c <= -1.45e+79) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -1.75e-16) {
		tmp = t_1;
	} else if (c <= 1.2e-141) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 2.5e+14) {
		tmp = t_1;
	} else if (c <= 5.8e+40) {
		tmp = 2.0 * ((z * t) - (b * (c * (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) :: tmp
    t_1 = 2.0d0 * ((x * y) - (i * (a * c)))
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.2d+161)) then
        tmp = t_2
    else if (c <= (-1.45d+79)) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= (-1.75d-16)) then
        tmp = t_1
    else if (c <= 1.2d-141) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else if (c <= 2.5d+14) then
        tmp = t_1
    else if (c <= 5.8d+40) then
        tmp = 2.0d0 * ((z * t) - (b * (c * (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 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+161) {
		tmp = t_2;
	} else if (c <= -1.45e+79) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= -1.75e-16) {
		tmp = t_1;
	} else if (c <= 1.2e-141) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 2.5e+14) {
		tmp = t_1;
	} else if (c <= 5.8e+40) {
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (i * (a * c)))
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.2e+161:
		tmp = t_2
	elif c <= -1.45e+79:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= -1.75e-16:
		tmp = t_1
	elif c <= 1.2e-141:
		tmp = 2.0 * ((z * t) + (x * y))
	elif c <= 2.5e+14:
		tmp = t_1
	elif c <= 5.8e+40:
		tmp = 2.0 * ((z * t) - (b * (c * (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(Float64(x * y) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.2e+161)
		tmp = t_2;
	elseif (c <= -1.45e+79)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= -1.75e-16)
		tmp = t_1;
	elseif (c <= 1.2e-141)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	elseif (c <= 2.5e+14)
		tmp = t_1;
	elseif (c <= 5.8e+40)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(b * Float64(c * Float64(c * 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 * ((x * y) - (i * (a * c)));
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.2e+161)
		tmp = t_2;
	elseif (c <= -1.45e+79)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= -1.75e-16)
		tmp = t_1;
	elseif (c <= 1.2e-141)
		tmp = 2.0 * ((z * t) + (x * y));
	elseif (c <= 2.5e+14)
		tmp = t_1;
	elseif (c <= 5.8e+40)
		tmp = 2.0 * ((z * t) - (b * (c * (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[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+161], t$95$2, If[LessEqual[c, -1.45e+79], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-16], t$95$1, If[LessEqual[c, 1.2e-141], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+14], t$95$1, If[LessEqual[c, 5.8e+40], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.1999999999999999e161 or 5.80000000000000035e40 < c

   1. Initial program 83.3%

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

   2. Taylor expanded in i around inf 85.0%

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

   if -1.1999999999999999e161 < c < -1.44999999999999996e79

   1. Initial program 88.8%

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

   2. Taylor expanded in a around inf 76.4%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*l* 75.0%

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

      4. *-commutative 75.0%

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

   5. Simplified 75.0%

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

      1. sub-neg 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-*r* 75.0%

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

   7. Applied egg-rr 75.0%

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

   if -1.44999999999999996e79 < c < -1.75000000000000009e-16 or 1.2e-141 < c < 2.5e14

   1. Initial program 97.4%

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

   2. Taylor expanded in a around inf 87.8%

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

   3. Taylor expanded in z around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*l* 73.7%

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

      4. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -1.75000000000000009e-16 < c < 1.2e-141

   1. Initial program 99.0%

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

   2. Taylor expanded in c around 0 86.9%

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

   if 2.5e14 < c < 5.80000000000000035e40

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 86.8%

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

   3. Taylor expanded in c around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*l* 87.0%

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

      4. unpow2 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in i around 0 87.0%

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

      1. unpow2 87.0%

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

      2. associate-*l* 87.0%

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

   8. Simplified 87.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+161}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+79}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 6: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 58000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* i (* a c)))))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -3.7e+145)
     t_2
     (if (<= c -4.9e+60)
       (* 2.0 (- (* z t) (* c (* i (* b c)))))
       (if (<= c -6.8e-16)
         t_1
         (if (<= c 1.35e-142)
           (* 2.0 (+ (* z t) (* x y)))
           (if (<= c 58000000000000.0)
             t_1
             (if (<= c 3.2e+39)
               (* 2.0 (- (* z t) (* b (* c (* 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 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.7e+145) {
		tmp = t_2;
	} else if (c <= -4.9e+60) {
		tmp = 2.0 * ((z * t) - (c * (i * (b * c))));
	} else if (c <= -6.8e-16) {
		tmp = t_1;
	} else if (c <= 1.35e-142) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 58000000000000.0) {
		tmp = t_1;
	} else if (c <= 3.2e+39) {
		tmp = 2.0 * ((z * t) - (b * (c * (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) :: tmp
    t_1 = 2.0d0 * ((x * y) - (i * (a * c)))
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-3.7d+145)) then
        tmp = t_2
    else if (c <= (-4.9d+60)) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (b * c))))
    else if (c <= (-6.8d-16)) then
        tmp = t_1
    else if (c <= 1.35d-142) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else if (c <= 58000000000000.0d0) then
        tmp = t_1
    else if (c <= 3.2d+39) then
        tmp = 2.0d0 * ((z * t) - (b * (c * (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 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -3.7e+145) {
		tmp = t_2;
	} else if (c <= -4.9e+60) {
		tmp = 2.0 * ((z * t) - (c * (i * (b * c))));
	} else if (c <= -6.8e-16) {
		tmp = t_1;
	} else if (c <= 1.35e-142) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 58000000000000.0) {
		tmp = t_1;
	} else if (c <= 3.2e+39) {
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (i * (a * c)))
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -3.7e+145:
		tmp = t_2
	elif c <= -4.9e+60:
		tmp = 2.0 * ((z * t) - (c * (i * (b * c))))
	elif c <= -6.8e-16:
		tmp = t_1
	elif c <= 1.35e-142:
		tmp = 2.0 * ((z * t) + (x * y))
	elif c <= 58000000000000.0:
		tmp = t_1
	elif c <= 3.2e+39:
		tmp = 2.0 * ((z * t) - (b * (c * (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(Float64(x * y) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -3.7e+145)
		tmp = t_2;
	elseif (c <= -4.9e+60)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(b * c)))));
	elseif (c <= -6.8e-16)
		tmp = t_1;
	elseif (c <= 1.35e-142)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	elseif (c <= 58000000000000.0)
		tmp = t_1;
	elseif (c <= 3.2e+39)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(b * Float64(c * Float64(c * 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 * ((x * y) - (i * (a * c)));
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -3.7e+145)
		tmp = t_2;
	elseif (c <= -4.9e+60)
		tmp = 2.0 * ((z * t) - (c * (i * (b * c))));
	elseif (c <= -6.8e-16)
		tmp = t_1;
	elseif (c <= 1.35e-142)
		tmp = 2.0 * ((z * t) + (x * y));
	elseif (c <= 58000000000000.0)
		tmp = t_1;
	elseif (c <= 3.2e+39)
		tmp = 2.0 * ((z * t) - (b * (c * (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[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+145], t$95$2, If[LessEqual[c, -4.9e+60], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e-16], t$95$1, If[LessEqual[c, 1.35e-142], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 58000000000000.0], t$95$1, If[LessEqual[c, 3.2e+39], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.69999999999999993e145 or 3.19999999999999993e39 < c

   1. Initial program 83.9%

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

   2. Taylor expanded in i around inf 84.4%

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

   if -3.69999999999999993e145 < c < -4.9000000000000003e60

   1. Initial program 88.8%

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

   2. Taylor expanded in x around 0 89.8%

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

   3. Taylor expanded in c around inf 74.3%

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

   if -4.9000000000000003e60 < c < -6.8e-16 or 1.3499999999999999e-142 < c < 5.8e13

   1. Initial program 97.2%

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

   2. Taylor expanded in a around inf 92.1%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. *-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. associate-*l* 76.9%

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

      4. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -6.8e-16 < c < 1.3499999999999999e-142

   1. Initial program 99.0%

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

   2. Taylor expanded in c around 0 86.9%

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

   if 5.8e13 < c < 3.19999999999999993e39

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 86.8%

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

   3. Taylor expanded in c around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*l* 87.0%

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

      4. unpow2 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in i around 0 87.0%

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

      1. unpow2 87.0%

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

      2. associate-*l* 87.0%

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

   8. Simplified 87.0%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 58000000000000:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 7: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_3 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* i (* a c)))))
        (t_2 (* 2.0 (- (* z t) (* a (* c i)))))
        (t_3 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.2e+161)
     t_3
     (if (<= c -1.1e+79)
       t_2
       (if (<= c -7e-16)
         t_1
         (if (<= c 1.25e-141)
           (* 2.0 (+ (* z t) (* x y)))
           (if (<= c 3.8e+24) t_1 (if (<= c 9.5e+40) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+161) {
		tmp = t_3;
	} else if (c <= -1.1e+79) {
		tmp = t_2;
	} else if (c <= -7e-16) {
		tmp = t_1;
	} else if (c <= 1.25e-141) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 3.8e+24) {
		tmp = t_1;
	} else if (c <= 9.5e+40) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (i * (a * c)))
    t_2 = 2.0d0 * ((z * t) - (a * (c * i)))
    t_3 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.2d+161)) then
        tmp = t_3
    else if (c <= (-1.1d+79)) then
        tmp = t_2
    else if (c <= (-7d-16)) then
        tmp = t_1
    else if (c <= 1.25d-141) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else if (c <= 3.8d+24) then
        tmp = t_1
    else if (c <= 9.5d+40) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+161) {
		tmp = t_3;
	} else if (c <= -1.1e+79) {
		tmp = t_2;
	} else if (c <= -7e-16) {
		tmp = t_1;
	} else if (c <= 1.25e-141) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 3.8e+24) {
		tmp = t_1;
	} else if (c <= 9.5e+40) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (i * (a * c)))
	t_2 = 2.0 * ((z * t) - (a * (c * i)))
	t_3 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.2e+161:
		tmp = t_3
	elif c <= -1.1e+79:
		tmp = t_2
	elif c <= -7e-16:
		tmp = t_1
	elif c <= 1.25e-141:
		tmp = 2.0 * ((z * t) + (x * y))
	elif c <= 3.8e+24:
		tmp = t_1
	elif c <= 9.5e+40:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))))
	t_3 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.2e+161)
		tmp = t_3;
	elseif (c <= -1.1e+79)
		tmp = t_2;
	elseif (c <= -7e-16)
		tmp = t_1;
	elseif (c <= 1.25e-141)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	elseif (c <= 3.8e+24)
		tmp = t_1;
	elseif (c <= 9.5e+40)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (i * (a * c)));
	t_2 = 2.0 * ((z * t) - (a * (c * i)));
	t_3 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.2e+161)
		tmp = t_3;
	elseif (c <= -1.1e+79)
		tmp = t_2;
	elseif (c <= -7e-16)
		tmp = t_1;
	elseif (c <= 1.25e-141)
		tmp = 2.0 * ((z * t) + (x * y));
	elseif (c <= 3.8e+24)
		tmp = t_1;
	elseif (c <= 9.5e+40)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+161], t$95$3, If[LessEqual[c, -1.1e+79], t$95$2, If[LessEqual[c, -7e-16], t$95$1, If[LessEqual[c, 1.25e-141], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+24], t$95$1, If[LessEqual[c, 9.5e+40], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.1999999999999999e161 or 9.5000000000000003e40 < c

   1. Initial program 83.3%

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

   2. Taylor expanded in i around inf 85.0%

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

   if -1.1999999999999999e161 < c < -1.0999999999999999e79 or 3.80000000000000015e24 < c < 9.5000000000000003e40

   1. Initial program 86.3%

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

   2. Taylor expanded in a around inf 76.1%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. *-commutative 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*l* 75.0%

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

      4. *-commutative 75.0%

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

   5. Simplified 75.0%

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

      1. sub-neg 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-*r* 79.6%

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

   7. Applied egg-rr 79.6%

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

   if -1.0999999999999999e79 < c < -7.00000000000000035e-16 or 1.25e-141 < c < 3.80000000000000015e24

   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 a around inf 86.4%

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

   3. Taylor expanded in z around 0 71.3%

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

      1. *-commutative 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*l* 73.2%

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

      4. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -7.00000000000000035e-16 < c < 1.25e-141

   1. Initial program 99.0%

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

   2. Taylor expanded in c around 0 86.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+161}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+79}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-16}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 8: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot c\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{if}\;c \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -4100000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+101} \lor \neg \left(c \leq 1.35 \cdot 10^{+240}\right):\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* a c))) (t_2 (* 2.0 (- (* z t) t_1))))
   (if (<= c -1.25e+161)
     (* c (* (* c (* b i)) -2.0))
     (if (<= c -4100000000000.0)
       t_2
       (if (<= c 3.6e-142)
         (* 2.0 (+ (* z t) (* x y)))
         (if (<= c 3.4e+53)
           (* 2.0 (- (* x y) t_1))
           (if (or (<= c 3.2e+101) (not (<= c 1.35e+240)))
             (* (* (* c c) (* b i)) -2.0)
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (a * c);
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -1.25e+161) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -4100000000000.0) {
		tmp = t_2;
	} else if (c <= 3.6e-142) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 3.4e+53) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((c <= 3.2e+101) || !(c <= 1.35e+240)) {
		tmp = ((c * c) * (b * i)) * -2.0;
	} 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 = i * (a * c)
    t_2 = 2.0d0 * ((z * t) - t_1)
    if (c <= (-1.25d+161)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-4100000000000.0d0)) then
        tmp = t_2
    else if (c <= 3.6d-142) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else if (c <= 3.4d+53) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((c <= 3.2d+101) .or. (.not. (c <= 1.35d+240))) then
        tmp = ((c * c) * (b * i)) * (-2.0d0)
    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 = i * (a * c);
	double t_2 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -1.25e+161) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -4100000000000.0) {
		tmp = t_2;
	} else if (c <= 3.6e-142) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else if (c <= 3.4e+53) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((c <= 3.2e+101) || !(c <= 1.35e+240)) {
		tmp = ((c * c) * (b * i)) * -2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * (a * c)
	t_2 = 2.0 * ((z * t) - t_1)
	tmp = 0
	if c <= -1.25e+161:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -4100000000000.0:
		tmp = t_2
	elif c <= 3.6e-142:
		tmp = 2.0 * ((z * t) + (x * y))
	elif c <= 3.4e+53:
		tmp = 2.0 * ((x * y) - t_1)
	elif (c <= 3.2e+101) or not (c <= 1.35e+240):
		tmp = ((c * c) * (b * i)) * -2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(a * c))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	tmp = 0.0
	if (c <= -1.25e+161)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -4100000000000.0)
		tmp = t_2;
	elseif (c <= 3.6e-142)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	elseif (c <= 3.4e+53)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif ((c <= 3.2e+101) || !(c <= 1.35e+240))
		tmp = Float64(Float64(Float64(c * c) * Float64(b * i)) * -2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i * (a * c);
	t_2 = 2.0 * ((z * t) - t_1);
	tmp = 0.0;
	if (c <= -1.25e+161)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -4100000000000.0)
		tmp = t_2;
	elseif (c <= 3.6e-142)
		tmp = 2.0 * ((z * t) + (x * y));
	elseif (c <= 3.4e+53)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((c <= 3.2e+101) || ~((c <= 1.35e+240)))
		tmp = ((c * c) * (b * i)) * -2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.25e+161], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4100000000000.0], t$95$2, If[LessEqual[c, 3.6e-142], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+53], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 3.2e+101], N[Not[LessEqual[c, 1.35e+240]], $MachinePrecision]], N[(N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.2499999999999999e161

   1. Initial program 81.6%

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

   2. Taylor expanded in b around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-rgt-neg-in 73.4%

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

      3. unpow2 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in c around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. unpow2 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l* 78.6%

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

      5. associate-*l* 78.6%

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

      6. *-commutative 78.6%

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

   7. Simplified 78.6%

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

   if -1.2499999999999999e161 < c < -4.1e12 or 3.20000000000000005e101 < c < 1.3499999999999999e240

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 70.0%

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

   3. Taylor expanded in x around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-*l* 61.9%

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

      4. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -4.1e12 < c < 3.6e-142

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 85.8%

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

   if 3.6e-142 < c < 3.39999999999999998e53

   1. Initial program 94.2%

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

   2. Taylor expanded in a around inf 85.9%

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

   3. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. *-commutative 64.1%

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

      3. associate-*l* 66.6%

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

      4. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if 3.39999999999999998e53 < c < 3.20000000000000005e101 or 1.3499999999999999e240 < c

   1. Initial program 94.8%

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

   2. Taylor expanded in b around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

      3. unpow2 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in c around 0 80.7%

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

      1. unpow2 80.7%

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

   7. Simplified 80.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -4100000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+101} \lor \neg \left(c \leq 1.35 \cdot 10^{+240}\right):\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 9: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+161} \lor \neg \left(x \cdot y \leq 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4e+161) (not (<= (* x y) 1e+38)))
   (* 2.0 (+ (* z t) (* x y)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4e+161) || !((x * y) <= 1e+38)) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-4d+161)) .or. (.not. ((x * y) <= 1d+38))) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4e+161) || !((x * y) <= 1e+38)) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -4e+161) or not ((x * y) <= 1e+38):
		tmp = 2.0 * ((z * t) + (x * y))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -4e+161) || !(Float64(x * y) <= 1e+38))
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -4e+161) || ~(((x * y) <= 1e+38)))
		tmp = 2.0 * ((z * t) + (x * y));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e+161], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+38]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.0000000000000002e161 or 9.99999999999999977e37 < (*.f64 x y)

   1. Initial program 93.3%

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

   2. Taylor expanded in c around 0 79.1%

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

   if -4.0000000000000002e161 < (*.f64 x y) < 9.99999999999999977e37

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0 89.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+161} \lor \neg \left(x \cdot y \leq 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+15} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* z t) -5e+15) (not (<= (* z t) 2e-15)))
     (* 2.0 (- (* z t) t_1))
     (* 2.0 (- (* x y) 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 (((z * t) <= -5e+15) || !((z * t) <= 2e-15)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - 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 (((z * t) <= (-5d+15)) .or. (.not. ((z * t) <= 2d-15))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * ((x * y) - 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 (((z * t) <= -5e+15) || !((z * t) <= 2e-15)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - 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 ((z * t) <= -5e+15) or not ((z * t) <= 2e-15):
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - 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 ((Float64(z * t) <= -5e+15) || !(Float64(z * t) <= 2e-15))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 (((z * t) <= -5e+15) || ~(((z * t) <= 2e-15)))
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * ((x * y) - 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[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e-15]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5e15 or 2.0000000000000002e-15 < (*.f64 z t)

   1. Initial program 89.7%

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

   2. Taylor expanded in x around 0 86.4%

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

   if -5e15 < (*.f64 z t) < 2.0000000000000002e-15

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 87.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+15} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 63.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* z t) (* x y)))))
   (if (<= (* x y) -1e+60)
     t_1
     (if (<= (* x y) 2e-17)
       (* 2.0 (- (* z t) (* i (* a c))))
       (if (<= (* x y) 1e+38) (* c (* (* c (* b i)) -2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if ((x * y) <= -1e+60) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if ((x * y) <= 1e+38) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) + (x * y))
    if ((x * y) <= (-1d+60)) then
        tmp = t_1
    else if ((x * y) <= 2d-17) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if ((x * y) <= 1d+38) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if ((x * y) <= -1e+60) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if ((x * y) <= 1e+38) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) + (x * y))
	tmp = 0
	if (x * y) <= -1e+60:
		tmp = t_1
	elif (x * y) <= 2e-17:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif (x * y) <= 1e+38:
		tmp = c * ((c * (b * i)) * -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+60)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-17)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) + (x * y));
	tmp = 0.0;
	if ((x * y) <= -1e+60)
		tmp = t_1;
	elseif ((x * y) <= 2e-17)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif ((x * y) <= 1e+38)
		tmp = c * ((c * (b * i)) * -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+60], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-17], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999995e59 or 9.99999999999999977e37 < (*.f64 x y)

   1. Initial program 92.0%

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

   2. Taylor expanded in c around 0 76.3%

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

   if -9.9999999999999995e59 < (*.f64 x y) < 2.00000000000000014e-17

   1. Initial program 93.5%

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

   2. Taylor expanded in a around inf 74.6%

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

   3. Taylor expanded in x around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 68.1%

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

      4. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 2.00000000000000014e-17 < (*.f64 x y) < 9.99999999999999977e37

   1. Initial program 88.5%

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

   2. Taylor expanded in b around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-in 78.2%

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

      3. unpow2 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in c around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. unpow2 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*l* 78.8%

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

      5. associate-*l* 78.8%

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

      6. *-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 12: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* z t) (* x y)))))
   (if (<= (* x y) -1e+134)
     t_1
     (if (<= (* x y) 2e-17)
       (* 2.0 (- (* z t) (* a (* c i))))
       (if (<= (* x y) 1e+38) (* c (* (* c (* b i)) -2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if ((x * y) <= -1e+134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((x * y) <= 1e+38) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) + (x * y))
    if ((x * y) <= (-1d+134)) then
        tmp = t_1
    else if ((x * y) <= 2d-17) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if ((x * y) <= 1d+38) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if ((x * y) <= -1e+134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-17) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if ((x * y) <= 1e+38) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) + (x * y))
	tmp = 0
	if (x * y) <= -1e+134:
		tmp = t_1
	elif (x * y) <= 2e-17:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif (x * y) <= 1e+38:
		tmp = c * ((c * (b * i)) * -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+134)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-17)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) + (x * y));
	tmp = 0.0;
	if ((x * y) <= -1e+134)
		tmp = t_1;
	elseif ((x * y) <= 2e-17)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif ((x * y) <= 1e+38)
		tmp = c * ((c * (b * i)) * -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+134], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-17], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999921e133 or 9.99999999999999977e37 < (*.f64 x y)

   1. Initial program 93.4%

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

   2. Taylor expanded in c around 0 78.3%

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

   if -9.99999999999999921e133 < (*.f64 x y) < 2.00000000000000014e-17

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 74.1%

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

   3. Taylor expanded in x around 0 68.2%

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

      1. *-commutative 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*l* 66.9%

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

      4. *-commutative 66.9%

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

   5. Simplified 66.9%

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

      1. sub-neg 66.9%

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

      2. *-commutative 66.9%

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

      3. *-commutative 66.9%

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

      4. *-commutative 66.9%

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

      5. associate-*r* 71.1%

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

   7. Applied egg-rr 71.1%

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

   if 2.00000000000000014e-17 < (*.f64 x y) < 9.99999999999999977e37

   1. Initial program 88.5%

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

   2. Taylor expanded in b around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-in 78.2%

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

      3. unpow2 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in c around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. unpow2 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*l* 78.8%

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

      5. associate-*l* 78.8%

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

      6. *-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+134}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 13: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+60} \lor \neg \left(c \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.25e+60) (not (<= c 3.1e+14)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* z t) (* x y)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.25e+60) || !(c <= 3.1e+14)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.25d+60)) .or. (.not. (c <= 3.1d+14))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.25e+60) || !(c <= 3.1e+14)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.25e+60) or not (c <= 3.1e+14):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.25e+60) || !(c <= 3.1e+14))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.25e+60) || ~((c <= 3.1e+14)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.25e+60], N[Not[LessEqual[c, 3.1e+14]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.24999999999999994e60 or 3.1e14 < c

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0 89.3%

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

   if -1.24999999999999994e60 < c < 3.1e14

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 94.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+60} \lor \neg \left(c \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 14: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.2e+62)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 2.6e+40)
       (* 2.0 (- (+ (* z t) (* x y)) (* a (* c i))))
       (* 2.0 (- (* x y) 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 <= -1.2e+62) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2.6e+40) {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - 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 <= (-1.2d+62)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 2.6d+40) then
        tmp = 2.0d0 * (((z * t) + (x * y)) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) - 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 <= -1.2e+62) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2.6e+40) {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - 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 <= -1.2e+62:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 2.6e+40:
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)))
	else:
		tmp = 2.0 * ((x * y) - 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 <= -1.2e+62)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 2.6e+40)
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 <= -1.2e+62)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 2.6e+40)
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	else
		tmp = 2.0 * ((x * y) - 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, -1.2e+62], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e+40], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2e62

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0 93.2%

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

   if -1.2e62 < c < 2.6000000000000001e40

   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. Step-by-step derivation

      1. associate-*l* 98.6%

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

      2. fma-def 99.3%

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

   3. Simplified 99.3%

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

      1. fma-def 98.6%

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

      2. +-commutative 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in a around inf 94.2%

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

   if 2.6000000000000001e40 < c

   1. Initial program 84.7%

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

   2. Taylor expanded in z around 0 84.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 15: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. associate-*l* 97.6%

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

   2. fma-def 98.0%

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

3. Simplified 98.0%

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

   1. fma-def 97.6%

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

   2. +-commutative 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 16: 36.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-18}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= z -1.35e+107)
     t_1
     (if (<= z -7.5e-217)
       (* 2.0 (* x y))
       (if (<= z 3e-18) (* (* c -2.0) (* 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 * (z * t);
	double tmp;
	if (z <= -1.35e+107) {
		tmp = t_1;
	} else if (z <= -7.5e-217) {
		tmp = 2.0 * (x * y);
	} else if (z <= 3e-18) {
		tmp = (c * -2.0) * (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 * (z * t)
    if (z <= (-1.35d+107)) then
        tmp = t_1
    else if (z <= (-7.5d-217)) then
        tmp = 2.0d0 * (x * y)
    else if (z <= 3d-18) then
        tmp = (c * (-2.0d0)) * (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 * (z * t);
	double tmp;
	if (z <= -1.35e+107) {
		tmp = t_1;
	} else if (z <= -7.5e-217) {
		tmp = 2.0 * (x * y);
	} else if (z <= 3e-18) {
		tmp = (c * -2.0) * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if z <= -1.35e+107:
		tmp = t_1
	elif z <= -7.5e-217:
		tmp = 2.0 * (x * y)
	elif z <= 3e-18:
		tmp = (c * -2.0) * (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(z * t))
	tmp = 0.0
	if (z <= -1.35e+107)
		tmp = t_1;
	elseif (z <= -7.5e-217)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (z <= 3e-18)
		tmp = Float64(Float64(c * -2.0) * 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 * (z * t);
	tmp = 0.0;
	if (z <= -1.35e+107)
		tmp = t_1;
	elseif (z <= -7.5e-217)
		tmp = 2.0 * (x * y);
	elseif (z <= 3e-18)
		tmp = (c * -2.0) * (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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+107], t$95$1, If[LessEqual[z, -7.5e-217], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-18], N[(N[(c * -2.0), $MachinePrecision] * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e107 or 2.99999999999999983e-18 < z

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 51.2%

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

   if -1.3500000000000001e107 < z < -7.50000000000000031e-217

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 36.3%

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

   if -7.50000000000000031e-217 < z < 2.99999999999999983e-18

   1. Initial program 90.1%

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

   2. Taylor expanded in a around inf 33.3%

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

      1. associate-*r* 33.3%

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

      2. neg-mul-1 33.3%

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

   4. Simplified 33.3%

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

   5. Taylor expanded in c around 0 33.3%

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

      1. associate-*r* 33.3%

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

      2. *-commutative 33.3%

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

   7. Simplified 33.3%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-217}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-18}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 17: 67.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+141} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3e+141) (not (<= c 3.2e+41)))
   (* (* (* c c) (* b i)) -2.0)
   (* 2.0 (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3e+141) || !(c <= 3.2e+41)) {
		tmp = ((c * c) * (b * i)) * -2.0;
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3d+141)) .or. (.not. (c <= 3.2d+41))) then
        tmp = ((c * c) * (b * i)) * (-2.0d0)
    else
        tmp = 2.0d0 * ((z * t) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3e+141) || !(c <= 3.2e+41)) {
		tmp = ((c * c) * (b * i)) * -2.0;
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3e+141) or not (c <= 3.2e+41):
		tmp = ((c * c) * (b * i)) * -2.0
	else:
		tmp = 2.0 * ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3e+141) || !(c <= 3.2e+41))
		tmp = Float64(Float64(Float64(c * c) * Float64(b * i)) * -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3e+141) || ~((c <= 3.2e+41)))
		tmp = ((c * c) * (b * i)) * -2.0;
	else
		tmp = 2.0 * ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3e+141], N[Not[LessEqual[c, 3.2e+41]], $MachinePrecision]], N[(N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.9999999999999999e141 or 3.2000000000000001e41 < c

   1. Initial program 84.3%

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

   2. Taylor expanded in b around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-rgt-neg-in 62.2%

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

      3. unpow2 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in c around 0 62.2%

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

      1. unpow2 62.2%

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

   7. Simplified 62.2%

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

   if -2.9999999999999999e141 < c < 3.2000000000000001e41

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 74.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+141} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 18: 68.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -3e+141)
   (* c (* (* c (* b i)) -2.0))
   (if (<= c 1.15e+42)
     (* 2.0 (+ (* z t) (* x y)))
     (* (* (* c c) (* b i)) -2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3e+141) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= 1.15e+42) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = ((c * c) * (b * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-3d+141)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= 1.15d+42) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else
        tmp = ((c * c) * (b * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3e+141) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= 1.15e+42) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = ((c * c) * (b * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -3e+141:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= 1.15e+42:
		tmp = 2.0 * ((z * t) + (x * y))
	else:
		tmp = ((c * c) * (b * i)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -3e+141)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= 1.15e+42)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(Float64(c * c) * Float64(b * i)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -3e+141)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= 1.15e+42)
		tmp = 2.0 * ((z * t) + (x * y));
	else
		tmp = ((c * c) * (b * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -3e+141], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e+42], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9999999999999999e141

   1. Initial program 83.8%

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

   2. Taylor expanded in b around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. unpow2 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in c around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. unpow2 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

      6. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if -2.9999999999999999e141 < c < 1.15e42

   1. Initial program 97.0%

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

   2. Taylor expanded in c around 0 74.3%

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

   if 1.15e42 < c

   1. Initial program 84.7%

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

   2. Taylor expanded in b around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-rgt-neg-in 55.2%

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

      3. unpow2 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in c around 0 55.2%

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

      1. unpow2 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 19: 38.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+115} \lor \neg \left(x \leq 4.6 \cdot 10^{-83}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -7.5e+115) (not (<= x 4.6e-83)))
   (* 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 <= -7.5e+115) || !(x <= 4.6e-83)) {
		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 <= (-7.5d+115)) .or. (.not. (x <= 4.6d-83))) 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 <= -7.5e+115) || !(x <= 4.6e-83)) {
		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 <= -7.5e+115) or not (x <= 4.6e-83):
		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 <= -7.5e+115) || !(x <= 4.6e-83))
		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 <= -7.5e+115) || ~((x <= 4.6e-83)))
		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, -7.5e+115], N[Not[LessEqual[x, 4.6e-83]], $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 < -7.4999999999999997e115 or 4.59999999999999979e-83 < x

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 46.1%

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

   if -7.4999999999999997e115 < x < 4.59999999999999979e-83

   1. Initial program 92.7%

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

   2. Taylor expanded in z around inf 37.5%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+115} \lor \neg \left(x \leq 4.6 \cdot 10^{-83}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 20: 29.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

2. Taylor expanded in z around inf 31.4%

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

3. Final simplification 31.4%

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

Developer target: 94.0% 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 2023215 
(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))))