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

Percentage Accurate: 90.1% → 95.3%

Time: 21.4s

Alternatives: 17

Speedup: 0.5×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.3% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

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

   1. Initial program 78.6%

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

   2. Taylor expanded in c around 0 92.9%

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

   if -inf.0 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.5%

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

      1. associate-*l* 95.7%

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

      2. fma-def 97.0%

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

   3. Simplified 97.0%

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

4. Final simplification 96.5%

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

Alternative 2: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t_1\right)\\ t_3 := c \cdot \left(t_1 \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_3\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))) (t_3 (* c (* t_1 i))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* x y) t_3))
     (if (<= t_2 5e+303)
       (* 2.0 (- (+ (* x y) (* z t)) t_2))
       (* 2.0 (- (* z t) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 5e+303) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((z * t) - t_3);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) - t_3);
	} else if (t_2 <= 5e+303) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((z * t) - t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	t_3 = c * (t_1 * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) - t_3)
	elif t_2 <= 5e+303:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((z * t) - t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	t_3 = Float64(c * Float64(t_1 * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_3));
	elseif (t_2 <= 5e+303)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	t_3 = c * (t_1 * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) - t_3);
	elseif (t_2 <= 5e+303)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((z * t) - t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+303], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0 88.5%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999997e303

   1. Initial program 98.5%

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

   if 4.9999999999999997e303 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 78.5%

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

   2. Taylor expanded in x around 0 94.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 5 \cdot 10^{+303}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 3: 96.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. associate-*l* 98.4%

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

      2. fma-def 98.4%

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

   3. Simplified 98.4%

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

      1. fma-def 98.4%

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

      2. +-commutative 98.4%

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

   5. Applied egg-rr 98.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 33.3%

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

   3. Taylor expanded in t around 0 50.4%

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

4. Final simplification 96.1%

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

Alternative 4: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ t_4 := -2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+67}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* a (* c i))))
        (t_3 (* (* x y) 2.0))
        (t_4 (* -2.0 (* c (* c (* b i))))))
   (if (<= c -1.15e+204)
     t_4
     (if (<= c -1.1e+180)
       t_2
       (if (<= c -5.8e+57)
         t_4
         (if (<= c -1.8e-17)
           t_1
           (if (<= c -3.4e-19)
             t_2
             (if (<= c -2.15e-176)
               t_3
               (if (<= c -8.6e-237)
                 t_1
                 (if (<= c 5.9e+23)
                   t_3
                   (if (<= c 2e+67)
                     (* -2.0 (* c (* a i)))
                     (* -2.0 (* c (* b (* c i)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double t_4 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_4;
	} else if (c <= -1.1e+180) {
		tmp = t_2;
	} else if (c <= -5.8e+57) {
		tmp = t_4;
	} else if (c <= -1.8e-17) {
		tmp = t_1;
	} else if (c <= -3.4e-19) {
		tmp = t_2;
	} else if (c <= -2.15e-176) {
		tmp = t_3;
	} else if (c <= -8.6e-237) {
		tmp = t_1;
	} else if (c <= 5.9e+23) {
		tmp = t_3;
	} else if (c <= 2e+67) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = -2.0 * (c * (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    t_3 = (x * y) * 2.0d0
    t_4 = (-2.0d0) * (c * (c * (b * i)))
    if (c <= (-1.15d+204)) then
        tmp = t_4
    else if (c <= (-1.1d+180)) then
        tmp = t_2
    else if (c <= (-5.8d+57)) then
        tmp = t_4
    else if (c <= (-1.8d-17)) then
        tmp = t_1
    else if (c <= (-3.4d-19)) then
        tmp = t_2
    else if (c <= (-2.15d-176)) then
        tmp = t_3
    else if (c <= (-8.6d-237)) then
        tmp = t_1
    else if (c <= 5.9d+23) then
        tmp = t_3
    else if (c <= 2d+67) then
        tmp = (-2.0d0) * (c * (a * i))
    else
        tmp = (-2.0d0) * (c * (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 t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double t_4 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_4;
	} else if (c <= -1.1e+180) {
		tmp = t_2;
	} else if (c <= -5.8e+57) {
		tmp = t_4;
	} else if (c <= -1.8e-17) {
		tmp = t_1;
	} else if (c <= -3.4e-19) {
		tmp = t_2;
	} else if (c <= -2.15e-176) {
		tmp = t_3;
	} else if (c <= -8.6e-237) {
		tmp = t_1;
	} else if (c <= 5.9e+23) {
		tmp = t_3;
	} else if (c <= 2e+67) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	t_3 = (x * y) * 2.0
	t_4 = -2.0 * (c * (c * (b * i)))
	tmp = 0
	if c <= -1.15e+204:
		tmp = t_4
	elif c <= -1.1e+180:
		tmp = t_2
	elif c <= -5.8e+57:
		tmp = t_4
	elif c <= -1.8e-17:
		tmp = t_1
	elif c <= -3.4e-19:
		tmp = t_2
	elif c <= -2.15e-176:
		tmp = t_3
	elif c <= -8.6e-237:
		tmp = t_1
	elif c <= 5.9e+23:
		tmp = t_3
	elif c <= 2e+67:
		tmp = -2.0 * (c * (a * i))
	else:
		tmp = -2.0 * (c * (b * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(a * Float64(c * i)))
	t_3 = Float64(Float64(x * y) * 2.0)
	t_4 = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -1.15e+204)
		tmp = t_4;
	elseif (c <= -1.1e+180)
		tmp = t_2;
	elseif (c <= -5.8e+57)
		tmp = t_4;
	elseif (c <= -1.8e-17)
		tmp = t_1;
	elseif (c <= -3.4e-19)
		tmp = t_2;
	elseif (c <= -2.15e-176)
		tmp = t_3;
	elseif (c <= -8.6e-237)
		tmp = t_1;
	elseif (c <= 5.9e+23)
		tmp = t_3;
	elseif (c <= 2e+67)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (a * (c * i));
	t_3 = (x * y) * 2.0;
	t_4 = -2.0 * (c * (c * (b * i)));
	tmp = 0.0;
	if (c <= -1.15e+204)
		tmp = t_4;
	elseif (c <= -1.1e+180)
		tmp = t_2;
	elseif (c <= -5.8e+57)
		tmp = t_4;
	elseif (c <= -1.8e-17)
		tmp = t_1;
	elseif (c <= -3.4e-19)
		tmp = t_2;
	elseif (c <= -2.15e-176)
		tmp = t_3;
	elseif (c <= -8.6e-237)
		tmp = t_1;
	elseif (c <= 5.9e+23)
		tmp = t_3;
	elseif (c <= 2e+67)
		tmp = -2.0 * (c * (a * i));
	else
		tmp = -2.0 * (c * (b * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$4 = N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+204], t$95$4, If[LessEqual[c, -1.1e+180], t$95$2, If[LessEqual[c, -5.8e+57], t$95$4, If[LessEqual[c, -1.8e-17], t$95$1, If[LessEqual[c, -3.4e-19], t$95$2, If[LessEqual[c, -2.15e-176], t$95$3, If[LessEqual[c, -8.6e-237], t$95$1, If[LessEqual[c, 5.9e+23], t$95$3, If[LessEqual[c, 2e+67], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.14999999999999995e204 or -1.1e180 < c < -5.8000000000000003e57

   1. Initial program 79.2%

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

   2. Taylor expanded in x around 0 73.0%

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

   3. Taylor expanded in c around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. unpow2 70.4%

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

      3. associate-*r* 68.4%

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

      4. associate-*r* 70.2%

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

      5. *-commutative 70.2%

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

   5. Simplified 70.2%

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

      1. expm1-log1p-u 40.1%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 39.9%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 36.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 36.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 39.9%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 39.9%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 40.1%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 70.3%

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

   9. Simplified 70.3%

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

   if -1.14999999999999995e204 < c < -1.1e180 or -1.79999999999999997e-17 < c < -3.4000000000000002e-19

   1. Initial program 76.2%

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

   2. Taylor expanded in x around 0 91.6%

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

   3. Taylor expanded in a around inf 74.1%

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

   if -5.8000000000000003e57 < c < -1.79999999999999997e-17 or -2.15000000000000006e-176 < c < -8.59999999999999965e-237

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.0%

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

   if -3.4000000000000002e-19 < c < -2.15000000000000006e-176 or -8.59999999999999965e-237 < c < 5.89999999999999987e23

   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 x around inf 53.0%

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

   if 5.89999999999999987e23 < c < 1.99999999999999997e67

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-*r* 70.3%

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

   5. Simplified 70.3%

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

   if 1.99999999999999997e67 < c

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 92.4%

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

   3. Taylor expanded in c around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. unpow2 67.4%

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

      3. associate-*r* 69.7%

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

      4. associate-*r* 75.6%

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

      5. *-commutative 75.6%

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

   5. Simplified 75.6%

      \[\leadsto \color{blue}{-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+23}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+67}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5: 48.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ t_4 := -2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.65 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+67}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* a (* c i))))
        (t_3 (* (* x y) 2.0))
        (t_4 (* -2.0 (* c (* c (* b i))))))
   (if (<= c -1.15e+204)
     t_4
     (if (<= c -1.1e+180)
       t_2
       (if (<= c -2.8e+57)
         t_4
         (if (<= c -3.1e-15)
           t_1
           (if (<= c -2.2e-19)
             t_2
             (if (<= c -2.65e-173)
               t_3
               (if (<= c -9.2e-237)
                 t_1
                 (if (<= c 1.2e+25)
                   t_3
                   (if (<= c 1.9e+67)
                     (* -2.0 (* c (* a i)))
                     (* -2.0 (* (* b c) (* c i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double t_4 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_4;
	} else if (c <= -1.1e+180) {
		tmp = t_2;
	} else if (c <= -2.8e+57) {
		tmp = t_4;
	} else if (c <= -3.1e-15) {
		tmp = t_1;
	} else if (c <= -2.2e-19) {
		tmp = t_2;
	} else if (c <= -2.65e-173) {
		tmp = t_3;
	} else if (c <= -9.2e-237) {
		tmp = t_1;
	} else if (c <= 1.2e+25) {
		tmp = t_3;
	} else if (c <= 1.9e+67) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = -2.0 * ((b * c) * (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    t_3 = (x * y) * 2.0d0
    t_4 = (-2.0d0) * (c * (c * (b * i)))
    if (c <= (-1.15d+204)) then
        tmp = t_4
    else if (c <= (-1.1d+180)) then
        tmp = t_2
    else if (c <= (-2.8d+57)) then
        tmp = t_4
    else if (c <= (-3.1d-15)) then
        tmp = t_1
    else if (c <= (-2.2d-19)) then
        tmp = t_2
    else if (c <= (-2.65d-173)) then
        tmp = t_3
    else if (c <= (-9.2d-237)) then
        tmp = t_1
    else if (c <= 1.2d+25) then
        tmp = t_3
    else if (c <= 1.9d+67) then
        tmp = (-2.0d0) * (c * (a * i))
    else
        tmp = (-2.0d0) * ((b * c) * (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 t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double t_3 = (x * y) * 2.0;
	double t_4 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_4;
	} else if (c <= -1.1e+180) {
		tmp = t_2;
	} else if (c <= -2.8e+57) {
		tmp = t_4;
	} else if (c <= -3.1e-15) {
		tmp = t_1;
	} else if (c <= -2.2e-19) {
		tmp = t_2;
	} else if (c <= -2.65e-173) {
		tmp = t_3;
	} else if (c <= -9.2e-237) {
		tmp = t_1;
	} else if (c <= 1.2e+25) {
		tmp = t_3;
	} else if (c <= 1.9e+67) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = -2.0 * ((b * c) * (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	t_3 = (x * y) * 2.0
	t_4 = -2.0 * (c * (c * (b * i)))
	tmp = 0
	if c <= -1.15e+204:
		tmp = t_4
	elif c <= -1.1e+180:
		tmp = t_2
	elif c <= -2.8e+57:
		tmp = t_4
	elif c <= -3.1e-15:
		tmp = t_1
	elif c <= -2.2e-19:
		tmp = t_2
	elif c <= -2.65e-173:
		tmp = t_3
	elif c <= -9.2e-237:
		tmp = t_1
	elif c <= 1.2e+25:
		tmp = t_3
	elif c <= 1.9e+67:
		tmp = -2.0 * (c * (a * i))
	else:
		tmp = -2.0 * ((b * c) * (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(a * Float64(c * i)))
	t_3 = Float64(Float64(x * y) * 2.0)
	t_4 = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -1.15e+204)
		tmp = t_4;
	elseif (c <= -1.1e+180)
		tmp = t_2;
	elseif (c <= -2.8e+57)
		tmp = t_4;
	elseif (c <= -3.1e-15)
		tmp = t_1;
	elseif (c <= -2.2e-19)
		tmp = t_2;
	elseif (c <= -2.65e-173)
		tmp = t_3;
	elseif (c <= -9.2e-237)
		tmp = t_1;
	elseif (c <= 1.2e+25)
		tmp = t_3;
	elseif (c <= 1.9e+67)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	else
		tmp = Float64(-2.0 * Float64(Float64(b * c) * Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (a * (c * i));
	t_3 = (x * y) * 2.0;
	t_4 = -2.0 * (c * (c * (b * i)));
	tmp = 0.0;
	if (c <= -1.15e+204)
		tmp = t_4;
	elseif (c <= -1.1e+180)
		tmp = t_2;
	elseif (c <= -2.8e+57)
		tmp = t_4;
	elseif (c <= -3.1e-15)
		tmp = t_1;
	elseif (c <= -2.2e-19)
		tmp = t_2;
	elseif (c <= -2.65e-173)
		tmp = t_3;
	elseif (c <= -9.2e-237)
		tmp = t_1;
	elseif (c <= 1.2e+25)
		tmp = t_3;
	elseif (c <= 1.9e+67)
		tmp = -2.0 * (c * (a * i));
	else
		tmp = -2.0 * ((b * c) * (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$4 = N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+204], t$95$4, If[LessEqual[c, -1.1e+180], t$95$2, If[LessEqual[c, -2.8e+57], t$95$4, If[LessEqual[c, -3.1e-15], t$95$1, If[LessEqual[c, -2.2e-19], t$95$2, If[LessEqual[c, -2.65e-173], t$95$3, If[LessEqual[c, -9.2e-237], t$95$1, If[LessEqual[c, 1.2e+25], t$95$3, If[LessEqual[c, 1.9e+67], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.14999999999999995e204 or -1.1e180 < c < -2.8e57

   1. Initial program 79.2%

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

   2. Taylor expanded in x around 0 73.0%

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

   3. Taylor expanded in c around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. unpow2 70.4%

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

      3. associate-*r* 68.4%

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

      4. associate-*r* 70.2%

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

      5. *-commutative 70.2%

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

   5. Simplified 70.2%

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

      1. expm1-log1p-u 40.1%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 39.9%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 36.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 36.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 39.9%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 39.9%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 40.1%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 70.3%

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

   9. Simplified 70.3%

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

   if -1.14999999999999995e204 < c < -1.1e180 or -3.0999999999999999e-15 < c < -2.1999999999999998e-19

   1. Initial program 76.2%

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

   2. Taylor expanded in x around 0 91.6%

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

   3. Taylor expanded in a around inf 74.1%

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

   if -2.8e57 < c < -3.0999999999999999e-15 or -2.64999999999999982e-173 < c < -9.20000000000000046e-237

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.0%

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

   if -2.1999999999999998e-19 < c < -2.64999999999999982e-173 or -9.20000000000000046e-237 < c < 1.19999999999999998e25

   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 x around inf 53.0%

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

   if 1.19999999999999998e25 < c < 1.9000000000000001e67

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-*r* 70.3%

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

   5. Simplified 70.3%

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

   if 1.9000000000000001e67 < c

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 92.4%

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

   3. Taylor expanded in c around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. unpow2 67.4%

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

      3. associate-*r* 69.7%

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

      4. associate-*r* 75.6%

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

      5. *-commutative 75.6%

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

   5. Simplified 75.6%

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

      1. expm1-log1p-u 37.9%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 30.8%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 30.8%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 30.8%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 36.7%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 74.4%

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

   9. Simplified 74.4%

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

   10. Taylor expanded in c around 0 67.4%

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

       1. unpow2 67.4%

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

       2. associate-*r* 69.7%

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

       3. associate-*r* 77.2%

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

       4. *-commutative 77.2%

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

   12. Simplified 77.2%

       \[\leadsto \color{blue}{-2 \cdot \left(\left(b \cdot c\right) \cdot \left(i \cdot c\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.65 \cdot 10^{-173}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+67}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-168}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i)))))
        (t_2 (* 2.0 (+ (* x y) (- (* z t) (* (* b c) (* c i)))))))
   (if (<= c -1.8e+134)
     t_1
     (if (<= c -4e-113)
       t_2
       (if (<= c 1.55e-168)
         (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
         (if (<= c 1e-57) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	double tmp;
	if (c <= -1.8e+134) {
		tmp = t_1;
	} else if (c <= -4e-113) {
		tmp = t_2;
	} else if (c <= 1.55e-168) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else if (c <= 1e-57) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    t_2 = 2.0d0 * ((x * y) + ((z * t) - ((b * c) * (c * i))))
    if (c <= (-1.8d+134)) then
        tmp = t_1
    else if (c <= (-4d-113)) then
        tmp = t_2
    else if (c <= 1.55d-168) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else if (c <= 1d-57) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	double tmp;
	if (c <= -1.8e+134) {
		tmp = t_1;
	} else if (c <= -4e-113) {
		tmp = t_2;
	} else if (c <= 1.55e-168) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else if (c <= 1e-57) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	t_2 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))))
	tmp = 0
	if c <= -1.8e+134:
		tmp = t_1
	elif c <= -4e-113:
		tmp = t_2
	elif c <= 1.55e-168:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	elif c <= 1e-57:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	t_2 = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(Float64(b * c) * Float64(c * i)))))
	tmp = 0.0
	if (c <= -1.8e+134)
		tmp = t_1;
	elseif (c <= -4e-113)
		tmp = t_2;
	elseif (c <= 1.55e-168)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	elseif (c <= 1e-57)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	t_2 = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	tmp = 0.0;
	if (c <= -1.8e+134)
		tmp = t_1;
	elseif (c <= -4e-113)
		tmp = t_2;
	elseif (c <= 1.55e-168)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	elseif (c <= 1e-57)
		tmp = t_2;
	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[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+134], t$95$1, If[LessEqual[c, -4e-113], t$95$2, If[LessEqual[c, 1.55e-168], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e-57], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.79999999999999994e134 or 9.99999999999999955e-58 < c

   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 z around 0 90.2%

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

   if -1.79999999999999994e134 < c < -3.99999999999999991e-113 or 1.55e-168 < c < 9.99999999999999955e-58

   1. Initial program 93.6%

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

   2. Taylor expanded in a around 0 93.8%

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

      1. associate--l+ 93.8%

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

      2. associate-*l* 93.8%

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

   4. Applied egg-rr 93.8%

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

   if -3.99999999999999991e-113 < c < 1.55e-168

   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 a around inf 98.5%

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

      1. *-commutative 98.5%

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

   4. Simplified 98.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-113}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-168}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 10^{-57}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-112}:\\ \;\;\;\;2 \cdot \left(t_2 - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-57}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i)))))
        (t_2 (+ (* x y) (* z t))))
   (if (<= c -3.5e+142)
     t_1
     (if (<= c -1.15e-112)
       (* 2.0 (- t_2 (* b (* c (* c i)))))
       (if (<= c 1.45e-168)
         (* 2.0 (- t_2 (* i (* a c))))
         (if (<= c 1.25e-57)
           (* 2.0 (+ (* x y) (- (* z t) (* (* b c) (* c i)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -3.5e+142) {
		tmp = t_1;
	} else if (c <= -1.15e-112) {
		tmp = 2.0 * (t_2 - (b * (c * (c * i))));
	} else if (c <= 1.45e-168) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 1.25e-57) {
		tmp = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * 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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    t_2 = (x * y) + (z * t)
    if (c <= (-3.5d+142)) then
        tmp = t_1
    else if (c <= (-1.15d-112)) then
        tmp = 2.0d0 * (t_2 - (b * (c * (c * i))))
    else if (c <= 1.45d-168) then
        tmp = 2.0d0 * (t_2 - (i * (a * c)))
    else if (c <= 1.25d-57) then
        tmp = 2.0d0 * ((x * y) + ((z * t) - ((b * c) * (c * 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 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -3.5e+142) {
		tmp = t_1;
	} else if (c <= -1.15e-112) {
		tmp = 2.0 * (t_2 - (b * (c * (c * i))));
	} else if (c <= 1.45e-168) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 1.25e-57) {
		tmp = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	t_2 = (x * y) + (z * t)
	tmp = 0
	if c <= -3.5e+142:
		tmp = t_1
	elif c <= -1.15e-112:
		tmp = 2.0 * (t_2 - (b * (c * (c * i))))
	elif c <= 1.45e-168:
		tmp = 2.0 * (t_2 - (i * (a * c)))
	elif c <= 1.25e-57:
		tmp = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * i))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -3.5e+142)
		tmp = t_1;
	elseif (c <= -1.15e-112)
		tmp = Float64(2.0 * Float64(t_2 - Float64(b * Float64(c * Float64(c * i)))));
	elseif (c <= 1.45e-168)
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(a * c))));
	elseif (c <= 1.25e-57)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(Float64(b * c) * Float64(c * 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 * ((x * y) - (c * ((a + (b * c)) * i)));
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -3.5e+142)
		tmp = t_1;
	elseif (c <= -1.15e-112)
		tmp = 2.0 * (t_2 - (b * (c * (c * i))));
	elseif (c <= 1.45e-168)
		tmp = 2.0 * (t_2 - (i * (a * c)));
	elseif (c <= 1.25e-57)
		tmp = 2.0 * ((x * y) + ((z * t) - ((b * c) * (c * 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[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+142], t$95$1, If[LessEqual[c, -1.15e-112], N[(2.0 * N[(t$95$2 - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-168], N[(2.0 * N[(t$95$2 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-57], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.49999999999999997e142 or 1.25e-57 < 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 z around 0 90.8%

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

   if -3.49999999999999997e142 < c < -1.14999999999999995e-112

   1. Initial program 90.6%

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

   2. Taylor expanded in a around 0 95.4%

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

      1. unpow2 95.4%

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

      2. associate-*r* 95.4%

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

   4. Simplified 95.4%

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

   if -1.14999999999999995e-112 < c < 1.4499999999999999e-168

   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 a around inf 98.5%

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

      1. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   if 1.4499999999999999e-168 < c < 1.25e-57

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0 95.5%

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

      1. associate--l+ 95.6%

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

      2. associate-*l* 95.6%

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

   4. Applied egg-rr 95.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-112}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-57}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 49.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+66}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* b (* c i))))))
   (if (<= c -1.15e+204)
     t_1
     (if (<= c -1.1e+180)
       (* -2.0 (* a (* c i)))
       (if (<= c -2.4e+58)
         t_1
         (if (<= c -8.6e-237)
           (* 2.0 (* z t))
           (if (<= c 1.6e+27)
             (* (* x y) 2.0)
             (if (<= c 6.8e+66) (* -2.0 (* c (* a i))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_1;
	} else if (c <= -1.1e+180) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -2.4e+58) {
		tmp = t_1;
	} else if (c <= -8.6e-237) {
		tmp = 2.0 * (z * t);
	} else if (c <= 1.6e+27) {
		tmp = (x * y) * 2.0;
	} else if (c <= 6.8e+66) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * (b * (c * i)))
    if (c <= (-1.15d+204)) then
        tmp = t_1
    else if (c <= (-1.1d+180)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (c <= (-2.4d+58)) then
        tmp = t_1
    else if (c <= (-8.6d-237)) then
        tmp = 2.0d0 * (z * t)
    else if (c <= 1.6d+27) then
        tmp = (x * y) * 2.0d0
    else if (c <= 6.8d+66) then
        tmp = (-2.0d0) * (c * (a * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_1;
	} else if (c <= -1.1e+180) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -2.4e+58) {
		tmp = t_1;
	} else if (c <= -8.6e-237) {
		tmp = 2.0 * (z * t);
	} else if (c <= 1.6e+27) {
		tmp = (x * y) * 2.0;
	} else if (c <= 6.8e+66) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * (b * (c * i)))
	tmp = 0
	if c <= -1.15e+204:
		tmp = t_1
	elif c <= -1.1e+180:
		tmp = -2.0 * (a * (c * i))
	elif c <= -2.4e+58:
		tmp = t_1
	elif c <= -8.6e-237:
		tmp = 2.0 * (z * t)
	elif c <= 1.6e+27:
		tmp = (x * y) * 2.0
	elif c <= 6.8e+66:
		tmp = -2.0 * (c * (a * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	tmp = 0.0
	if (c <= -1.15e+204)
		tmp = t_1;
	elseif (c <= -1.1e+180)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (c <= -2.4e+58)
		tmp = t_1;
	elseif (c <= -8.6e-237)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (c <= 1.6e+27)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (c <= 6.8e+66)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * (b * (c * i)));
	tmp = 0.0;
	if (c <= -1.15e+204)
		tmp = t_1;
	elseif (c <= -1.1e+180)
		tmp = -2.0 * (a * (c * i));
	elseif (c <= -2.4e+58)
		tmp = t_1;
	elseif (c <= -8.6e-237)
		tmp = 2.0 * (z * t);
	elseif (c <= 1.6e+27)
		tmp = (x * y) * 2.0;
	elseif (c <= 6.8e+66)
		tmp = -2.0 * (c * (a * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+204], t$95$1, If[LessEqual[c, -1.1e+180], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.4e+58], t$95$1, If[LessEqual[c, -8.6e-237], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+27], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 6.8e+66], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.14999999999999995e204 or -1.1e180 < c < -2.4e58 or 6.8000000000000006e66 < c

   1. Initial program 82.6%

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

   2. Taylor expanded in x around 0 83.8%

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

   3. Taylor expanded in c around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. unpow2 68.7%

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

      3. associate-*r* 69.1%

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

      4. associate-*r* 73.2%

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

      5. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -1.14999999999999995e204 < c < -1.1e180

   1. Initial program 71.5%

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

   2. Taylor expanded in x around 0 89.9%

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

   3. Taylor expanded in a around inf 68.9%

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

   if -2.4e58 < c < -8.59999999999999965e-237

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -8.59999999999999965e-237 < c < 1.60000000000000008e27

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 53.9%

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

   if 1.60000000000000008e27 < c < 6.8000000000000006e66

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in a around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-*r* 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+66}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 9: 68.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* -2.0 (* c (* c (* b i))))))
   (if (<= c -1.15e+204)
     t_2
     (if (<= c -1.1e+180)
       (* -2.0 (* a (* c i)))
       (if (<= c -2.8e+88)
         t_2
         (if (<= c 1.85e+28)
           t_1
           (if (<= c 1.06e+48)
             (* -2.0 (* c (* a i)))
             (if (<= c 9.2e+61) t_1 (* -2.0 (* (* b c) (* c i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_2;
	} else if (c <= -1.1e+180) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -2.8e+88) {
		tmp = t_2;
	} else if (c <= 1.85e+28) {
		tmp = t_1;
	} else if (c <= 1.06e+48) {
		tmp = -2.0 * (c * (a * i));
	} else if (c <= 9.2e+61) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((b * c) * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (c * (c * (b * i)))
    if (c <= (-1.15d+204)) then
        tmp = t_2
    else if (c <= (-1.1d+180)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (c <= (-2.8d+88)) then
        tmp = t_2
    else if (c <= 1.85d+28) then
        tmp = t_1
    else if (c <= 1.06d+48) then
        tmp = (-2.0d0) * (c * (a * i))
    else if (c <= 9.2d+61) then
        tmp = t_1
    else
        tmp = (-2.0d0) * ((b * c) * (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 t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1.15e+204) {
		tmp = t_2;
	} else if (c <= -1.1e+180) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -2.8e+88) {
		tmp = t_2;
	} else if (c <= 1.85e+28) {
		tmp = t_1;
	} else if (c <= 1.06e+48) {
		tmp = -2.0 * (c * (a * i));
	} else if (c <= 9.2e+61) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((b * c) * (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (c * (c * (b * i)))
	tmp = 0
	if c <= -1.15e+204:
		tmp = t_2
	elif c <= -1.1e+180:
		tmp = -2.0 * (a * (c * i))
	elif c <= -2.8e+88:
		tmp = t_2
	elif c <= 1.85e+28:
		tmp = t_1
	elif c <= 1.06e+48:
		tmp = -2.0 * (c * (a * i))
	elif c <= 9.2e+61:
		tmp = t_1
	else:
		tmp = -2.0 * ((b * c) * (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -1.15e+204)
		tmp = t_2;
	elseif (c <= -1.1e+180)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (c <= -2.8e+88)
		tmp = t_2;
	elseif (c <= 1.85e+28)
		tmp = t_1;
	elseif (c <= 1.06e+48)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	elseif (c <= 9.2e+61)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(Float64(b * c) * Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (c * (c * (b * i)));
	tmp = 0.0;
	if (c <= -1.15e+204)
		tmp = t_2;
	elseif (c <= -1.1e+180)
		tmp = -2.0 * (a * (c * i));
	elseif (c <= -2.8e+88)
		tmp = t_2;
	elseif (c <= 1.85e+28)
		tmp = t_1;
	elseif (c <= 1.06e+48)
		tmp = -2.0 * (c * (a * i));
	elseif (c <= 9.2e+61)
		tmp = t_1;
	else
		tmp = -2.0 * ((b * c) * (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+204], t$95$2, If[LessEqual[c, -1.1e+180], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.8e+88], t$95$2, If[LessEqual[c, 1.85e+28], t$95$1, If[LessEqual[c, 1.06e+48], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+61], t$95$1, N[(-2.0 * N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.14999999999999995e204 or -1.1e180 < c < -2.79999999999999989e88

   1. Initial program 78.4%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in c around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. unpow2 75.4%

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

      3. associate-*r* 73.1%

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

      4. associate-*r* 75.3%

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

      5. *-commutative 75.3%

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

   5. Simplified 75.3%

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

      1. expm1-log1p-u 43.5%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 43.3%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 41.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 41.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 43.3%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 43.3%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 43.5%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 75.3%

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

   9. Simplified 75.3%

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

   if -1.14999999999999995e204 < c < -1.1e180

   1. Initial program 71.5%

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

   2. Taylor expanded in x around 0 89.9%

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

   3. Taylor expanded in a around inf 68.9%

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

   if -2.79999999999999989e88 < c < 1.85e28 or 1.06e48 < c < 9.1999999999999998e61

   1. Initial program 97.1%

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

   2. Taylor expanded in c around 0 82.9%

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

   if 1.85e28 < c < 1.06e48

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in a around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r* 100.0%

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

   5. Simplified 100.0%

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

   if 9.1999999999999998e61 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 92.8%

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

   3. Taylor expanded in c around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. unpow2 65.7%

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

      3. associate-*r* 68.0%

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

      4. associate-*r* 73.6%

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

      5. *-commutative 73.6%

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

   5. Simplified 73.6%

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

      1. expm1-log1p-u 37.7%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 31.0%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 31.0%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 31.0%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 36.5%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 72.4%

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

   9. Simplified 72.4%

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

   10. Taylor expanded in c around 0 65.7%

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

       1. unpow2 65.7%

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

       2. associate-*r* 68.0%

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

       3. associate-*r* 75.1%

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

       4. *-commutative 75.1%

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

   12. Simplified 75.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+204}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+88}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+28}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+61}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 68.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := \left(b \cdot -2\right) \cdot \left(i \cdot \left(c \cdot c\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+177}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* (* b -2.0) (* i (* c c)))))
   (if (<= c -1.2e+204)
     t_2
     (if (<= c -5.8e+177)
       (* -2.0 (* a (* c i)))
       (if (<= c -3e+82)
         t_2
         (if (<= c 3.3e+28)
           t_1
           (if (<= c 2.65e+48)
             (* -2.0 (* c (* a i)))
             (if (<= c 4.9e+61) t_1 (* -2.0 (* (* b c) (* c i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (b * -2.0) * (i * (c * c));
	double tmp;
	if (c <= -1.2e+204) {
		tmp = t_2;
	} else if (c <= -5.8e+177) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -3e+82) {
		tmp = t_2;
	} else if (c <= 3.3e+28) {
		tmp = t_1;
	} else if (c <= 2.65e+48) {
		tmp = -2.0 * (c * (a * i));
	} else if (c <= 4.9e+61) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((b * c) * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (b * (-2.0d0)) * (i * (c * c))
    if (c <= (-1.2d+204)) then
        tmp = t_2
    else if (c <= (-5.8d+177)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (c <= (-3d+82)) then
        tmp = t_2
    else if (c <= 3.3d+28) then
        tmp = t_1
    else if (c <= 2.65d+48) then
        tmp = (-2.0d0) * (c * (a * i))
    else if (c <= 4.9d+61) then
        tmp = t_1
    else
        tmp = (-2.0d0) * ((b * c) * (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 t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (b * -2.0) * (i * (c * c));
	double tmp;
	if (c <= -1.2e+204) {
		tmp = t_2;
	} else if (c <= -5.8e+177) {
		tmp = -2.0 * (a * (c * i));
	} else if (c <= -3e+82) {
		tmp = t_2;
	} else if (c <= 3.3e+28) {
		tmp = t_1;
	} else if (c <= 2.65e+48) {
		tmp = -2.0 * (c * (a * i));
	} else if (c <= 4.9e+61) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((b * c) * (c * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = (b * -2.0) * (i * (c * c))
	tmp = 0
	if c <= -1.2e+204:
		tmp = t_2
	elif c <= -5.8e+177:
		tmp = -2.0 * (a * (c * i))
	elif c <= -3e+82:
		tmp = t_2
	elif c <= 3.3e+28:
		tmp = t_1
	elif c <= 2.65e+48:
		tmp = -2.0 * (c * (a * i))
	elif c <= 4.9e+61:
		tmp = t_1
	else:
		tmp = -2.0 * ((b * c) * (c * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(Float64(b * -2.0) * Float64(i * Float64(c * c)))
	tmp = 0.0
	if (c <= -1.2e+204)
		tmp = t_2;
	elseif (c <= -5.8e+177)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (c <= -3e+82)
		tmp = t_2;
	elseif (c <= 3.3e+28)
		tmp = t_1;
	elseif (c <= 2.65e+48)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	elseif (c <= 4.9e+61)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(Float64(b * c) * Float64(c * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = (b * -2.0) * (i * (c * c));
	tmp = 0.0;
	if (c <= -1.2e+204)
		tmp = t_2;
	elseif (c <= -5.8e+177)
		tmp = -2.0 * (a * (c * i));
	elseif (c <= -3e+82)
		tmp = t_2;
	elseif (c <= 3.3e+28)
		tmp = t_1;
	elseif (c <= 2.65e+48)
		tmp = -2.0 * (c * (a * i));
	elseif (c <= 4.9e+61)
		tmp = t_1;
	else
		tmp = -2.0 * ((b * c) * (c * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * -2.0), $MachinePrecision] * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+204], t$95$2, If[LessEqual[c, -5.8e+177], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e+82], t$95$2, If[LessEqual[c, 3.3e+28], t$95$1, If[LessEqual[c, 2.65e+48], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e+61], t$95$1, N[(-2.0 * N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.2e204 or -5.80000000000000027e177 < c < -2.99999999999999989e82

   1. Initial program 79.7%

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

   2. Taylor expanded in x around 0 74.8%

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

   3. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. unpow2 78.9%

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

      3. associate-*r* 74.1%

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

      4. associate-*r* 76.3%

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

      5. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in c around 0 78.9%

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

      1. associate-*r* 78.9%

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

      2. unpow2 78.9%

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

   8. Simplified 78.9%

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

   if -1.2e204 < c < -5.80000000000000027e177

   1. Initial program 68.6%

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

   2. Taylor expanded in x around 0 91.4%

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

   3. Taylor expanded in a around inf 65.8%

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

   if -2.99999999999999989e82 < c < 3.3e28 or 2.65e48 < c < 4.90000000000000025e61

   1. Initial program 97.1%

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

   2. Taylor expanded in c around 0 82.9%

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

   if 3.3e28 < c < 2.65e48

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in a around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r* 100.0%

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

   5. Simplified 100.0%

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

   if 4.90000000000000025e61 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 92.8%

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

   3. Taylor expanded in c around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. unpow2 65.7%

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

      3. associate-*r* 68.0%

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

      4. associate-*r* 73.6%

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

      5. *-commutative 73.6%

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

   5. Simplified 73.6%

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

      1. expm1-log1p-u 37.7%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 31.0%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. associate-*r* 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(b \cdot c\right) \cdot i}\right)} - 1\right)\right) \]

      4. *-commutative 32.4%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot b\right)} \cdot i\right)} - 1\right)\right) \]

      5. associate-*l* 31.0%

         \[\leadsto -2 \cdot \left(c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot \left(b \cdot i\right)}\right)} - 1\right)\right) \]

   7. Applied egg-rr 31.0%

      \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)} - 1\right)}\right) \]
   8. Step-by-step derivation

      1. expm1-def 36.5%

         \[\leadsto -2 \cdot \left(c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      2. expm1-log1p 72.4%

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

   9. Simplified 72.4%

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

   10. Taylor expanded in c around 0 65.7%

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

       1. unpow2 65.7%

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

       2. associate-*r* 68.0%

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

       3. associate-*r* 75.1%

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

       4. *-commutative 75.1%

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

   12. Simplified 75.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+204}:\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(i \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+177}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{+82}:\\ \;\;\;\;\left(b \cdot -2\right) \cdot \left(i \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+61}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.4 \cdot 10^{-19} \lor \neg \left(c \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.4e-19) (not (<= c 1.4e-37)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.4e-19) || !(c <= 1.4e-37)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-8.4d-19)) .or. (.not. (c <= 1.4d-37))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.4e-19) || !(c <= 1.4e-37)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.4e-19) or not (c <= 1.4e-37):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.4e-19) || !(c <= 1.4e-37))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8.4e-19) || ~((c <= 1.4e-37)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.4e-19], N[Not[LessEqual[c, 1.4e-37]], $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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.3999999999999996e-19 or 1.4000000000000001e-37 < 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 x around 0 83.8%

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

   if -8.3999999999999996e-19 < c < 1.4000000000000001e-37

   1. Initial program 97.1%

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

   2. Taylor expanded in c around 0 87.0%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.4 \cdot 10^{-19} \lor \neg \left(c \leq 1.4 \cdot 10^{-37}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 12: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+80} \lor \neg \left(c \leq 1.25 \cdot 10^{-57}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.05e+80) (not (<= c 1.25e-57)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e+80) || !(c <= 1.25e-57)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.05d+80)) .or. (.not. (c <= 1.25d-57))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e+80) || !(c <= 1.25e-57)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.05e+80) or not (c <= 1.25e-57):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.05e+80) || !(c <= 1.25e-57))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.05e+80) || ~((c <= 1.25e-57)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.05e+80], N[Not[LessEqual[c, 1.25e-57]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.05000000000000001e80 or 1.25e-57 < c

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 90.0%

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

   if -1.05000000000000001e80 < c < 1.25e-57

   1. Initial program 96.7%

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

   2. Taylor expanded in c around 0 84.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+80} \lor \neg \left(c \leq 1.25 \cdot 10^{-57}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 13: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+84} \lor \neg \left(c \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.8e+84) (not (<= c 2.4e-27)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e+84) || !(c <= 2.4e-27)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.8d+84)) .or. (.not. (c <= 2.4d-27))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.8e+84) || !(c <= 2.4e-27)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.8e+84) or not (c <= 2.4e-27):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.8e+84) || !(c <= 2.4e-27))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.8e+84) || ~((c <= 2.4e-27)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.8e+84], N[Not[LessEqual[c, 2.4e-27]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8e84 or 2.40000000000000002e-27 < c

   1. Initial program 83.2%

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

   2. Taylor expanded in z around 0 90.4%

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

   if -1.8e84 < c < 2.40000000000000002e-27

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 89.8%

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

      1. *-commutative 89.8%

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

   4. Simplified 89.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+84} \lor \neg \left(c \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 14: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+80} \lor \neg \left(c \leq 1.55 \cdot 10^{+23}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.1e+80) (not (<= c 1.55e+23)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+80) || !(c <= 1.55e+23)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.1d+80)) .or. (.not. (c <= 1.55d+23))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+80) || !(c <= 1.55e+23)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.1e+80) or not (c <= 1.55e+23):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.1e+80) || !(c <= 1.55e+23))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.1e+80) || ~((c <= 1.55e+23)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.1e+80], N[Not[LessEqual[c, 1.55e+23]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.10000000000000001e80 or 1.54999999999999985e23 < c

   1. Initial program 82.3%

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

   2. Taylor expanded in x around 0 86.4%

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

   3. Taylor expanded in t around 0 85.4%

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

   if -2.10000000000000001e80 < c < 1.54999999999999985e23

   1. Initial program 97.1%

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

   2. Taylor expanded in c around 0 82.6%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+80} \lor \neg \left(c \leq 1.55 \cdot 10^{+23}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 15: 39.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* x y) 2.0)) (t_2 (* 2.0 (* z t))))
   (if (<= t -2.65e-92)
     t_2
     (if (<= t 4.3e-18)
       t_1
       (if (<= t 1.75e+53)
         (* -2.0 (* a (* c i)))
         (if (<= t 7.5e+95) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.65e-92) {
		tmp = t_2;
	} else if (t <= 4.3e-18) {
		tmp = t_1;
	} else if (t <= 1.75e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if (t <= 7.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) * 2.0d0
    t_2 = 2.0d0 * (z * t)
    if (t <= (-2.65d-92)) then
        tmp = t_2
    else if (t <= 4.3d-18) then
        tmp = t_1
    else if (t <= 1.75d+53) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (t <= 7.5d+95) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) * 2.0;
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.65e-92) {
		tmp = t_2;
	} else if (t <= 4.3e-18) {
		tmp = t_1;
	} else if (t <= 1.75e+53) {
		tmp = -2.0 * (a * (c * i));
	} else if (t <= 7.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) * 2.0
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -2.65e-92:
		tmp = t_2
	elif t <= 4.3e-18:
		tmp = t_1
	elif t <= 1.75e+53:
		tmp = -2.0 * (a * (c * i))
	elif t <= 7.5e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) * 2.0)
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -2.65e-92)
		tmp = t_2;
	elseif (t <= 4.3e-18)
		tmp = t_1;
	elseif (t <= 1.75e+53)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (t <= 7.5e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) * 2.0;
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -2.65e-92)
		tmp = t_2;
	elseif (t <= 4.3e-18)
		tmp = t_1;
	elseif (t <= 1.75e+53)
		tmp = -2.0 * (a * (c * i));
	elseif (t <= 7.5e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e-92], t$95$2, If[LessEqual[t, 4.3e-18], t$95$1, If[LessEqual[t, 1.75e+53], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+95], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.65000000000000015e-92 or 7.5000000000000001e95 < t

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 44.7%

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

   if -2.65000000000000015e-92 < t < 4.3000000000000002e-18 or 1.75000000000000009e53 < t < 7.5000000000000001e95

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 39.8%

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

   if 4.3000000000000002e-18 < t < 1.75000000000000009e53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.3%

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

   3. Taylor expanded in a around inf 20.8%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-92}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-18}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+53}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 40.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-92} \lor \neg \left(t \leq 7.2 \cdot 10^{+95}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -2.3e-92) (not (<= t 7.2e+95)))
   (* 2.0 (* z t))
   (* (* x y) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -2.3e-92) || !(t <= 7.2e+95)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 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 ((t <= (-2.3d-92)) .or. (.not. (t <= 7.2d+95))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (x * y) * 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 ((t <= -2.3e-92) || !(t <= 7.2e+95)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -2.3e-92) or not (t <= 7.2e+95):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -2.3e-92) || !(t <= 7.2e+95))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -2.3e-92) || ~((t <= 7.2e+95)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -2.3e-92], N[Not[LessEqual[t, 7.2e+95]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000016e-92 or 7.19999999999999955e95 < t

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 44.7%

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

   if -2.30000000000000016e-92 < t < 7.19999999999999955e95

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 37.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-92} \lor \neg \left(t \leq 7.2 \cdot 10^{+95}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 17: 28.9% 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 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 z around inf 28.5%

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

3. Final simplification 28.5%

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

Developer target: 94.3% 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 2023285 
(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))))