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

Percentage Accurate: 89.8% → 96.1%

Time: 12.7s

Alternatives: 17

Speedup: 0.5×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* z t) (* x y)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* 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 tmp;
	if ((((z * t) + (x * y)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (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))
	tmp = 0.0
	if (Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

      1. associate-*l* 97.8%

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

      2. fma-def 97.8%

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

   3. Simplified 97.8%

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

   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 i around inf 62.8%

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

   3. Taylor expanded in i around 0 62.8%

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

4. Final simplification 95.7%

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

Alternative 2: 92.8% accurate, 0.5× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

   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 i around inf 62.8%

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

   3. Taylor expanded in i around 0 62.8%

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

4. Final simplification 94.6%

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

Alternative 3: 96.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(-2.0 * Float64(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 = (z * t) + (x * y);
	tmp = 0.0;
	if ((t_2 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = -2.0 * (c * (t_1 * i));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

      1. associate-*l* 97.8%

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

      2. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-def 97.8%

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

      2. +-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

   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 i around inf 62.8%

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

   3. Taylor expanded in i around 0 62.8%

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

4. Final simplification 95.7%

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

Alternative 4: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* 2.0 (* x y)))
        (t_3 (* -2.0 (* c (* b (* c i))))))
   (if (<= c -2.8e+100)
     t_3
     (if (<= c -6.6e+26)
       t_1
       (if (<= c -2.25e-94)
         (* 2.0 (* i (* c (- a))))
         (if (<= c 1.3e-285)
           t_1
           (if (<= c 7e-152)
             t_2
             (if (<= c 1.28e-76) t_1 (if (<= c 3.2e-14) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2.8e+100) {
		tmp = t_3;
	} else if (c <= -6.6e+26) {
		tmp = t_1;
	} else if (c <= -2.25e-94) {
		tmp = 2.0 * (i * (c * -a));
	} else if (c <= 1.3e-285) {
		tmp = t_1;
	} else if (c <= 7e-152) {
		tmp = t_2;
	} else if (c <= 1.28e-76) {
		tmp = t_1;
	} else if (c <= 3.2e-14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    t_3 = (-2.0d0) * (c * (b * (c * i)))
    if (c <= (-2.8d+100)) then
        tmp = t_3
    else if (c <= (-6.6d+26)) then
        tmp = t_1
    else if (c <= (-2.25d-94)) then
        tmp = 2.0d0 * (i * (c * -a))
    else if (c <= 1.3d-285) then
        tmp = t_1
    else if (c <= 7d-152) then
        tmp = t_2
    else if (c <= 1.28d-76) then
        tmp = t_1
    else if (c <= 3.2d-14) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2.8e+100) {
		tmp = t_3;
	} else if (c <= -6.6e+26) {
		tmp = t_1;
	} else if (c <= -2.25e-94) {
		tmp = 2.0 * (i * (c * -a));
	} else if (c <= 1.3e-285) {
		tmp = t_1;
	} else if (c <= 7e-152) {
		tmp = t_2;
	} else if (c <= 1.28e-76) {
		tmp = t_1;
	} else if (c <= 3.2e-14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	t_3 = -2.0 * (c * (b * (c * i)))
	tmp = 0
	if c <= -2.8e+100:
		tmp = t_3
	elif c <= -6.6e+26:
		tmp = t_1
	elif c <= -2.25e-94:
		tmp = 2.0 * (i * (c * -a))
	elif c <= 1.3e-285:
		tmp = t_1
	elif c <= 7e-152:
		tmp = t_2
	elif c <= 1.28e-76:
		tmp = t_1
	elif c <= 3.2e-14:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	t_3 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	tmp = 0.0
	if (c <= -2.8e+100)
		tmp = t_3;
	elseif (c <= -6.6e+26)
		tmp = t_1;
	elseif (c <= -2.25e-94)
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(-a))));
	elseif (c <= 1.3e-285)
		tmp = t_1;
	elseif (c <= 7e-152)
		tmp = t_2;
	elseif (c <= 1.28e-76)
		tmp = t_1;
	elseif (c <= 3.2e-14)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	t_3 = -2.0 * (c * (b * (c * i)));
	tmp = 0.0;
	if (c <= -2.8e+100)
		tmp = t_3;
	elseif (c <= -6.6e+26)
		tmp = t_1;
	elseif (c <= -2.25e-94)
		tmp = 2.0 * (i * (c * -a));
	elseif (c <= 1.3e-285)
		tmp = t_1;
	elseif (c <= 7e-152)
		tmp = t_2;
	elseif (c <= 1.28e-76)
		tmp = t_1;
	elseif (c <= 3.2e-14)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+100], t$95$3, If[LessEqual[c, -6.6e+26], t$95$1, If[LessEqual[c, -2.25e-94], N[(2.0 * N[(i * N[(c * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-285], t$95$1, If[LessEqual[c, 7e-152], t$95$2, If[LessEqual[c, 1.28e-76], t$95$1, If[LessEqual[c, 3.2e-14], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.7999999999999998e100 or 3.2000000000000002e-14 < c

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. *-commutative 68.5%

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

      3. distribute-rgt-neg-in 68.5%

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

      4. unpow2 68.5%

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

      5. distribute-rgt-neg-in 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in i around 0 68.5%

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

      1. unpow2 68.5%

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

      2. associate-*r* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in c around 0 68.5%

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

      1. unpow2 68.5%

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

      2. associate-*r* 70.3%

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

      3. associate-*r* 69.6%

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

      4. *-commutative 69.6%

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

   10. Simplified 69.6%

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

   if -2.7999999999999998e100 < c < -6.59999999999999987e26 or -2.2500000000000001e-94 < c < 1.3000000000000001e-285 or 7.0000000000000002e-152 < c < 1.28e-76

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 61.5%

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

   if -6.59999999999999987e26 < c < -2.2500000000000001e-94

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 79.6%

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

   3. Taylor expanded in z around 0 59.9%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-*r* 39.3%

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

      3. distribute-rgt-neg-in 39.3%

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

      4. *-commutative 39.3%

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

      5. associate-*r* 39.4%

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

   8. Simplified 39.4%

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

   if 1.3000000000000001e-285 < c < 7.0000000000000002e-152 or 1.28e-76 < c < 3.2000000000000002e-14

   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 x around inf 54.0%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-152}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.28 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := -2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* 2.0 (* x y)))
        (t_3 (* -2.0 (* b (* i (* c c))))))
   (if (<= c -2.05e+62)
     t_3
     (if (<= c -6.6e+26)
       t_1
       (if (<= c -1.05e-90)
         (* 2.0 (* i (* c (- a))))
         (if (<= c 4.8e-285)
           t_1
           (if (<= c 1e-149)
             t_2
             (if (<= c 2.2e-76) t_1 (if (<= c 3.35e-15) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (b * (i * (c * c)));
	double tmp;
	if (c <= -2.05e+62) {
		tmp = t_3;
	} else if (c <= -6.6e+26) {
		tmp = t_1;
	} else if (c <= -1.05e-90) {
		tmp = 2.0 * (i * (c * -a));
	} else if (c <= 4.8e-285) {
		tmp = t_1;
	} else if (c <= 1e-149) {
		tmp = t_2;
	} else if (c <= 2.2e-76) {
		tmp = t_1;
	} else if (c <= 3.35e-15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    t_3 = (-2.0d0) * (b * (i * (c * c)))
    if (c <= (-2.05d+62)) then
        tmp = t_3
    else if (c <= (-6.6d+26)) then
        tmp = t_1
    else if (c <= (-1.05d-90)) then
        tmp = 2.0d0 * (i * (c * -a))
    else if (c <= 4.8d-285) then
        tmp = t_1
    else if (c <= 1d-149) then
        tmp = t_2
    else if (c <= 2.2d-76) then
        tmp = t_1
    else if (c <= 3.35d-15) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (b * (i * (c * c)));
	double tmp;
	if (c <= -2.05e+62) {
		tmp = t_3;
	} else if (c <= -6.6e+26) {
		tmp = t_1;
	} else if (c <= -1.05e-90) {
		tmp = 2.0 * (i * (c * -a));
	} else if (c <= 4.8e-285) {
		tmp = t_1;
	} else if (c <= 1e-149) {
		tmp = t_2;
	} else if (c <= 2.2e-76) {
		tmp = t_1;
	} else if (c <= 3.35e-15) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	t_3 = -2.0 * (b * (i * (c * c)))
	tmp = 0
	if c <= -2.05e+62:
		tmp = t_3
	elif c <= -6.6e+26:
		tmp = t_1
	elif c <= -1.05e-90:
		tmp = 2.0 * (i * (c * -a))
	elif c <= 4.8e-285:
		tmp = t_1
	elif c <= 1e-149:
		tmp = t_2
	elif c <= 2.2e-76:
		tmp = t_1
	elif c <= 3.35e-15:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	t_3 = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))))
	tmp = 0.0
	if (c <= -2.05e+62)
		tmp = t_3;
	elseif (c <= -6.6e+26)
		tmp = t_1;
	elseif (c <= -1.05e-90)
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(-a))));
	elseif (c <= 4.8e-285)
		tmp = t_1;
	elseif (c <= 1e-149)
		tmp = t_2;
	elseif (c <= 2.2e-76)
		tmp = t_1;
	elseif (c <= 3.35e-15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	t_3 = -2.0 * (b * (i * (c * c)));
	tmp = 0.0;
	if (c <= -2.05e+62)
		tmp = t_3;
	elseif (c <= -6.6e+26)
		tmp = t_1;
	elseif (c <= -1.05e-90)
		tmp = 2.0 * (i * (c * -a));
	elseif (c <= 4.8e-285)
		tmp = t_1;
	elseif (c <= 1e-149)
		tmp = t_2;
	elseif (c <= 2.2e-76)
		tmp = t_1;
	elseif (c <= 3.35e-15)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.05e+62], t$95$3, If[LessEqual[c, -6.6e+26], t$95$1, If[LessEqual[c, -1.05e-90], N[(2.0 * N[(i * N[(c * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e-285], t$95$1, If[LessEqual[c, 1e-149], t$95$2, If[LessEqual[c, 2.2e-76], t$95$1, If[LessEqual[c, 3.35e-15], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.04999999999999992e62 or 3.35e-15 < c

   1. Initial program 81.8%

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

   2. Taylor expanded in b around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. *-commutative 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. unpow2 66.6%

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

      5. distribute-rgt-neg-in 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in i around 0 66.6%

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

      1. unpow2 66.6%

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

      2. associate-*r* 70.4%

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

   7. Simplified 70.4%

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

   if -2.04999999999999992e62 < c < -6.59999999999999987e26 or -1.05e-90 < c < 4.8000000000000001e-285 or 9.99999999999999979e-150 < c < 2.19999999999999999e-76

   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 z around inf 63.5%

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

   if -6.59999999999999987e26 < c < -1.05e-90

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 79.6%

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

   3. Taylor expanded in z around 0 59.9%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-*r* 39.3%

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

      3. distribute-rgt-neg-in 39.3%

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

      4. *-commutative 39.3%

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

      5. associate-*r* 39.4%

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

   8. Simplified 39.4%

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

   if 4.8000000000000001e-285 < c < 9.99999999999999979e-150 or 2.19999999999999999e-76 < c < 3.35e-15

   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 x around inf 54.0%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+62}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 10^{-149}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 520000:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))))
   (if (<= a -7.8e+70)
     (* 2.0 (- t_1 (* i (* a c))))
     (if (<= a 520000.0)
       (* 2.0 (- t_1 (* c (* c (* b i)))))
       (* 2.0 (- t_1 (* a (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if (a <= -7.8e+70) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 520000.0) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else {
		tmp = 2.0 * (t_1 - (a * (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) :: tmp
    t_1 = (z * t) + (x * y)
    if (a <= (-7.8d+70)) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (a <= 520000.0d0) then
        tmp = 2.0d0 * (t_1 - (c * (c * (b * i))))
    else
        tmp = 2.0d0 * (t_1 - (a * (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 = (z * t) + (x * y);
	double tmp;
	if (a <= -7.8e+70) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (a <= 520000.0) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else {
		tmp = 2.0 * (t_1 - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	tmp = 0
	if a <= -7.8e+70:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif a <= 520000.0:
		tmp = 2.0 * (t_1 - (c * (c * (b * i))))
	else:
		tmp = 2.0 * (t_1 - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (a <= -7.8e+70)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (a <= 520000.0)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(b * i)))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	tmp = 0.0;
	if (a <= -7.8e+70)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (a <= 520000.0)
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	else
		tmp = 2.0 * (t_1 - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+70], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 520000.0], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.79999999999999949e70

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 86.5%

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

   if -7.79999999999999949e70 < a < 5.2e5

   1. Initial program 90.5%

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

   2. Taylor expanded in a around 0 85.2%

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

      1. unpow2 85.2%

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

      2. associate-*r* 91.1%

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

   4. Simplified 91.1%

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

   if 5.2e5 < a

   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. Step-by-step derivation

      1. associate-*l* 92.3%

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

      2. fma-def 95.6%

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

   3. Simplified 95.6%

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

      1. fma-def 92.3%

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

      2. +-commutative 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in a around inf 84.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 520000:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-295}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+148}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= t -2.05e-82)
     t_2
     (if (<= t -9.5e-205)
       t_1
       (if (<= t 7e-295)
         (* 2.0 (* i (* c (- a))))
         (if (<= t 8.5e+50)
           t_1
           (if (or (<= t 4.2e+130) (not (<= t 1.95e+148)))
             t_2
             (* -2.0 (* c (* a 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 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.05e-82) {
		tmp = t_2;
	} else if (t <= -9.5e-205) {
		tmp = t_1;
	} else if (t <= 7e-295) {
		tmp = 2.0 * (i * (c * -a));
	} else if (t <= 8.5e+50) {
		tmp = t_1;
	} else if ((t <= 4.2e+130) || !(t <= 1.95e+148)) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (c * (a * 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 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (t <= (-2.05d-82)) then
        tmp = t_2
    else if (t <= (-9.5d-205)) then
        tmp = t_1
    else if (t <= 7d-295) then
        tmp = 2.0d0 * (i * (c * -a))
    else if (t <= 8.5d+50) then
        tmp = t_1
    else if ((t <= 4.2d+130) .or. (.not. (t <= 1.95d+148))) then
        tmp = t_2
    else
        tmp = (-2.0d0) * (c * (a * 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 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -2.05e-82) {
		tmp = t_2;
	} else if (t <= -9.5e-205) {
		tmp = t_1;
	} else if (t <= 7e-295) {
		tmp = 2.0 * (i * (c * -a));
	} else if (t <= 8.5e+50) {
		tmp = t_1;
	} else if ((t <= 4.2e+130) || !(t <= 1.95e+148)) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (c * (a * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -2.05e-82:
		tmp = t_2
	elif t <= -9.5e-205:
		tmp = t_1
	elif t <= 7e-295:
		tmp = 2.0 * (i * (c * -a))
	elif t <= 8.5e+50:
		tmp = t_1
	elif (t <= 4.2e+130) or not (t <= 1.95e+148):
		tmp = t_2
	else:
		tmp = -2.0 * (c * (a * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -2.05e-82)
		tmp = t_2;
	elseif (t <= -9.5e-205)
		tmp = t_1;
	elseif (t <= 7e-295)
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(-a))));
	elseif (t <= 8.5e+50)
		tmp = t_1;
	elseif ((t <= 4.2e+130) || !(t <= 1.95e+148))
		tmp = t_2;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -2.05e-82)
		tmp = t_2;
	elseif (t <= -9.5e-205)
		tmp = t_1;
	elseif (t <= 7e-295)
		tmp = 2.0 * (i * (c * -a));
	elseif (t <= 8.5e+50)
		tmp = t_1;
	elseif ((t <= 4.2e+130) || ~((t <= 1.95e+148)))
		tmp = t_2;
	else
		tmp = -2.0 * (c * (a * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e-82], t$95$2, If[LessEqual[t, -9.5e-205], t$95$1, If[LessEqual[t, 7e-295], N[(2.0 * N[(i * N[(c * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+50], t$95$1, If[Or[LessEqual[t, 4.2e+130], N[Not[LessEqual[t, 1.95e+148]], $MachinePrecision]], t$95$2, N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.04999999999999998e-82 or 8.49999999999999961e50 < t < 4.19999999999999981e130 or 1.95000000000000001e148 < t

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf 53.0%

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

   if -2.04999999999999998e-82 < t < -9.49999999999999957e-205 or 6.99999999999999977e-295 < t < 8.49999999999999961e50

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 39.3%

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

   if -9.49999999999999957e-205 < t < 6.99999999999999977e-295

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf 57.9%

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

   3. Taylor expanded in z around 0 39.5%

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

      1. associate-*r* 53.1%

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

      2. *-commutative 53.1%

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

      3. *-commutative 53.1%

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

      4. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in y around 0 26.0%

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

      1. mul-1-neg 26.0%

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

      2. associate-*r* 30.3%

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

      3. distribute-rgt-neg-in 30.3%

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

      4. *-commutative 30.3%

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

      5. associate-*r* 39.6%

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

   8. Simplified 39.6%

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

   if 4.19999999999999981e130 < t < 1.95000000000000001e148

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 79.7%

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

   3. Taylor expanded in z around 0 60.5%

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

      1. associate-*r* 60.1%

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

      2. *-commutative 60.1%

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

      3. *-commutative 60.1%

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

      4. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-*r* 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. *-commutative 60.2%

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

      5. associate-*r* 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in i around 0 60.5%

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

       1. *-commutative 60.5%

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

   11. Simplified 60.5%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-205}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-295}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+148}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -2.25 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= c -2.25e+100)
     (* -2.0 (* c (* c (* b i))))
     (if (<= c 1.1e-285)
       t_1
       (if (<= c 2e-149)
         t_2
         (if (<= c 6.5e-76)
           t_1
           (if (<= c 1.02e-14) t_2 (* -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 * (x * y);
	double tmp;
	if (c <= -2.25e+100) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else if (c <= 1.1e-285) {
		tmp = t_1;
	} else if (c <= 2e-149) {
		tmp = t_2;
	} else if (c <= 6.5e-76) {
		tmp = t_1;
	} else if (c <= 1.02e-14) {
		tmp = t_2;
	} 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) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-2.25d+100)) then
        tmp = (-2.0d0) * (c * (c * (b * i)))
    else if (c <= 1.1d-285) then
        tmp = t_1
    else if (c <= 2d-149) then
        tmp = t_2
    else if (c <= 6.5d-76) then
        tmp = t_1
    else if (c <= 1.02d-14) then
        tmp = t_2
    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 * (x * y);
	double tmp;
	if (c <= -2.25e+100) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else if (c <= 1.1e-285) {
		tmp = t_1;
	} else if (c <= 2e-149) {
		tmp = t_2;
	} else if (c <= 6.5e-76) {
		tmp = t_1;
	} else if (c <= 1.02e-14) {
		tmp = t_2;
	} 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 * (x * y)
	tmp = 0
	if c <= -2.25e+100:
		tmp = -2.0 * (c * (c * (b * i)))
	elif c <= 1.1e-285:
		tmp = t_1
	elif c <= 2e-149:
		tmp = t_2
	elif c <= 6.5e-76:
		tmp = t_1
	elif c <= 1.02e-14:
		tmp = t_2
	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(x * y))
	tmp = 0.0
	if (c <= -2.25e+100)
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	elseif (c <= 1.1e-285)
		tmp = t_1;
	elseif (c <= 2e-149)
		tmp = t_2;
	elseif (c <= 6.5e-76)
		tmp = t_1;
	elseif (c <= 1.02e-14)
		tmp = t_2;
	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 * (x * y);
	tmp = 0.0;
	if (c <= -2.25e+100)
		tmp = -2.0 * (c * (c * (b * i)));
	elseif (c <= 1.1e-285)
		tmp = t_1;
	elseif (c <= 2e-149)
		tmp = t_2;
	elseif (c <= 6.5e-76)
		tmp = t_1;
	elseif (c <= 1.02e-14)
		tmp = t_2;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.25e+100], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e-285], t$95$1, If[LessEqual[c, 2e-149], t$95$2, If[LessEqual[c, 6.5e-76], t$95$1, If[LessEqual[c, 1.02e-14], t$95$2, N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.25000000000000018e100

   1. Initial program 78.0%

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

   2. Taylor expanded in b around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. *-commutative 76.0%

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

      3. distribute-rgt-neg-in 76.0%

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

      4. unpow2 76.0%

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

      5. distribute-rgt-neg-in 76.0%

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

   4. Simplified 76.0%

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

   5. Taylor expanded in i around 0 76.0%

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

      1. unpow2 76.0%

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

      2. associate-*r* 78.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in c around 0 76.0%

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

      1. unpow2 76.0%

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

      2. associate-*r* 78.3%

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

   10. Simplified 78.3%

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

   if -2.25000000000000018e100 < c < 1.1e-285 or 1.99999999999999996e-149 < c < 6.5e-76

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 50.0%

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

   if 1.1e-285 < c < 1.99999999999999996e-149 or 6.5e-76 < c < 1.02e-14

   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 x around inf 54.0%

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

   if 1.02e-14 < c

   1. Initial program 82.9%

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

   2. Taylor expanded in b around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. *-commutative 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

      4. unpow2 64.2%

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

      5. distribute-rgt-neg-in 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in i around 0 64.2%

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

      1. unpow2 64.2%

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

      2. associate-*r* 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in c around 0 64.2%

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

      1. unpow2 64.2%

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

      2. associate-*r* 65.7%

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

      3. associate-*r* 65.9%

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

      4. *-commutative 65.9%

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

   10. Simplified 65.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{+100}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 9: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+52} \lor \neg \left(c \leq -6.6 \cdot 10^{+26}\right) \land \left(c \leq -1.14 \cdot 10^{-85} \lor \neg \left(c \leq 1.12 \cdot 10^{-13}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8e+52)
         (and (not (<= c -6.6e+26))
              (or (<= c -1.14e-85) (not (<= c 1.12e-13)))))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* 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 ((c <= -8e+52) || (!(c <= -6.6e+26) && ((c <= -1.14e-85) || !(c <= 1.12e-13)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((z * t) + (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 ((c <= (-8d+52)) .or. (.not. (c <= (-6.6d+26))) .and. (c <= (-1.14d-85)) .or. (.not. (c <= 1.12d-13))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((z * t) + (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 ((c <= -8e+52) || (!(c <= -6.6e+26) && ((c <= -1.14e-85) || !(c <= 1.12e-13)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8e+52) or (not (c <= -6.6e+26) and ((c <= -1.14e-85) or not (c <= 1.12e-13))):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8e+52) || (!(c <= -6.6e+26) && ((c <= -1.14e-85) || !(c <= 1.12e-13))))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(z * t) + 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 ((c <= -8e+52) || (~((c <= -6.6e+26)) && ((c <= -1.14e-85) || ~((c <= 1.12e-13)))))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8e+52], And[N[Not[LessEqual[c, -6.6e+26]], $MachinePrecision], Or[LessEqual[c, -1.14e-85], N[Not[LessEqual[c, 1.12e-13]], $MachinePrecision]]]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.9999999999999999e52 or -6.59999999999999987e26 < c < -1.1400000000000001e-85 or 1.12e-13 < c

   1. Initial program 84.7%

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

   2. Taylor expanded in i around inf 75.7%

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

   3. Taylor expanded in i around 0 75.7%

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

   if -7.9999999999999999e52 < c < -6.59999999999999987e26 or -1.1400000000000001e-85 < c < 1.12e-13

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 85.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+52} \lor \neg \left(c \leq -6.6 \cdot 10^{+26}\right) \land \left(c \leq -1.14 \cdot 10^{-85} \lor \neg \left(c \leq 1.12 \cdot 10^{-13}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 10: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.14 \cdot 10^{-85} \lor \neg \left(c \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -2.4e+62)
     t_1
     (if (<= c -6.6e+26)
       (* 2.0 (- (* z t) (* c (* a i))))
       (if (or (<= c -1.14e-85) (not (<= c 1.15e-13)))
         t_1
         (* (+ (* 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 t_1 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -2.4e+62) {
		tmp = t_1;
	} else if (c <= -6.6e+26) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((c <= -1.14e-85) || !(c <= 1.15e-13)) {
		tmp = t_1;
	} else {
		tmp = ((z * t) + (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) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-2.4d+62)) then
        tmp = t_1
    else if (c <= (-6.6d+26)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if ((c <= (-1.14d-85)) .or. (.not. (c <= 1.15d-13))) then
        tmp = t_1
    else
        tmp = ((z * t) + (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 t_1 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -2.4e+62) {
		tmp = t_1;
	} else if (c <= -6.6e+26) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((c <= -1.14e-85) || !(c <= 1.15e-13)) {
		tmp = t_1;
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -2.4e+62:
		tmp = t_1
	elif c <= -6.6e+26:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif (c <= -1.14e-85) or not (c <= 1.15e-13):
		tmp = t_1
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -2.4e+62)
		tmp = t_1;
	elseif (c <= -6.6e+26)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif ((c <= -1.14e-85) || !(c <= 1.15e-13))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -2.4e+62)
		tmp = t_1;
	elseif (c <= -6.6e+26)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif ((c <= -1.14e-85) || ~((c <= 1.15e-13)))
		tmp = t_1;
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.4e+62], t$95$1, If[LessEqual[c, -6.6e+26], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -1.14e-85], N[Not[LessEqual[c, 1.15e-13]], $MachinePrecision]], t$95$1, N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.4e62 or -6.59999999999999987e26 < c < -1.1400000000000001e-85 or 1.1499999999999999e-13 < c

   1. Initial program 84.6%

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

   2. Taylor expanded in i around inf 75.5%

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

   3. Taylor expanded in i around 0 75.5%

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

   if -2.4e62 < c < -6.59999999999999987e26

   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 a around inf 73.7%

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

   3. Taylor expanded in x around 0 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -1.1400000000000001e-85 < c < 1.1499999999999999e-13

   1. Initial program 98.1%

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

   2. Taylor expanded in c around 0 86.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.14 \cdot 10^{-85} \lor \neg \left(c \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 11: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+139} \lor \neg \left(c \leq 1.12 \cdot 10^{+32}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.5e+139) (not (<= c 1.12e+32)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (- (+ (* z t) (* x y)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.5e+139) || !(c <= 1.12e+32)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.5d+139)) .or. (.not. (c <= 1.12d+32))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.5e+139) || !(c <= 1.12e+32)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.5e+139) or not (c <= 1.12e+32):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.5e+139) || !(c <= 1.12e+32))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.5e+139) || ~((c <= 1.12e+32)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.5e+139], N[Not[LessEqual[c, 1.12e+32]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.49999999999999978e139 or 1.12000000000000007e32 < c

   1. Initial program 80.3%

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

   2. Taylor expanded in i around inf 83.9%

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

   3. Taylor expanded in i around 0 83.9%

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

   if -3.49999999999999978e139 < c < 1.12000000000000007e32

   1. Initial program 95.8%

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

   2. Taylor expanded in a around inf 87.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+139} \lor \neg \left(c \leq 1.12 \cdot 10^{+32}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 12: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+137} \lor \neg \left(c \leq 1.25 \cdot 10^{+39}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.5e+137) (not (<= c 1.25e+39)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (- (+ (* z t) (* x y)) (* a (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.5e+137) || !(c <= 1.25e+39)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.5d+137)) .or. (.not. (c <= 1.25d+39))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.5e+137) || !(c <= 1.25e+39)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.5e+137) or not (c <= 1.25e+39):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.5e+137) || !(c <= 1.25e+39))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.5e+137) || ~((c <= 1.25e+39)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.5e+137], N[Not[LessEqual[c, 1.25e+39]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.5e137 or 1.25000000000000004e39 < c

   1. Initial program 80.3%

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

   2. Taylor expanded in i around inf 83.9%

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

   3. Taylor expanded in i around 0 83.9%

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

   if -1.5e137 < c < 1.25000000000000004e39

   1. Initial program 95.8%

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

      1. associate-*l* 96.2%

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

      2. fma-def 96.8%

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

   3. Simplified 96.8%

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

      1. fma-def 96.2%

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

      2. +-commutative 96.2%

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

   5. Applied egg-rr 96.2%

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

   6. Taylor expanded in a around inf 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+137} \lor \neg \left(c \leq 1.25 \cdot 10^{+39}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 13: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+148}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -3.6e-71)
     t_1
     (if (<= t 5.7e+47)
       (* 2.0 (* x y))
       (if (or (<= t 5e+130) (not (<= t 1.95e+148)))
         t_1
         (* -2.0 (* c (* a 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 tmp;
	if (t <= -3.6e-71) {
		tmp = t_1;
	} else if (t <= 5.7e+47) {
		tmp = 2.0 * (x * y);
	} else if ((t <= 5e+130) || !(t <= 1.95e+148)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-3.6d-71)) then
        tmp = t_1
    else if (t <= 5.7d+47) then
        tmp = 2.0d0 * (x * y)
    else if ((t <= 5d+130) .or. (.not. (t <= 1.95d+148))) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (a * 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 tmp;
	if (t <= -3.6e-71) {
		tmp = t_1;
	} else if (t <= 5.7e+47) {
		tmp = 2.0 * (x * y);
	} else if ((t <= 5e+130) || !(t <= 1.95e+148)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -3.6e-71:
		tmp = t_1
	elif t <= 5.7e+47:
		tmp = 2.0 * (x * y)
	elif (t <= 5e+130) or not (t <= 1.95e+148):
		tmp = t_1
	else:
		tmp = -2.0 * (c * (a * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -3.6e-71)
		tmp = t_1;
	elseif (t <= 5.7e+47)
		tmp = Float64(2.0 * Float64(x * y));
	elseif ((t <= 5e+130) || !(t <= 1.95e+148))
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -3.6e-71)
		tmp = t_1;
	elseif (t <= 5.7e+47)
		tmp = 2.0 * (x * y);
	elseif ((t <= 5e+130) || ~((t <= 1.95e+148)))
		tmp = t_1;
	else
		tmp = -2.0 * (c * (a * 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]}, If[LessEqual[t, -3.6e-71], t$95$1, If[LessEqual[t, 5.7e+47], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5e+130], N[Not[LessEqual[t, 1.95e+148]], $MachinePrecision]], t$95$1, N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e-71 or 5.6999999999999997e47 < t < 4.9999999999999996e130 or 1.95000000000000001e148 < t

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf 53.0%

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

   if -3.6e-71 < t < 5.6999999999999997e47

   1. Initial program 94.0%

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

   2. Taylor expanded in x around inf 36.8%

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

   if 4.9999999999999996e130 < t < 1.95000000000000001e148

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 79.7%

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

   3. Taylor expanded in z around 0 60.5%

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

      1. associate-*r* 60.1%

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

      2. *-commutative 60.1%

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

      3. *-commutative 60.1%

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

      4. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-*r* 60.2%

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

      3. distribute-rgt-neg-in 60.2%

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

      4. *-commutative 60.2%

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

      5. associate-*r* 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in i around 0 60.5%

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

       1. *-commutative 60.5%

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

   11. Simplified 60.5%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-71}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+130} \lor \neg \left(t \leq 1.95 \cdot 10^{+148}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 14: 68.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+77} \lor \neg \left(c \leq 2.25 \cdot 10^{+38}\right):\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -6.2e+77) (not (<= c 2.25e+38)))
   (* -2.0 (* b (* i (* c c))))
   (* (+ (* 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 ((c <= -6.2e+77) || !(c <= 2.25e+38)) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else {
		tmp = ((z * t) + (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 ((c <= (-6.2d+77)) .or. (.not. (c <= 2.25d+38))) then
        tmp = (-2.0d0) * (b * (i * (c * c)))
    else
        tmp = ((z * t) + (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 ((c <= -6.2e+77) || !(c <= 2.25e+38)) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -6.2e+77) or not (c <= 2.25e+38):
		tmp = -2.0 * (b * (i * (c * c)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -6.2e+77) || !(c <= 2.25e+38))
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	else
		tmp = Float64(Float64(Float64(z * t) + 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 ((c <= -6.2e+77) || ~((c <= 2.25e+38)))
		tmp = -2.0 * (b * (i * (c * c)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -6.2e+77], N[Not[LessEqual[c, 2.25e+38]], $MachinePrecision]], N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.19999999999999997e77 or 2.2499999999999999e38 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in b around inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. unpow2 69.3%

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

      5. distribute-rgt-neg-in 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in i around 0 69.3%

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

      1. unpow2 69.3%

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

      2. associate-*r* 73.6%

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

   7. Simplified 73.6%

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

   if -6.19999999999999997e77 < c < 2.2499999999999999e38

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 74.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+77} \lor \neg \left(c \leq 2.25 \cdot 10^{+38}\right):\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 15: 68.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;\left(c \cdot \left(b \cdot c\right)\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -4.5e+125)
   (* (* c (* b c)) (* i -2.0))
   (if (<= c 7.6e+37)
     (* (+ (* z t) (* x y)) 2.0)
     (* -2.0 (* b (* i (* c c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.5e+125) {
		tmp = (c * (b * c)) * (i * -2.0);
	} else if (c <= 7.6e+37) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = -2.0 * (b * (i * (c * 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 <= (-4.5d+125)) then
        tmp = (c * (b * c)) * (i * (-2.0d0))
    else if (c <= 7.6d+37) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = (-2.0d0) * (b * (i * (c * 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 <= -4.5e+125) {
		tmp = (c * (b * c)) * (i * -2.0);
	} else if (c <= 7.6e+37) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = -2.0 * (b * (i * (c * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -4.5e+125:
		tmp = (c * (b * c)) * (i * -2.0)
	elif c <= 7.6e+37:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = -2.0 * (b * (i * (c * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -4.5e+125)
		tmp = Float64(Float64(c * Float64(b * c)) * Float64(i * -2.0));
	elseif (c <= 7.6e+37)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -4.5e+125)
		tmp = (c * (b * c)) * (i * -2.0);
	elseif (c <= 7.6e+37)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = -2.0 * (b * (i * (c * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -4.5e+125], N[(N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+37], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.5e125

   1. Initial program 80.6%

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

   2. Taylor expanded in b around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. unpow2 78.3%

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

      5. distribute-rgt-neg-in 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in i around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. unpow2 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 81.7%

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

      5. *-commutative 81.7%

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

      6. associate-*l* 81.7%

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

      7. *-commutative 81.7%

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

      8. associate-*l* 84.3%

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

   7. Simplified 84.3%

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

   if -4.5e125 < c < 7.59999999999999979e37

   1. Initial program 95.8%

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

   2. Taylor expanded in c around 0 73.5%

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

   if 7.59999999999999979e37 < c

   1. Initial program 80.8%

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

   2. Taylor expanded in b around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

      4. unpow2 66.7%

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

      5. distribute-rgt-neg-in 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in i around 0 66.7%

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

      1. unpow2 66.7%

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

      2. associate-*r* 70.4%

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

   7. Simplified 70.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;\left(c \cdot \left(b \cdot c\right)\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 16: 39.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-67} \lor \neg \left(t \leq 1.1 \cdot 10^{+50}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -4.1e-67) (not (<= t 1.1e+50)))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -4.1e-67) || !(t <= 1.1e+50)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-4.1d-67)) .or. (.not. (t <= 1.1d+50))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -4.1e-67) || !(t <= 1.1e+50)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -4.1e-67) or not (t <= 1.1e+50):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -4.1e-67) || !(t <= 1.1e+50))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -4.1e-67) || ~((t <= 1.1e+50)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -4.1e-67], N[Not[LessEqual[t, 1.1e+50]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0999999999999997e-67 or 1.10000000000000008e50 < t

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 51.8%

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

   if -4.0999999999999997e-67 < t < 1.10000000000000008e50

   1. Initial program 94.0%

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

   2. Taylor expanded in x around inf 36.8%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-67} \lor \neg \left(t \leq 1.1 \cdot 10^{+50}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 28.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

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

2. Taylor expanded in z around inf 33.3%

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

3. Final simplification 33.3%

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

Developer target: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023187 
(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))))