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

Percentage Accurate: 90.0% → 96.4%

Time: 17.8s

Alternatives: 16

Speedup: 0.5×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% 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: 96.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 - \left(c \cdot t\_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t\_2 - t\_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t\_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

      1. fma-define 95.6%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. fma-define 99.9%

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

      2. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 66.8%

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

   4. Taylor expanded in i around 0 66.8%

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

4. Final simplification 97.6%

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

Alternative 2: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := c \cdot t\_1\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+276}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_3 \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* c t_1)))
   (if (<= t_3 -2e+276)
     (* 2.0 (- (* z t) t_2))
     (if (<= t_3 2e+302)
       (* (- (+ (* x y) (* z t)) (* t_3 i)) 2.0)
       (* -2.0 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -2e+276) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 2e+302) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = -2.0 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = c * (t_1 * i)
    t_3 = c * t_1
    if (t_3 <= (-2d+276)) then
        tmp = 2.0d0 * ((z * t) - t_2)
    else if (t_3 <= 2d+302) then
        tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0d0
    else
        tmp = (-2.0d0) * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = c * t_1;
	double tmp;
	if (t_3 <= -2e+276) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 2e+302) {
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	} else {
		tmp = -2.0 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = c * t_1
	tmp = 0
	if t_3 <= -2e+276:
		tmp = 2.0 * ((z * t) - t_2)
	elif t_3 <= 2e+302:
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0
	else:
		tmp = -2.0 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(c * t_1)
	tmp = 0.0
	if (t_3 <= -2e+276)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	elseif (t_3 <= 2e+302)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(t_3 * i)) * 2.0);
	else
		tmp = Float64(-2.0 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	t_3 = c * t_1;
	tmp = 0.0;
	if (t_3 <= -2e+276)
		tmp = 2.0 * ((z * t) - t_2);
	elseif (t_3 <= 2e+302)
		tmp = (((x * y) + (z * t)) - (t_3 * i)) * 2.0;
	else
		tmp = -2.0 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+276], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+302], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * i), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -2.0000000000000001e276

   1. Initial program 65.3%

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

   3. Taylor expanded in x around 0 84.6%

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

   if -2.0000000000000001e276 < (*.f64 (+.f64 a (*.f64 b c)) c) < 2.0000000000000002e302

   1. Initial program 98.8%

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

   if 2.0000000000000002e302 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 68.1%

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

   3. Taylor expanded in i around inf 92.6%

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

   4. Taylor expanded in i around 0 92.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -2 \cdot 10^{+276}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -1.75 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-183}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-95}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* (* c (+ a (* b c))) (- i)))))
   (if (<= i -1.75e+98)
     t_1
     (if (<= i -4.9e-183)
       (* 2.0 (- (* z t) (* c (* b (* c i)))))
       (if (<= i 1.35e-95)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= i 1.7e-28)
           (* 2.0 (- (* z t) (* b (* c (* c i)))))
           (if (<= i 2.5e+27) (* 2.0 (- (* z t) (* c (* a i)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((c * (a + (b * c))) * -i);
	double tmp;
	if (i <= -1.75e+98) {
		tmp = t_1;
	} else if (i <= -4.9e-183) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (i <= 1.35e-95) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 1.7e-28) {
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))));
	} else if (i <= 2.5e+27) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((c * (a + (b * c))) * -i)
    if (i <= (-1.75d+98)) then
        tmp = t_1
    else if (i <= (-4.9d-183)) then
        tmp = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    else if (i <= 1.35d-95) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (i <= 1.7d-28) then
        tmp = 2.0d0 * ((z * t) - (b * (c * (c * i))))
    else if (i <= 2.5d+27) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((c * (a + (b * c))) * -i);
	double tmp;
	if (i <= -1.75e+98) {
		tmp = t_1;
	} else if (i <= -4.9e-183) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (i <= 1.35e-95) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 1.7e-28) {
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))));
	} else if (i <= 2.5e+27) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((c * (a + (b * c))) * -i)
	tmp = 0
	if i <= -1.75e+98:
		tmp = t_1
	elif i <= -4.9e-183:
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))))
	elif i <= 1.35e-95:
		tmp = ((x * y) + (z * t)) * 2.0
	elif i <= 1.7e-28:
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))))
	elif i <= 2.5e+27:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(c * Float64(a + Float64(b * c))) * Float64(-i)))
	tmp = 0.0
	if (i <= -1.75e+98)
		tmp = t_1;
	elseif (i <= -4.9e-183)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (i <= 1.35e-95)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (i <= 1.7e-28)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(b * Float64(c * Float64(c * i)))));
	elseif (i <= 2.5e+27)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((c * (a + (b * c))) * -i);
	tmp = 0.0;
	if (i <= -1.75e+98)
		tmp = t_1;
	elseif (i <= -4.9e-183)
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	elseif (i <= 1.35e-95)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (i <= 1.7e-28)
		tmp = 2.0 * ((z * t) - (b * (c * (c * i))));
	elseif (i <= 2.5e+27)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.75e+98], t$95$1, If[LessEqual[i, -4.9e-183], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e-95], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[i, 1.7e-28], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(b * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+27], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.75e98 or 2.4999999999999999e27 < i

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 74.6%

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

   4. Taylor expanded in i around inf 84.1%

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

   5. Taylor expanded in t around 0 76.8%

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

   if -1.75e98 < i < -4.9e-183

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 76.3%

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

   4. Taylor expanded in a around 0 70.1%

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

   if -4.9e-183 < i < 1.35e-95

   1. Initial program 87.2%

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

   3. Taylor expanded in c around 0 84.0%

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

   if 1.35e-95 < i < 1.7e-28

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 88.2%

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

   4. Taylor expanded in a around 0 71.0%

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

      1. *-un-lft-identity 71.0%

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

      2. *-commutative 71.0%

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

      3. associate-*r* 71.1%

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

      4. *-commutative 71.1%

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

      5. associate-*l* 71.2%

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

   6. Applied egg-rr 71.2%

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

   if 1.7e-28 < i < 2.4999999999999999e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.5%

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

   4. Taylor expanded in c around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. +-commutative 86.5%

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

      3. sub-neg 86.5%

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

      4. *-commutative 86.5%

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

      5. associate-*l* 86.5%

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

   6. Simplified 86.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-183}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-95}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(z \cdot t - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := 2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-95}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+30}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* b (* c i))))))
        (t_2 (* 2.0 (* (* c (+ a (* b c))) (- i)))))
   (if (<= i -1.85e+99)
     t_2
     (if (<= i -6.2e-181)
       t_1
       (if (<= i 1.3e-95)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= i 7.6e-31)
           t_1
           (if (<= i 3e+30) (* 2.0 (- (* z t) (* c (* a i)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	double t_2 = 2.0 * ((c * (a + (b * c))) * -i);
	double tmp;
	if (i <= -1.85e+99) {
		tmp = t_2;
	} else if (i <= -6.2e-181) {
		tmp = t_1;
	} else if (i <= 1.3e-95) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 7.6e-31) {
		tmp = t_1;
	} else if (i <= 3e+30) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    t_2 = 2.0d0 * ((c * (a + (b * c))) * -i)
    if (i <= (-1.85d+99)) then
        tmp = t_2
    else if (i <= (-6.2d-181)) then
        tmp = t_1
    else if (i <= 1.3d-95) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (i <= 7.6d-31) then
        tmp = t_1
    else if (i <= 3d+30) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	double t_2 = 2.0 * ((c * (a + (b * c))) * -i);
	double tmp;
	if (i <= -1.85e+99) {
		tmp = t_2;
	} else if (i <= -6.2e-181) {
		tmp = t_1;
	} else if (i <= 1.3e-95) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (i <= 7.6e-31) {
		tmp = t_1;
	} else if (i <= 3e+30) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (b * (c * i))))
	t_2 = 2.0 * ((c * (a + (b * c))) * -i)
	tmp = 0
	if i <= -1.85e+99:
		tmp = t_2
	elif i <= -6.2e-181:
		tmp = t_1
	elif i <= 1.3e-95:
		tmp = ((x * y) + (z * t)) * 2.0
	elif i <= 7.6e-31:
		tmp = t_1
	elif i <= 3e+30:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))))
	t_2 = Float64(2.0 * Float64(Float64(c * Float64(a + Float64(b * c))) * Float64(-i)))
	tmp = 0.0
	if (i <= -1.85e+99)
		tmp = t_2;
	elseif (i <= -6.2e-181)
		tmp = t_1;
	elseif (i <= 1.3e-95)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (i <= 7.6e-31)
		tmp = t_1;
	elseif (i <= 3e+30)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (b * (c * i))));
	t_2 = 2.0 * ((c * (a + (b * c))) * -i);
	tmp = 0.0;
	if (i <= -1.85e+99)
		tmp = t_2;
	elseif (i <= -6.2e-181)
		tmp = t_1;
	elseif (i <= 1.3e-95)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (i <= 7.6e-31)
		tmp = t_1;
	elseif (i <= 3e+30)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e+99], t$95$2, If[LessEqual[i, -6.2e-181], t$95$1, If[LessEqual[i, 1.3e-95], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[i, 7.6e-31], t$95$1, If[LessEqual[i, 3e+30], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.85000000000000005e99 or 2.99999999999999978e30 < i

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 74.6%

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

   4. Taylor expanded in i around inf 84.1%

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

   5. Taylor expanded in t around 0 76.8%

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

   if -1.85000000000000005e99 < i < -6.20000000000000043e-181 or 1.3e-95 < i < 7.5999999999999999e-31

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 79.2%

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

   4. Taylor expanded in a around 0 70.3%

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

   if -6.20000000000000043e-181 < i < 1.3e-95

   1. Initial program 87.2%

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

   3. Taylor expanded in c around 0 84.0%

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

   if 7.5999999999999999e-31 < i < 2.99999999999999978e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.5%

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

   4. Taylor expanded in c around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. +-commutative 86.5%

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

      3. sub-neg 86.5%

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

      4. *-commutative 86.5%

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

      5. associate-*l* 86.5%

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

   6. Simplified 86.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-95}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+30}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;z \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= z -1.78e+137)
     t_1
     (if (<= z -7.1e+19)
       (* -2.0 (* a (* c i)))
       (if (<= z -6.3e-221)
         t_2
         (if (<= z 1.1e-292)
           (* 2.0 (* i (* c (- a))))
           (if (<= z 5.4e-32) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (z <= -1.78e+137) {
		tmp = t_1;
	} else if (z <= -7.1e+19) {
		tmp = -2.0 * (a * (c * i));
	} else if (z <= -6.3e-221) {
		tmp = t_2;
	} else if (z <= 1.1e-292) {
		tmp = 2.0 * (i * (c * -a));
	} else if (z <= 5.4e-32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if (z <= (-1.78d+137)) then
        tmp = t_1
    else if (z <= (-7.1d+19)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (z <= (-6.3d-221)) then
        tmp = t_2
    else if (z <= 1.1d-292) then
        tmp = 2.0d0 * (i * (c * -a))
    else if (z <= 5.4d-32) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if (z <= -1.78e+137) {
		tmp = t_1;
	} else if (z <= -7.1e+19) {
		tmp = -2.0 * (a * (c * i));
	} else if (z <= -6.3e-221) {
		tmp = t_2;
	} else if (z <= 1.1e-292) {
		tmp = 2.0 * (i * (c * -a));
	} else if (z <= 5.4e-32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if z <= -1.78e+137:
		tmp = t_1
	elif z <= -7.1e+19:
		tmp = -2.0 * (a * (c * i))
	elif z <= -6.3e-221:
		tmp = t_2
	elif z <= 1.1e-292:
		tmp = 2.0 * (i * (c * -a))
	elif z <= 5.4e-32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (z <= -1.78e+137)
		tmp = t_1;
	elseif (z <= -7.1e+19)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (z <= -6.3e-221)
		tmp = t_2;
	elseif (z <= 1.1e-292)
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(-a))));
	elseif (z <= 5.4e-32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if (z <= -1.78e+137)
		tmp = t_1;
	elseif (z <= -7.1e+19)
		tmp = -2.0 * (a * (c * i));
	elseif (z <= -6.3e-221)
		tmp = t_2;
	elseif (z <= 1.1e-292)
		tmp = 2.0 * (i * (c * -a));
	elseif (z <= 5.4e-32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[z, -1.78e+137], t$95$1, If[LessEqual[z, -7.1e+19], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.3e-221], t$95$2, If[LessEqual[z, 1.1e-292], N[(2.0 * N[(i * N[(c * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-32], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.77999999999999997e137 or 5.39999999999999962e-32 < z

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf 47.9%

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

   if -1.77999999999999997e137 < z < -7.1e19

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 37.7%

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

      1. mul-1-neg 37.7%

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

      2. *-commutative 37.7%

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

      3. associate-*l* 29.1%

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

      4. *-commutative 29.1%

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

      5. distribute-rgt-neg-in 29.1%

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

      6. *-commutative 29.1%

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

      7. distribute-rgt-neg-in 29.1%

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

   5. Simplified 29.1%

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

   6. Taylor expanded in c around 0 37.7%

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

   if -7.1e19 < z < -6.29999999999999958e-221 or 1.10000000000000006e-292 < z < 5.39999999999999962e-32

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 42.2%

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

   if -6.29999999999999958e-221 < z < 1.10000000000000006e-292

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0 73.4%

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

   4. Taylor expanded in i around inf 73.1%

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

   5. Taylor expanded in a around inf 31.2%

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

      1. associate-*r* 31.2%

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

      2. mul-1-neg 31.2%

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

   7. Simplified 31.2%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.78 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-221}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-220}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-35}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* a (* c i))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= z -7.5e+137)
     t_2
     (if (<= z -1.55e+20)
       t_1
       (if (<= z -2.45e-220)
         t_3
         (if (<= z 3.05e-292) t_1 (if (<= z 4e-35) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (z <= -7.5e+137) {
		tmp = t_2;
	} else if (z <= -1.55e+20) {
		tmp = t_1;
	} else if (z <= -2.45e-220) {
		tmp = t_3;
	} else if (z <= 3.05e-292) {
		tmp = t_1;
	} else if (z <= 4e-35) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-2.0d0) * (a * (c * i))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if (z <= (-7.5d+137)) then
        tmp = t_2
    else if (z <= (-1.55d+20)) then
        tmp = t_1
    else if (z <= (-2.45d-220)) then
        tmp = t_3
    else if (z <= 3.05d-292) then
        tmp = t_1
    else if (z <= 4d-35) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (z <= -7.5e+137) {
		tmp = t_2;
	} else if (z <= -1.55e+20) {
		tmp = t_1;
	} else if (z <= -2.45e-220) {
		tmp = t_3;
	} else if (z <= 3.05e-292) {
		tmp = t_1;
	} else if (z <= 4e-35) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (a * (c * i))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if z <= -7.5e+137:
		tmp = t_2
	elif z <= -1.55e+20:
		tmp = t_1
	elif z <= -2.45e-220:
		tmp = t_3
	elif z <= 3.05e-292:
		tmp = t_1
	elif z <= 4e-35:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(a * Float64(c * i)))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (z <= -7.5e+137)
		tmp = t_2;
	elseif (z <= -1.55e+20)
		tmp = t_1;
	elseif (z <= -2.45e-220)
		tmp = t_3;
	elseif (z <= 3.05e-292)
		tmp = t_1;
	elseif (z <= 4e-35)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (a * (c * i));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if (z <= -7.5e+137)
		tmp = t_2;
	elseif (z <= -1.55e+20)
		tmp = t_1;
	elseif (z <= -2.45e-220)
		tmp = t_3;
	elseif (z <= 3.05e-292)
		tmp = t_1;
	elseif (z <= 4e-35)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[z, -7.5e+137], t$95$2, If[LessEqual[z, -1.55e+20], t$95$1, If[LessEqual[z, -2.45e-220], t$95$3, If[LessEqual[z, 3.05e-292], t$95$1, If[LessEqual[z, 4e-35], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000025e137 or 4.00000000000000003e-35 < z

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf 47.9%

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

   if -7.50000000000000025e137 < z < -1.55e20 or -2.4500000000000001e-220 < z < 3.04999999999999982e-292

   1. Initial program 83.2%

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

   3. Taylor expanded in a around inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. *-commutative 36.2%

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

      3. associate-*l* 28.4%

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

      4. *-commutative 28.4%

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

      5. distribute-rgt-neg-in 28.4%

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

      6. *-commutative 28.4%

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

      7. distribute-rgt-neg-in 28.4%

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

   5. Simplified 28.4%

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

   6. Taylor expanded in c around 0 36.2%

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

   if -1.55e20 < z < -2.4500000000000001e-220 or 3.04999999999999982e-292 < z < 4.00000000000000003e-35

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 42.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+20}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-220}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-292}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;-2 \cdot t\_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+22} \lor \neg \left(c \leq 1.7 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.55e+164)
     (* -2.0 t_1)
     (if (or (<= c -3.5e+22) (not (<= c 1.7e-47)))
       (* 2.0 (- (* z t) t_1))
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.55e+164) {
		tmp = -2.0 * t_1;
	} else if ((c <= -3.5e+22) || !(c <= 1.7e-47)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-1.55d+164)) then
        tmp = (-2.0d0) * t_1
    else if ((c <= (-3.5d+22)) .or. (.not. (c <= 1.7d-47))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.55e+164) {
		tmp = -2.0 * t_1;
	} else if ((c <= -3.5e+22) || !(c <= 1.7e-47)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.55e+164:
		tmp = -2.0 * t_1
	elif (c <= -3.5e+22) or not (c <= 1.7e-47):
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.55e+164)
		tmp = Float64(-2.0 * t_1);
	elseif ((c <= -3.5e+22) || !(c <= 1.7e-47))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.55e+164)
		tmp = -2.0 * t_1;
	elseif ((c <= -3.5e+22) || ~((c <= 1.7e-47)))
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+164], N[(-2.0 * t$95$1), $MachinePrecision], If[Or[LessEqual[c, -3.5e+22], N[Not[LessEqual[c, 1.7e-47]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5500000000000001e164

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf 90.1%

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

   4. Taylor expanded in i around 0 90.1%

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

   if -1.5500000000000001e164 < c < -3.5e22 or 1.7000000000000001e-47 < c

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 81.9%

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

   if -3.5e22 < c < 1.7000000000000001e-47

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+22} \lor \neg \left(c \leq 1.7 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{+164}:\\ \;\;\;\;-2 \cdot t\_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+22} \lor \neg \left(c \leq 6.8 \cdot 10^{-49}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -4e+164)
     (* -2.0 t_1)
     (if (or (<= c -2e+22) (not (<= c 6.8e-49)))
       (* 2.0 (- (* z t) t_1))
       (* 2.0 (- (+ (* x y) (* z t)) (* 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -4e+164) {
		tmp = -2.0 * t_1;
	} else if ((c <= -2e+22) || !(c <= 6.8e-49)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (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 = c * ((a + (b * c)) * i)
    if (c <= (-4d+164)) then
        tmp = (-2.0d0) * t_1
    else if ((c <= (-2d+22)) .or. (.not. (c <= 6.8d-49))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (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 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -4e+164) {
		tmp = -2.0 * t_1;
	} else if ((c <= -2e+22) || !(c <= 6.8e-49)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -4e+164:
		tmp = -2.0 * t_1
	elif (c <= -2e+22) or not (c <= 6.8e-49):
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -4e+164)
		tmp = Float64(-2.0 * t_1);
	elseif ((c <= -2e+22) || !(c <= 6.8e-49))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -4e+164)
		tmp = -2.0 * t_1;
	elseif ((c <= -2e+22) || ~((c <= 6.8e-49)))
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e+164], N[(-2.0 * t$95$1), $MachinePrecision], If[Or[LessEqual[c, -2e+22], N[Not[LessEqual[c, 6.8e-49]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4e164

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf 90.1%

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

   4. Taylor expanded in i around 0 90.1%

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

   if -4e164 < c < -2e22 or 6.8000000000000001e-49 < c

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 81.9%

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

   if -2e22 < c < 6.8000000000000001e-49

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 92.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+164}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+22} \lor \neg \left(c \leq 6.8 \cdot 10^{-49}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{+170}:\\ \;\;\;\;-2 \cdot t\_2\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (* c (* (+ a (* b c)) i))))
   (if (<= c -5.8e+170)
     (* -2.0 t_2)
     (if (<= c -1.15e-38)
       (* 2.0 (- t_1 (* (* b c) (* c i))))
       (if (<= c 2.3e-47)
         (* 2.0 (- t_1 (* i (* a c))))
         (* 2.0 (- (* z t) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5.8e+170) {
		tmp = -2.0 * t_2;
	} else if (c <= -1.15e-38) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else if (c <= 2.3e-47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = c * ((a + (b * c)) * i)
    if (c <= (-5.8d+170)) then
        tmp = (-2.0d0) * t_2
    else if (c <= (-1.15d-38)) then
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    else if (c <= 2.3d-47) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5.8e+170) {
		tmp = -2.0 * t_2;
	} else if (c <= -1.15e-38) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else if (c <= 2.3e-47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -5.8e+170:
		tmp = -2.0 * t_2
	elif c <= -1.15e-38:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	elif c <= 2.3e-47:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -5.8e+170)
		tmp = Float64(-2.0 * t_2);
	elseif (c <= -1.15e-38)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	elseif (c <= 2.3e-47)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -5.8e+170)
		tmp = -2.0 * t_2;
	elseif (c <= -1.15e-38)
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	elseif (c <= 2.3e-47)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.8e+170], N[(-2.0 * t$95$2), $MachinePrecision], If[LessEqual[c, -1.15e-38], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-47], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.8000000000000001e170

   1. Initial program 72.2%

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

   3. Taylor expanded in i around inf 96.5%

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

   4. Taylor expanded in i around 0 96.5%

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

   if -5.8000000000000001e170 < c < -1.15000000000000001e-38

   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. Step-by-step derivation

      1. fma-define 90.7%

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

      2. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

      1. fma-define 97.6%

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

      2. +-commutative 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in a around 0 88.6%

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

   if -1.15000000000000001e-38 < c < 2.29999999999999982e-47

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   if 2.29999999999999982e-47 < c

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+170}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+169}:\\ \;\;\;\;-2 \cdot t\_2\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (* c (* (+ a (* b c)) i))))
   (if (<= c -7e+169)
     (* -2.0 t_2)
     (if (<= c -1.25e-38)
       (* 2.0 (- t_1 (* i (* c (* b c)))))
       (if (<= c 5.8e-47)
         (* 2.0 (- t_1 (* i (* a c))))
         (* 2.0 (- (* z t) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -7e+169) {
		tmp = -2.0 * t_2;
	} else if (c <= -1.25e-38) {
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	} else if (c <= 5.8e-47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = c * ((a + (b * c)) * i)
    if (c <= (-7d+169)) then
        tmp = (-2.0d0) * t_2
    else if (c <= (-1.25d-38)) then
        tmp = 2.0d0 * (t_1 - (i * (c * (b * c))))
    else if (c <= 5.8d-47) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -7e+169) {
		tmp = -2.0 * t_2;
	} else if (c <= -1.25e-38) {
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	} else if (c <= 5.8e-47) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -7e+169:
		tmp = -2.0 * t_2
	elif c <= -1.25e-38:
		tmp = 2.0 * (t_1 - (i * (c * (b * c))))
	elif c <= 5.8e-47:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -7e+169)
		tmp = Float64(-2.0 * t_2);
	elseif (c <= -1.25e-38)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(b * c)))));
	elseif (c <= 5.8e-47)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -7e+169)
		tmp = -2.0 * t_2;
	elseif (c <= -1.25e-38)
		tmp = 2.0 * (t_1 - (i * (c * (b * c))));
	elseif (c <= 5.8e-47)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+169], N[(-2.0 * t$95$2), $MachinePrecision], If[LessEqual[c, -1.25e-38], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e-47], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.00000000000000038e169

   1. Initial program 72.2%

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

   3. Taylor expanded in i around inf 96.5%

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

   4. Taylor expanded in i around 0 96.5%

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

   if -7.00000000000000038e169 < c < -1.25000000000000008e-38

   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. Add Preprocessing

   3. Taylor expanded in a around 0 84.2%

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

   if -1.25000000000000008e-38 < c < 5.8000000000000001e-47

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   if 5.8000000000000001e-47 < c

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+169}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.9 \cdot 10^{-182} \lor \neg \left(i \leq 5 \cdot 10^{-142}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -5.9e-182) (not (<= i 5e-142)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.9e-182) || !(i <= 5e-142)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-5.9d-182)) .or. (.not. (i <= 5d-142))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.9e-182) || !(i <= 5e-142)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -5.9e-182) or not (i <= 5e-142):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -5.9e-182) || !(i <= 5e-142))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -5.9e-182) || ~((i <= 5e-142)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -5.9e-182], N[Not[LessEqual[i, 5e-142]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.89999999999999968e-182 or 5.0000000000000002e-142 < i

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 76.0%

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

   if -5.89999999999999968e-182 < i < 5.0000000000000002e-142

   1. Initial program 93.4%

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

   3. Taylor expanded in c around 0 90.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.9 \cdot 10^{-182} \lor \neg \left(i \leq 5 \cdot 10^{-142}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+97} \lor \neg \left(i \leq 9500\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1e+97) (not (<= i 9500.0)))
   (* 2.0 (* (* c (+ a (* b c))) (- i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1e+97) || !(i <= 9500.0)) {
		tmp = 2.0 * ((c * (a + (b * c))) * -i);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1d+97)) .or. (.not. (i <= 9500.0d0))) then
        tmp = 2.0d0 * ((c * (a + (b * c))) * -i)
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1e+97) || !(i <= 9500.0)) {
		tmp = 2.0 * ((c * (a + (b * c))) * -i);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1e+97) or not (i <= 9500.0):
		tmp = 2.0 * ((c * (a + (b * c))) * -i)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1e+97) || !(i <= 9500.0))
		tmp = Float64(2.0 * Float64(Float64(c * Float64(a + Float64(b * c))) * Float64(-i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1e+97) || ~((i <= 9500.0)))
		tmp = 2.0 * ((c * (a + (b * c))) * -i);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1e+97], N[Not[LessEqual[i, 9500.0]], $MachinePrecision]], N[(2.0 * N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.0000000000000001e97 or 9500 < i

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 75.8%

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

   4. Taylor expanded in i around inf 84.9%

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

   5. Taylor expanded in t around 0 76.0%

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

   if -1.0000000000000001e97 < i < 9500

   1. Initial program 88.3%

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

   3. Taylor expanded in c around 0 70.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+97} \lor \neg \left(i \leq 9500\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+25} \lor \neg \left(c \leq 3.2 \cdot 10^{-21}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.35e+25) (not (<= c 3.2e-21)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.35e+25) || !(c <= 3.2e-21)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.35d+25)) .or. (.not. (c <= 3.2d-21))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.35e+25) || !(c <= 3.2e-21)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.35e+25) or not (c <= 3.2e-21):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.35e+25) || !(c <= 3.2e-21))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.35e+25) || ~((c <= 3.2e-21)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.35e+25], N[Not[LessEqual[c, 3.2e-21]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.35e25 or 3.2000000000000002e-21 < c

   1. Initial program 79.4%

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

   3. Taylor expanded in i around inf 73.3%

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

   4. Taylor expanded in i around 0 73.3%

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

   if -1.35e25 < c < 3.2000000000000002e-21

   1. Initial program 97.7%

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

   3. Taylor expanded in c around 0 73.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+25} \lor \neg \left(c \leq 3.2 \cdot 10^{-21}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+127} \lor \neg \left(i \leq 5.8 \cdot 10^{+74}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -5.8e+127) (not (<= i 5.8e+74)))
   (* -2.0 (* a (* c i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.8e+127) || !(i <= 5.8e+74)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-5.8d+127)) .or. (.not. (i <= 5.8d+74))) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -5.8e+127) || !(i <= 5.8e+74)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -5.8e+127) or not (i <= 5.8e+74):
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -5.8e+127) || !(i <= 5.8e+74))
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -5.8e+127) || ~((i <= 5.8e+74)))
		tmp = -2.0 * (a * (c * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -5.8e+127], N[Not[LessEqual[i, 5.8e+74]], $MachinePrecision]], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.8000000000000004e127 or 5.8000000000000005e74 < i

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. *-commutative 48.2%

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

      3. associate-*l* 35.1%

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

      4. *-commutative 35.1%

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

      5. distribute-rgt-neg-in 35.1%

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

      6. *-commutative 35.1%

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

      7. distribute-rgt-neg-in 35.1%

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

   5. Simplified 35.1%

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

   6. Taylor expanded in c around 0 48.2%

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

   if -5.8000000000000004e127 < i < 5.8000000000000005e74

   1. Initial program 88.3%

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

   3. Taylor expanded in c around 0 67.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+127} \lor \neg \left(i \leq 5.8 \cdot 10^{+74}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -11000000000000 \lor \neg \left(z \leq 1.85 \cdot 10^{-39}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -11000000000000.0) (not (<= z 1.85e-39)))
   (* 2.0 (* z t))
   (* (* x y) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -11000000000000.0) || !(z <= 1.85e-39)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-11000000000000.0d0)) .or. (.not. (z <= 1.85d-39))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (x * y) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -11000000000000.0) || !(z <= 1.85e-39)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -11000000000000.0) or not (z <= 1.85e-39):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -11000000000000.0) || !(z <= 1.85e-39))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -11000000000000.0) || ~((z <= 1.85e-39)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -11000000000000.0], N[Not[LessEqual[z, 1.85e-39]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e13 or 1.85000000000000007e-39 < z

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf 45.8%

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

   if -1.1e13 < z < 1.85000000000000007e-39

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 40.0%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11000000000000 \lor \neg \left(z \leq 1.85 \cdot 10^{-39}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.0% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

3. Taylor expanded in z around inf 29.6%

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

4. Final simplification 29.6%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))