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

Percentage Accurate: 90.7% → 97.1%

Time: 16.4s

Alternatives: 22

Speedup: 0.5×

• 45.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.5× speedup

Math

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

FPCore

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

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 * (z * (t - (c * (((a * i) / z) + ((b * (c * i)) / z)))));
	}
	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 * (z * (t - (c * (((a * i) / z) + ((b * (c * i)) / z)))));
	}
	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 * (z * (t - (c * (((a * i) / z) + ((b * (c * i)) / z)))))
	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(z * Float64(t - Float64(c * Float64(Float64(Float64(a * i) / z) + Float64(Float64(b * Float64(c * i)) / z))))));
	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 * (z * (t - (c * (((a * i) / z) + ((b * (c * i)) / z)))));
	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[(z * N[(t - N[(c * N[(N[(N[(a * i), $MachinePrecision] / z), $MachinePrecision] + N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.0%

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

      1. fma-define 96.0%

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

      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 z around inf 35.7%

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

   4. Taylor expanded in c around 0 57.1%

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

      1. associate-/l* 64.3%

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

      2. associate-/l* 64.3%

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

      3. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in x around 0 64.3%

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

4. Final simplification 97.9%

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

Alternative 2: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ t_2 := a \cdot \left(c \cdot i\right)\\ t_3 := 2 \cdot \left(x \cdot y - t\_2\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{+126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* (* b c) (- i)))))
        (t_2 (* a (* c i)))
        (t_3 (* 2.0 (- (* x y) t_2))))
   (if (<= c -1e+167)
     t_1
     (if (<= c -7.6e+126)
       t_3
       (if (<= c -6.8e+91)
         (* 2.0 (* c (* b (* c (- i)))))
         (if (<= c -2.4e+62)
           t_3
           (if (<= c -6.6e+47)
             t_1
             (if (<= c 2.9e-150)
               (* (+ (* x y) (* z t)) 2.0)
               (if (<= c 3.2e+167) (* 2.0 (- (* z t) 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 * (c * ((b * c) * -i));
	double t_2 = a * (c * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -1e+167) {
		tmp = t_1;
	} else if (c <= -7.6e+126) {
		tmp = t_3;
	} else if (c <= -6.8e+91) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= -2.4e+62) {
		tmp = t_3;
	} else if (c <= -6.6e+47) {
		tmp = t_1;
	} else if (c <= 2.9e-150) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.2e+167) {
		tmp = 2.0 * ((z * t) - 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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (c * ((b * c) * -i))
    t_2 = a * (c * i)
    t_3 = 2.0d0 * ((x * y) - t_2)
    if (c <= (-1d+167)) then
        tmp = t_1
    else if (c <= (-7.6d+126)) then
        tmp = t_3
    else if (c <= (-6.8d+91)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= (-2.4d+62)) then
        tmp = t_3
    else if (c <= (-6.6d+47)) then
        tmp = t_1
    else if (c <= 2.9d-150) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 3.2d+167) then
        tmp = 2.0d0 * ((z * t) - 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 * (c * ((b * c) * -i));
	double t_2 = a * (c * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -1e+167) {
		tmp = t_1;
	} else if (c <= -7.6e+126) {
		tmp = t_3;
	} else if (c <= -6.8e+91) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= -2.4e+62) {
		tmp = t_3;
	} else if (c <= -6.6e+47) {
		tmp = t_1;
	} else if (c <= 2.9e-150) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.2e+167) {
		tmp = 2.0 * ((z * t) - t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * ((b * c) * -i))
	t_2 = a * (c * i)
	t_3 = 2.0 * ((x * y) - t_2)
	tmp = 0
	if c <= -1e+167:
		tmp = t_1
	elif c <= -7.6e+126:
		tmp = t_3
	elif c <= -6.8e+91:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= -2.4e+62:
		tmp = t_3
	elif c <= -6.6e+47:
		tmp = t_1
	elif c <= 2.9e-150:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 3.2e+167:
		tmp = 2.0 * ((z * t) - 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(c * Float64(Float64(b * c) * Float64(-i))))
	t_2 = Float64(a * Float64(c * i))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - t_2))
	tmp = 0.0
	if (c <= -1e+167)
		tmp = t_1;
	elseif (c <= -7.6e+126)
		tmp = t_3;
	elseif (c <= -6.8e+91)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= -2.4e+62)
		tmp = t_3;
	elseif (c <= -6.6e+47)
		tmp = t_1;
	elseif (c <= 2.9e-150)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 3.2e+167)
		tmp = Float64(2.0 * Float64(Float64(z * t) - 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 * (c * ((b * c) * -i));
	t_2 = a * (c * i);
	t_3 = 2.0 * ((x * y) - t_2);
	tmp = 0.0;
	if (c <= -1e+167)
		tmp = t_1;
	elseif (c <= -7.6e+126)
		tmp = t_3;
	elseif (c <= -6.8e+91)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= -2.4e+62)
		tmp = t_3;
	elseif (c <= -6.6e+47)
		tmp = t_1;
	elseif (c <= 2.9e-150)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 3.2e+167)
		tmp = 2.0 * ((z * t) - 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[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+167], t$95$1, If[LessEqual[c, -7.6e+126], t$95$3, If[LessEqual[c, -6.8e+91], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.4e+62], t$95$3, If[LessEqual[c, -6.6e+47], t$95$1, If[LessEqual[c, 2.9e-150], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 3.2e+167], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1e167 or -2.4e62 < c < -6.5999999999999998e47 or 3.19999999999999981e167 < c

   1. Initial program 86.8%

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

   3. Taylor expanded in i around inf 94.1%

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

   4. Taylor expanded in a around 0 86.8%

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

   if -1e167 < c < -7.60000000000000033e126 or -6.8000000000000002e91 < c < -2.4e62

   1. Initial program 86.9%

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

   3. Taylor expanded in a around inf 74.6%

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

      1. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in z around 0 66.2%

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

   if -7.60000000000000033e126 < c < -6.8000000000000002e91

   1. Initial program 64.0%

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

   3. Taylor expanded in i around inf 87.1%

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

   4. Taylor expanded in a around 0 87.7%

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

   5. Taylor expanded in i around 0 87.9%

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

   if -6.5999999999999998e47 < c < 2.8999999999999998e-150

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 77.5%

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

   if 2.8999999999999998e-150 < c < 3.19999999999999981e167

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in x around 0 54.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{+126}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+167}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ t_3 := 2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+88}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (- (* z t) (* a (* c i)))))
        (t_3 (* 2.0 (* c (* (* b c) (- i))))))
   (if (<= c -4.8e+158)
     t_3
     (if (<= c -1.65e+127)
       t_1
       (if (<= c -3.8e+88)
         (* 2.0 (* c (* b (* c (- i)))))
         (if (<= c -1.95e+62)
           t_2
           (if (<= c -6e+48)
             t_3
             (if (<= c 1.55e-149) t_1 (if (<= c 2.7e+166) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = 2.0 * (c * ((b * c) * -i));
	double tmp;
	if (c <= -4.8e+158) {
		tmp = t_3;
	} else if (c <= -1.65e+127) {
		tmp = t_1;
	} else if (c <= -3.8e+88) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= -1.95e+62) {
		tmp = t_2;
	} else if (c <= -6e+48) {
		tmp = t_3;
	} else if (c <= 1.55e-149) {
		tmp = t_1;
	} else if (c <= 2.7e+166) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * ((z * t) - (a * (c * i)))
    t_3 = 2.0d0 * (c * ((b * c) * -i))
    if (c <= (-4.8d+158)) then
        tmp = t_3
    else if (c <= (-1.65d+127)) then
        tmp = t_1
    else if (c <= (-3.8d+88)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= (-1.95d+62)) then
        tmp = t_2
    else if (c <= (-6d+48)) then
        tmp = t_3
    else if (c <= 1.55d-149) then
        tmp = t_1
    else if (c <= 2.7d+166) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * ((z * t) - (a * (c * i)));
	double t_3 = 2.0 * (c * ((b * c) * -i));
	double tmp;
	if (c <= -4.8e+158) {
		tmp = t_3;
	} else if (c <= -1.65e+127) {
		tmp = t_1;
	} else if (c <= -3.8e+88) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= -1.95e+62) {
		tmp = t_2;
	} else if (c <= -6e+48) {
		tmp = t_3;
	} else if (c <= 1.55e-149) {
		tmp = t_1;
	} else if (c <= 2.7e+166) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * ((z * t) - (a * (c * i)))
	t_3 = 2.0 * (c * ((b * c) * -i))
	tmp = 0
	if c <= -4.8e+158:
		tmp = t_3
	elif c <= -1.65e+127:
		tmp = t_1
	elif c <= -3.8e+88:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= -1.95e+62:
		tmp = t_2
	elif c <= -6e+48:
		tmp = t_3
	elif c <= 1.55e-149:
		tmp = t_1
	elif c <= 2.7e+166:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))))
	t_3 = Float64(2.0 * Float64(c * Float64(Float64(b * c) * Float64(-i))))
	tmp = 0.0
	if (c <= -4.8e+158)
		tmp = t_3;
	elseif (c <= -1.65e+127)
		tmp = t_1;
	elseif (c <= -3.8e+88)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= -1.95e+62)
		tmp = t_2;
	elseif (c <= -6e+48)
		tmp = t_3;
	elseif (c <= 1.55e-149)
		tmp = t_1;
	elseif (c <= 2.7e+166)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * ((z * t) - (a * (c * i)));
	t_3 = 2.0 * (c * ((b * c) * -i));
	tmp = 0.0;
	if (c <= -4.8e+158)
		tmp = t_3;
	elseif (c <= -1.65e+127)
		tmp = t_1;
	elseif (c <= -3.8e+88)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= -1.95e+62)
		tmp = t_2;
	elseif (c <= -6e+48)
		tmp = t_3;
	elseif (c <= 1.55e-149)
		tmp = t_1;
	elseif (c <= 2.7e+166)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e+158], t$95$3, If[LessEqual[c, -1.65e+127], t$95$1, If[LessEqual[c, -3.8e+88], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.95e+62], t$95$2, If[LessEqual[c, -6e+48], t$95$3, If[LessEqual[c, 1.55e-149], t$95$1, If[LessEqual[c, 2.7e+166], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.80000000000000016e158 or -1.95e62 < c < -5.9999999999999999e48 or 2.70000000000000012e166 < c

   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 i around inf 94.3%

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

   4. Taylor expanded in a around 0 85.7%

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

   if -4.80000000000000016e158 < c < -1.64999999999999988e127 or -5.9999999999999999e48 < c < 1.54999999999999994e-149

   1. Initial program 95.5%

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

   3. Taylor expanded in c around 0 76.1%

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

   if -1.64999999999999988e127 < c < -3.7999999999999997e88

   1. Initial program 68.0%

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

   3. Taylor expanded in i around inf 77.5%

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

   4. Taylor expanded in a around 0 78.1%

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

   5. Taylor expanded in i around 0 78.3%

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

   if -3.7999999999999997e88 < c < -1.95e62 or 1.54999999999999994e-149 < c < 2.70000000000000012e166

   1. Initial program 89.5%

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

   3. Taylor expanded in a around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in x around 0 56.5%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+158}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+88}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-149}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t\_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (* c (* t_1 (- i))))
     (if (<= t_2 2e+304)
       (* (- (+ (* x y) (* z t)) t_2) 2.0)
       (* 2.0 (- (* z t) (* c (* t_1 i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 2e+304) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (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 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else if (t_2 <= 2e+304) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * (c * (t_1 * -i))
	elif t_2 <= 2e+304:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	elseif (t_2 <= 2e+304)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * (c * (t_1 * -i));
	elseif (t_2 <= 2e+304)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+304], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 82.1%

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

   3. Taylor expanded in i around inf 96.4%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e304

   1. Initial program 98.6%

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

   if 1.9999999999999999e304 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 90.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-195}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+208}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+177)
   (* (* x y) 2.0)
   (if (<= (* x y) -2e-195)
     (* 2.0 (* x (* t (/ z x))))
     (if (<= (* x y) 0.0)
       (* 2.0 (* i (* a (- c))))
       (if (<= (* x y) 5e-109)
         (* 2.0 (* z t))
         (if (<= (* x y) 2e+208)
           (* 2.0 (* (* c i) (- a)))
           (* 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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= -2e-195) {
		tmp = 2.0 * (x * (t * (z / x)));
	} else if ((x * y) <= 0.0) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 5e-109) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2e+208) {
		tmp = 2.0 * ((c * i) * -a);
	} 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 ((x * y) <= (-2d+177)) then
        tmp = (x * y) * 2.0d0
    else if ((x * y) <= (-2d-195)) then
        tmp = 2.0d0 * (x * (t * (z / x)))
    else if ((x * y) <= 0.0d0) then
        tmp = 2.0d0 * (i * (a * -c))
    else if ((x * y) <= 5d-109) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 2d+208) then
        tmp = 2.0d0 * ((c * i) * -a)
    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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= -2e-195) {
		tmp = 2.0 * (x * (t * (z / x)));
	} else if ((x * y) <= 0.0) {
		tmp = 2.0 * (i * (a * -c));
	} else if ((x * y) <= 5e-109) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2e+208) {
		tmp = 2.0 * ((c * i) * -a);
	} else {
		tmp = x * (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+177:
		tmp = (x * y) * 2.0
	elif (x * y) <= -2e-195:
		tmp = 2.0 * (x * (t * (z / x)))
	elif (x * y) <= 0.0:
		tmp = 2.0 * (i * (a * -c))
	elif (x * y) <= 5e-109:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 2e+208:
		tmp = 2.0 * ((c * i) * -a)
	else:
		tmp = x * (y * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+177)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (Float64(x * y) <= -2e-195)
		tmp = Float64(2.0 * Float64(x * Float64(t * Float64(z / x))));
	elseif (Float64(x * y) <= 0.0)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	elseif (Float64(x * y) <= 5e-109)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 2e+208)
		tmp = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+177)
		tmp = (x * y) * 2.0;
	elseif ((x * y) <= -2e-195)
		tmp = 2.0 * (x * (t * (z / x)));
	elseif ((x * y) <= 0.0)
		tmp = 2.0 * (i * (a * -c));
	elseif ((x * y) <= 5e-109)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 2e+208)
		tmp = 2.0 * ((c * i) * -a);
	else
		tmp = x * (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+177], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-195], N[(2.0 * N[(x * N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-109], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+208], N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -2e177

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf 67.0%

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

   if -2e177 < (*.f64 x y) < -2.0000000000000002e-195

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 62.2%

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

      1. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in x around inf 60.7%

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

   7. Taylor expanded in t around inf 31.8%

      \[\leadsto 2 \cdot \left(x \cdot \color{blue}{\frac{t \cdot z}{x}}\right) \]
   8. Step-by-step derivation

      1. associate-/l* 33.4%

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

   9. Simplified 33.4%

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

   if -2.0000000000000002e-195 < (*.f64 x y) < 0.0

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf 41.9%

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

      1. mul-1-neg 41.9%

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

      2. *-commutative 41.9%

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

      3. associate-*l* 35.3%

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

      4. *-commutative 35.3%

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

      5. distribute-rgt-neg-in 35.3%

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

      6. *-commutative 35.3%

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

      7. distribute-rgt-neg-in 35.3%

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

   5. Simplified 35.3%

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

      1. distribute-rgt-neg-out 35.3%

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

      2. *-commutative 35.3%

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

      3. distribute-rgt-neg-out 35.3%

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

      4. associate-*r* 44.0%

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

   7. Applied egg-rr 44.0%

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

   if 0.0 < (*.f64 x y) < 5.0000000000000002e-109

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 46.2%

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

   if 5.0000000000000002e-109 < (*.f64 x y) < 2e208

   1. Initial program 91.8%

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

      1. fma-define 91.8%

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

      2. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

      1. fma-define 98.1%

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

      2. +-commutative 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in c around 0 83.5%

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

   8. Taylor expanded in a around inf 32.2%

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

      1. associate-*r* 32.2%

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

      2. mul-1-neg 32.2%

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

   10. Simplified 32.2%

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

   if 2e208 < (*.f64 x y)

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. pow1 61.2%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 61.2%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 61.2%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 61.2%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-195}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+208}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 0.5× speedup

Math

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

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 (- (* b (* c (- i))) (* a 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 * ((b * (c * -i)) - (a * 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 * ((b * (c * -i)) - (a * 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 * ((b * (c * -i)) - (a * 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(Float64(b * Float64(c * Float64(-i))) - Float64(a * 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 * ((b * (c * -i)) - (a * 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[(N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.0%

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

      1. fma-define 96.0%

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

      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 43.1%

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

      1. distribute-rgt-in 43.1%

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

      2. *-commutative 43.1%

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

      3. associate-*r* 43.1%

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

   5. Applied egg-rr 43.1%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(i \cdot a + b \cdot \left(c \cdot i\right)\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

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

Alternative 7: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-174}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* i (* a (- c)))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* x (* y 2.0))))
   (if (<= z -1.1e+122)
     t_2
     (if (<= z -4.7e-8)
       t_1
       (if (<= z -2.5e-229)
         t_3
         (if (<= z 1.32e-278)
           t_1
           (if (<= z 1.9e-174)
             t_3
             (if (<= z 7.2e+21) (* 2.0 (* (* c i) (- a))) 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 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -1.1e+122) {
		tmp = t_2;
	} else if (z <= -4.7e-8) {
		tmp = t_1;
	} else if (z <= -2.5e-229) {
		tmp = t_3;
	} else if (z <= 1.32e-278) {
		tmp = t_1;
	} else if (z <= 1.9e-174) {
		tmp = t_3;
	} else if (z <= 7.2e+21) {
		tmp = 2.0 * ((c * i) * -a);
	} 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 * (i * (a * -c))
    t_2 = 2.0d0 * (z * t)
    t_3 = x * (y * 2.0d0)
    if (z <= (-1.1d+122)) then
        tmp = t_2
    else if (z <= (-4.7d-8)) then
        tmp = t_1
    else if (z <= (-2.5d-229)) then
        tmp = t_3
    else if (z <= 1.32d-278) then
        tmp = t_1
    else if (z <= 1.9d-174) then
        tmp = t_3
    else if (z <= 7.2d+21) then
        tmp = 2.0d0 * ((c * i) * -a)
    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 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -1.1e+122) {
		tmp = t_2;
	} else if (z <= -4.7e-8) {
		tmp = t_1;
	} else if (z <= -2.5e-229) {
		tmp = t_3;
	} else if (z <= 1.32e-278) {
		tmp = t_1;
	} else if (z <= 1.9e-174) {
		tmp = t_3;
	} else if (z <= 7.2e+21) {
		tmp = 2.0 * ((c * i) * -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (i * (a * -c))
	t_2 = 2.0 * (z * t)
	t_3 = x * (y * 2.0)
	tmp = 0
	if z <= -1.1e+122:
		tmp = t_2
	elif z <= -4.7e-8:
		tmp = t_1
	elif z <= -2.5e-229:
		tmp = t_3
	elif z <= 1.32e-278:
		tmp = t_1
	elif z <= 1.9e-174:
		tmp = t_3
	elif z <= 7.2e+21:
		tmp = 2.0 * ((c * i) * -a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(i * Float64(a * Float64(-c))))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (z <= -1.1e+122)
		tmp = t_2;
	elseif (z <= -4.7e-8)
		tmp = t_1;
	elseif (z <= -2.5e-229)
		tmp = t_3;
	elseif (z <= 1.32e-278)
		tmp = t_1;
	elseif (z <= 1.9e-174)
		tmp = t_3;
	elseif (z <= 7.2e+21)
		tmp = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)));
	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 * (i * (a * -c));
	t_2 = 2.0 * (z * t);
	t_3 = x * (y * 2.0);
	tmp = 0.0;
	if (z <= -1.1e+122)
		tmp = t_2;
	elseif (z <= -4.7e-8)
		tmp = t_1;
	elseif (z <= -2.5e-229)
		tmp = t_3;
	elseif (z <= 1.32e-278)
		tmp = t_1;
	elseif (z <= 1.9e-174)
		tmp = t_3;
	elseif (z <= 7.2e+21)
		tmp = 2.0 * ((c * i) * -a);
	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[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+122], t$95$2, If[LessEqual[z, -4.7e-8], t$95$1, If[LessEqual[z, -2.5e-229], t$95$3, If[LessEqual[z, 1.32e-278], t$95$1, If[LessEqual[z, 1.9e-174], t$95$3, If[LessEqual[z, 7.2e+21], N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e122 or 7.2e21 < z

   1. Initial program 85.8%

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

   3. Taylor expanded in z around inf 43.2%

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

   if -1.1e122 < z < -4.6999999999999997e-8 or -2.50000000000000008e-229 < z < 1.32e-278

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. *-commutative 36.8%

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

      3. associate-*l* 34.9%

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

      4. *-commutative 34.9%

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

      5. distribute-rgt-neg-in 34.9%

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

      6. *-commutative 34.9%

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

      7. distribute-rgt-neg-in 34.9%

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

   5. Simplified 34.9%

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

      1. distribute-rgt-neg-out 34.9%

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

      2. *-commutative 34.9%

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

      3. distribute-rgt-neg-out 34.9%

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

      4. associate-*r* 34.9%

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

   7. Applied egg-rr 34.9%

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

   if -4.6999999999999997e-8 < z < -2.50000000000000008e-229 or 1.32e-278 < z < 1.9000000000000001e-174

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 41.3%

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

      1. pow1 41.3%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 41.3%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 41.3%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 41.3%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 41.3%

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

      2. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   if 1.9000000000000001e-174 < z < 7.2e21

   1. Initial program 97.4%

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

      1. fma-define 97.4%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in c around 0 90.0%

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

   8. Taylor expanded in a around inf 29.4%

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

      1. associate-*r* 29.4%

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

      2. mul-1-neg 29.4%

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

   10. Simplified 29.4%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-278}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-170}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* i (* a (- c)))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* x (* y 2.0))))
   (if (<= z -2.3e+122)
     t_2
     (if (<= z -2.1e-8)
       t_1
       (if (<= z -3.6e-228)
         t_3
         (if (<= z 1.3e-281)
           t_1
           (if (<= z 4.5e-170) t_3 (if (<= z 3e+19) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -2.3e+122) {
		tmp = t_2;
	} else if (z <= -2.1e-8) {
		tmp = t_1;
	} else if (z <= -3.6e-228) {
		tmp = t_3;
	} else if (z <= 1.3e-281) {
		tmp = t_1;
	} else if (z <= 4.5e-170) {
		tmp = t_3;
	} else if (z <= 3e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (i * (a * -c))
    t_2 = 2.0d0 * (z * t)
    t_3 = x * (y * 2.0d0)
    if (z <= (-2.3d+122)) then
        tmp = t_2
    else if (z <= (-2.1d-8)) then
        tmp = t_1
    else if (z <= (-3.6d-228)) then
        tmp = t_3
    else if (z <= 1.3d-281) then
        tmp = t_1
    else if (z <= 4.5d-170) then
        tmp = t_3
    else if (z <= 3d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -2.3e+122) {
		tmp = t_2;
	} else if (z <= -2.1e-8) {
		tmp = t_1;
	} else if (z <= -3.6e-228) {
		tmp = t_3;
	} else if (z <= 1.3e-281) {
		tmp = t_1;
	} else if (z <= 4.5e-170) {
		tmp = t_3;
	} else if (z <= 3e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (i * (a * -c))
	t_2 = 2.0 * (z * t)
	t_3 = x * (y * 2.0)
	tmp = 0
	if z <= -2.3e+122:
		tmp = t_2
	elif z <= -2.1e-8:
		tmp = t_1
	elif z <= -3.6e-228:
		tmp = t_3
	elif z <= 1.3e-281:
		tmp = t_1
	elif z <= 4.5e-170:
		tmp = t_3
	elif z <= 3e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(i * Float64(a * Float64(-c))))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (z <= -2.3e+122)
		tmp = t_2;
	elseif (z <= -2.1e-8)
		tmp = t_1;
	elseif (z <= -3.6e-228)
		tmp = t_3;
	elseif (z <= 1.3e-281)
		tmp = t_1;
	elseif (z <= 4.5e-170)
		tmp = t_3;
	elseif (z <= 3e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (i * (a * -c));
	t_2 = 2.0 * (z * t);
	t_3 = x * (y * 2.0);
	tmp = 0.0;
	if (z <= -2.3e+122)
		tmp = t_2;
	elseif (z <= -2.1e-8)
		tmp = t_1;
	elseif (z <= -3.6e-228)
		tmp = t_3;
	elseif (z <= 1.3e-281)
		tmp = t_1;
	elseif (z <= 4.5e-170)
		tmp = t_3;
	elseif (z <= 3e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+122], t$95$2, If[LessEqual[z, -2.1e-8], t$95$1, If[LessEqual[z, -3.6e-228], t$95$3, If[LessEqual[z, 1.3e-281], t$95$1, If[LessEqual[z, 4.5e-170], t$95$3, If[LessEqual[z, 3e+19], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3000000000000001e122 or 3e19 < z

   1. Initial program 85.8%

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

   3. Taylor expanded in z around inf 43.2%

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

   if -2.3000000000000001e122 < z < -2.09999999999999994e-8 or -3.6000000000000002e-228 < z < 1.30000000000000002e-281 or 4.50000000000000002e-170 < z < 3e19

   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 a around inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. *-commutative 33.9%

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

      3. associate-*l* 29.6%

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

      4. *-commutative 29.6%

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

      5. distribute-rgt-neg-in 29.6%

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

      6. *-commutative 29.6%

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

      7. distribute-rgt-neg-in 29.6%

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

   5. Simplified 29.6%

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

      1. distribute-rgt-neg-out 29.6%

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

      2. *-commutative 29.6%

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

      3. distribute-rgt-neg-out 29.6%

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

      4. associate-*r* 31.7%

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

   7. Applied egg-rr 31.7%

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

   if -2.09999999999999994e-8 < z < -3.6000000000000002e-228 or 1.30000000000000002e-281 < z < 4.50000000000000002e-170

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 40.8%

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

      1. pow1 40.8%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 40.8%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 40.8%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 40.8%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 40.8%

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

      2. *-commutative 40.8%

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

   7. Simplified 40.8%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+122}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot \left(y \cdot 2\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 90000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* i (* a (- c)))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* x (* y 2.0))))
   (if (<= z -5.6e+121)
     t_2
     (if (<= z -1.8e-8)
       t_1
       (if (<= z -1.6e-229)
         t_3
         (if (<= z 6.8e-286)
           t_1
           (if (<= z 4.2e-175) t_3 (if (<= z 90000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -5.6e+121) {
		tmp = t_2;
	} else if (z <= -1.8e-8) {
		tmp = t_1;
	} else if (z <= -1.6e-229) {
		tmp = t_3;
	} else if (z <= 6.8e-286) {
		tmp = t_1;
	} else if (z <= 4.2e-175) {
		tmp = t_3;
	} else if (z <= 90000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (i * (a * -c))
    t_2 = 2.0d0 * (z * t)
    t_3 = x * (y * 2.0d0)
    if (z <= (-5.6d+121)) then
        tmp = t_2
    else if (z <= (-1.8d-8)) then
        tmp = t_1
    else if (z <= (-1.6d-229)) then
        tmp = t_3
    else if (z <= 6.8d-286) then
        tmp = t_1
    else if (z <= 4.2d-175) then
        tmp = t_3
    else if (z <= 90000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (i * (a * -c));
	double t_2 = 2.0 * (z * t);
	double t_3 = x * (y * 2.0);
	double tmp;
	if (z <= -5.6e+121) {
		tmp = t_2;
	} else if (z <= -1.8e-8) {
		tmp = t_1;
	} else if (z <= -1.6e-229) {
		tmp = t_3;
	} else if (z <= 6.8e-286) {
		tmp = t_1;
	} else if (z <= 4.2e-175) {
		tmp = t_3;
	} else if (z <= 90000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (i * (a * -c))
	t_2 = 2.0 * (z * t)
	t_3 = x * (y * 2.0)
	tmp = 0
	if z <= -5.6e+121:
		tmp = t_2
	elif z <= -1.8e-8:
		tmp = t_1
	elif z <= -1.6e-229:
		tmp = t_3
	elif z <= 6.8e-286:
		tmp = t_1
	elif z <= 4.2e-175:
		tmp = t_3
	elif z <= 90000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(i * Float64(a * Float64(-c))))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(x * Float64(y * 2.0))
	tmp = 0.0
	if (z <= -5.6e+121)
		tmp = t_2;
	elseif (z <= -1.8e-8)
		tmp = t_1;
	elseif (z <= -1.6e-229)
		tmp = t_3;
	elseif (z <= 6.8e-286)
		tmp = t_1;
	elseif (z <= 4.2e-175)
		tmp = t_3;
	elseif (z <= 90000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (i * (a * -c));
	t_2 = 2.0 * (z * t);
	t_3 = x * (y * 2.0);
	tmp = 0.0;
	if (z <= -5.6e+121)
		tmp = t_2;
	elseif (z <= -1.8e-8)
		tmp = t_1;
	elseif (z <= -1.6e-229)
		tmp = t_3;
	elseif (z <= 6.8e-286)
		tmp = t_1;
	elseif (z <= 4.2e-175)
		tmp = t_3;
	elseif (z <= 90000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+121], t$95$2, If[LessEqual[z, -1.8e-8], t$95$1, If[LessEqual[z, -1.6e-229], t$95$3, If[LessEqual[z, 6.8e-286], t$95$1, If[LessEqual[z, 4.2e-175], t$95$3, If[LessEqual[z, 90000000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000012e121 or 9e10 < z

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf 42.8%

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

   if -5.60000000000000012e121 < z < -1.79999999999999991e-8 or -1.60000000000000007e-229 < z < 6.8000000000000002e-286 or 4.2e-175 < z < 9e10

   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. Step-by-step derivation

      1. fma-define 93.4%

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

      2. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

      1. fma-define 97.7%

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

      2. +-commutative 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in a around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. associate-*r* 30.6%

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

      3. distribute-lft-neg-out 30.6%

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

      4. *-commutative 30.6%

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

      5. distribute-rgt-neg-out 30.6%

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

      6. *-commutative 30.6%

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

   9. Simplified 30.6%

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

   if -1.79999999999999991e-8 < z < -1.60000000000000007e-229 or 6.8000000000000002e-286 < z < 4.2e-175

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 41.3%

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

      1. pow1 41.3%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 41.3%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 41.3%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 41.3%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 41.3%

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

      2. *-commutative 41.3%

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

   7. Simplified 41.3%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-286}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;z \leq 90000000000:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -42000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+37} \lor \neg \left(c \leq 1.05 \cdot 10^{+118}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (* c i))) (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -42000000000.0)
     t_2
     (if (<= c 1.22e-148)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 4.1e-61)
         (* 2.0 (- (* z t) t_1))
         (if (or (<= c 6.8e+37) (not (<= c 1.05e+118)))
           t_2
           (* 2.0 (- (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -42000000000.0) {
		tmp = t_2;
	} else if (c <= 1.22e-148) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 4.1e-61) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((c <= 6.8e+37) || !(c <= 1.05e+118)) {
		tmp = t_2;
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * i)
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-42000000000.0d0)) then
        tmp = t_2
    else if (c <= 1.22d-148) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 4.1d-61) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if ((c <= 6.8d+37) .or. (.not. (c <= 1.05d+118))) then
        tmp = t_2
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a * (c * i);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -42000000000.0) {
		tmp = t_2;
	} else if (c <= 1.22e-148) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 4.1e-61) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((c <= 6.8e+37) || !(c <= 1.05e+118)) {
		tmp = t_2;
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a * (c * i)
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -42000000000.0:
		tmp = t_2
	elif c <= 1.22e-148:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 4.1e-61:
		tmp = 2.0 * ((z * t) - t_1)
	elif (c <= 6.8e+37) or not (c <= 1.05e+118):
		tmp = t_2
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(c * i))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -42000000000.0)
		tmp = t_2;
	elseif (c <= 1.22e-148)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 4.1e-61)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif ((c <= 6.8e+37) || !(c <= 1.05e+118))
		tmp = t_2;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (c * i);
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -42000000000.0)
		tmp = t_2;
	elseif (c <= 1.22e-148)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 4.1e-61)
		tmp = 2.0 * ((z * t) - t_1);
	elseif ((c <= 6.8e+37) || ~((c <= 1.05e+118)))
		tmp = t_2;
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -42000000000.0], t$95$2, If[LessEqual[c, 1.22e-148], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 4.1e-61], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 6.8e+37], N[Not[LessEqual[c, 1.05e+118]], $MachinePrecision]], t$95$2, N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.2e10 or 4.09999999999999999e-61 < c < 6.80000000000000011e37 or 1.05e118 < c

   1. Initial program 86.2%

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

   3. Taylor expanded in i around inf 80.2%

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

   if -4.2e10 < c < 1.21999999999999992e-148

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 79.8%

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

   if 1.21999999999999992e-148 < c < 4.09999999999999999e-61

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 91.7%

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

      1. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in x around 0 81.0%

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

   if 6.80000000000000011e37 < c < 1.05e118

   1. Initial program 78.2%

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

   3. Taylor expanded in a around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around 0 63.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -42000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-148}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+37} \lor \neg \left(c \leq 1.05 \cdot 10^{+118}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := x \cdot y + z \cdot t\\ t_3 := 2 \cdot \left(t\_2 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(t\_2 - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (+ (* x y) (* z t)))
        (t_3 (* 2.0 (- t_2 (* i (* a c))))))
   (if (<= c -8.5e-10)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 3.1e-59)
       t_3
       (if (<= c 7.6e+49)
         (* 2.0 (- t_2 (* i (* c (* b c)))))
         (if (<= c 2.2e+85) t_3 (* 2.0 (- (* z t) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = (x * y) + (z * t);
	double t_3 = 2.0 * (t_2 - (i * (a * c)));
	double tmp;
	if (c <= -8.5e-10) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.1e-59) {
		tmp = t_3;
	} else if (c <= 7.6e+49) {
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	} else if (c <= 2.2e+85) {
		tmp = t_3;
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = (x * y) + (z * t)
    t_3 = 2.0d0 * (t_2 - (i * (a * c)))
    if (c <= (-8.5d-10)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 3.1d-59) then
        tmp = t_3
    else if (c <= 7.6d+49) then
        tmp = 2.0d0 * (t_2 - (i * (c * (b * c))))
    else if (c <= 2.2d+85) then
        tmp = t_3
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = (x * y) + (z * t);
	double t_3 = 2.0 * (t_2 - (i * (a * c)));
	double tmp;
	if (c <= -8.5e-10) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.1e-59) {
		tmp = t_3;
	} else if (c <= 7.6e+49) {
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	} else if (c <= 2.2e+85) {
		tmp = t_3;
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = (x * y) + (z * t)
	t_3 = 2.0 * (t_2 - (i * (a * c)))
	tmp = 0
	if c <= -8.5e-10:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 3.1e-59:
		tmp = t_3
	elif c <= 7.6e+49:
		tmp = 2.0 * (t_2 - (i * (c * (b * c))))
	elif c <= 2.2e+85:
		tmp = t_3
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	t_3 = Float64(2.0 * Float64(t_2 - Float64(i * Float64(a * c))))
	tmp = 0.0
	if (c <= -8.5e-10)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 3.1e-59)
		tmp = t_3;
	elseif (c <= 7.6e+49)
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(c * Float64(b * c)))));
	elseif (c <= 2.2e+85)
		tmp = t_3;
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = (x * y) + (z * t);
	t_3 = 2.0 * (t_2 - (i * (a * c)));
	tmp = 0.0;
	if (c <= -8.5e-10)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 3.1e-59)
		tmp = t_3;
	elseif (c <= 7.6e+49)
		tmp = 2.0 * (t_2 - (i * (c * (b * c))));
	elseif (c <= 2.2e+85)
		tmp = t_3;
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(t$95$2 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e-10], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e-59], t$95$3, If[LessEqual[c, 7.6e+49], N[(2.0 * N[(t$95$2 - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+85], t$95$3, N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.4999999999999996e-10

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 87.8%

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

   if -8.4999999999999996e-10 < c < 3.09999999999999999e-59 or 7.5999999999999997e49 < c < 2.2000000000000002e85

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   if 3.09999999999999999e-59 < c < 7.5999999999999997e49

   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 a around 0 83.5%

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

   if 2.2000000000000002e85 < c

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 98.1%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(t\_2 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;2 \cdot \left(t\_2 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))) (t_2 (+ (* x y) (* z t))))
   (if (<= c -2.75e-11)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 3.4e-59)
       (* 2.0 (- t_2 (* i (* a c))))
       (if (<= c 2.2e+67)
         (* 2.0 (- t_2 (* (* b c) (* c i))))
         (* 2.0 (- (* z t) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.75e-11) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.4e-59) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 2.2e+67) {
		tmp = 2.0 * (t_2 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = (x * y) + (z * t)
    if (c <= (-2.75d-11)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 3.4d-59) then
        tmp = 2.0d0 * (t_2 - (i * (a * c)))
    else if (c <= 2.2d+67) then
        tmp = 2.0d0 * (t_2 - ((b * c) * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.75e-11) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 3.4e-59) {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	} else if (c <= 2.2e+67) {
		tmp = 2.0 * (t_2 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if c <= -2.75e-11:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 3.4e-59:
		tmp = 2.0 * (t_2 - (i * (a * c)))
	elif c <= 2.2e+67:
		tmp = 2.0 * (t_2 - ((b * c) * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -2.75e-11)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 3.4e-59)
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(a * c))));
	elseif (c <= 2.2e+67)
		tmp = Float64(2.0 * Float64(t_2 - Float64(Float64(b * c) * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -2.75e-11)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 3.4e-59)
		tmp = 2.0 * (t_2 - (i * (a * c)));
	elseif (c <= 2.2e+67)
		tmp = 2.0 * (t_2 - ((b * c) * (c * i)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.75e-11], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e-59], N[(2.0 * N[(t$95$2 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+67], N[(2.0 * N[(t$95$2 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.74999999999999987e-11

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 87.8%

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

   if -2.74999999999999987e-11 < c < 3.40000000000000018e-59

   1. Initial program 98.9%

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

   3. Taylor expanded in a around inf 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   if 3.40000000000000018e-59 < c < 2.2e67

   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. Step-by-step derivation

      1. fma-define 89.1%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

      1. fma-define 89.1%

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

      2. +-commutative 89.1%

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

   6. Applied egg-rr 89.1%

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

   7. Taylor expanded in a around 0 82.3%

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

   if 2.2e67 < c

   1. Initial program 85.0%

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

   3. Taylor expanded in x around 0 96.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+67}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+159} \lor \neg \left(c \leq -1.35 \cdot 10^{+127}\right) \land \left(c \leq -9.6 \cdot 10^{+46} \lor \neg \left(c \leq 7.6 \cdot 10^{+81}\right)\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3e+159)
         (and (not (<= c -1.35e+127))
              (or (<= c -9.6e+46) (not (<= c 7.6e+81)))))
   (* 2.0 (* c (* 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 <= -3e+159) || (!(c <= -1.35e+127) && ((c <= -9.6e+46) || !(c <= 7.6e+81)))) {
		tmp = 2.0 * (c * (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 <= (-3d+159)) .or. (.not. (c <= (-1.35d+127))) .and. (c <= (-9.6d+46)) .or. (.not. (c <= 7.6d+81))) then
        tmp = 2.0d0 * (c * (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 <= -3e+159) || (!(c <= -1.35e+127) && ((c <= -9.6e+46) || !(c <= 7.6e+81)))) {
		tmp = 2.0 * (c * (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 <= -3e+159) or (not (c <= -1.35e+127) and ((c <= -9.6e+46) or not (c <= 7.6e+81))):
		tmp = 2.0 * (c * (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 <= -3e+159) || (!(c <= -1.35e+127) && ((c <= -9.6e+46) || !(c <= 7.6e+81))))
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(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 ((c <= -3e+159) || (~((c <= -1.35e+127)) && ((c <= -9.6e+46) || ~((c <= 7.6e+81)))))
		tmp = 2.0 * (c * (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, -3e+159], And[N[Not[LessEqual[c, -1.35e+127]], $MachinePrecision], Or[LessEqual[c, -9.6e+46], N[Not[LessEqual[c, 7.6e+81]], $MachinePrecision]]]], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.0000000000000002e159 or -1.3500000000000001e127 < c < -9.60000000000000034e46 or 7.599999999999999e81 < c

   1. Initial program 85.9%

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

   3. Taylor expanded in i around inf 89.5%

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

   4. Taylor expanded in a around 0 70.6%

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

   5. Taylor expanded in i around 0 70.6%

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

   if -3.0000000000000002e159 < c < -1.3500000000000001e127 or -9.60000000000000034e46 < c < 7.599999999999999e81

   1. Initial program 94.1%

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

   3. Taylor expanded in c around 0 68.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+159} \lor \neg \left(c \leq -1.35 \cdot 10^{+127}\right) \land \left(c \leq -9.6 \cdot 10^{+46} \lor \neg \left(c \leq 7.6 \cdot 10^{+81}\right)\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.55 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* c (* (* b c) (- i))))))
   (if (<= c -6.2e+158)
     t_2
     (if (<= c -3.3e+124)
       t_1
       (if (<= c -3.55e+47)
         (* 2.0 (* c (* b (* c (- i)))))
         (if (<= c 2.7e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((b * c) * -i));
	double tmp;
	if (c <= -6.2e+158) {
		tmp = t_2;
	} else if (c <= -3.3e+124) {
		tmp = t_1;
	} else if (c <= -3.55e+47) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 2.7e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (c * ((b * c) * -i))
    if (c <= (-6.2d+158)) then
        tmp = t_2
    else if (c <= (-3.3d+124)) then
        tmp = t_1
    else if (c <= (-3.55d+47)) then
        tmp = 2.0d0 * (c * (b * (c * -i)))
    else if (c <= 2.7d+84) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((b * c) * -i));
	double tmp;
	if (c <= -6.2e+158) {
		tmp = t_2;
	} else if (c <= -3.3e+124) {
		tmp = t_1;
	} else if (c <= -3.55e+47) {
		tmp = 2.0 * (c * (b * (c * -i)));
	} else if (c <= 2.7e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * (c * ((b * c) * -i))
	tmp = 0
	if c <= -6.2e+158:
		tmp = t_2
	elif c <= -3.3e+124:
		tmp = t_1
	elif c <= -3.55e+47:
		tmp = 2.0 * (c * (b * (c * -i)))
	elif c <= 2.7e+84:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(b * c) * Float64(-i))))
	tmp = 0.0
	if (c <= -6.2e+158)
		tmp = t_2;
	elseif (c <= -3.3e+124)
		tmp = t_1;
	elseif (c <= -3.55e+47)
		tmp = Float64(2.0 * Float64(c * Float64(b * Float64(c * Float64(-i)))));
	elseif (c <= 2.7e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (c * ((b * c) * -i));
	tmp = 0.0;
	if (c <= -6.2e+158)
		tmp = t_2;
	elseif (c <= -3.3e+124)
		tmp = t_1;
	elseif (c <= -3.55e+47)
		tmp = 2.0 * (c * (b * (c * -i)));
	elseif (c <= 2.7e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(b * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+158], t$95$2, If[LessEqual[c, -3.3e+124], t$95$1, If[LessEqual[c, -3.55e+47], N[(2.0 * N[(c * N[(b * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.2000000000000004e158 or 2.7e84 < c

   1. Initial program 85.5%

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

   3. Taylor expanded in i around inf 91.5%

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

   4. Taylor expanded in a around 0 74.5%

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

   if -6.2000000000000004e158 < c < -3.30000000000000015e124 or -3.5500000000000001e47 < c < 2.7e84

   1. Initial program 94.1%

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

   3. Taylor expanded in c around 0 68.5%

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

   if -3.30000000000000015e124 < c < -3.5500000000000001e47

   1. Initial program 87.4%

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

   3. Taylor expanded in i around inf 82.6%

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

   4. Taylor expanded in a around 0 57.0%

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

   5. Taylor expanded in i around 0 57.0%

      \[\leadsto 2 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+158}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -3.55 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+139} \lor \neg \left(i \leq -2.2 \cdot 10^{+91} \lor \neg \left(i \leq -1.05 \cdot 10^{-46}\right) \land i \leq 8.5 \cdot 10^{+149}\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2e+139)
         (not
          (or (<= i -2.2e+91) (and (not (<= i -1.05e-46)) (<= i 8.5e+149)))))
   (* 2.0 (* (* c i) (- a)))
   (* (+ (* 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 <= -2e+139) || !((i <= -2.2e+91) || (!(i <= -1.05e-46) && (i <= 8.5e+149)))) {
		tmp = 2.0 * ((c * i) * -a);
	} 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 <= (-2d+139)) .or. (.not. (i <= (-2.2d+91)) .or. (.not. (i <= (-1.05d-46))) .and. (i <= 8.5d+149))) then
        tmp = 2.0d0 * ((c * i) * -a)
    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 <= -2e+139) || !((i <= -2.2e+91) || (!(i <= -1.05e-46) && (i <= 8.5e+149)))) {
		tmp = 2.0 * ((c * i) * -a);
	} 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 <= -2e+139) or not ((i <= -2.2e+91) or (not (i <= -1.05e-46) and (i <= 8.5e+149))):
		tmp = 2.0 * ((c * i) * -a)
	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 <= -2e+139) || !((i <= -2.2e+91) || (!(i <= -1.05e-46) && (i <= 8.5e+149))))
		tmp = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)));
	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 <= -2e+139) || ~(((i <= -2.2e+91) || (~((i <= -1.05e-46)) && (i <= 8.5e+149)))))
		tmp = 2.0 * ((c * i) * -a);
	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, -2e+139], N[Not[Or[LessEqual[i, -2.2e+91], And[N[Not[LessEqual[i, -1.05e-46]], $MachinePrecision], LessEqual[i, 8.5e+149]]]], $MachinePrecision]], N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if i < -2.00000000000000007e139

   1. Initial program 90.8%

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

   3. Taylor expanded in a around inf 58.1%

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

      1. mul-1-neg 58.1%

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

   5. Simplified 58.1%

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

   if -2.00000000000000007e139 < i < -2.19999999999999999e91 or -1.04999999999999994e-46 < i < 8.49999999999999956e149

   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 c around 0 62.8%

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

   if -2.19999999999999999e91 < i < -1.04999999999999994e-46 or 8.49999999999999956e149 < i

   1. Initial program 94.1%

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

      1. fma-define 94.1%

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

      2. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

      1. fma-define 94.2%

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

      2. +-commutative 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in c around 0 69.0%

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

   8. Taylor expanded in a around inf 48.7%

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

      1. associate-*r* 48.7%

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

      2. mul-1-neg 48.7%

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

   10. Simplified 48.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+139} \lor \neg \left(i \leq -2.2 \cdot 10^{+91} \lor \neg \left(i \leq -1.05 \cdot 10^{-46}\right) \land i \leq 8.5 \cdot 10^{+149}\right):\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+208}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+177)
   (* (* x y) 2.0)
   (if (<= (* x y) 5e-109)
     (* 2.0 (* z t))
     (if (<= (* x y) 2e+208) (* 2.0 (* (* c i) (- a))) (* 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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e-109) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2e+208) {
		tmp = 2.0 * ((c * i) * -a);
	} 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 ((x * y) <= (-2d+177)) then
        tmp = (x * y) * 2.0d0
    else if ((x * y) <= 5d-109) then
        tmp = 2.0d0 * (z * t)
    else if ((x * y) <= 2d+208) then
        tmp = 2.0d0 * ((c * i) * -a)
    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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e-109) {
		tmp = 2.0 * (z * t);
	} else if ((x * y) <= 2e+208) {
		tmp = 2.0 * ((c * i) * -a);
	} else {
		tmp = x * (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+177:
		tmp = (x * y) * 2.0
	elif (x * y) <= 5e-109:
		tmp = 2.0 * (z * t)
	elif (x * y) <= 2e+208:
		tmp = 2.0 * ((c * i) * -a)
	else:
		tmp = x * (y * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+177)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (Float64(x * y) <= 5e-109)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(x * y) <= 2e+208)
		tmp = Float64(2.0 * Float64(Float64(c * i) * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+177)
		tmp = (x * y) * 2.0;
	elseif ((x * y) <= 5e-109)
		tmp = 2.0 * (z * t);
	elseif ((x * y) <= 2e+208)
		tmp = 2.0 * ((c * i) * -a);
	else
		tmp = x * (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+177], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-109], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+208], N[(2.0 * N[(N[(c * i), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2e177

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf 67.0%

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

   if -2e177 < (*.f64 x y) < 5.0000000000000002e-109

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 37.1%

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

   if 5.0000000000000002e-109 < (*.f64 x y) < 2e208

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 32.2%

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

      1. mul-1-neg 32.2%

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

   5. Simplified 32.2%

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

   if 2e208 < (*.f64 x y)

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. pow1 61.2%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 61.2%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 61.2%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 61.2%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 61.2%

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

      2. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-109}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+208}:\\ \;\;\;\;2 \cdot \left(\left(c \cdot i\right) \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{-36} \lor \neg \left(c \leq 8.4 \cdot 10^{-169}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.05e-36) (not (<= c 8.4e-169)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e-36) || !(c <= 8.4e-169)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.05d-36)) .or. (.not. (c <= 8.4d-169))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e-36) || !(c <= 8.4e-169)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.05e-36) or not (c <= 8.4e-169):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.05e-36) || !(c <= 8.4e-169))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.05e-36) || ~((c <= 8.4e-169)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.05e-36], N[Not[LessEqual[c, 8.4e-169]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.04999999999999995e-36 or 8.4000000000000002e-169 < c

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0 83.1%

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

   if -1.04999999999999995e-36 < c < 8.4000000000000002e-169

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0 82.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{-36} \lor \neg \left(c \leq 8.4 \cdot 10^{-169}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -2.75e-11)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 5e-59)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.75e-11) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 5e-59) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-2.75d-11)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 5d-59) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -2.75e-11) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 5e-59) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -2.75e-11:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 5e-59:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -2.75e-11)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 5e-59)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -2.75e-11)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 5e-59)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.75e-11], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e-59], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.74999999999999987e-11

   1. Initial program 85.2%

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

   3. Taylor expanded in z around 0 87.8%

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

   if -2.74999999999999987e-11 < c < 5.0000000000000001e-59

   1. Initial program 98.9%

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

   3. Taylor expanded in a around inf 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   if 5.0000000000000001e-59 < c

   1. Initial program 86.3%

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

   3. Taylor expanded in x around 0 87.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{elif}\;c \leq 1.56 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.3e-42)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 1.56e-169)
       (* (+ (* x y) (* z t)) 2.0)
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.3e-42) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.56e-169) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-1.3d-42)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 1.56d-169) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.3e-42) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 1.56e-169) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.3e-42:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 1.56e-169:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.3e-42)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 1.56e-169)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.3e-42)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 1.56e-169)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e-42], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.56e-169], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.3e-42

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 87.0%

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

   if -1.3e-42 < c < 1.56000000000000008e-169

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0 82.5%

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

   if 1.56000000000000008e-169 < c

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 85.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.56 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.32 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 3.3 \cdot 10^{+90}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.32e+177) (not (<= (* x y) 3.3e+90)))
   (* (* x y) 2.0)
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.32e+177) || !((x * y) <= 3.3e+90)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.32d+177)) .or. (.not. ((x * y) <= 3.3d+90))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.32e+177) || !((x * y) <= 3.3e+90)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.32e+177) or not ((x * y) <= 3.3e+90):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.32e+177) || !(Float64(x * y) <= 3.3e+90))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.32e+177) || ~(((x * y) <= 3.3e+90)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.32e+177], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.3e+90]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.3200000000000001e177 or 3.30000000000000008e90 < (*.f64 x y)

   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 x around inf 55.8%

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

   if -1.3200000000000001e177 < (*.f64 x y) < 3.30000000000000008e90

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 33.4%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.32 \cdot 10^{+177} \lor \neg \left(x \cdot y \leq 3.3 \cdot 10^{+90}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 44.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+177)
   (* (* x y) 2.0)
   (if (<= (* x y) 5e+89) (* 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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e+89) {
		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 ((x * y) <= (-2d+177)) then
        tmp = (x * y) * 2.0d0
    else if ((x * y) <= 5d+89) 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 ((x * y) <= -2e+177) {
		tmp = (x * y) * 2.0;
	} else if ((x * y) <= 5e+89) {
		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 (x * y) <= -2e+177:
		tmp = (x * y) * 2.0
	elif (x * y) <= 5e+89:
		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 (Float64(x * y) <= -2e+177)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (Float64(x * y) <= 5e+89)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(x * Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -2e+177)
		tmp = (x * y) * 2.0;
	elseif ((x * y) <= 5e+89)
		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[LessEqual[N[(x * y), $MachinePrecision], -2e+177], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+89], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e177

   1. Initial program 90.6%

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

   3. Taylor expanded in x around inf 67.0%

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

   if -2e177 < (*.f64 x y) < 4.99999999999999983e89

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 33.4%

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

   if 4.99999999999999983e89 < (*.f64 x y)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf 49.2%

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

      1. pow1 49.2%

         \[\leadsto \color{blue}{{\left(2 \cdot \left(x \cdot y\right)\right)}^{1}} \]

      2. *-commutative 49.2%

         \[\leadsto {\left(2 \cdot \color{blue}{\left(y \cdot x\right)}\right)}^{1} \]

      3. associate-*r* 49.2%

         \[\leadsto {\color{blue}{\left(\left(2 \cdot y\right) \cdot x\right)}}^{1} \]

   5. Applied egg-rr 49.2%

      \[\leadsto \color{blue}{{\left(\left(2 \cdot y\right) \cdot x\right)}^{1}} \]
   6. Step-by-step derivation

      1. unpow1 49.2%

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

      2. *-commutative 49.2%

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

   7. Simplified 49.2%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+177}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

3. Taylor expanded in z around inf 25.2%

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

4. Final simplification 25.2%

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

Developer target: 94.8% 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 2024103 
(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))))