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

Percentage Accurate: 89.8% → 95.2%

Time: 25.3s

Alternatives: 19

Speedup: 0.7×

• 46.9% 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: 89.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ 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 (- (* x y) (* (* b c) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 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 * ((x * y) - ((b * c) * (c * 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 * ((x * y) - ((b * c) * (c * 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 * ((x * y) - ((b * c) * (c * 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(Float64(x * y) - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 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 * ((x * y) - ((b * c) * (c * 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[(N[(x * y), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * 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 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. associate-*l* 98.2%

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

      2. fma-def 98.2%

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

   3. Simplified 98.2%

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

      1. fma-def 98.2%

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

      2. +-commutative 98.2%

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

   5. Applied egg-rr 98.2%

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

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

   1. Initial program 0.0%

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

      1. associate-*r* 16.7%

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

      2. *-commutative 16.7%

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

      3. flip-+ 0.0%

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

      4. associate-*r/ 0.0%

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

      5. pow2 0.0%

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

   3. Applied egg-rr 0.0%

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

      1. associate-/l* 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in a around 0 25.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\color{blue}{\frac{1}{b \cdot c}}}\right) \]
   7. Step-by-step derivation

      1. associate-/r* 25.0%

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

   8. Simplified 25.0%

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

   9. Taylor expanded in z around 0 66.7%

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

       1. unpow2 66.7%

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

       2. associate-*r* 66.7%

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

       3. associate-*l* 66.7%

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

       4. *-commutative 66.7%

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

       5. *-commutative 66.7%

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

       6. *-commutative 66.7%

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

   11. Simplified 66.7%

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

4. Final simplification 96.7%

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

Alternative 2: 43.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* a (* c i)) (- 2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -4.5e+49)
     t_3
     (if (<= (* x y) -6e-92)
       t_1
       (if (<= (* x y) 2.7e-180)
         t_2
         (if (<= (* x y) 3.2e-129)
           t_1
           (if (<= (* x y) 1.95e-47)
             t_2
             (if (<= (* x y) 3.6e+14) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * (c * i)) * -2.0;
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.5e+49) {
		tmp = t_3;
	} else if ((x * y) <= -6e-92) {
		tmp = t_1;
	} else if ((x * y) <= 2.7e-180) {
		tmp = t_2;
	} else if ((x * y) <= 3.2e-129) {
		tmp = t_1;
	} else if ((x * y) <= 1.95e-47) {
		tmp = t_2;
	} else if ((x * y) <= 3.6e+14) {
		tmp = t_1;
	} 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 = (a * (c * i)) * -2.0d0
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-4.5d+49)) then
        tmp = t_3
    else if ((x * y) <= (-6d-92)) then
        tmp = t_1
    else if ((x * y) <= 2.7d-180) then
        tmp = t_2
    else if ((x * y) <= 3.2d-129) then
        tmp = t_1
    else if ((x * y) <= 1.95d-47) then
        tmp = t_2
    else if ((x * y) <= 3.6d+14) then
        tmp = t_1
    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 = (a * (c * i)) * -2.0;
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.5e+49) {
		tmp = t_3;
	} else if ((x * y) <= -6e-92) {
		tmp = t_1;
	} else if ((x * y) <= 2.7e-180) {
		tmp = t_2;
	} else if ((x * y) <= 3.2e-129) {
		tmp = t_1;
	} else if ((x * y) <= 1.95e-47) {
		tmp = t_2;
	} else if ((x * y) <= 3.6e+14) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * (c * i)) * -2.0
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -4.5e+49:
		tmp = t_3
	elif (x * y) <= -6e-92:
		tmp = t_1
	elif (x * y) <= 2.7e-180:
		tmp = t_2
	elif (x * y) <= 3.2e-129:
		tmp = t_1
	elif (x * y) <= 1.95e-47:
		tmp = t_2
	elif (x * y) <= 3.6e+14:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * Float64(c * i)) * Float64(-2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -4.5e+49)
		tmp = t_3;
	elseif (Float64(x * y) <= -6e-92)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.7e-180)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.2e-129)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.95e-47)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.6e+14)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * (c * i)) * -2.0;
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -4.5e+49)
		tmp = t_3;
	elseif ((x * y) <= -6e-92)
		tmp = t_1;
	elseif ((x * y) <= 2.7e-180)
		tmp = t_2;
	elseif ((x * y) <= 3.2e-129)
		tmp = t_1;
	elseif ((x * y) <= 1.95e-47)
		tmp = t_2;
	elseif ((x * y) <= 3.6e+14)
		tmp = t_1;
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+49], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -6e-92], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.7e-180], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-129], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.95e-47], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.6e+14], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.49999999999999982e49 or 3.6e14 < (*.f64 x y)

   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. Taylor expanded in x around inf 54.7%

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

   if -4.49999999999999982e49 < (*.f64 x y) < -6.00000000000000027e-92 or 2.70000000000000014e-180 < (*.f64 x y) < 3.2000000000000003e-129 or 1.94999999999999989e-47 < (*.f64 x y) < 3.6e14

   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. Step-by-step derivation

      1. associate-*l* 92.4%

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

      2. fma-def 92.4%

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

   3. Simplified 92.4%

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

      1. fma-def 92.4%

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

      2. +-commutative 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in a around inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. distribute-rgt-neg-in 51.2%

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

      3. distribute-rgt-neg-in 51.2%

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

   8. Simplified 51.2%

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

   if -6.00000000000000027e-92 < (*.f64 x y) < 2.70000000000000014e-180 or 3.2000000000000003e-129 < (*.f64 x y) < 1.94999999999999989e-47

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 45.9%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-92}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-180}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 3: 43.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 130000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* a (* c i)) (- 2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -4.5e+49)
     t_3
     (if (<= (* x y) -8e-91)
       t_1
       (if (<= (* x y) 1.42e-176)
         t_2
         (if (<= (* x y) 6.2e-130)
           t_1
           (if (<= (* x y) 3.2e-47)
             t_2
             (if (<= (* x y) 130000000000.0)
               (* 2.0 (* c (* a (- i))))
               t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * (c * i)) * -2.0;
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.5e+49) {
		tmp = t_3;
	} else if ((x * y) <= -8e-91) {
		tmp = t_1;
	} else if ((x * y) <= 1.42e-176) {
		tmp = t_2;
	} else if ((x * y) <= 6.2e-130) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-47) {
		tmp = t_2;
	} else if ((x * y) <= 130000000000.0) {
		tmp = 2.0 * (c * (a * -i));
	} 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 = (a * (c * i)) * -2.0d0
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-4.5d+49)) then
        tmp = t_3
    else if ((x * y) <= (-8d-91)) then
        tmp = t_1
    else if ((x * y) <= 1.42d-176) then
        tmp = t_2
    else if ((x * y) <= 6.2d-130) then
        tmp = t_1
    else if ((x * y) <= 3.2d-47) then
        tmp = t_2
    else if ((x * y) <= 130000000000.0d0) then
        tmp = 2.0d0 * (c * (a * -i))
    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 = (a * (c * i)) * -2.0;
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.5e+49) {
		tmp = t_3;
	} else if ((x * y) <= -8e-91) {
		tmp = t_1;
	} else if ((x * y) <= 1.42e-176) {
		tmp = t_2;
	} else if ((x * y) <= 6.2e-130) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-47) {
		tmp = t_2;
	} else if ((x * y) <= 130000000000.0) {
		tmp = 2.0 * (c * (a * -i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * (c * i)) * -2.0
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -4.5e+49:
		tmp = t_3
	elif (x * y) <= -8e-91:
		tmp = t_1
	elif (x * y) <= 1.42e-176:
		tmp = t_2
	elif (x * y) <= 6.2e-130:
		tmp = t_1
	elif (x * y) <= 3.2e-47:
		tmp = t_2
	elif (x * y) <= 130000000000.0:
		tmp = 2.0 * (c * (a * -i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * Float64(c * i)) * Float64(-2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -4.5e+49)
		tmp = t_3;
	elseif (Float64(x * y) <= -8e-91)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.42e-176)
		tmp = t_2;
	elseif (Float64(x * y) <= 6.2e-130)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-47)
		tmp = t_2;
	elseif (Float64(x * y) <= 130000000000.0)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * (c * i)) * -2.0;
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -4.5e+49)
		tmp = t_3;
	elseif ((x * y) <= -8e-91)
		tmp = t_1;
	elseif ((x * y) <= 1.42e-176)
		tmp = t_2;
	elseif ((x * y) <= 6.2e-130)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-47)
		tmp = t_2;
	elseif ((x * y) <= 130000000000.0)
		tmp = 2.0 * (c * (a * -i));
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+49], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -8e-91], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.42e-176], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6.2e-130], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-47], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 130000000000.0], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.49999999999999982e49 or 1.3e11 < (*.f64 x y)

   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. Taylor expanded in x around inf 54.7%

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

   if -4.49999999999999982e49 < (*.f64 x y) < -8.00000000000000018e-91 or 1.42000000000000009e-176 < (*.f64 x y) < 6.20000000000000021e-130

   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. Step-by-step derivation

      1. associate-*l* 91.8%

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

      2. fma-def 91.8%

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

   3. Simplified 91.8%

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

      1. fma-def 91.8%

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

      2. +-commutative 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in a around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. distribute-rgt-neg-in 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

   8. Simplified 57.8%

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

   if -8.00000000000000018e-91 < (*.f64 x y) < 1.42000000000000009e-176 or 6.20000000000000021e-130 < (*.f64 x y) < 3.1999999999999999e-47

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 45.9%

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

   if 3.1999999999999999e-47 < (*.f64 x y) < 1.3e11

   1. Initial program 82.8%

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

   2. Taylor expanded in a around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. *-commutative 37.6%

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

      3. associate-*l* 37.7%

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

      4. *-commutative 37.7%

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

      5. distribute-rgt-neg-in 37.7%

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

      6. *-commutative 37.7%

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

   4. Simplified 37.7%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -8 \cdot 10^{-91}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{-176}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-130}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 130000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 4: 42.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1.15 \cdot 10^{-98}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* (* x y) 2.0)))
   (if (<= (* x y) -4.4e+49)
     t_2
     (if (<= (* x y) -1.15e-98)
       (* 2.0 (* (* a c) (- i)))
       (if (<= (* x y) 2.1e-178)
         t_1
         (if (<= (* x y) 5.7e-129)
           (* (* a (* c i)) (- 2.0))
           (if (<= (* x y) 2.1e-47)
             t_1
             (if (<= (* x y) 3.2e+14) (* 2.0 (* c (* a (- i)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.4e+49) {
		tmp = t_2;
	} else if ((x * y) <= -1.15e-98) {
		tmp = 2.0 * ((a * c) * -i);
	} else if ((x * y) <= 2.1e-178) {
		tmp = t_1;
	} else if ((x * y) <= 5.7e-129) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 2.1e-47) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+14) {
		tmp = 2.0 * (c * (a * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    if ((x * y) <= (-4.4d+49)) then
        tmp = t_2
    else if ((x * y) <= (-1.15d-98)) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if ((x * y) <= 2.1d-178) then
        tmp = t_1
    else if ((x * y) <= 5.7d-129) then
        tmp = (a * (c * i)) * -2.0d0
    else if ((x * y) <= 2.1d-47) then
        tmp = t_1
    else if ((x * y) <= 3.2d+14) then
        tmp = 2.0d0 * (c * (a * -i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -4.4e+49) {
		tmp = t_2;
	} else if ((x * y) <= -1.15e-98) {
		tmp = 2.0 * ((a * c) * -i);
	} else if ((x * y) <= 2.1e-178) {
		tmp = t_1;
	} else if ((x * y) <= 5.7e-129) {
		tmp = (a * (c * i)) * -2.0;
	} else if ((x * y) <= 2.1e-47) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e+14) {
		tmp = 2.0 * (c * (a * -i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -4.4e+49:
		tmp = t_2
	elif (x * y) <= -1.15e-98:
		tmp = 2.0 * ((a * c) * -i)
	elif (x * y) <= 2.1e-178:
		tmp = t_1
	elif (x * y) <= 5.7e-129:
		tmp = (a * (c * i)) * -2.0
	elif (x * y) <= 2.1e-47:
		tmp = t_1
	elif (x * y) <= 3.2e+14:
		tmp = 2.0 * (c * (a * -i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -4.4e+49)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.15e-98)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (Float64(x * y) <= 2.1e-178)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.7e-129)
		tmp = Float64(Float64(a * Float64(c * i)) * Float64(-2.0));
	elseif (Float64(x * y) <= 2.1e-47)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e+14)
		tmp = Float64(2.0 * Float64(c * Float64(a * Float64(-i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -4.4e+49)
		tmp = t_2;
	elseif ((x * y) <= -1.15e-98)
		tmp = 2.0 * ((a * c) * -i);
	elseif ((x * y) <= 2.1e-178)
		tmp = t_1;
	elseif ((x * y) <= 5.7e-129)
		tmp = (a * (c * i)) * -2.0;
	elseif ((x * y) <= 2.1e-47)
		tmp = t_1;
	elseif ((x * y) <= 3.2e+14)
		tmp = 2.0 * (c * (a * -i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.4e+49], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.15e-98], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.1e-178], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.7e-129], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.1e-47], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e+14], N[(2.0 * N[(c * N[(a * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.4000000000000001e49 or 3.2e14 < (*.f64 x y)

   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. Taylor expanded in x around inf 54.7%

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

   if -4.4000000000000001e49 < (*.f64 x y) < -1.15e-98

   1. Initial program 99.9%

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

      1. associate-*r* 93.3%

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

      2. *-commutative 93.3%

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

      3. flip-+ 62.4%

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

      4. associate-*r/ 52.8%

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

      5. pow2 52.8%

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

   3. Applied egg-rr 52.8%

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

      1. associate-/l* 62.3%

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

   5. Simplified 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-/l* 58.4%

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

      3. clear-num 58.4%

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

      4. unpow2 58.4%

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

      5. flip-+ 92.4%

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

      6. +-commutative 92.4%

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

      7. fma-def 92.4%

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

   7. Applied egg-rr 92.4%

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

   8. Taylor expanded in a around inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. *-commutative 49.2%

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

      3. *-commutative 49.2%

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

      4. associate-*r* 52.7%

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

      5. neg-mul-1 52.7%

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

   10. Simplified 52.7%

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

   if -1.15e-98 < (*.f64 x y) < 2.1e-178 or 5.7000000000000001e-129 < (*.f64 x y) < 2.1000000000000001e-47

   1. Initial program 91.6%

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

   2. Taylor expanded in z around inf 47.1%

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

   if 2.1e-178 < (*.f64 x y) < 5.7000000000000001e-129

   1. Initial program 82.2%

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

      1. associate-*l* 82.4%

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

      2. fma-def 82.4%

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

   3. Simplified 82.4%

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

      1. fma-def 82.4%

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

      2. +-commutative 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in a around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-rgt-neg-in 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

   8. Simplified 63.7%

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

   if 2.1000000000000001e-47 < (*.f64 x y) < 3.2e14

   1. Initial program 82.8%

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

   2. Taylor expanded in a around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. *-commutative 37.6%

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

      3. associate-*l* 37.7%

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

      4. *-commutative 37.7%

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

      5. distribute-rgt-neg-in 37.7%

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

      6. *-commutative 37.7%

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

   4. Simplified 37.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -1.15 \cdot 10^{-98}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.7 \cdot 10^{-129}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(a \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 5: 92.2% accurate, 0.7× speedup

Math

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

FPCore

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

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 * ((x * y) - (c * (t_1 * i)));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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 * ((x * y) - (c * (t_1 * i)));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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 * ((x * y) - (c * (t_1 * i)))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	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(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	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 * ((x * y) - (c * (t_1 * i)));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	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[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 69.7%

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

   2. Taylor expanded in z around 0 90.6%

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

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

   1. Initial program 96.3%

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

4. Final simplification 94.9%

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

Alternative 6: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;x \cdot y \leq 460000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= (* x y) -2.4e-68)
     (* 2.0 (- (* x y) t_1))
     (if (<= (* x y) 460000000000.0)
       (* 2.0 (- (* z t) t_1))
       (* 2.0 (- (+ (* x y) (* z t)) (* (* b c) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -2.4e-68) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 460000000000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - ((b * c) * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if ((x * y) <= (-2.4d-68)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if ((x * y) <= 460000000000.0d0) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - ((b * c) * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if ((x * y) <= -2.4e-68) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if ((x * y) <= 460000000000.0) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - ((b * c) * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if (x * y) <= -2.4e-68:
		tmp = 2.0 * ((x * y) - t_1)
	elif (x * y) <= 460000000000.0:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - ((b * c) * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (Float64(x * y) <= -2.4e-68)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (Float64(x * y) <= 460000000000.0)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if ((x * y) <= -2.4e-68)
		tmp = 2.0 * ((x * y) - t_1);
	elseif ((x * y) <= 460000000000.0)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * (((x * y) + (z * t)) - ((b * c) * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.4e-68], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 460000000000.0], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.39999999999999991e-68

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 80.9%

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

   if -2.39999999999999991e-68 < (*.f64 x y) < 4.6e11

   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. Taylor expanded in x around 0 91.5%

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

   if 4.6e11 < (*.f64 x y)

   1. Initial program 91.3%

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

      1. associate-*l* 98.2%

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

      2. fma-def 98.2%

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

   3. Simplified 98.2%

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

      1. fma-def 98.2%

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

      2. +-commutative 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in a around 0 91.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 460000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+159}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))))
   (if (<= c -8.2e+112)
     (* (* (* b c) (* c i)) (- 2.0))
     (if (<= c -4.0)
       t_1
       (if (<= c -2.05e-22)
         (* c (* (* c (* b i)) -2.0))
         (if (<= c -1.5e-116)
           (* 2.0 (- (* z t) (* c (* a i))))
           (if (<= c 1.12e+30)
             t_1
             (if (<= c 1.1e+159)
               (* 2.0 (- (* x y) (* a (* c i))))
               (* 2.0 (* b (* c (* c (- i)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -8.2e+112) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -4.0) {
		tmp = t_1;
	} else if (c <= -2.05e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -1.5e-116) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 1.12e+30) {
		tmp = t_1;
	} else if (c <= 1.1e+159) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    if (c <= (-8.2d+112)) then
        tmp = ((b * c) * (c * i)) * -2.0d0
    else if (c <= (-4.0d0)) then
        tmp = t_1
    else if (c <= (-2.05d-22)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-1.5d-116)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (c <= 1.12d+30) then
        tmp = t_1
    else if (c <= 1.1d+159) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else
        tmp = 2.0d0 * (b * (c * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -8.2e+112) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -4.0) {
		tmp = t_1;
	} else if (c <= -2.05e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -1.5e-116) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 1.12e+30) {
		tmp = t_1;
	} else if (c <= 1.1e+159) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	tmp = 0
	if c <= -8.2e+112:
		tmp = ((b * c) * (c * i)) * -2.0
	elif c <= -4.0:
		tmp = t_1
	elif c <= -2.05e-22:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -1.5e-116:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif c <= 1.12e+30:
		tmp = t_1
	elif c <= 1.1e+159:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	else:
		tmp = 2.0 * (b * (c * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (c <= -8.2e+112)
		tmp = Float64(Float64(Float64(b * c) * Float64(c * i)) * Float64(-2.0));
	elseif (c <= -4.0)
		tmp = t_1;
	elseif (c <= -2.05e-22)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -1.5e-116)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (c <= 1.12e+30)
		tmp = t_1;
	elseif (c <= 1.1e+159)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(b * Float64(c * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	tmp = 0.0;
	if (c <= -8.2e+112)
		tmp = ((b * c) * (c * i)) * -2.0;
	elseif (c <= -4.0)
		tmp = t_1;
	elseif (c <= -2.05e-22)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -1.5e-116)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (c <= 1.12e+30)
		tmp = t_1;
	elseif (c <= 1.1e+159)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	else
		tmp = 2.0 * (b * (c * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+112], N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, -4.0], t$95$1, If[LessEqual[c, -2.05e-22], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e-116], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.12e+30], t$95$1, If[LessEqual[c, 1.1e+159], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(b * N[(c * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -8.19999999999999951e112

   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. Step-by-step derivation

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. flip-+ 39.2%

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

      4. associate-*r/ 39.2%

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

      5. pow2 39.2%

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

   3. Applied egg-rr 39.2%

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

      1. associate-/l* 39.2%

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

   5. Simplified 39.2%

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

      1. associate--l+ 39.2%

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

      2. associate-/l* 39.2%

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

      3. clear-num 39.2%

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

      4. unpow2 39.2%

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

      5. flip-+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 95.1%

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in c around inf 81.2%

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

      1. unpow2 81.2%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

      4. neg-mul-1 81.1%

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

      5. distribute-rgt-neg-in 81.1%

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

      6. *-commutative 81.1%

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

      7. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   if -8.19999999999999951e112 < c < -4 or -1.50000000000000013e-116 < c < 1.12e30

   1. Initial program 94.6%

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

   2. Taylor expanded in c around 0 74.0%

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

   if -4 < c < -2.05e-22

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. unpow2 83.2%

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

      5. associate-*r* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in c around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-*l* 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. associate-*r* 83.2%

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

      9. *-commutative 83.2%

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

      10. associate-*l* 83.8%

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

   7. Simplified 83.8%

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

   if -2.05e-22 < c < -1.50000000000000013e-116

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 78.6%

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

   3. Taylor expanded in a around inf 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 1.12e30 < c < 1.1e159

   1. Initial program 85.1%

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

   2. Taylor expanded in a around inf 61.3%

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

      1. *-commutative 61.3%

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

   4. Simplified 61.3%

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

   5. Taylor expanded in z around 0 60.9%

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

   if 1.1e159 < c

   1. Initial program 74.5%

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

   2. Taylor expanded in b around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. unpow2 69.2%

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

      5. associate-*r* 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -4:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+30}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+159}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t_1\right)\\ t_3 := 2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.65 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 19:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (* 2.0 (- (* x y) t_1)))
        (t_3 (* 2.0 (- (* z t) t_1))))
   (if (<= c -3.8e+43)
     t_2
     (if (<= c -2.3e-56)
       t_3
       (if (<= c -3.65e-75)
         t_2
         (if (<= c 19.0)
           (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -3.8e+43) {
		tmp = t_2;
	} else if (c <= -2.3e-56) {
		tmp = t_3;
	} else if (c <= -3.65e-75) {
		tmp = t_2;
	} else if (c <= 19.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    t_3 = 2.0d0 * ((z * t) - t_1)
    if (c <= (-3.8d+43)) then
        tmp = t_2
    else if (c <= (-2.3d-56)) then
        tmp = t_3
    else if (c <= (-3.65d-75)) then
        tmp = t_2
    else if (c <= 19.0d0) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double t_3 = 2.0 * ((z * t) - t_1);
	double tmp;
	if (c <= -3.8e+43) {
		tmp = t_2;
	} else if (c <= -2.3e-56) {
		tmp = t_3;
	} else if (c <= -3.65e-75) {
		tmp = t_2;
	} else if (c <= 19.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((x * y) - t_1)
	t_3 = 2.0 * ((z * t) - t_1)
	tmp = 0
	if c <= -3.8e+43:
		tmp = t_2
	elif c <= -2.3e-56:
		tmp = t_3
	elif c <= -3.65e-75:
		tmp = t_2
	elif c <= 19.0:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = t_3
	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(2.0 * Float64(Float64(x * y) - t_1))
	t_3 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	tmp = 0.0
	if (c <= -3.8e+43)
		tmp = t_2;
	elseif (c <= -2.3e-56)
		tmp = t_3;
	elseif (c <= -3.65e-75)
		tmp = t_2;
	elseif (c <= 19.0)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = t_3;
	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 = 2.0 * ((x * y) - t_1);
	t_3 = 2.0 * ((z * t) - t_1);
	tmp = 0.0;
	if (c <= -3.8e+43)
		tmp = t_2;
	elseif (c <= -2.3e-56)
		tmp = t_3;
	elseif (c <= -3.65e-75)
		tmp = t_2;
	elseif (c <= 19.0)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+43], t$95$2, If[LessEqual[c, -2.3e-56], t$95$3, If[LessEqual[c, -3.65e-75], t$95$2, If[LessEqual[c, 19.0], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.80000000000000008e43 or -2.30000000000000002e-56 < c < -3.6499999999999999e-75

   1. Initial program 81.4%

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

   2. Taylor expanded in z around 0 92.1%

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

   if -3.80000000000000008e43 < c < -2.30000000000000002e-56 or 19 < c

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0 88.1%

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

   if -3.6499999999999999e-75 < c < 19

   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. Taylor expanded in a around inf 91.7%

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

      1. *-commutative 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-56}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.65 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 19:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+49} \lor \neg \left(x \cdot y \leq 1.22 \cdot 10^{+66}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4.4e+49) (not (<= (* x y) 1.22e+66)))
   (* 2.0 (- (* x y) (* (* b c) (* c i))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4.4e+49) || !((x * y) <= 1.22e+66)) {
		tmp = 2.0 * ((x * y) - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-4.4d+49)) .or. (.not. ((x * y) <= 1.22d+66))) then
        tmp = 2.0d0 * ((x * y) - ((b * c) * (c * i)))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4.4e+49) || !((x * y) <= 1.22e+66)) {
		tmp = 2.0 * ((x * y) - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -4.4e+49) or not ((x * y) <= 1.22e+66):
		tmp = 2.0 * ((x * y) - ((b * c) * (c * i)))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -4.4e+49) || !(Float64(x * y) <= 1.22e+66))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(Float64(b * c) * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -4.4e+49) || ~(((x * y) <= 1.22e+66)))
		tmp = 2.0 * ((x * y) - ((b * c) * (c * i)));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.4e+49], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.22e+66]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.4000000000000001e49 or 1.21999999999999993e66 < (*.f64 x y)

   1. Initial program 87.8%

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

      1. associate-*r* 93.8%

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

      2. *-commutative 93.8%

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

      3. flip-+ 61.2%

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

      4. associate-*r/ 61.2%

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

      5. pow2 61.2%

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

   3. Applied egg-rr 61.2%

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

      1. associate-/l* 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in a around 0 87.7%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\color{blue}{\frac{1}{b \cdot c}}}\right) \]
   7. Step-by-step derivation

      1. associate-/r* 87.7%

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

   8. Simplified 87.7%

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

   9. Taylor expanded in z around 0 78.0%

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

       1. unpow2 78.0%

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

       2. associate-*r* 78.9%

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

       3. associate-*l* 81.0%

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

       4. *-commutative 81.0%

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

       5. *-commutative 81.0%

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

       6. *-commutative 81.0%

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

   11. Simplified 81.0%

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

   if -4.4000000000000001e49 < (*.f64 x y) < 1.21999999999999993e66

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 86.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+49} \lor \neg \left(x \cdot y \leq 1.22 \cdot 10^{+66}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{-68} \lor \neg \left(x \cdot y \leq 4.15 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* x y) -2.8e-68) (not (<= (* x y) 4.15e-47)))
     (* 2.0 (- (* x y) t_1))
     (* 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 (((x * y) <= -2.8e-68) || !((x * y) <= 4.15e-47)) {
		tmp = 2.0 * ((x * y) - t_1);
	} 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 (((x * y) <= (-2.8d-68)) .or. (.not. ((x * y) <= 4.15d-47))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    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 (((x * y) <= -2.8e-68) || !((x * y) <= 4.15e-47)) {
		tmp = 2.0 * ((x * y) - t_1);
	} 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 ((x * y) <= -2.8e-68) or not ((x * y) <= 4.15e-47):
		tmp = 2.0 * ((x * y) - t_1)
	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 ((Float64(x * y) <= -2.8e-68) || !(Float64(x * y) <= 4.15e-47))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	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 (((x * y) <= -2.8e-68) || ~(((x * y) <= 4.15e-47)))
		tmp = 2.0 * ((x * y) - t_1);
	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[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e-68], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.15e-47]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8000000000000001e-68 or 4.1499999999999998e-47 < (*.f64 x y)

   1. Initial program 88.4%

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

   2. Taylor expanded in z around 0 82.6%

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

   if -2.8000000000000001e-68 < (*.f64 x y) < 4.1499999999999998e-47

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 92.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{-68} \lor \neg \left(x \cdot y \leq 4.15 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))))
   (if (<= c -3.8e+111)
     (* (* (* b c) (* c i)) (- 2.0))
     (if (<= c -4.0)
       t_1
       (if (<= c -8.8e-23)
         (* c (* (* c (* b i)) -2.0))
         (if (<= c -8.6e-115)
           (* 2.0 (* (* a c) (- i)))
           (if (<= c 7e+82) t_1 (* 2.0 (* b (* c (* c (- i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -3.8e+111) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -4.0) {
		tmp = t_1;
	} else if (c <= -8.8e-23) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 7e+82) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    if (c <= (-3.8d+111)) then
        tmp = ((b * c) * (c * i)) * -2.0d0
    else if (c <= (-4.0d0)) then
        tmp = t_1
    else if (c <= (-8.8d-23)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-8.6d-115)) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if (c <= 7d+82) then
        tmp = t_1
    else
        tmp = 2.0d0 * (b * (c * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -3.8e+111) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -4.0) {
		tmp = t_1;
	} else if (c <= -8.8e-23) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 7e+82) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	tmp = 0
	if c <= -3.8e+111:
		tmp = ((b * c) * (c * i)) * -2.0
	elif c <= -4.0:
		tmp = t_1
	elif c <= -8.8e-23:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -8.6e-115:
		tmp = 2.0 * ((a * c) * -i)
	elif c <= 7e+82:
		tmp = t_1
	else:
		tmp = 2.0 * (b * (c * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (c <= -3.8e+111)
		tmp = Float64(Float64(Float64(b * c) * Float64(c * i)) * Float64(-2.0));
	elseif (c <= -4.0)
		tmp = t_1;
	elseif (c <= -8.8e-23)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -8.6e-115)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (c <= 7e+82)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(b * Float64(c * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	tmp = 0.0;
	if (c <= -3.8e+111)
		tmp = ((b * c) * (c * i)) * -2.0;
	elseif (c <= -4.0)
		tmp = t_1;
	elseif (c <= -8.8e-23)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -8.6e-115)
		tmp = 2.0 * ((a * c) * -i);
	elseif (c <= 7e+82)
		tmp = t_1;
	else
		tmp = 2.0 * (b * (c * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+111], N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, -4.0], t$95$1, If[LessEqual[c, -8.8e-23], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.6e-115], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e+82], t$95$1, N[(2.0 * N[(b * N[(c * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.79999999999999976e111

   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. Step-by-step derivation

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. flip-+ 39.2%

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

      4. associate-*r/ 39.2%

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

      5. pow2 39.2%

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

   3. Applied egg-rr 39.2%

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

      1. associate-/l* 39.2%

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

   5. Simplified 39.2%

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

      1. associate--l+ 39.2%

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

      2. associate-/l* 39.2%

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

      3. clear-num 39.2%

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

      4. unpow2 39.2%

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

      5. flip-+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 95.1%

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in c around inf 81.2%

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

      1. unpow2 81.2%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

      4. neg-mul-1 81.1%

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

      5. distribute-rgt-neg-in 81.1%

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

      6. *-commutative 81.1%

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

      7. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   if -3.79999999999999976e111 < c < -4 or -8.6000000000000008e-115 < c < 7.0000000000000001e82

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 71.7%

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

   if -4 < c < -8.7999999999999998e-23

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. unpow2 83.2%

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

      5. associate-*r* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in c around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-*l* 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. associate-*r* 83.2%

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

      9. *-commutative 83.2%

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

      10. associate-*l* 83.8%

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

   7. Simplified 83.8%

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

   if -8.7999999999999998e-23 < c < -8.6000000000000008e-115

   1. Initial program 99.4%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

      3. flip-+ 54.6%

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

      4. associate-*r/ 54.5%

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

      5. pow2 54.5%

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

   3. Applied egg-rr 54.5%

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

      1. associate-/l* 54.5%

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

   5. Simplified 54.5%

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

      1. associate--l+ 54.5%

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

      2. associate-/l* 53.0%

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

      3. clear-num 53.1%

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

      4. unpow2 53.1%

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

      5. flip-+ 92.3%

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

      6. +-commutative 92.3%

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

      7. fma-def 92.3%

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

   7. Applied egg-rr 92.3%

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

   8. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*r* 55.8%

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

      5. neg-mul-1 55.8%

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

   10. Simplified 55.8%

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

   if 7.0000000000000001e82 < c

   1. Initial program 74.9%

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

   2. Taylor expanded in b around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. unpow2 61.9%

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

      5. associate-*r* 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -4:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -0.0058:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))))
   (if (<= c -8.2e+112)
     (* (* (* b c) (* c i)) (- 2.0))
     (if (<= c -0.0058)
       t_1
       (if (<= c -2.05e-22)
         (* c (* (* c (* b i)) -2.0))
         (if (<= c -8e-115)
           (* 2.0 (- (* z t) (* c (* a i))))
           (if (<= c 1.7e+83) t_1 (* 2.0 (* b (* c (* c (- i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -8.2e+112) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -0.0058) {
		tmp = t_1;
	} else if (c <= -2.05e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8e-115) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 1.7e+83) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    if (c <= (-8.2d+112)) then
        tmp = ((b * c) * (c * i)) * -2.0d0
    else if (c <= (-0.0058d0)) then
        tmp = t_1
    else if (c <= (-2.05d-22)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-8d-115)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (c <= 1.7d+83) then
        tmp = t_1
    else
        tmp = 2.0d0 * (b * (c * (c * -i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -8.2e+112) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -0.0058) {
		tmp = t_1;
	} else if (c <= -2.05e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8e-115) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= 1.7e+83) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (b * (c * (c * -i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	tmp = 0
	if c <= -8.2e+112:
		tmp = ((b * c) * (c * i)) * -2.0
	elif c <= -0.0058:
		tmp = t_1
	elif c <= -2.05e-22:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -8e-115:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif c <= 1.7e+83:
		tmp = t_1
	else:
		tmp = 2.0 * (b * (c * (c * -i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (c <= -8.2e+112)
		tmp = Float64(Float64(Float64(b * c) * Float64(c * i)) * Float64(-2.0));
	elseif (c <= -0.0058)
		tmp = t_1;
	elseif (c <= -2.05e-22)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -8e-115)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (c <= 1.7e+83)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(b * Float64(c * Float64(c * Float64(-i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	tmp = 0.0;
	if (c <= -8.2e+112)
		tmp = ((b * c) * (c * i)) * -2.0;
	elseif (c <= -0.0058)
		tmp = t_1;
	elseif (c <= -2.05e-22)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -8e-115)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (c <= 1.7e+83)
		tmp = t_1;
	else
		tmp = 2.0 * (b * (c * (c * -i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+112], N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, -0.0058], t$95$1, If[LessEqual[c, -2.05e-22], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e-115], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+83], t$95$1, N[(2.0 * N[(b * N[(c * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8.19999999999999951e112

   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. Step-by-step derivation

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. flip-+ 39.2%

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

      4. associate-*r/ 39.2%

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

      5. pow2 39.2%

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

   3. Applied egg-rr 39.2%

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

      1. associate-/l* 39.2%

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

   5. Simplified 39.2%

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

      1. associate--l+ 39.2%

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

      2. associate-/l* 39.2%

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

      3. clear-num 39.2%

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

      4. unpow2 39.2%

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

      5. flip-+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 95.1%

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in c around inf 81.2%

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

      1. unpow2 81.2%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

      4. neg-mul-1 81.1%

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

      5. distribute-rgt-neg-in 81.1%

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

      6. *-commutative 81.1%

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

      7. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   if -8.19999999999999951e112 < c < -0.0058 or -8.0000000000000004e-115 < c < 1.6999999999999999e83

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 71.7%

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

   if -0.0058 < c < -2.05e-22

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. unpow2 83.2%

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

      5. associate-*r* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in c around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-*l* 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. associate-*r* 83.2%

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

      9. *-commutative 83.2%

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

      10. associate-*l* 83.8%

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

   7. Simplified 83.8%

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

   if -2.05e-22 < c < -8.0000000000000004e-115

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 78.6%

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

   3. Taylor expanded in a around inf 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if 1.6999999999999999e83 < c

   1. Initial program 74.9%

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

   2. Taylor expanded in b around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. unpow2 61.9%

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

      5. associate-*r* 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -0.0058:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(c \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 13: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -0.175:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))) (t_2 (* c (* (* c (* b i)) -2.0))))
   (if (<= c -4e+113)
     t_2
     (if (<= c -0.175)
       t_1
       (if (<= c -1.25e-22)
         t_2
         (if (<= c -8.6e-115)
           (* 2.0 (* (* a c) (- i)))
           (if (<= c 6.2e+83) 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 * ((x * y) + (z * t));
	double t_2 = c * ((c * (b * i)) * -2.0);
	double tmp;
	if (c <= -4e+113) {
		tmp = t_2;
	} else if (c <= -0.175) {
		tmp = t_1;
	} else if (c <= -1.25e-22) {
		tmp = t_2;
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 6.2e+83) {
		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 = 2.0d0 * ((x * y) + (z * t))
    t_2 = c * ((c * (b * i)) * (-2.0d0))
    if (c <= (-4d+113)) then
        tmp = t_2
    else if (c <= (-0.175d0)) then
        tmp = t_1
    else if (c <= (-1.25d-22)) then
        tmp = t_2
    else if (c <= (-8.6d-115)) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if (c <= 6.2d+83) 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 * ((x * y) + (z * t));
	double t_2 = c * ((c * (b * i)) * -2.0);
	double tmp;
	if (c <= -4e+113) {
		tmp = t_2;
	} else if (c <= -0.175) {
		tmp = t_1;
	} else if (c <= -1.25e-22) {
		tmp = t_2;
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 6.2e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = c * ((c * (b * i)) * -2.0)
	tmp = 0
	if c <= -4e+113:
		tmp = t_2
	elif c <= -0.175:
		tmp = t_1
	elif c <= -1.25e-22:
		tmp = t_2
	elif c <= -8.6e-115:
		tmp = 2.0 * ((a * c) * -i)
	elif c <= 6.2e+83:
		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(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0))
	tmp = 0.0
	if (c <= -4e+113)
		tmp = t_2;
	elseif (c <= -0.175)
		tmp = t_1;
	elseif (c <= -1.25e-22)
		tmp = t_2;
	elseif (c <= -8.6e-115)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (c <= 6.2e+83)
		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 * ((x * y) + (z * t));
	t_2 = c * ((c * (b * i)) * -2.0);
	tmp = 0.0;
	if (c <= -4e+113)
		tmp = t_2;
	elseif (c <= -0.175)
		tmp = t_1;
	elseif (c <= -1.25e-22)
		tmp = t_2;
	elseif (c <= -8.6e-115)
		tmp = 2.0 * ((a * c) * -i);
	elseif (c <= 6.2e+83)
		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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e+113], t$95$2, If[LessEqual[c, -0.175], t$95$1, If[LessEqual[c, -1.25e-22], t$95$2, If[LessEqual[c, -8.6e-115], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e+83], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4e113 or -0.17499999999999999 < c < -1.24999999999999988e-22 or 6.19999999999999984e83 < c

   1. Initial program 80.7%

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

   2. Taylor expanded in b around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. *-commutative 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

      4. unpow2 71.0%

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

      5. associate-*r* 73.8%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in c around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. unpow2 71.0%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-*l* 73.7%

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

      6. *-commutative 73.7%

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

      7. associate-*l* 73.7%

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

      8. associate-*r* 71.9%

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

      9. *-commutative 71.9%

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

      10. associate-*l* 71.9%

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

   7. Simplified 71.9%

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

   if -4e113 < c < -0.17499999999999999 or -8.6000000000000008e-115 < c < 6.19999999999999984e83

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 71.7%

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

   if -1.24999999999999988e-22 < c < -8.6000000000000008e-115

   1. Initial program 99.4%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

      3. flip-+ 54.6%

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

      4. associate-*r/ 54.5%

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

      5. pow2 54.5%

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

   3. Applied egg-rr 54.5%

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

      1. associate-/l* 54.5%

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

   5. Simplified 54.5%

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

      1. associate--l+ 54.5%

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

      2. associate-/l* 53.0%

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

      3. clear-num 53.1%

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

      4. unpow2 53.1%

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

      5. flip-+ 92.3%

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

      6. +-commutative 92.3%

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

      7. fma-def 92.3%

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

   7. Applied egg-rr 92.3%

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

   8. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*r* 55.8%

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

      5. neg-mul-1 55.8%

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

   10. Simplified 55.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+113}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -0.175:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \end{array} \]

Alternative 14: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -0.0046:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))) (t_2 (* -2.0 (* c (* b (* c i))))))
   (if (<= c -2.4e+112)
     t_2
     (if (<= c -0.0046)
       t_1
       (if (<= c -3.7e-23)
         (* c (* (* c (* b i)) -2.0))
         (if (<= c -8.6e-115)
           (* 2.0 (* (* a c) (- i)))
           (if (<= c 8.5e+82) 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 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2.4e+112) {
		tmp = t_2;
	} else if (c <= -0.0046) {
		tmp = t_1;
	} else if (c <= -3.7e-23) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 8.5e+82) {
		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 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * (b * (c * i)))
    if (c <= (-2.4d+112)) then
        tmp = t_2
    else if (c <= (-0.0046d0)) then
        tmp = t_1
    else if (c <= (-3.7d-23)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-8.6d-115)) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if (c <= 8.5d+82) 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 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -2.4e+112) {
		tmp = t_2;
	} else if (c <= -0.0046) {
		tmp = t_1;
	} else if (c <= -3.7e-23) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 8.5e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * (b * (c * i)))
	tmp = 0
	if c <= -2.4e+112:
		tmp = t_2
	elif c <= -0.0046:
		tmp = t_1
	elif c <= -3.7e-23:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -8.6e-115:
		tmp = 2.0 * ((a * c) * -i)
	elif c <= 8.5e+82:
		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(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	tmp = 0.0
	if (c <= -2.4e+112)
		tmp = t_2;
	elseif (c <= -0.0046)
		tmp = t_1;
	elseif (c <= -3.7e-23)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -8.6e-115)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (c <= 8.5e+82)
		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 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * (b * (c * i)));
	tmp = 0.0;
	if (c <= -2.4e+112)
		tmp = t_2;
	elseif (c <= -0.0046)
		tmp = t_1;
	elseif (c <= -3.7e-23)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -8.6e-115)
		tmp = 2.0 * ((a * c) * -i);
	elseif (c <= 8.5e+82)
		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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.4e+112], t$95$2, If[LessEqual[c, -0.0046], t$95$1, If[LessEqual[c, -3.7e-23], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.6e-115], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+82], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.4e112 or 8.4999999999999995e82 < c

   1. Initial program 79.6%

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

   2. Taylor expanded in b around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. unpow2 70.3%

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

      5. associate-*r* 73.2%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in c around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. unpow2 70.3%

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

      3. associate-*r* 73.2%

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

      4. *-commutative 73.2%

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

      5. associate-*l* 73.1%

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

   7. Simplified 73.1%

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

   if -2.4e112 < c < -0.0045999999999999999 or -8.6000000000000008e-115 < c < 8.4999999999999995e82

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 71.7%

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

   if -0.0045999999999999999 < c < -3.7000000000000003e-23

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. unpow2 83.2%

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

      5. associate-*r* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in c around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-*l* 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. associate-*r* 83.2%

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

      9. *-commutative 83.2%

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

      10. associate-*l* 83.8%

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

   7. Simplified 83.8%

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

   if -3.7000000000000003e-23 < c < -8.6000000000000008e-115

   1. Initial program 99.4%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

      3. flip-+ 54.6%

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

      4. associate-*r/ 54.5%

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

      5. pow2 54.5%

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

   3. Applied egg-rr 54.5%

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

      1. associate-/l* 54.5%

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

   5. Simplified 54.5%

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

      1. associate--l+ 54.5%

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

      2. associate-/l* 53.0%

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

      3. clear-num 53.1%

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

      4. unpow2 53.1%

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

      5. flip-+ 92.3%

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

      6. +-commutative 92.3%

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

      7. fma-def 92.3%

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

   7. Applied egg-rr 92.3%

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

   8. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*r* 55.8%

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

      5. neg-mul-1 55.8%

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

   10. Simplified 55.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+112}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -0.0046:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 15: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -0.0052:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t)))))
   (if (<= c -4.5e+111)
     (* (* (* b c) (* c i)) (- 2.0))
     (if (<= c -0.0052)
       t_1
       (if (<= c -1.25e-22)
         (* c (* (* c (* b i)) -2.0))
         (if (<= c -8.6e-115)
           (* 2.0 (* (* a c) (- i)))
           (if (<= c 8e+82) t_1 (* -2.0 (* c (* b (* c i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -4.5e+111) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -0.0052) {
		tmp = t_1;
	} else if (c <= -1.25e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 8e+82) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    if (c <= (-4.5d+111)) then
        tmp = ((b * c) * (c * i)) * -2.0d0
    else if (c <= (-0.0052d0)) then
        tmp = t_1
    else if (c <= (-1.25d-22)) then
        tmp = c * ((c * (b * i)) * (-2.0d0))
    else if (c <= (-8.6d-115)) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if (c <= 8d+82) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (b * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double tmp;
	if (c <= -4.5e+111) {
		tmp = ((b * c) * (c * i)) * -2.0;
	} else if (c <= -0.0052) {
		tmp = t_1;
	} else if (c <= -1.25e-22) {
		tmp = c * ((c * (b * i)) * -2.0);
	} else if (c <= -8.6e-115) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (c <= 8e+82) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (b * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	tmp = 0
	if c <= -4.5e+111:
		tmp = ((b * c) * (c * i)) * -2.0
	elif c <= -0.0052:
		tmp = t_1
	elif c <= -1.25e-22:
		tmp = c * ((c * (b * i)) * -2.0)
	elif c <= -8.6e-115:
		tmp = 2.0 * ((a * c) * -i)
	elif c <= 8e+82:
		tmp = t_1
	else:
		tmp = -2.0 * (c * (b * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (c <= -4.5e+111)
		tmp = Float64(Float64(Float64(b * c) * Float64(c * i)) * Float64(-2.0));
	elseif (c <= -0.0052)
		tmp = t_1;
	elseif (c <= -1.25e-22)
		tmp = Float64(c * Float64(Float64(c * Float64(b * i)) * -2.0));
	elseif (c <= -8.6e-115)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (c <= 8e+82)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	tmp = 0.0;
	if (c <= -4.5e+111)
		tmp = ((b * c) * (c * i)) * -2.0;
	elseif (c <= -0.0052)
		tmp = t_1;
	elseif (c <= -1.25e-22)
		tmp = c * ((c * (b * i)) * -2.0);
	elseif (c <= -8.6e-115)
		tmp = 2.0 * ((a * c) * -i);
	elseif (c <= 8e+82)
		tmp = t_1;
	else
		tmp = -2.0 * (c * (b * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e+111], N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, -0.0052], t$95$1, If[LessEqual[c, -1.25e-22], N[(c * N[(N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.6e-115], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+82], t$95$1, N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.50000000000000001e111

   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. Step-by-step derivation

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. flip-+ 39.2%

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

      4. associate-*r/ 39.2%

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

      5. pow2 39.2%

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

   3. Applied egg-rr 39.2%

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

      1. associate-/l* 39.2%

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

   5. Simplified 39.2%

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

      1. associate--l+ 39.2%

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

      2. associate-/l* 39.2%

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

      3. clear-num 39.2%

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

      4. unpow2 39.2%

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

      5. flip-+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 95.1%

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in c around inf 81.2%

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

      1. unpow2 81.2%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

      4. neg-mul-1 81.1%

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

      5. distribute-rgt-neg-in 81.1%

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

      6. *-commutative 81.1%

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

      7. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   if -4.50000000000000001e111 < c < -0.0051999999999999998 or -8.6000000000000008e-115 < c < 7.9999999999999997e82

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 71.7%

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

   if -0.0051999999999999998 < c < -1.24999999999999988e-22

   1. Initial program 99.2%

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

   2. Taylor expanded in b around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. unpow2 83.2%

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

      5. associate-*r* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in c around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. unpow2 83.2%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-*l* 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. associate-*r* 83.2%

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

      9. *-commutative 83.2%

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

      10. associate-*l* 83.8%

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

   7. Simplified 83.8%

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

   if -1.24999999999999988e-22 < c < -8.6000000000000008e-115

   1. Initial program 99.4%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

      3. flip-+ 54.6%

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

      4. associate-*r/ 54.5%

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

      5. pow2 54.5%

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

   3. Applied egg-rr 54.5%

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

      1. associate-/l* 54.5%

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

   5. Simplified 54.5%

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

      1. associate--l+ 54.5%

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

      2. associate-/l* 53.0%

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

      3. clear-num 53.1%

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

      4. unpow2 53.1%

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

      5. flip-+ 92.3%

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

      6. +-commutative 92.3%

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

      7. fma-def 92.3%

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

   7. Applied egg-rr 92.3%

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

   8. Taylor expanded in a around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*r* 55.8%

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

      5. neg-mul-1 55.8%

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

   10. Simplified 55.8%

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

   if 7.9999999999999997e82 < c

   1. Initial program 74.9%

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

   2. Taylor expanded in b around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. unpow2 61.9%

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

      5. associate-*r* 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in c around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. unpow2 61.9%

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

      3. associate-*r* 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-*l* 65.4%

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

   7. Simplified 65.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq -0.0052:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(b \cdot i\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-115}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 16: 71.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{-115} \lor \neg \left(c \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.6e-115) (not (<= c 1.2e+32)))
   (* (* c (* (+ a (* b c)) i)) (- 2.0))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.6e-115) || !(c <= 1.2e+32)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (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 ((c <= (-8.6d-115)) .or. (.not. (c <= 1.2d+32))) then
        tmp = (c * ((a + (b * c)) * i)) * -2.0d0
    else
        tmp = 2.0d0 * ((x * y) + (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 ((c <= -8.6e-115) || !(c <= 1.2e+32)) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.6e-115) or not (c <= 1.2e+32):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.6e-115) || !(c <= 1.2e+32))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * Float64(-2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8.6e-115) || ~((c <= 1.2e+32)))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.6e-115], N[Not[LessEqual[c, 1.2e+32]], $MachinePrecision]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.6000000000000008e-115 or 1.19999999999999996e32 < c

   1. Initial program 83.9%

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

   2. Taylor expanded in i around inf 76.9%

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

   if -8.6000000000000008e-115 < c < 1.19999999999999996e32

   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. Taylor expanded in c around 0 79.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{-115} \lor \neg \left(c \leq 1.2 \cdot 10^{+32}\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 17: 42.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{-92} \lor \neg \left(x \cdot y \leq 3.2 \cdot 10^{-40}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -3.8e-92) (not (<= (* x y) 3.2e-40)))
   (* (* 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) <= -3.8e-92) || !((x * y) <= 3.2e-40)) {
		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) <= (-3.8d-92)) .or. (.not. ((x * y) <= 3.2d-40))) 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) <= -3.8e-92) || !((x * y) <= 3.2e-40)) {
		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) <= -3.8e-92) or not ((x * y) <= 3.2e-40):
		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) <= -3.8e-92) || !(Float64(x * y) <= 3.2e-40))
		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) <= -3.8e-92) || ~(((x * y) <= 3.2e-40)))
		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], -3.8e-92], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.2e-40]], $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) < -3.8000000000000001e-92 or 3.20000000000000002e-40 < (*.f64 x y)

   1. Initial program 88.6%

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

   2. Taylor expanded in x around inf 44.6%

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

   if -3.8000000000000001e-92 < (*.f64 x y) < 3.20000000000000002e-40

   1. Initial program 91.1%

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

   2. Taylor expanded in z around inf 41.1%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{-92} \lor \neg \left(x \cdot y \leq 3.2 \cdot 10^{-40}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 18: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+189} \lor \neg \left(i \leq 8.8 \cdot 10^{+106}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2.1e+189) (not (<= i 8.8e+106)))
   (* (* a (* c i)) (- 2.0))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.1e+189) || !(i <= 8.8e+106)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (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 ((i <= (-2.1d+189)) .or. (.not. (i <= 8.8d+106))) then
        tmp = (a * (c * i)) * -2.0d0
    else
        tmp = 2.0d0 * ((x * y) + (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 ((i <= -2.1e+189) || !(i <= 8.8e+106)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -2.1e+189) or not (i <= 8.8e+106):
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -2.1e+189) || !(i <= 8.8e+106))
		tmp = Float64(Float64(a * Float64(c * i)) * Float64(-2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -2.1e+189) || ~((i <= 8.8e+106)))
		tmp = (a * (c * i)) * -2.0;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -2.1e+189], N[Not[LessEqual[i, 8.8e+106]], $MachinePrecision]], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.09999999999999992e189 or 8.79999999999999966e106 < i

   1. Initial program 95.0%

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

      1. associate-*l* 92.0%

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

      2. fma-def 92.0%

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

   3. Simplified 92.0%

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

      1. fma-def 92.0%

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

      2. +-commutative 92.0%

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

   5. Applied egg-rr 92.0%

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

   6. Taylor expanded in a around inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. distribute-rgt-neg-in 50.0%

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

      3. distribute-rgt-neg-in 50.0%

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

   8. Simplified 50.0%

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

   if -2.09999999999999992e189 < i < 8.79999999999999966e106

   1. Initial program 88.0%

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

   2. Taylor expanded in c around 0 60.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+189} \lor \neg \left(i \leq 8.8 \cdot 10^{+106}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 19: 30.1% 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 89.7%

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

2. Taylor expanded in z around inf 26.4%

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

3. Final simplification 26.4%

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

Developer target: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023287 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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