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

Percentage Accurate: 89.8% → 94.7%

Time: 15.9s

Alternatives: 16

Speedup: 1.0×

• 47.5% 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: 94.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 65.3%

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

   2. Taylor expanded in z around 0 88.1%

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

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

   1. Initial program 98.6%

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

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

   1. Initial program 78.0%

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

   2. Taylor expanded in x around 0 91.7%

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

4. Final simplification 95.3%

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

Alternative 2: 94.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

   1. associate-*l* 92.7%

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

   2. fma-def 93.4%

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

3. Simplified 93.4%

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

4. Final simplification 93.4%

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

Alternative 3: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+79} \lor \neg \left(c \leq -4.6 \cdot 10^{+61} \lor \neg \left(c \leq -3 \cdot 10^{-25}\right) \land \left(c \leq 4.2 \cdot 10^{-72} \lor \neg \left(c \leq 2.9 \cdot 10^{-51}\right) \land c \leq 11500000\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (* (+ a (* b c)) i)) -2.0)))
   (if (<= c -3e+144)
     t_1
     (if (<= c -8.6e+98)
       (* 2.0 (- (* z t) (* c (* a i))))
       (if (or (<= c -8e+79)
               (not
                (or (<= c -4.6e+61)
                    (and (not (<= c -3e-25))
                         (or (<= c 4.2e-72)
                             (and (not (<= c 2.9e-51)) (<= c 11500000.0)))))))
         t_1
         (* 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 t_1 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -3e+144) {
		tmp = t_1;
	} else if (c <= -8.6e+98) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((c <= -8e+79) || !((c <= -4.6e+61) || (!(c <= -3e-25) && ((c <= 4.2e-72) || (!(c <= 2.9e-51) && (c <= 11500000.0)))))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (c * ((a + (b * c)) * i)) * (-2.0d0)
    if (c <= (-3d+144)) then
        tmp = t_1
    else if (c <= (-8.6d+98)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if ((c <= (-8d+79)) .or. (.not. (c <= (-4.6d+61)) .or. (.not. (c <= (-3d-25))) .and. (c <= 4.2d-72) .or. (.not. (c <= 2.9d-51)) .and. (c <= 11500000.0d0))) then
        tmp = t_1
    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 t_1 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (c <= -3e+144) {
		tmp = t_1;
	} else if (c <= -8.6e+98) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if ((c <= -8e+79) || !((c <= -4.6e+61) || (!(c <= -3e-25) && ((c <= 4.2e-72) || (!(c <= 2.9e-51) && (c <= 11500000.0)))))) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * ((a + (b * c)) * i)) * -2.0
	tmp = 0
	if c <= -3e+144:
		tmp = t_1
	elif c <= -8.6e+98:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif (c <= -8e+79) or not ((c <= -4.6e+61) or (not (c <= -3e-25) and ((c <= 4.2e-72) or (not (c <= 2.9e-51) and (c <= 11500000.0))))):
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0)
	tmp = 0.0
	if (c <= -3e+144)
		tmp = t_1;
	elseif (c <= -8.6e+98)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif ((c <= -8e+79) || !((c <= -4.6e+61) || (!(c <= -3e-25) && ((c <= 4.2e-72) || (!(c <= 2.9e-51) && (c <= 11500000.0))))))
		tmp = t_1;
	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)
	t_1 = (c * ((a + (b * c)) * i)) * -2.0;
	tmp = 0.0;
	if (c <= -3e+144)
		tmp = t_1;
	elseif (c <= -8.6e+98)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif ((c <= -8e+79) || ~(((c <= -4.6e+61) || (~((c <= -3e-25)) && ((c <= 4.2e-72) || (~((c <= 2.9e-51)) && (c <= 11500000.0)))))))
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -3e+144], t$95$1, If[LessEqual[c, -8.6e+98], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -8e+79], N[Not[Or[LessEqual[c, -4.6e+61], And[N[Not[LessEqual[c, -3e-25]], $MachinePrecision], Or[LessEqual[c, 4.2e-72], And[N[Not[LessEqual[c, 2.9e-51]], $MachinePrecision], LessEqual[c, 11500000.0]]]]]], $MachinePrecision]], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9999999999999999e144 or -8.6000000000000003e98 < c < -7.99999999999999974e79 or -4.5999999999999999e61 < c < -2.9999999999999998e-25 or 4.2e-72 < c < 2.89999999999999973e-51 or 1.15e7 < c

   1. Initial program 78.3%

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

      1. associate-*l* 89.3%

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

      2. fma-def 90.1%

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

   3. Simplified 90.1%

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

      1. fma-def 89.3%

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

      2. +-commutative 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in c around inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

      3. unpow2 66.3%

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

      4. distribute-lft-neg-in 66.3%

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

      5. associate-*l* 73.9%

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

      6. *-commutative 73.9%

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

      7. associate-*r* 73.4%

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

      8. neg-mul-1 73.4%

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

      9. distribute-lft-neg-in 73.4%

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

      10. distribute-lft-in 79.3%

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

      11. distribute-rgt-in 80.9%

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

      12. +-commutative 80.9%

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

      13. *-commutative 80.9%

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

      14. associate-*r* 80.2%

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

      15. distribute-lft-neg-in 80.2%

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

      16. *-commutative 80.2%

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

      17. distribute-rgt-neg-in 80.2%

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

      18. *-commutative 80.2%

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

      19. +-commutative 80.2%

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

      20. fma-def 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in i around 0 80.9%

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

   if -2.9999999999999999e144 < c < -8.6000000000000003e98

   1. Initial program 90.4%

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

   2. Taylor expanded in a around inf 83.0%

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

   3. Taylor expanded in x around 0 92.6%

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

      1. *-commutative 92.6%

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

   5. Simplified 92.6%

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

   if -7.99999999999999974e79 < c < -4.5999999999999999e61 or -2.9999999999999998e-25 < c < 4.2e-72 or 2.89999999999999973e-51 < c < 1.15e7

   1. Initial program 97.6%

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

   2. Taylor expanded in c around 0 77.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+98}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+79} \lor \neg \left(c \leq -4.6 \cdot 10^{+61} \lor \neg \left(c \leq -3 \cdot 10^{-25}\right) \land \left(c \leq 4.2 \cdot 10^{-72} \lor \neg \left(c \leq 2.9 \cdot 10^{-51}\right) \land c \leq 11500000\right)\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.16 \cdot 10^{+80} \lor \neg \left(c \leq -4.6 \cdot 10^{+61} \lor \neg \left(c \leq -1.25 \cdot 10^{-24}\right) \land \left(c \leq 2.3 \cdot 10^{-71} \lor \neg \left(c \leq 2.6 \cdot 10^{-51}\right) \land c \leq 7000000\right)\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.16e+80)
         (not
          (or (<= c -4.6e+61)
              (and (not (<= c -1.25e-24))
                   (or (<= c 2.3e-71)
                       (and (not (<= c 2.6e-51)) (<= c 7000000.0)))))))
   (* (* 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 <= -1.16e+80) || !((c <= -4.6e+61) || (!(c <= -1.25e-24) && ((c <= 2.3e-71) || (!(c <= 2.6e-51) && (c <= 7000000.0)))))) {
		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 <= (-1.16d+80)) .or. (.not. (c <= (-4.6d+61)) .or. (.not. (c <= (-1.25d-24))) .and. (c <= 2.3d-71) .or. (.not. (c <= 2.6d-51)) .and. (c <= 7000000.0d0))) 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 <= -1.16e+80) || !((c <= -4.6e+61) || (!(c <= -1.25e-24) && ((c <= 2.3e-71) || (!(c <= 2.6e-51) && (c <= 7000000.0)))))) {
		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 <= -1.16e+80) or not ((c <= -4.6e+61) or (not (c <= -1.25e-24) and ((c <= 2.3e-71) or (not (c <= 2.6e-51) and (c <= 7000000.0))))):
		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 <= -1.16e+80) || !((c <= -4.6e+61) || (!(c <= -1.25e-24) && ((c <= 2.3e-71) || (!(c <= 2.6e-51) && (c <= 7000000.0))))))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -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 <= -1.16e+80) || ~(((c <= -4.6e+61) || (~((c <= -1.25e-24)) && ((c <= 2.3e-71) || (~((c <= 2.6e-51)) && (c <= 7000000.0)))))))
		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, -1.16e+80], N[Not[Or[LessEqual[c, -4.6e+61], And[N[Not[LessEqual[c, -1.25e-24]], $MachinePrecision], Or[LessEqual[c, 2.3e-71], And[N[Not[LessEqual[c, 2.6e-51]], $MachinePrecision], LessEqual[c, 7000000.0]]]]]], $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 < -1.15999999999999997e80 or -4.5999999999999999e61 < c < -1.24999999999999995e-24 or 2.2999999999999998e-71 < c < 2.6e-51 or 7e6 < c

   1. Initial program 79.2%

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

      1. associate-*l* 90.1%

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

      2. fma-def 90.9%

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

   3. Simplified 90.9%

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

      1. fma-def 90.1%

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

      2. +-commutative 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in c around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. neg-mul-1 64.4%

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

      3. unpow2 64.4%

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

      4. distribute-lft-neg-in 64.4%

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

      5. associate-*l* 71.4%

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

      6. *-commutative 71.4%

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

      7. associate-*r* 71.0%

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

      8. neg-mul-1 71.0%

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

      9. distribute-lft-neg-in 71.0%

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

      10. distribute-lft-in 77.1%

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

      11. distribute-rgt-in 78.7%

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

      12. +-commutative 78.7%

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

      13. *-commutative 78.7%

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

      14. associate-*r* 77.9%

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

      15. distribute-lft-neg-in 77.9%

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

      16. *-commutative 77.9%

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

      17. distribute-rgt-neg-in 77.9%

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

      18. *-commutative 77.9%

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

      19. +-commutative 77.9%

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

      20. fma-def 78.0%

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

   8. Simplified 78.0%

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

   9. Taylor expanded in i around 0 78.7%

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

   if -1.15999999999999997e80 < c < -4.5999999999999999e61 or -1.24999999999999995e-24 < c < 2.2999999999999998e-71 or 2.6e-51 < c < 7e6

   1. Initial program 97.6%

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

   2. Taylor expanded in c around 0 77.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.16 \cdot 10^{+80} \lor \neg \left(c \leq -4.6 \cdot 10^{+61} \lor \neg \left(c \leq -1.25 \cdot 10^{-24}\right) \land \left(c \leq 2.3 \cdot 10^{-71} \lor \neg \left(c \leq 2.6 \cdot 10^{-51}\right) \land c \leq 7000000\right)\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 5: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+153}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))
   (if (<= x -1.3e+153)
     (* 2.0 (- (* x y) (* c (* i (* b c)))))
     (if (<= x -6.2e+107)
       t_1
       (if (<= x -4.5e+23)
         (* 2.0 (- (* x y) (* c (* a i))))
         (if (<= x 7.4e-96) t_1 (* 2.0 (- (* x y) (* i (* a c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (x <= -1.3e+153) {
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	} else if (x <= -6.2e+107) {
		tmp = t_1;
	} else if (x <= -4.5e+23) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (x <= 7.4e-96) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    if (x <= (-1.3d+153)) then
        tmp = 2.0d0 * ((x * y) - (c * (i * (b * c))))
    else if (x <= (-6.2d+107)) then
        tmp = t_1
    else if (x <= (-4.5d+23)) then
        tmp = 2.0d0 * ((x * y) - (c * (a * i)))
    else if (x <= 7.4d-96) then
        tmp = t_1
    else
        tmp = 2.0d0 * ((x * y) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (x <= -1.3e+153) {
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	} else if (x <= -6.2e+107) {
		tmp = t_1;
	} else if (x <= -4.5e+23) {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	} else if (x <= 7.4e-96) {
		tmp = t_1;
	} else {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	tmp = 0
	if x <= -1.3e+153:
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))))
	elif x <= -6.2e+107:
		tmp = t_1
	elif x <= -4.5e+23:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	elif x <= 7.4e-96:
		tmp = t_1
	else:
		tmp = 2.0 * ((x * y) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	tmp = 0.0
	if (x <= -1.3e+153)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(i * Float64(b * c)))));
	elseif (x <= -6.2e+107)
		tmp = t_1;
	elseif (x <= -4.5e+23)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))));
	elseif (x <= 7.4e-96)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	tmp = 0.0;
	if (x <= -1.3e+153)
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	elseif (x <= -6.2e+107)
		tmp = t_1;
	elseif (x <= -4.5e+23)
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	elseif (x <= 7.4e-96)
		tmp = t_1;
	else
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+153], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e+107], t$95$1, If[LessEqual[x, -4.5e+23], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-96], t$95$1, N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2999999999999999e153

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 83.8%

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

   3. Taylor expanded in c around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-*l* 76.3%

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

      3. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   if -1.2999999999999999e153 < x < -6.20000000000000052e107 or -4.49999999999999979e23 < x < 7.39999999999999972e-96

   1. Initial program 86.3%

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

   2. Taylor expanded in x around 0 80.9%

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

   if -6.20000000000000052e107 < x < -4.49999999999999979e23

   1. Initial program 87.8%

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

   2. Taylor expanded in a around inf 82.0%

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

   3. Taylor expanded in z around 0 81.9%

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

   if 7.39999999999999972e-96 < x

   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 0 71.2%

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

   3. Taylor expanded in c around 0 52.8%

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

      1. neg-mul-1 52.8%

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

      2. sub-neg 52.8%

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

      3. associate-*r* 56.0%

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

   5. Simplified 56.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+153}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-96}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 6: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;i \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* (* c (* (+ a (* b c)) i)) -2.0)))
   (if (<= i -3.9e+87)
     t_2
     (if (<= i 1.6e-178)
       t_1
       (if (<= i 8.2e-23)
         t_2
         (if (<= i 2.2e+20)
           t_1
           (if (<= i 2.25e+57) t_2 (* 2.0 (- (* x y) (* i (* a c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (i <= -3.9e+87) {
		tmp = t_2;
	} else if (i <= 1.6e-178) {
		tmp = t_1;
	} else if (i <= 8.2e-23) {
		tmp = t_2;
	} else if (i <= 2.2e+20) {
		tmp = t_1;
	} else if (i <= 2.25e+57) {
		tmp = t_2;
	} else {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (c * ((a + (b * c)) * i)) * (-2.0d0)
    if (i <= (-3.9d+87)) then
        tmp = t_2
    else if (i <= 1.6d-178) then
        tmp = t_1
    else if (i <= 8.2d-23) then
        tmp = t_2
    else if (i <= 2.2d+20) then
        tmp = t_1
    else if (i <= 2.25d+57) then
        tmp = t_2
    else
        tmp = 2.0d0 * ((x * y) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = (c * ((a + (b * c)) * i)) * -2.0;
	double tmp;
	if (i <= -3.9e+87) {
		tmp = t_2;
	} else if (i <= 1.6e-178) {
		tmp = t_1;
	} else if (i <= 8.2e-23) {
		tmp = t_2;
	} else if (i <= 2.2e+20) {
		tmp = t_1;
	} else if (i <= 2.25e+57) {
		tmp = t_2;
	} else {
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = (c * ((a + (b * c)) * i)) * -2.0
	tmp = 0
	if i <= -3.9e+87:
		tmp = t_2
	elif i <= 1.6e-178:
		tmp = t_1
	elif i <= 8.2e-23:
		tmp = t_2
	elif i <= 2.2e+20:
		tmp = t_1
	elif i <= 2.25e+57:
		tmp = t_2
	else:
		tmp = 2.0 * ((x * y) - (i * (a * c)))
	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(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0)
	tmp = 0.0
	if (i <= -3.9e+87)
		tmp = t_2;
	elseif (i <= 1.6e-178)
		tmp = t_1;
	elseif (i <= 8.2e-23)
		tmp = t_2;
	elseif (i <= 2.2e+20)
		tmp = t_1;
	elseif (i <= 2.25e+57)
		tmp = t_2;
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = (c * ((a + (b * c)) * i)) * -2.0;
	tmp = 0.0;
	if (i <= -3.9e+87)
		tmp = t_2;
	elseif (i <= 1.6e-178)
		tmp = t_1;
	elseif (i <= 8.2e-23)
		tmp = t_2;
	elseif (i <= 2.2e+20)
		tmp = t_1;
	elseif (i <= 2.25e+57)
		tmp = t_2;
	else
		tmp = 2.0 * ((x * y) - (i * (a * c)));
	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[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[i, -3.9e+87], t$95$2, If[LessEqual[i, 1.6e-178], t$95$1, If[LessEqual[i, 8.2e-23], t$95$2, If[LessEqual[i, 2.2e+20], t$95$1, If[LessEqual[i, 2.25e+57], t$95$2, N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.9000000000000002e87 or 1.6e-178 < i < 8.20000000000000059e-23 or 2.2e20 < i < 2.24999999999999998e57

   1. Initial program 92.2%

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

      1. associate-*l* 92.1%

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

      2. fma-def 93.2%

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

   3. Simplified 93.2%

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

      1. fma-def 92.1%

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

      2. +-commutative 92.1%

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

   5. Applied egg-rr 92.1%

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

   6. Taylor expanded in c around inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

      3. unpow2 51.4%

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

      4. distribute-lft-neg-in 51.4%

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

      5. associate-*l* 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-*r* 63.5%

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

      8. neg-mul-1 63.5%

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

      9. distribute-lft-neg-in 63.5%

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

      10. distribute-lft-in 69.2%

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

      11. distribute-rgt-in 70.4%

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

      12. +-commutative 70.4%

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

      13. *-commutative 70.4%

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

      14. associate-*r* 69.3%

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

      15. distribute-lft-neg-in 69.3%

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

      16. *-commutative 69.3%

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

      17. distribute-rgt-neg-in 69.3%

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

      18. *-commutative 69.3%

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

      19. +-commutative 69.3%

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

      20. fma-def 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in i around 0 70.4%

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

   if -3.9000000000000002e87 < i < 1.6e-178 or 8.20000000000000059e-23 < i < 2.2e20

   1. Initial program 82.9%

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

   2. Taylor expanded in c around 0 72.5%

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

   if 2.24999999999999998e57 < i

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 71.4%

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

   3. Taylor expanded in c around 0 54.3%

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

      1. neg-mul-1 54.3%

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

      2. sub-neg 54.3%

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

      3. associate-*r* 66.7%

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

   5. Simplified 66.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-178}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{+57}:\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 7: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-137} \lor \neg \left(y \leq 1.12 \cdot 10^{+76}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= y -7.5e-137) (not (<= y 1.12e+76)))
     (* 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 ((y <= -7.5e-137) || !(y <= 1.12e+76)) {
		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 ((y <= (-7.5d-137)) .or. (.not. (y <= 1.12d+76))) 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 ((y <= -7.5e-137) || !(y <= 1.12e+76)) {
		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 (y <= -7.5e-137) or not (y <= 1.12e+76):
		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 ((y <= -7.5e-137) || !(y <= 1.12e+76))
		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 ((y <= -7.5e-137) || ~((y <= 1.12e+76)))
		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[y, -7.5e-137], N[Not[LessEqual[y, 1.12e+76]], $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 y < -7.4999999999999995e-137 or 1.12000000000000005e76 < 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. Taylor expanded in z around 0 81.6%

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

   if -7.4999999999999995e-137 < y < 1.12000000000000005e76

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 79.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-137} \lor \neg \left(y \leq 1.12 \cdot 10^{+76}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -9 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{elif}\;c \leq 9000000:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -9e-23)
     (* 2.0 (- (* x y) t_1))
     (if (<= c 9000000.0)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -9e-23) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 9000000.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-9d-23)) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else if (c <= 9000000.0d0) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -9e-23) {
		tmp = 2.0 * ((x * y) - t_1);
	} else if (c <= 9000000.0) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -9e-23:
		tmp = 2.0 * ((x * y) - t_1)
	elif c <= 9000000.0:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -9e-23)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	elseif (c <= 9000000.0)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -9e-23)
		tmp = 2.0 * ((x * y) - t_1);
	elseif (c <= 9000000.0)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9e-23], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9000000.0], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.9999999999999995e-23

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0 85.8%

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

   if -8.9999999999999995e-23 < c < 9e6

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 92.1%

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

   if 9e6 < c

   1. Initial program 73.1%

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

   2. Taylor expanded in x around 0 85.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 9000000:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 94.0% 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]

Derivation

1. Initial program 88.2%

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

   1. associate-*l* 92.7%

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

   2. fma-def 93.4%

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

3. Simplified 93.4%

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

   1. fma-def 92.7%

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

   2. +-commutative 92.7%

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

5. Applied egg-rr 92.7%

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

6. Final simplification 92.7%

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

Alternative 10: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 11500000:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* -2.0 (* c (* b i))))))
   (if (<= c -3e+144)
     t_1
     (if (<= c 11500000.0)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 5.5e+60) (* -2.0 (* c (* a i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (-2.0 * (c * (b * i)));
	double tmp;
	if (c <= -3e+144) {
		tmp = t_1;
	} else if (c <= 11500000.0) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.5e+60) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((-2.0d0) * (c * (b * i)))
    if (c <= (-3d+144)) then
        tmp = t_1
    else if (c <= 11500000.0d0) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 5.5d+60) then
        tmp = (-2.0d0) * (c * (a * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (-2.0 * (c * (b * i)));
	double tmp;
	if (c <= -3e+144) {
		tmp = t_1;
	} else if (c <= 11500000.0) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.5e+60) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (-2.0 * (c * (b * i)))
	tmp = 0
	if c <= -3e+144:
		tmp = t_1
	elif c <= 11500000.0:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 5.5e+60:
		tmp = -2.0 * (c * (a * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(-2.0 * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -3e+144)
		tmp = t_1;
	elseif (c <= 11500000.0)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 5.5e+60)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (-2.0 * (c * (b * i)));
	tmp = 0.0;
	if (c <= -3e+144)
		tmp = t_1;
	elseif (c <= 11500000.0)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 5.5e+60)
		tmp = -2.0 * (c * (a * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(-2.0 * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+144], t$95$1, If[LessEqual[c, 11500000.0], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e+60], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9999999999999999e144 or 5.5000000000000001e60 < c

   1. Initial program 72.9%

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

   2. Taylor expanded in b around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-rgt-neg-in 67.9%

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

      3. unpow2 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in c around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. unpow2 67.9%

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

      3. associate-*r* 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-*l* 72.0%

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

      6. *-commutative 72.0%

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

   7. Simplified 72.0%

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

   if -2.9999999999999999e144 < c < 1.15e7

   1. Initial program 95.8%

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

   2. Taylor expanded in c around 0 68.7%

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

   if 1.15e7 < c < 5.5000000000000001e60

   1. Initial program 90.8%

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

   2. Taylor expanded in a around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. neg-mul-1 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in c around 0 67.7%

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

      1. *-commutative 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 11500000:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 11: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(c \cdot \left(-b\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 11000000:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -3e+144)
   (* 2.0 (* c (* i (* c (- b)))))
   (if (<= c 11000000.0)
     (* 2.0 (+ (* x y) (* z t)))
     (if (<= c 6.5e+55) (* -2.0 (* c (* a i))) (* c (* -2.0 (* c (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3e+144) {
		tmp = 2.0 * (c * (i * (c * -b)));
	} else if (c <= 11000000.0) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.5e+55) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = c * (-2.0 * (c * (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-3d+144)) then
        tmp = 2.0d0 * (c * (i * (c * -b)))
    else if (c <= 11000000.0d0) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 6.5d+55) then
        tmp = (-2.0d0) * (c * (a * i))
    else
        tmp = c * ((-2.0d0) * (c * (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3e+144) {
		tmp = 2.0 * (c * (i * (c * -b)));
	} else if (c <= 11000000.0) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 6.5e+55) {
		tmp = -2.0 * (c * (a * i));
	} else {
		tmp = c * (-2.0 * (c * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -3e+144:
		tmp = 2.0 * (c * (i * (c * -b)))
	elif c <= 11000000.0:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 6.5e+55:
		tmp = -2.0 * (c * (a * i))
	else:
		tmp = c * (-2.0 * (c * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -3e+144)
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(c * Float64(-b)))));
	elseif (c <= 11000000.0)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 6.5e+55)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	else
		tmp = Float64(c * Float64(-2.0 * Float64(c * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -3e+144)
		tmp = 2.0 * (c * (i * (c * -b)));
	elseif (c <= 11000000.0)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 6.5e+55)
		tmp = -2.0 * (c * (a * i));
	else
		tmp = c * (-2.0 * (c * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -3e+144], N[(2.0 * N[(c * N[(i * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 11000000.0], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+55], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(-2.0 * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9999999999999999e144

   1. Initial program 78.8%

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

      1. associate-*l* 90.6%

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

      2. fma-def 90.6%

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

   3. Simplified 90.6%

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

      1. fma-def 90.6%

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

      2. +-commutative 90.6%

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

   5. Applied egg-rr 90.6%

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

   6. Taylor expanded in a around 0 84.6%

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

   7. Taylor expanded in c around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. associate-*l* 79.0%

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

      3. unpow2 79.0%

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

      4. associate-*l* 81.9%

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

      5. associate-*r* 78.8%

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

      6. *-commutative 78.8%

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

      7. *-commutative 78.8%

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

      8. distribute-lft-neg-in 78.8%

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

      9. *-commutative 78.8%

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

      10. associate-*r* 78.9%

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

      11. *-commutative 78.9%

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

      12. distribute-rgt-neg-in 78.9%

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

   9. Simplified 78.9%

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

   if -2.9999999999999999e144 < c < 1.1e7

   1. Initial program 95.8%

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

   2. Taylor expanded in c around 0 68.7%

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

   if 1.1e7 < c < 6.50000000000000027e55

   1. Initial program 90.8%

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

   2. Taylor expanded in a around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. neg-mul-1 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in c around 0 67.7%

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

      1. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   if 6.50000000000000027e55 < c

   1. Initial program 69.2%

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

   2. Taylor expanded in b around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-rgt-neg-in 61.0%

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

      3. unpow2 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in c around 0 61.0%

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

      1. *-commutative 61.0%

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

      2. unpow2 61.0%

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

      3. associate-*r* 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-*l* 69.5%

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

      6. *-commutative 69.5%

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

   7. Simplified 69.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+144}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(c \cdot \left(-b\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 11000000:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 12: 38.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-104}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -3.15e-142)
     t_2
     (if (<= y 7.2e-181)
       t_1
       (if (<= y 1e-104)
         (* 2.0 (* (* a c) (- i)))
         (if (<= y 4.9e+58) 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 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.15e-142) {
		tmp = t_2;
	} else if (y <= 7.2e-181) {
		tmp = t_1;
	} else if (y <= 1e-104) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (y <= 4.9e+58) {
		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 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-3.15d-142)) then
        tmp = t_2
    else if (y <= 7.2d-181) then
        tmp = t_1
    else if (y <= 1d-104) then
        tmp = 2.0d0 * ((a * c) * -i)
    else if (y <= 4.9d+58) 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 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.15e-142) {
		tmp = t_2;
	} else if (y <= 7.2e-181) {
		tmp = t_1;
	} else if (y <= 1e-104) {
		tmp = 2.0 * ((a * c) * -i);
	} else if (y <= 4.9e+58) {
		tmp = t_1;
	} 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 = 2.0 * (x * y)
	tmp = 0
	if y <= -3.15e-142:
		tmp = t_2
	elif y <= 7.2e-181:
		tmp = t_1
	elif y <= 1e-104:
		tmp = 2.0 * ((a * c) * -i)
	elif y <= 4.9e+58:
		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(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -3.15e-142)
		tmp = t_2;
	elseif (y <= 7.2e-181)
		tmp = t_1;
	elseif (y <= 1e-104)
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	elseif (y <= 4.9e+58)
		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 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -3.15e-142)
		tmp = t_2;
	elseif (y <= 7.2e-181)
		tmp = t_1;
	elseif (y <= 1e-104)
		tmp = 2.0 * ((a * c) * -i);
	elseif (y <= 4.9e+58)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e-142], t$95$2, If[LessEqual[y, 7.2e-181], t$95$1, If[LessEqual[y, 1e-104], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1499999999999999e-142 or 4.90000000000000018e58 < y

   1. Initial program 87.4%

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

   2. Taylor expanded in x around inf 47.2%

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

   if -3.1499999999999999e-142 < y < 7.1999999999999998e-181 or 9.99999999999999927e-105 < y < 4.90000000000000018e58

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 37.8%

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

   if 7.1999999999999998e-181 < y < 9.99999999999999927e-105

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 30.8%

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

      1. associate-*r* 30.8%

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

      2. neg-mul-1 30.8%

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

   4. Simplified 30.8%

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

   5. Taylor expanded in c around 0 30.8%

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

      1. mul-1-neg 30.8%

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

      2. associate-*r* 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-104}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 38.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-105}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -3.8e-136)
     t_2
     (if (<= y 4.2e-152)
       t_1
       (if (<= y 9.5e-105)
         (* -2.0 (* c (* a i)))
         (if (<= y 7.2e+58) 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 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.8e-136) {
		tmp = t_2;
	} else if (y <= 4.2e-152) {
		tmp = t_1;
	} else if (y <= 9.5e-105) {
		tmp = -2.0 * (c * (a * i));
	} else if (y <= 7.2e+58) {
		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 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-3.8d-136)) then
        tmp = t_2
    else if (y <= 4.2d-152) then
        tmp = t_1
    else if (y <= 9.5d-105) then
        tmp = (-2.0d0) * (c * (a * i))
    else if (y <= 7.2d+58) 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 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.8e-136) {
		tmp = t_2;
	} else if (y <= 4.2e-152) {
		tmp = t_1;
	} else if (y <= 9.5e-105) {
		tmp = -2.0 * (c * (a * i));
	} else if (y <= 7.2e+58) {
		tmp = t_1;
	} 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 = 2.0 * (x * y)
	tmp = 0
	if y <= -3.8e-136:
		tmp = t_2
	elif y <= 4.2e-152:
		tmp = t_1
	elif y <= 9.5e-105:
		tmp = -2.0 * (c * (a * i))
	elif y <= 7.2e+58:
		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(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -3.8e-136)
		tmp = t_2;
	elseif (y <= 4.2e-152)
		tmp = t_1;
	elseif (y <= 9.5e-105)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	elseif (y <= 7.2e+58)
		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 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -3.8e-136)
		tmp = t_2;
	elseif (y <= 4.2e-152)
		tmp = t_1;
	elseif (y <= 9.5e-105)
		tmp = -2.0 * (c * (a * i));
	elseif (y <= 7.2e+58)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-136], t$95$2, If[LessEqual[y, 4.2e-152], t$95$1, If[LessEqual[y, 9.5e-105], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000003e-136 or 7.19999999999999993e58 < y

   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 x around inf 47.5%

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

   if -3.8000000000000003e-136 < y < 4.19999999999999998e-152 or 9.5000000000000002e-105 < y < 7.19999999999999993e58

   1. Initial program 87.6%

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

   2. Taylor expanded in z around inf 39.3%

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

   if 4.19999999999999998e-152 < y < 9.5000000000000002e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 46.2%

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

      1. associate-*r* 46.2%

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

      2. neg-mul-1 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in c around 0 46.2%

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

      1. *-commutative 46.2%

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

   7. Simplified 46.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-136}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-152}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-105}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 55.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.05e+99) (* 2.0 (+ (* x y) (* z t))) (* 2.0 (* (* a c) (- i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.05e+99) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((a * c) * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.05d+99) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((a * c) * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.05e+99) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((a * c) * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.05e+99:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((a * c) * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.05e+99)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(a * c) * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.05e+99)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((a * c) * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.05e+99], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(a * c), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.0499999999999999e99

   1. Initial program 89.2%

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

   2. Taylor expanded in c around 0 59.2%

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

   if 2.0499999999999999e99 < a

   1. Initial program 82.7%

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

   2. Taylor expanded in a around inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. neg-mul-1 49.4%

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

   4. Simplified 49.4%

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

   5. Taylor expanded in c around 0 49.4%

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

      1. mul-1-neg 49.4%

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

      2. associate-*r* 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. *-commutative 63.7%

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

   7. Simplified 63.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.05 \cdot 10^{+99}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot c\right) \cdot \left(-i\right)\right)\\ \end{array} \]

Alternative 15: 39.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-136} \lor \neg \left(y \leq 1.75 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -2.35e-136) (not (<= y 1.75e+58)))
   (* 2.0 (* x y))
   (* 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 ((y <= -2.35e-136) || !(y <= 1.75e+58)) {
		tmp = 2.0 * (x * y);
	} 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 ((y <= (-2.35d-136)) .or. (.not. (y <= 1.75d+58))) then
        tmp = 2.0d0 * (x * y)
    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 ((y <= -2.35e-136) || !(y <= 1.75e+58)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -2.35e-136) or not (y <= 1.75e+58):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -2.35e-136) || !(y <= 1.75e+58))
		tmp = Float64(2.0 * Float64(x * y));
	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 ((y <= -2.35e-136) || ~((y <= 1.75e+58)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -2.35e-136], N[Not[LessEqual[y, 1.75e+58]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35000000000000011e-136 or 1.7499999999999999e58 < y

   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 x around inf 47.5%

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

   if -2.35000000000000011e-136 < y < 1.7499999999999999e58

   1. Initial program 88.5%

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

   2. Taylor expanded in z around inf 37.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-136} \lor \neg \left(y \leq 1.75 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 29.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

2. Taylor expanded in z around inf 29.0%

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

3. Final simplification 29.0%

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

Developer target: 94.0% 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 2023214 
(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))))