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

Percentage Accurate: 90.0% → 94.9%

Time: 14.1s

Alternatives: 17

Speedup: 0.5×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_2\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+281)))
     (* -2.0 (* c (* t_1 i)))
     (* (- (+ (* z t) (* x y)) t_2) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+281)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+281)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+281):
		tmp = -2.0 * (c * (t_1 * i))
	else:
		tmp = (((z * t) + (x * y)) - t_2) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+281))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	else
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - t_2) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+281)))
		tmp = -2.0 * (c * (t_1 * i));
	else
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+281]], $MachinePrecision]], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 2.0000000000000001e281 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.3%

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

   2. Taylor expanded in i around inf 94.9%

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

   3. Taylor expanded in i around 0 94.9%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.0000000000000001e281

   1. Initial program 98.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

      1. associate-*l* 97.9%

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

      2. fma-def 97.9%

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

   3. Simplified 97.9%

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

      1. fma-def 97.9%

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

      2. +-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 67.1%

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

   3. Taylor expanded in i around 0 67.1%

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

4. Final simplification 96.5%

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

Alternative 3: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ t_3 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.95 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* a i)))))
        (t_2 (* 2.0 (+ (* z t) (* x y))))
        (t_3 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -1.15e+44)
     t_3
     (if (<= c -2.4e+14)
       t_2
       (if (<= c -1.4e-61)
         t_1
         (if (<= c 1e-88)
           t_2
           (if (<= c 3.95e+34) t_1 (if (<= c 1.5e+47) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.15e+44) {
		tmp = t_3;
	} else if (c <= -2.4e+14) {
		tmp = t_2;
	} else if (c <= -1.4e-61) {
		tmp = t_1;
	} else if (c <= 1e-88) {
		tmp = t_2;
	} else if (c <= 3.95e+34) {
		tmp = t_1;
	} else if (c <= 1.5e+47) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (a * i)))
    t_2 = 2.0d0 * ((z * t) + (x * y))
    t_3 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-1.15d+44)) then
        tmp = t_3
    else if (c <= (-2.4d+14)) then
        tmp = t_2
    else if (c <= (-1.4d-61)) then
        tmp = t_1
    else if (c <= 1d-88) then
        tmp = t_2
    else if (c <= 3.95d+34) then
        tmp = t_1
    else if (c <= 1.5d+47) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.15e+44) {
		tmp = t_3;
	} else if (c <= -2.4e+14) {
		tmp = t_2;
	} else if (c <= -1.4e-61) {
		tmp = t_1;
	} else if (c <= 1e-88) {
		tmp = t_2;
	} else if (c <= 3.95e+34) {
		tmp = t_1;
	} else if (c <= 1.5e+47) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (a * i)))
	t_2 = 2.0 * ((z * t) + (x * y))
	t_3 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.15e+44:
		tmp = t_3
	elif c <= -2.4e+14:
		tmp = t_2
	elif c <= -1.4e-61:
		tmp = t_1
	elif c <= 1e-88:
		tmp = t_2
	elif c <= 3.95e+34:
		tmp = t_1
	elif c <= 1.5e+47:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.15e+44)
		tmp = t_3;
	elseif (c <= -2.4e+14)
		tmp = t_2;
	elseif (c <= -1.4e-61)
		tmp = t_1;
	elseif (c <= 1e-88)
		tmp = t_2;
	elseif (c <= 3.95e+34)
		tmp = t_1;
	elseif (c <= 1.5e+47)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (a * i)));
	t_2 = 2.0 * ((z * t) + (x * y));
	t_3 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.15e+44)
		tmp = t_3;
	elseif (c <= -2.4e+14)
		tmp = t_2;
	elseif (c <= -1.4e-61)
		tmp = t_1;
	elseif (c <= 1e-88)
		tmp = t_2;
	elseif (c <= 3.95e+34)
		tmp = t_1;
	elseif (c <= 1.5e+47)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+44], t$95$3, If[LessEqual[c, -2.4e+14], t$95$2, If[LessEqual[c, -1.4e-61], t$95$1, If[LessEqual[c, 1e-88], t$95$2, If[LessEqual[c, 3.95e+34], t$95$1, If[LessEqual[c, 1.5e+47], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.15000000000000002e44 or 1.5000000000000001e47 < c

   1. Initial program 81.5%

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

   2. Taylor expanded in i around inf 89.8%

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

   3. Taylor expanded in i around 0 89.8%

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

   if -1.15000000000000002e44 < c < -2.4e14 or -1.4000000000000001e-61 < c < 9.99999999999999934e-89 or 3.94999999999999999e34 < c < 1.5000000000000001e47

   1. Initial program 97.8%

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

   2. Taylor expanded in c around 0 83.5%

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

   if -2.4e14 < c < -1.4000000000000001e-61 or 9.99999999999999934e-89 < c < 3.94999999999999999e34

   1. Initial program 97.9%

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

      1. associate-*l* 97.7%

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

      2. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. fma-def 97.7%

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

      2. +-commutative 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in a around inf 88.9%

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

      1. associate-*r* 89.0%

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

      2. *-commutative 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in x around 0 82.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 10^{-88}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.95 \cdot 10^{+34}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;c \leq -7.4 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9.4 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* a i)))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i))))
        (t_3 (* 2.0 (+ (* z t) (* x y)))))
   (if (<= c -7.4e+51)
     t_2
     (if (<= c -9.4e+14)
       (* 2.0 (- (* x y) (* c (* i (* b c)))))
       (if (<= c -1.3e-61)
         t_1
         (if (<= c 1.06e-88)
           t_3
           (if (<= c 4.1e+35) t_1 (if (<= c 1.45e+47) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double t_3 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -7.4e+51) {
		tmp = t_2;
	} else if (c <= -9.4e+14) {
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	} else if (c <= -1.3e-61) {
		tmp = t_1;
	} else if (c <= 1.06e-88) {
		tmp = t_3;
	} else if (c <= 4.1e+35) {
		tmp = t_1;
	} else if (c <= 1.45e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * (a * i)))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    t_3 = 2.0d0 * ((z * t) + (x * y))
    if (c <= (-7.4d+51)) then
        tmp = t_2
    else if (c <= (-9.4d+14)) then
        tmp = 2.0d0 * ((x * y) - (c * (i * (b * c))))
    else if (c <= (-1.3d-61)) then
        tmp = t_1
    else if (c <= 1.06d-88) then
        tmp = t_3
    else if (c <= 4.1d+35) then
        tmp = t_1
    else if (c <= 1.45d+47) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (a * i)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double t_3 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -7.4e+51) {
		tmp = t_2;
	} else if (c <= -9.4e+14) {
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	} else if (c <= -1.3e-61) {
		tmp = t_1;
	} else if (c <= 1.06e-88) {
		tmp = t_3;
	} else if (c <= 4.1e+35) {
		tmp = t_1;
	} else if (c <= 1.45e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (a * i)))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	t_3 = 2.0 * ((z * t) + (x * y))
	tmp = 0
	if c <= -7.4e+51:
		tmp = t_2
	elif c <= -9.4e+14:
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))))
	elif c <= -1.3e-61:
		tmp = t_1
	elif c <= 1.06e-88:
		tmp = t_3
	elif c <= 4.1e+35:
		tmp = t_1
	elif c <= 1.45e+47:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	t_3 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (c <= -7.4e+51)
		tmp = t_2;
	elseif (c <= -9.4e+14)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(i * Float64(b * c)))));
	elseif (c <= -1.3e-61)
		tmp = t_1;
	elseif (c <= 1.06e-88)
		tmp = t_3;
	elseif (c <= 4.1e+35)
		tmp = t_1;
	elseif (c <= 1.45e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (a * i)));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	t_3 = 2.0 * ((z * t) + (x * y));
	tmp = 0.0;
	if (c <= -7.4e+51)
		tmp = t_2;
	elseif (c <= -9.4e+14)
		tmp = 2.0 * ((x * y) - (c * (i * (b * c))));
	elseif (c <= -1.3e-61)
		tmp = t_1;
	elseif (c <= 1.06e-88)
		tmp = t_3;
	elseif (c <= 4.1e+35)
		tmp = t_1;
	elseif (c <= 1.45e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.4e+51], t$95$2, If[LessEqual[c, -9.4e+14], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-61], t$95$1, If[LessEqual[c, 1.06e-88], t$95$3, If[LessEqual[c, 4.1e+35], t$95$1, If[LessEqual[c, 1.45e+47], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.4000000000000005e51 or 1.4499999999999999e47 < c

   1. Initial program 81.1%

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

   2. Taylor expanded in i around inf 89.6%

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

   3. Taylor expanded in i around 0 89.6%

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

   if -7.4000000000000005e51 < c < -9.4e14

   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 0 99.9%

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

      1. unpow2 99.9%

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

      2. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.8%

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

      1. unpow2 90.8%

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

      2. associate-*r* 90.8%

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

      3. associate-*r* 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-*l* 90.8%

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

      6. *-commutative 90.8%

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

      7. *-commutative 90.8%

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

   7. Simplified 90.8%

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

   if -9.4e14 < c < -1.30000000000000005e-61 or 1.06e-88 < c < 4.0999999999999998e35

   1. Initial program 97.9%

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

      1. associate-*l* 97.7%

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

      2. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. fma-def 97.7%

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

      2. +-commutative 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in a around inf 88.9%

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

      1. associate-*r* 89.0%

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

      2. *-commutative 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in x around 0 82.9%

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

   if -1.30000000000000005e-61 < c < 1.06e-88 or 4.0999999999999998e35 < c < 1.4499999999999999e47

   1. Initial program 98.8%

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

   2. Taylor expanded in c around 0 84.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.4 \cdot 10^{+51}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.4 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-61}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+43} \lor \neg \left(c \leq -1.16 \cdot 10^{+27}\right) \land \left(c \leq -1.35 \cdot 10^{-61} \lor \neg \left(c \leq 1.1 \cdot 10^{-88}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8.5e+43)
         (and (not (<= c -1.16e+27))
              (or (<= c -1.35e-61) (not (<= c 1.1e-88)))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.5e+43) || (!(c <= -1.16e+27) && ((c <= -1.35e-61) || !(c <= 1.1e-88)))) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-8.5d+43)) .or. (.not. (c <= (-1.16d+27))) .and. (c <= (-1.35d-61)) .or. (.not. (c <= 1.1d-88))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((z * t) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8.5e+43) || (!(c <= -1.16e+27) && ((c <= -1.35e-61) || !(c <= 1.1e-88)))) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8.5e+43) or (not (c <= -1.16e+27) and ((c <= -1.35e-61) or not (c <= 1.1e-88))):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8.5e+43) || (!(c <= -1.16e+27) && ((c <= -1.35e-61) || !(c <= 1.1e-88))))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8.5e+43) || (~((c <= -1.16e+27)) && ((c <= -1.35e-61) || ~((c <= 1.1e-88)))))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8.5e+43], And[N[Not[LessEqual[c, -1.16e+27]], $MachinePrecision], Or[LessEqual[c, -1.35e-61], N[Not[LessEqual[c, 1.1e-88]], $MachinePrecision]]]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.5e43 or -1.16e27 < c < -1.34999999999999997e-61 or 1.10000000000000002e-88 < c

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0 90.3%

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

   if -8.5e43 < c < -1.16e27 or -1.34999999999999997e-61 < c < 1.10000000000000002e-88

   1. Initial program 97.7%

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

   2. Taylor expanded in c around 0 84.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+43} \lor \neg \left(c \leq -1.16 \cdot 10^{+27}\right) \land \left(c \leq -1.35 \cdot 10^{-61} \lor \neg \left(c \leq 1.1 \cdot 10^{-88}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 6: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ t_3 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot t_3\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(t_3 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (* 2.0 (- (* z t) t_1)))
        (t_3 (+ (* z t) (* x y))))
   (if (<= c -8.5e+43)
     t_2
     (if (<= c -1.4e+27)
       (* 2.0 t_3)
       (if (<= c -3.05e-46)
         t_2
         (if (<= c 1.45e+47)
           (* 2.0 (- t_3 (* i (* a c))))
           (* 2.0 (- (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -8.5e+43) {
		tmp = t_2;
	} else if (c <= -1.4e+27) {
		tmp = 2.0 * t_3;
	} else if (c <= -3.05e-46) {
		tmp = t_2;
	} else if (c <= 1.45e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    t_3 = (z * t) + (x * y)
    if (c <= (-8.5d+43)) then
        tmp = t_2
    else if (c <= (-1.4d+27)) then
        tmp = 2.0d0 * t_3
    else if (c <= (-3.05d-46)) then
        tmp = t_2
    else if (c <= 1.45d+47) then
        tmp = 2.0d0 * (t_3 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -8.5e+43) {
		tmp = t_2;
	} else if (c <= -1.4e+27) {
		tmp = 2.0 * t_3;
	} else if (c <= -3.05e-46) {
		tmp = t_2;
	} else if (c <= 1.45e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((z * t) - t_1)
	t_3 = (z * t) + (x * y)
	tmp = 0
	if c <= -8.5e+43:
		tmp = t_2
	elif c <= -1.4e+27:
		tmp = 2.0 * t_3
	elif c <= -3.05e-46:
		tmp = t_2
	elif c <= 1.45e+47:
		tmp = 2.0 * (t_3 - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	t_3 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (c <= -8.5e+43)
		tmp = t_2;
	elseif (c <= -1.4e+27)
		tmp = Float64(2.0 * t_3);
	elseif (c <= -3.05e-46)
		tmp = t_2;
	elseif (c <= 1.45e+47)
		tmp = Float64(2.0 * Float64(t_3 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = 2.0 * ((z * t) - t_1);
	t_3 = (z * t) + (x * y);
	tmp = 0.0;
	if (c <= -8.5e+43)
		tmp = t_2;
	elseif (c <= -1.4e+27)
		tmp = 2.0 * t_3;
	elseif (c <= -3.05e-46)
		tmp = t_2;
	elseif (c <= 1.45e+47)
		tmp = 2.0 * (t_3 - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+43], t$95$2, If[LessEqual[c, -1.4e+27], N[(2.0 * t$95$3), $MachinePrecision], If[LessEqual[c, -3.05e-46], t$95$2, If[LessEqual[c, 1.45e+47], N[(2.0 * N[(t$95$3 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.5e43 or -1.4e27 < c < -3.05000000000000018e-46

   1. Initial program 87.9%

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

   2. Taylor expanded in x around 0 94.9%

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

   if -8.5e43 < c < -1.4e27

   1. Initial program 83.3%

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

   2. Taylor expanded in c around 0 100.0%

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

   if -3.05000000000000018e-46 < c < 1.4499999999999999e47

   1. Initial program 99.1%

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

      1. associate-*l* 99.1%

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

      2. fma-def 99.1%

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

   3. Simplified 99.1%

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

      1. fma-def 99.1%

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

      2. +-commutative 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in a around inf 91.3%

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

      1. associate-*r* 95.5%

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

      2. *-commutative 95.5%

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

   8. Simplified 95.5%

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

   if 1.4499999999999999e47 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 88.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ t_3 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(t_3 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(t_3 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (* 2.0 (- (* z t) t_1)))
        (t_3 (+ (* z t) (* x y))))
   (if (<= c -1.9e+52)
     t_2
     (if (<= c -1.6e+14)
       (* 2.0 (- t_3 (* c (* c (* b i)))))
       (if (<= c -3.05e-46)
         t_2
         (if (<= c 3.35e+47)
           (* 2.0 (- t_3 (* i (* a c))))
           (* 2.0 (- (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -1.9e+52) {
		tmp = t_2;
	} else if (c <= -1.6e+14) {
		tmp = 2.0 * (t_3 - (c * (c * (b * i))));
	} else if (c <= -3.05e-46) {
		tmp = t_2;
	} else if (c <= 3.35e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    t_3 = (z * t) + (x * y)
    if (c <= (-1.9d+52)) then
        tmp = t_2
    else if (c <= (-1.6d+14)) then
        tmp = 2.0d0 * (t_3 - (c * (c * (b * i))))
    else if (c <= (-3.05d-46)) then
        tmp = t_2
    else if (c <= 3.35d+47) then
        tmp = 2.0d0 * (t_3 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -1.9e+52) {
		tmp = t_2;
	} else if (c <= -1.6e+14) {
		tmp = 2.0 * (t_3 - (c * (c * (b * i))));
	} else if (c <= -3.05e-46) {
		tmp = t_2;
	} else if (c <= 3.35e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((z * t) - t_1)
	t_3 = (z * t) + (x * y)
	tmp = 0
	if c <= -1.9e+52:
		tmp = t_2
	elif c <= -1.6e+14:
		tmp = 2.0 * (t_3 - (c * (c * (b * i))))
	elif c <= -3.05e-46:
		tmp = t_2
	elif c <= 3.35e+47:
		tmp = 2.0 * (t_3 - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	t_3 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (c <= -1.9e+52)
		tmp = t_2;
	elseif (c <= -1.6e+14)
		tmp = Float64(2.0 * Float64(t_3 - Float64(c * Float64(c * Float64(b * i)))));
	elseif (c <= -3.05e-46)
		tmp = t_2;
	elseif (c <= 3.35e+47)
		tmp = Float64(2.0 * Float64(t_3 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = 2.0 * ((z * t) - t_1);
	t_3 = (z * t) + (x * y);
	tmp = 0.0;
	if (c <= -1.9e+52)
		tmp = t_2;
	elseif (c <= -1.6e+14)
		tmp = 2.0 * (t_3 - (c * (c * (b * i))));
	elseif (c <= -3.05e-46)
		tmp = t_2;
	elseif (c <= 3.35e+47)
		tmp = 2.0 * (t_3 - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e+52], t$95$2, If[LessEqual[c, -1.6e+14], N[(2.0 * N[(t$95$3 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.05e-46], t$95$2, If[LessEqual[c, 3.35e+47], N[(2.0 * N[(t$95$3 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.9e52 or -1.6e14 < c < -3.05000000000000018e-46

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 96.9%

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

   if -1.9e52 < c < -1.6e14

   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 0 99.9%

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

      1. unpow2 99.9%

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

      2. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

   if -3.05000000000000018e-46 < c < 3.34999999999999986e47

   1. Initial program 99.1%

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

      1. associate-*l* 99.1%

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

      2. fma-def 99.1%

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

   3. Simplified 99.1%

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

      1. fma-def 99.1%

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

      2. +-commutative 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in a around inf 91.3%

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

      1. associate-*r* 95.5%

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

      2. *-commutative 95.5%

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

   8. Simplified 95.5%

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

   if 3.34999999999999986e47 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 88.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-46}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.35 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(z \cdot t - t_1\right)\\ t_3 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -45000000000000:\\ \;\;\;\;2 \cdot \left(t_3 - \left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(t_3 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i)))
        (t_2 (* 2.0 (- (* z t) t_1)))
        (t_3 (+ (* z t) (* x y))))
   (if (<= c -1e+52)
     t_2
     (if (<= c -45000000000000.0)
       (* 2.0 (- t_3 (* (* c i) (* b c))))
       (if (<= c -2.9e-50)
         t_2
         (if (<= c 6e+47)
           (* 2.0 (- t_3 (* i (* a c))))
           (* 2.0 (- (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -1e+52) {
		tmp = t_2;
	} else if (c <= -45000000000000.0) {
		tmp = 2.0 * (t_3 - ((c * i) * (b * c)));
	} else if (c <= -2.9e-50) {
		tmp = t_2;
	} else if (c <= 6e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((z * t) - t_1)
    t_3 = (z * t) + (x * y)
    if (c <= (-1d+52)) then
        tmp = t_2
    else if (c <= (-45000000000000.0d0)) then
        tmp = 2.0d0 * (t_3 - ((c * i) * (b * c)))
    else if (c <= (-2.9d-50)) then
        tmp = t_2
    else if (c <= 6d+47) then
        tmp = 2.0d0 * (t_3 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((z * t) - t_1);
	double t_3 = (z * t) + (x * y);
	double tmp;
	if (c <= -1e+52) {
		tmp = t_2;
	} else if (c <= -45000000000000.0) {
		tmp = 2.0 * (t_3 - ((c * i) * (b * c)));
	} else if (c <= -2.9e-50) {
		tmp = t_2;
	} else if (c <= 6e+47) {
		tmp = 2.0 * (t_3 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	t_2 = 2.0 * ((z * t) - t_1)
	t_3 = (z * t) + (x * y)
	tmp = 0
	if c <= -1e+52:
		tmp = t_2
	elif c <= -45000000000000.0:
		tmp = 2.0 * (t_3 - ((c * i) * (b * c)))
	elif c <= -2.9e-50:
		tmp = t_2
	elif c <= 6e+47:
		tmp = 2.0 * (t_3 - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - t_1))
	t_3 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (c <= -1e+52)
		tmp = t_2;
	elseif (c <= -45000000000000.0)
		tmp = Float64(2.0 * Float64(t_3 - Float64(Float64(c * i) * Float64(b * c))));
	elseif (c <= -2.9e-50)
		tmp = t_2;
	elseif (c <= 6e+47)
		tmp = Float64(2.0 * Float64(t_3 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	t_2 = 2.0 * ((z * t) - t_1);
	t_3 = (z * t) + (x * y);
	tmp = 0.0;
	if (c <= -1e+52)
		tmp = t_2;
	elseif (c <= -45000000000000.0)
		tmp = 2.0 * (t_3 - ((c * i) * (b * c)));
	elseif (c <= -2.9e-50)
		tmp = t_2;
	elseif (c <= 6e+47)
		tmp = 2.0 * (t_3 - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+52], t$95$2, If[LessEqual[c, -45000000000000.0], N[(2.0 * N[(t$95$3 - N[(N[(c * i), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.9e-50], t$95$2, If[LessEqual[c, 6e+47], N[(2.0 * N[(t$95$3 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.9999999999999999e51 or -4.5e13 < c < -2.90000000000000008e-50

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 96.9%

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

   if -9.9999999999999999e51 < c < -4.5e13

   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. Step-by-step derivation

      1. associate-*l* 90.9%

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

      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 90.9%

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

      2. +-commutative 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in a around 0 100.0%

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

   if -2.90000000000000008e-50 < c < 6.0000000000000003e47

   1. Initial program 99.1%

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

      1. associate-*l* 99.1%

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

      2. fma-def 99.1%

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

   3. Simplified 99.1%

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

      1. fma-def 99.1%

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

      2. +-commutative 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in a around inf 91.3%

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

      1. associate-*r* 95.5%

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

      2. *-commutative 95.5%

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

   8. Simplified 95.5%

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

   if 6.0000000000000003e47 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in z around 0 88.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -45000000000000:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot i\right) \cdot \left(b \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := -2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* 2.0 (* x y)))
        (t_3 (* -2.0 (* c (* c (* b i))))))
   (if (<= c -1e+44)
     t_3
     (if (<= c -8.8e+14)
       t_2
       (if (<= c -6.4e-14)
         (* i (* -2.0 (* a c)))
         (if (<= c 4.8e-204)
           t_1
           (if (<= c 1.95e-82) t_2 (if (<= c 1.6e+47) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1e+44) {
		tmp = t_3;
	} else if (c <= -8.8e+14) {
		tmp = t_2;
	} else if (c <= -6.4e-14) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 4.8e-204) {
		tmp = t_1;
	} else if (c <= 1.95e-82) {
		tmp = t_2;
	} else if (c <= 1.6e+47) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    t_3 = (-2.0d0) * (c * (c * (b * i)))
    if (c <= (-1d+44)) then
        tmp = t_3
    else if (c <= (-8.8d+14)) then
        tmp = t_2
    else if (c <= (-6.4d-14)) then
        tmp = i * ((-2.0d0) * (a * c))
    else if (c <= 4.8d-204) then
        tmp = t_1
    else if (c <= 1.95d-82) then
        tmp = t_2
    else if (c <= 1.6d+47) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double t_3 = -2.0 * (c * (c * (b * i)));
	double tmp;
	if (c <= -1e+44) {
		tmp = t_3;
	} else if (c <= -8.8e+14) {
		tmp = t_2;
	} else if (c <= -6.4e-14) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 4.8e-204) {
		tmp = t_1;
	} else if (c <= 1.95e-82) {
		tmp = t_2;
	} else if (c <= 1.6e+47) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	t_3 = -2.0 * (c * (c * (b * i)))
	tmp = 0
	if c <= -1e+44:
		tmp = t_3
	elif c <= -8.8e+14:
		tmp = t_2
	elif c <= -6.4e-14:
		tmp = i * (-2.0 * (a * c))
	elif c <= 4.8e-204:
		tmp = t_1
	elif c <= 1.95e-82:
		tmp = t_2
	elif c <= 1.6e+47:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	t_3 = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))))
	tmp = 0.0
	if (c <= -1e+44)
		tmp = t_3;
	elseif (c <= -8.8e+14)
		tmp = t_2;
	elseif (c <= -6.4e-14)
		tmp = Float64(i * Float64(-2.0 * Float64(a * c)));
	elseif (c <= 4.8e-204)
		tmp = t_1;
	elseif (c <= 1.95e-82)
		tmp = t_2;
	elseif (c <= 1.6e+47)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	t_3 = -2.0 * (c * (c * (b * i)));
	tmp = 0.0;
	if (c <= -1e+44)
		tmp = t_3;
	elseif (c <= -8.8e+14)
		tmp = t_2;
	elseif (c <= -6.4e-14)
		tmp = i * (-2.0 * (a * c));
	elseif (c <= 4.8e-204)
		tmp = t_1;
	elseif (c <= 1.95e-82)
		tmp = t_2;
	elseif (c <= 1.6e+47)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+44], t$95$3, If[LessEqual[c, -8.8e+14], t$95$2, If[LessEqual[c, -6.4e-14], N[(i * N[(-2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e-204], t$95$1, If[LessEqual[c, 1.95e-82], t$95$2, If[LessEqual[c, 1.6e+47], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.0000000000000001e44 or 1.6e47 < c

   1. Initial program 81.5%

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

   2. Taylor expanded in i around inf 89.8%

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

   3. Taylor expanded in c around inf 68.0%

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

      1. unpow2 68.0%

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

      2. associate-*r* 72.1%

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

      3. associate-*r* 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-*l* 72.2%

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

      6. *-commutative 72.2%

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

      7. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in i around 0 72.1%

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

   if -1.0000000000000001e44 < c < -8.8e14 or 4.8e-204 < c < 1.94999999999999987e-82

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 58.4%

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

   if -8.8e14 < c < -6.4000000000000005e-14

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. neg-mul-1 76.5%

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

      3. *-commutative 76.5%

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

      4. associate-*r* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-*l* 76.7%

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

   10. Simplified 76.7%

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

   if -6.4000000000000005e-14 < c < 4.8e-204 or 1.94999999999999987e-82 < c < 1.6e47

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 50.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 10: 48.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= c -1.15e+44)
     (* -2.0 (* c (* i (* b c))))
     (if (<= c -1.9e+16)
       t_2
       (if (<= c -6.6e-19)
         (* i (* -2.0 (* a c)))
         (if (<= c 5.6e-202)
           t_1
           (if (<= c 1.1e-82)
             t_2
             (if (<= c 1.9e+48) t_1 (* -2.0 (* c (* c (* b i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -1.15e+44) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -1.9e+16) {
		tmp = t_2;
	} else if (c <= -6.6e-19) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 5.6e-202) {
		tmp = t_1;
	} else if (c <= 1.1e-82) {
		tmp = t_2;
	} else if (c <= 1.9e+48) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-1.15d+44)) then
        tmp = (-2.0d0) * (c * (i * (b * c)))
    else if (c <= (-1.9d+16)) then
        tmp = t_2
    else if (c <= (-6.6d-19)) then
        tmp = i * ((-2.0d0) * (a * c))
    else if (c <= 5.6d-202) then
        tmp = t_1
    else if (c <= 1.1d-82) then
        tmp = t_2
    else if (c <= 1.9d+48) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (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 t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -1.15e+44) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -1.9e+16) {
		tmp = t_2;
	} else if (c <= -6.6e-19) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 5.6e-202) {
		tmp = t_1;
	} else if (c <= 1.1e-82) {
		tmp = t_2;
	} else if (c <= 1.9e+48) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (c * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if c <= -1.15e+44:
		tmp = -2.0 * (c * (i * (b * c)))
	elif c <= -1.9e+16:
		tmp = t_2
	elif c <= -6.6e-19:
		tmp = i * (-2.0 * (a * c))
	elif c <= 5.6e-202:
		tmp = t_1
	elif c <= 1.1e-82:
		tmp = t_2
	elif c <= 1.9e+48:
		tmp = t_1
	else:
		tmp = -2.0 * (c * (c * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -1.15e+44)
		tmp = Float64(-2.0 * Float64(c * Float64(i * Float64(b * c))));
	elseif (c <= -1.9e+16)
		tmp = t_2;
	elseif (c <= -6.6e-19)
		tmp = Float64(i * Float64(-2.0 * Float64(a * c)));
	elseif (c <= 5.6e-202)
		tmp = t_1;
	elseif (c <= 1.1e-82)
		tmp = t_2;
	elseif (c <= 1.9e+48)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -1.15e+44)
		tmp = -2.0 * (c * (i * (b * c)));
	elseif (c <= -1.9e+16)
		tmp = t_2;
	elseif (c <= -6.6e-19)
		tmp = i * (-2.0 * (a * c));
	elseif (c <= 5.6e-202)
		tmp = t_1;
	elseif (c <= 1.1e-82)
		tmp = t_2;
	elseif (c <= 1.9e+48)
		tmp = t_1;
	else
		tmp = -2.0 * (c * (c * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+44], N[(-2.0 * N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e+16], t$95$2, If[LessEqual[c, -6.6e-19], N[(i * N[(-2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e-202], t$95$1, If[LessEqual[c, 1.1e-82], t$95$2, If[LessEqual[c, 1.9e+48], t$95$1, N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.15000000000000002e44

   1. Initial program 85.5%

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

   2. Taylor expanded in i around inf 94.4%

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

   3. Taylor expanded in c around inf 76.5%

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

      1. unpow2 76.5%

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

      2. associate-*r* 81.8%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*l* 83.7%

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

      6. *-commutative 83.7%

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

      7. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -1.15000000000000002e44 < c < -1.9e16 or 5.6000000000000002e-202 < c < 1.09999999999999993e-82

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 58.4%

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

   if -1.9e16 < c < -6.5999999999999995e-19

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. neg-mul-1 76.5%

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

      3. *-commutative 76.5%

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

      4. associate-*r* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-*l* 76.7%

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

   10. Simplified 76.7%

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

   if -6.5999999999999995e-19 < c < 5.6000000000000002e-202 or 1.09999999999999993e-82 < c < 1.9e48

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 50.7%

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

   if 1.9e48 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in i around inf 85.8%

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

   3. Taylor expanded in c around inf 60.4%

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

      1. unpow2 60.4%

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

      2. associate-*r* 63.6%

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

      3. associate-*r* 66.7%

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

      4. *-commutative 66.7%

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

      5. associate-*l* 62.1%

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

      6. *-commutative 62.1%

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

      7. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in i around 0 63.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{+16}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-82}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 11: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+43} \lor \neg \left(c \leq -1.2 \cdot 10^{+24}\right) \land \left(c \leq -1.55 \cdot 10^{-61} \lor \neg \left(c \leq 1.9 \cdot 10^{+47}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -9e+43)
         (and (not (<= c -1.2e+24))
              (or (<= c -1.55e-61) (not (<= c 1.9e+47)))))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9e+43) || (!(c <= -1.2e+24) && ((c <= -1.55e-61) || !(c <= 1.9e+47)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-9d+43)) .or. (.not. (c <= (-1.2d+24))) .and. (c <= (-1.55d-61)) .or. (.not. (c <= 1.9d+47))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * ((z * t) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9e+43) || (!(c <= -1.2e+24) && ((c <= -1.55e-61) || !(c <= 1.9e+47)))) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -9e+43) or (not (c <= -1.2e+24) and ((c <= -1.55e-61) or not (c <= 1.9e+47))):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -9e+43) || (!(c <= -1.2e+24) && ((c <= -1.55e-61) || !(c <= 1.9e+47))))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -9e+43) || (~((c <= -1.2e+24)) && ((c <= -1.55e-61) || ~((c <= 1.9e+47)))))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -9e+43], And[N[Not[LessEqual[c, -1.2e+24]], $MachinePrecision], Or[LessEqual[c, -1.55e-61], N[Not[LessEqual[c, 1.9e+47]], $MachinePrecision]]]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9e43 or -1.2e24 < c < -1.54999999999999997e-61 or 1.9000000000000002e47 < c

   1. Initial program 83.7%

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

   2. Taylor expanded in i around inf 86.0%

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

   3. Taylor expanded in i around 0 86.0%

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

   if -9e43 < c < -1.2e24 or -1.54999999999999997e-61 < c < 1.9000000000000002e47

   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 c around 0 79.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{+43} \lor \neg \left(c \leq -1.2 \cdot 10^{+24}\right) \land \left(c \leq -1.55 \cdot 10^{-61} \lor \neg \left(c \leq 1.9 \cdot 10^{+47}\right)\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 12: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* z t) (* x y)))))
   (if (<= c -9.5e+43)
     (* -2.0 (* c (* i (* b c))))
     (if (<= c -1400000000.0)
       t_1
       (if (<= c -3.45e-15)
         (* i (* -2.0 (* a c)))
         (if (<= c 1.8e+58) t_1 (* -2.0 (* c (* c (* b i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -9.5e+43) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -1400000000.0) {
		tmp = t_1;
	} else if (c <= -3.45e-15) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 1.8e+58) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) + (x * y))
    if (c <= (-9.5d+43)) then
        tmp = (-2.0d0) * (c * (i * (b * c)))
    else if (c <= (-1400000000.0d0)) then
        tmp = t_1
    else if (c <= (-3.45d-15)) then
        tmp = i * ((-2.0d0) * (a * c))
    else if (c <= 1.8d+58) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (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 t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -9.5e+43) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -1400000000.0) {
		tmp = t_1;
	} else if (c <= -3.45e-15) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 1.8e+58) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (c * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) + (x * y))
	tmp = 0
	if c <= -9.5e+43:
		tmp = -2.0 * (c * (i * (b * c)))
	elif c <= -1400000000.0:
		tmp = t_1
	elif c <= -3.45e-15:
		tmp = i * (-2.0 * (a * c))
	elif c <= 1.8e+58:
		tmp = t_1
	else:
		tmp = -2.0 * (c * (c * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (c <= -9.5e+43)
		tmp = Float64(-2.0 * Float64(c * Float64(i * Float64(b * c))));
	elseif (c <= -1400000000.0)
		tmp = t_1;
	elseif (c <= -3.45e-15)
		tmp = Float64(i * Float64(-2.0 * Float64(a * c)));
	elseif (c <= 1.8e+58)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) + (x * y));
	tmp = 0.0;
	if (c <= -9.5e+43)
		tmp = -2.0 * (c * (i * (b * c)));
	elseif (c <= -1400000000.0)
		tmp = t_1;
	elseif (c <= -3.45e-15)
		tmp = i * (-2.0 * (a * c));
	elseif (c <= 1.8e+58)
		tmp = t_1;
	else
		tmp = -2.0 * (c * (c * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e+43], N[(-2.0 * N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1400000000.0], t$95$1, If[LessEqual[c, -3.45e-15], N[(i * N[(-2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+58], t$95$1, N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.5000000000000004e43

   1. Initial program 85.5%

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

   2. Taylor expanded in i around inf 94.4%

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

   3. Taylor expanded in c around inf 76.5%

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

      1. unpow2 76.5%

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

      2. associate-*r* 81.8%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*l* 83.7%

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

      6. *-commutative 83.7%

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

      7. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -9.5000000000000004e43 < c < -1.4e9 or -3.45000000000000005e-15 < c < 1.79999999999999998e58

   1. Initial program 97.1%

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

   2. Taylor expanded in c around 0 74.9%

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

   if -1.4e9 < c < -3.45000000000000005e-15

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. neg-mul-1 76.5%

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

      3. *-commutative 76.5%

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

      4. associate-*r* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-*l* 76.7%

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

   10. Simplified 76.7%

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

   if 1.79999999999999998e58 < c

   1. Initial program 78.4%

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

   2. Taylor expanded in i around inf 86.6%

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

   3. Taylor expanded in c around inf 63.2%

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

      1. unpow2 63.2%

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

      2. associate-*r* 66.5%

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

      3. associate-*r* 68.1%

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

      4. *-commutative 68.1%

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

      5. associate-*l* 64.9%

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

      6. *-commutative 64.9%

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

      7. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in i around 0 66.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1400000000:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{-15}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 13: 68.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;c \leq -1.36 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -2150000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* z t) (* x y)))))
   (if (<= c -1.36e+44)
     (* -2.0 (* c (* i (* b c))))
     (if (<= c -2150000000.0)
       t_1
       (if (<= c -1.12e-13)
         (* i (* -2.0 (* a c)))
         (if (<= c 8.2e+47) t_1 (* b (* -2.0 (* c (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -1.36e+44) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -2150000000.0) {
		tmp = t_1;
	} else if (c <= -1.12e-13) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 8.2e+47) {
		tmp = t_1;
	} else {
		tmp = b * (-2.0 * (c * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) + (x * y))
    if (c <= (-1.36d+44)) then
        tmp = (-2.0d0) * (c * (i * (b * c)))
    else if (c <= (-2150000000.0d0)) then
        tmp = t_1
    else if (c <= (-1.12d-13)) then
        tmp = i * ((-2.0d0) * (a * c))
    else if (c <= 8.2d+47) then
        tmp = t_1
    else
        tmp = b * ((-2.0d0) * (c * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) + (x * y));
	double tmp;
	if (c <= -1.36e+44) {
		tmp = -2.0 * (c * (i * (b * c)));
	} else if (c <= -2150000000.0) {
		tmp = t_1;
	} else if (c <= -1.12e-13) {
		tmp = i * (-2.0 * (a * c));
	} else if (c <= 8.2e+47) {
		tmp = t_1;
	} else {
		tmp = b * (-2.0 * (c * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) + (x * y))
	tmp = 0
	if c <= -1.36e+44:
		tmp = -2.0 * (c * (i * (b * c)))
	elif c <= -2150000000.0:
		tmp = t_1
	elif c <= -1.12e-13:
		tmp = i * (-2.0 * (a * c))
	elif c <= 8.2e+47:
		tmp = t_1
	else:
		tmp = b * (-2.0 * (c * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (c <= -1.36e+44)
		tmp = Float64(-2.0 * Float64(c * Float64(i * Float64(b * c))));
	elseif (c <= -2150000000.0)
		tmp = t_1;
	elseif (c <= -1.12e-13)
		tmp = Float64(i * Float64(-2.0 * Float64(a * c)));
	elseif (c <= 8.2e+47)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(-2.0 * Float64(c * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) + (x * y));
	tmp = 0.0;
	if (c <= -1.36e+44)
		tmp = -2.0 * (c * (i * (b * c)));
	elseif (c <= -2150000000.0)
		tmp = t_1;
	elseif (c <= -1.12e-13)
		tmp = i * (-2.0 * (a * c));
	elseif (c <= 8.2e+47)
		tmp = t_1;
	else
		tmp = b * (-2.0 * (c * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.36e+44], N[(-2.0 * N[(c * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2150000000.0], t$95$1, If[LessEqual[c, -1.12e-13], N[(i * N[(-2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.2e+47], t$95$1, N[(b * N[(-2.0 * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.36000000000000005e44

   1. Initial program 85.5%

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

   2. Taylor expanded in i around inf 94.4%

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

   3. Taylor expanded in c around inf 76.5%

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

      1. unpow2 76.5%

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

      2. associate-*r* 81.8%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-*l* 83.7%

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

      6. *-commutative 83.7%

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

      7. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if -1.36000000000000005e44 < c < -2.15e9 or -1.12e-13 < c < 8.2000000000000002e47

   1. Initial program 97.7%

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

   2. Taylor expanded in c around 0 76.0%

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

   if -2.15e9 < c < -1.12e-13

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. neg-mul-1 76.5%

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

      3. *-commutative 76.5%

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

      4. associate-*r* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in c around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-*l* 76.7%

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

   10. Simplified 76.7%

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

   if 8.2000000000000002e47 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in i around inf 85.8%

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

   3. Taylor expanded in c around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-*r* 66.9%

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

      3. unpow2 66.9%

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

      4. associate-*r* 67.0%

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

      5. *-commutative 67.0%

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

      6. associate-*l* 67.0%

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

   5. Simplified 67.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.36 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -2150000000:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 14: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1860000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* -2.0 (* a c)))) (t_2 (* 2.0 (* z t))))
   (if (<= t -1860000.0)
     t_2
     (if (<= t -1.9e-130)
       t_1
       (if (<= t -9e-237) (* 2.0 (* x y)) (if (<= t 3.4e+37) 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 = i * (-2.0 * (a * c));
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1860000.0) {
		tmp = t_2;
	} else if (t <= -1.9e-130) {
		tmp = t_1;
	} else if (t <= -9e-237) {
		tmp = 2.0 * (x * y);
	} else if (t <= 3.4e+37) {
		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 = i * ((-2.0d0) * (a * c))
    t_2 = 2.0d0 * (z * t)
    if (t <= (-1860000.0d0)) then
        tmp = t_2
    else if (t <= (-1.9d-130)) then
        tmp = t_1
    else if (t <= (-9d-237)) then
        tmp = 2.0d0 * (x * y)
    else if (t <= 3.4d+37) 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 = i * (-2.0 * (a * c));
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (t <= -1860000.0) {
		tmp = t_2;
	} else if (t <= -1.9e-130) {
		tmp = t_1;
	} else if (t <= -9e-237) {
		tmp = 2.0 * (x * y);
	} else if (t <= 3.4e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * (-2.0 * (a * c))
	t_2 = 2.0 * (z * t)
	tmp = 0
	if t <= -1860000.0:
		tmp = t_2
	elif t <= -1.9e-130:
		tmp = t_1
	elif t <= -9e-237:
		tmp = 2.0 * (x * y)
	elif t <= 3.4e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(-2.0 * Float64(a * c)))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1860000.0)
		tmp = t_2;
	elseif (t <= -1.9e-130)
		tmp = t_1;
	elseif (t <= -9e-237)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (t <= 3.4e+37)
		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 = i * (-2.0 * (a * c));
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1860000.0)
		tmp = t_2;
	elseif (t <= -1.9e-130)
		tmp = t_1;
	elseif (t <= -9e-237)
		tmp = 2.0 * (x * y);
	elseif (t <= 3.4e+37)
		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[(i * N[(-2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1860000.0], t$95$2, If[LessEqual[t, -1.9e-130], t$95$1, If[LessEqual[t, -9e-237], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.86e6 or 3.40000000000000006e37 < t

   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 43.8%

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

   if -1.86e6 < t < -1.8999999999999999e-130 or -9.00000000000000019e-237 < t < 3.40000000000000006e37

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

      3. *-commutative 36.5%

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

      4. associate-*r* 37.4%

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

   4. Simplified 37.4%

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

   5. Taylor expanded in c around 0 36.5%

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

      1. *-commutative 36.5%

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

   7. Simplified 36.5%

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

   8. Taylor expanded in c around 0 36.5%

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

      1. *-commutative 36.5%

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

      2. *-commutative 36.5%

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

      3. associate-*r* 37.4%

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

      4. *-commutative 37.4%

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

      5. associate-*l* 38.2%

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

   10. Simplified 38.2%

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

   if -1.8999999999999999e-130 < t < -9.00000000000000019e-237

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 25.8%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1860000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-237}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 33.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+232} \lor \neg \left(z \leq -2.85 \cdot 10^{+21}\right) \land z \leq 6 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -1.1e+232) (and (not (<= z -2.85e+21)) (<= z 6e-75)))
   (* 2.0 (* a (* c (- i))))
   (* 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 ((z <= -1.1e+232) || (!(z <= -2.85e+21) && (z <= 6e-75))) {
		tmp = 2.0 * (a * (c * -i));
	} 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 ((z <= (-1.1d+232)) .or. (.not. (z <= (-2.85d+21))) .and. (z <= 6d-75)) then
        tmp = 2.0d0 * (a * (c * -i))
    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 ((z <= -1.1e+232) || (!(z <= -2.85e+21) && (z <= 6e-75))) {
		tmp = 2.0 * (a * (c * -i));
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -1.1e+232) or (not (z <= -2.85e+21) and (z <= 6e-75)):
		tmp = 2.0 * (a * (c * -i))
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -1.1e+232) || (!(z <= -2.85e+21) && (z <= 6e-75)))
		tmp = Float64(2.0 * Float64(a * Float64(c * Float64(-i))));
	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 ((z <= -1.1e+232) || (~((z <= -2.85e+21)) && (z <= 6e-75)))
		tmp = 2.0 * (a * (c * -i));
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -1.1e+232], And[N[Not[LessEqual[z, -2.85e+21]], $MachinePrecision], LessEqual[z, 6e-75]]], N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e232 or -2.85e21 < z < 5.9999999999999997e-75

   1. Initial program 87.7%

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

      1. associate-*l* 92.8%

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

      2. fma-def 92.8%

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

   3. Simplified 92.8%

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

      1. fma-def 92.8%

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

      2. +-commutative 92.8%

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

   5. Applied egg-rr 92.8%

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

   6. Taylor expanded in a around inf 41.2%

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

      1. mul-1-neg 41.2%

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

      2. *-commutative 41.2%

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

      3. distribute-rgt-neg-in 41.2%

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

      4. *-commutative 41.2%

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

      5. associate-*l* 42.0%

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

   8. Simplified 42.0%

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

   if -1.1e232 < z < -2.85e21 or 5.9999999999999997e-75 < z

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 43.9%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+232} \lor \neg \left(z \leq -2.85 \cdot 10^{+21}\right) \land z \leq 6 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 38.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+179} \lor \neg \left(x \leq 2.85 \cdot 10^{+51}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+179) (not (<= x 2.85e+51)))
   (* 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 ((x <= -2.3e+179) || !(x <= 2.85e+51)) {
		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 ((x <= (-2.3d+179)) .or. (.not. (x <= 2.85d+51))) 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 ((x <= -2.3e+179) || !(x <= 2.85e+51)) {
		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 (x <= -2.3e+179) or not (x <= 2.85e+51):
		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 ((x <= -2.3e+179) || !(x <= 2.85e+51))
		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 ((x <= -2.3e+179) || ~((x <= 2.85e+51)))
		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[x, -2.3e+179], N[Not[LessEqual[x, 2.85e+51]], $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 x < -2.29999999999999994e179 or 2.8500000000000001e51 < x

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 44.8%

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

   if -2.29999999999999994e179 < x < 2.8500000000000001e51

   1. Initial program 90.9%

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

   2. Taylor expanded in z around inf 29.5%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+179} \lor \neg \left(x \leq 2.85 \cdot 10^{+51}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 17: 29.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.5%

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

2. Taylor expanded in z around inf 27.3%

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

3. Final simplification 27.3%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023230 
(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))))