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

Percentage Accurate: 90.0% → 96.0%

Time: 12.2s

Alternatives: 15

Speedup: 0.5×

• 47.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i))))
     (* (* i (* b (* c c))) -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 tmp;
	if ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	} else {
		tmp = (i * (b * (c * c))) * -2.0;
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(b * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -2.0), $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 93.8%

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

      1. associate-*l* 99.5%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

   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 63.6%

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

   3. Taylor expanded in c around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*r* 72.8%

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

      3. unpow2 72.8%

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

   5. Simplified 72.8%

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

4. Final simplification 98.3%

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

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t_2\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+307)))
     (* -2.0 (* c (* t_1 i)))
     (* (- (+ (* x y) (* z t)) t_2) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+307)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+307)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+307):
		tmp = -2.0 * (c * (t_1 * i))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+307))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+307)))
		tmp = -2.0 * (c * (t_1 * i));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+307]], $MachinePrecision]], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 1.99999999999999997e307 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 75.2%

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

   2. Taylor expanded in i around inf 93.8%

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

   3. Taylor expanded in i around 0 93.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.99999999999999997e307

   1. Initial program 99.9%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]

Alternative 3: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -3.1e+59)
     t_2
     (if (<= c 1.25e-102)
       t_1
       (if (<= c 1.55e-90)
         (* (* c i) (* a -2.0))
         (if (<= c 2.4e-7) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -3.1e+59) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 2.4e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-3.1d+59)) then
        tmp = t_2
    else if (c <= 1.25d-102) then
        tmp = t_1
    else if (c <= 1.55d-90) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= 2.4d-7) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -3.1e+59) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 2.4e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -3.1e+59:
		tmp = t_2
	elif c <= 1.25e-102:
		tmp = t_1
	elif c <= 1.55e-90:
		tmp = (c * i) * (a * -2.0)
	elif c <= 2.4e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -3.1e+59)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= 2.4e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -3.1e+59)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= 2.4e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.1e+59], t$95$2, If[LessEqual[c, 1.25e-102], t$95$1, If[LessEqual[c, 1.55e-90], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e-7], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.10000000000000015e59 or 2.39999999999999979e-7 < c

   1. Initial program 80.9%

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

   2. Taylor expanded in i around inf 83.3%

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

   3. Taylor expanded in i around 0 83.3%

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

   if -3.10000000000000015e59 < c < 1.25000000000000006e-102 or 1.5500000000000001e-90 < c < 2.39999999999999979e-7

   1. Initial program 96.9%

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

   2. Taylor expanded in c around 0 80.1%

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

   if 1.25000000000000006e-102 < c < 1.5500000000000001e-90

   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 78.1%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 67.5%

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

      4. neg-mul-1 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in a around 0 78.1%

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

      1. associate-*r* 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+59}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -1.6e+57)
     t_2
     (if (<= c 6.8e-104)
       t_1
       (if (<= c 1.85e-90)
         (* 2.0 (- (* z t) (* a (* c i))))
         (if (<= c 5.4e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.6e+57) {
		tmp = t_2;
	} else if (c <= 6.8e-104) {
		tmp = t_1;
	} else if (c <= 1.85e-90) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 5.4e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-1.6d+57)) then
        tmp = t_2
    else if (c <= 6.8d-104) then
        tmp = t_1
    else if (c <= 1.85d-90) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= 5.4d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.6e+57) {
		tmp = t_2;
	} else if (c <= 6.8e-104) {
		tmp = t_1;
	} else if (c <= 1.85e-90) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 5.4e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.6e+57:
		tmp = t_2
	elif c <= 6.8e-104:
		tmp = t_1
	elif c <= 1.85e-90:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= 5.4e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.6e+57)
		tmp = t_2;
	elseif (c <= 6.8e-104)
		tmp = t_1;
	elseif (c <= 1.85e-90)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= 5.4e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.6e+57)
		tmp = t_2;
	elseif (c <= 6.8e-104)
		tmp = t_1;
	elseif (c <= 1.85e-90)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= 5.4e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.6e+57], t$95$2, If[LessEqual[c, 6.8e-104], t$95$1, If[LessEqual[c, 1.85e-90], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.60000000000000015e57 or 5.39999999999999999e-16 < c

   1. Initial program 80.9%

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

   2. Taylor expanded in i around inf 83.3%

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

   3. Taylor expanded in i around 0 83.3%

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

   if -1.60000000000000015e57 < c < 6.80000000000000031e-104 or 1.85000000000000009e-90 < c < 5.39999999999999999e-16

   1. Initial program 96.9%

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

   2. Taylor expanded in c around 0 80.1%

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

   if 6.80000000000000031e-104 < c < 1.85000000000000009e-90

   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 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-*l* 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in x around 0 78.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-104}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-16}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -1.7e+57)
     t_2
     (if (<= c 1.35e-110)
       t_1
       (if (<= c 3.1e-62)
         (* 2.0 (- (* x y) (* a (* c i))))
         (if (<= c 2.2e-13) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.7e+57) {
		tmp = t_2;
	} else if (c <= 1.35e-110) {
		tmp = t_1;
	} else if (c <= 3.1e-62) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 2.2e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-1.7d+57)) then
        tmp = t_2
    else if (c <= 1.35d-110) then
        tmp = t_1
    else if (c <= 3.1d-62) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if (c <= 2.2d-13) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -1.7e+57) {
		tmp = t_2;
	} else if (c <= 1.35e-110) {
		tmp = t_1;
	} else if (c <= 3.1e-62) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 2.2e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -1.7e+57:
		tmp = t_2
	elif c <= 1.35e-110:
		tmp = t_1
	elif c <= 3.1e-62:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif c <= 2.2e-13:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -1.7e+57)
		tmp = t_2;
	elseif (c <= 1.35e-110)
		tmp = t_1;
	elseif (c <= 3.1e-62)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (c <= 2.2e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -1.7e+57)
		tmp = t_2;
	elseif (c <= 1.35e-110)
		tmp = t_1;
	elseif (c <= 3.1e-62)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif (c <= 2.2e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.7e+57], t$95$2, If[LessEqual[c, 1.35e-110], t$95$1, If[LessEqual[c, 3.1e-62], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-13], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.69999999999999996e57 or 2.19999999999999997e-13 < c

   1. Initial program 80.9%

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

   2. Taylor expanded in i around inf 83.3%

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

   3. Taylor expanded in i around 0 83.3%

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

   if -1.69999999999999996e57 < c < 1.3499999999999999e-110 or 3.0999999999999999e-62 < c < 2.19999999999999997e-13

   1. Initial program 96.7%

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

   2. Taylor expanded in c around 0 80.4%

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

   if 1.3499999999999999e-110 < c < 3.0999999999999999e-62

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l* 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in z around 0 88.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-110}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-13}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+63} \lor \neg \left(c \leq 670000000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.6e+63) (not (<= c 670000000000.0)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (- (+ (* x y) (* z t)) (* c (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e+63) || !(c <= 670000000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.6d+63)) .or. (.not. (c <= 670000000000.0d0))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (c * (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.6e+63) || !(c <= 670000000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.6e+63) or not (c <= 670000000000.0):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.6e+63) || !(c <= 670000000000.0))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(c * Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.6e+63) || ~((c <= 670000000000.0)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (c * (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.6e+63], N[Not[LessEqual[c, 670000000000.0]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.59999999999999999e63 or 6.7e11 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in i around inf 84.9%

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

   3. Taylor expanded in i around 0 84.9%

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

   if -3.59999999999999999e63 < c < 6.7e11

   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 a around inf 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l* 86.4%

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

   4. Simplified 86.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.6 \cdot 10^{+63} \lor \neg \left(c \leq 670000000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+62} \lor \neg \left(c \leq 720000000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.5e+62) (not (<= c 720000000000.0)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.5e+62) || !(c <= 720000000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.5d+62)) .or. (.not. (c <= 720000000000.0d0))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.5e+62) || !(c <= 720000000000.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.5e+62) or not (c <= 720000000000.0):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.5e+62) || !(c <= 720000000000.0))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.5e+62) || ~((c <= 720000000000.0)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.5e+62], N[Not[LessEqual[c, 720000000000.0]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.49999999999999999e62 or 7.2e11 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in i around inf 84.9%

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

   3. Taylor expanded in i around 0 84.9%

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

   if -4.49999999999999999e62 < c < 7.2e11

   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 a around inf 88.1%

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

      1. *-commutative 88.1%

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

   4. Simplified 88.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+62} \lor \neg \left(c \leq 720000000000\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 8: 56.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+104} \lor \neg \left(c \leq 1.25 \cdot 10^{-102}\right) \land \left(c \leq 1.55 \cdot 10^{-90} \lor \neg \left(c \leq 4.9 \cdot 10^{+163}\right)\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.5e+104)
         (and (not (<= c 1.25e-102))
              (or (<= c 1.55e-90) (not (<= c 4.9e+163)))))
   (* (* c i) (* a -2.0))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.5e+104) || (!(c <= 1.25e-102) && ((c <= 1.55e-90) || !(c <= 4.9e+163)))) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.5d+104)) .or. (.not. (c <= 1.25d-102)) .and. (c <= 1.55d-90) .or. (.not. (c <= 4.9d+163))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.5e+104) || (!(c <= 1.25e-102) && ((c <= 1.55e-90) || !(c <= 4.9e+163)))) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.5e+104) or (not (c <= 1.25e-102) and ((c <= 1.55e-90) or not (c <= 4.9e+163))):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.5e+104) || (!(c <= 1.25e-102) && ((c <= 1.55e-90) || !(c <= 4.9e+163))))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.5e+104) || (~((c <= 1.25e-102)) && ((c <= 1.55e-90) || ~((c <= 4.9e+163)))))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.5e+104], And[N[Not[LessEqual[c, 1.25e-102]], $MachinePrecision], Or[LessEqual[c, 1.55e-90], N[Not[LessEqual[c, 4.9e+163]], $MachinePrecision]]]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.4999999999999998e104 or 1.25000000000000006e-102 < c < 1.5500000000000001e-90 or 4.9e163 < c

   1. Initial program 77.9%

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

   2. Taylor expanded in a around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. *-commutative 50.9%

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

      3. associate-*r* 43.6%

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

      4. neg-mul-1 43.6%

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

   4. Simplified 43.6%

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

   5. Taylor expanded in a around 0 50.9%

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

      1. associate-*r* 50.9%

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

   7. Simplified 50.9%

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

   if -2.4999999999999998e104 < c < 1.25000000000000006e-102 or 1.5500000000000001e-90 < c < 4.9e163

   1. Initial program 95.0%

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

   2. Taylor expanded in c around 0 69.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+104} \lor \neg \left(c \leq 1.25 \cdot 10^{-102}\right) \land \left(c \leq 1.55 \cdot 10^{-90} \lor \neg \left(c \leq 4.9 \cdot 10^{+163}\right)\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 9: 67.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -7.7 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* c (* (* c i) (* b -2.0)))))
   (if (<= c -7.7e+62)
     t_2
     (if (<= c 1.25e-102)
       t_1
       (if (<= c 1.55e-90)
         (* (* c i) (* a -2.0))
         (if (<= c 760000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = c * ((c * i) * (b * -2.0));
	double tmp;
	if (c <= -7.7e+62) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = c * ((c * i) * (b * (-2.0d0)))
    if (c <= (-7.7d+62)) then
        tmp = t_2
    else if (c <= 1.25d-102) then
        tmp = t_1
    else if (c <= 1.55d-90) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= 760000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = c * ((c * i) * (b * -2.0));
	double tmp;
	if (c <= -7.7e+62) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = c * ((c * i) * (b * -2.0))
	tmp = 0
	if c <= -7.7e+62:
		tmp = t_2
	elif c <= 1.25e-102:
		tmp = t_1
	elif c <= 1.55e-90:
		tmp = (c * i) * (a * -2.0)
	elif c <= 760000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(c * Float64(Float64(c * i) * Float64(b * -2.0)))
	tmp = 0.0
	if (c <= -7.7e+62)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = c * ((c * i) * (b * -2.0));
	tmp = 0.0;
	if (c <= -7.7e+62)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(c * i), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.7e+62], t$95$2, If[LessEqual[c, 1.25e-102], t$95$1, If[LessEqual[c, 1.55e-90], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 760000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.7000000000000003e62 or 7.6e11 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in i around inf 84.9%

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

   3. Taylor expanded in c around inf 63.7%

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

      1. associate-*r* 63.7%

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

      2. unpow2 63.7%

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

      3. associate-*l* 65.0%

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

      4. *-commutative 65.0%

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

      5. rem-log-exp 61.0%

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

      6. log-pow 61.0%

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

      7. associate-*l* 61.0%

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

      8. *-commutative 61.0%

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

      9. associate-*l* 61.0%

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

      10. *-commutative 61.0%

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

      11. log-pow 61.0%

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

      12. rem-log-exp 66.6%

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

      13. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -7.7000000000000003e62 < c < 1.25000000000000006e-102 or 1.5500000000000001e-90 < c < 7.6e11

   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 78.3%

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

   if 1.25000000000000006e-102 < c < 1.5500000000000001e-90

   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 78.1%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 67.5%

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

      4. neg-mul-1 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in a around 0 78.1%

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

      1. associate-*r* 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.7 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot i\right) \cdot \left(b \cdot -2\right)\right)\\ \end{array} \]

Alternative 10: 67.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := \left(c \cdot i\right) \cdot \left(\left(b \cdot c\right) \cdot -2\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* (* c i) (* (* b c) -2.0))))
   (if (<= c -5.2e+61)
     t_2
     (if (<= c 1.25e-102)
       t_1
       (if (<= c 1.55e-90)
         (* (* c i) (* a -2.0))
         (if (<= c 760000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (c * i) * ((b * c) * -2.0);
	double tmp;
	if (c <= -5.2e+61) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = (c * i) * ((b * c) * (-2.0d0))
    if (c <= (-5.2d+61)) then
        tmp = t_2
    else if (c <= 1.25d-102) then
        tmp = t_1
    else if (c <= 1.55d-90) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= 760000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = (c * i) * ((b * c) * -2.0);
	double tmp;
	if (c <= -5.2e+61) {
		tmp = t_2;
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = (c * i) * ((b * c) * -2.0)
	tmp = 0
	if c <= -5.2e+61:
		tmp = t_2
	elif c <= 1.25e-102:
		tmp = t_1
	elif c <= 1.55e-90:
		tmp = (c * i) * (a * -2.0)
	elif c <= 760000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(Float64(c * i) * Float64(Float64(b * c) * -2.0))
	tmp = 0.0
	if (c <= -5.2e+61)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = (c * i) * ((b * c) * -2.0);
	tmp = 0.0;
	if (c <= -5.2e+61)
		tmp = t_2;
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] * N[(N[(b * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+61], t$95$2, If[LessEqual[c, 1.25e-102], t$95$1, If[LessEqual[c, 1.55e-90], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 760000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.19999999999999945e61 or 7.6e11 < c

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. *-commutative 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. unpow2 63.7%

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

      5. associate-*r* 65.0%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in c around 0 63.7%

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

      1. associate-*r* 63.7%

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

      2. unpow2 63.7%

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

      3. associate-*r* 65.0%

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

      4. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in c around 0 63.7%

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

   10. Simplified 66.7%

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

   if -5.19999999999999945e61 < c < 1.25000000000000006e-102 or 1.5500000000000001e-90 < c < 7.6e11

   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 78.3%

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

   if 1.25000000000000006e-102 < c < 1.5500000000000001e-90

   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 78.1%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 67.5%

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

      4. neg-mul-1 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in a around 0 78.1%

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

      1. associate-*r* 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(\left(b \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(\left(b \cdot c\right) \cdot -2\right)\\ \end{array} \]

Alternative 11: 67.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{if}\;c \leq -4.7 \cdot 10^{+63}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(\left(b \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot i\right)\right) \cdot \left(b \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)))
   (if (<= c -4.7e+63)
     (* (* c i) (* (* b c) -2.0))
     (if (<= c 1.25e-102)
       t_1
       (if (<= c 1.55e-90)
         (* (* c i) (* a -2.0))
         (if (<= c 760000000000.0) t_1 (* (* c (* c i)) (* b -2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -4.7e+63) {
		tmp = (c * i) * ((b * c) * -2.0);
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = (c * (c * i)) * (b * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    if (c <= (-4.7d+63)) then
        tmp = (c * i) * ((b * c) * (-2.0d0))
    else if (c <= 1.25d-102) then
        tmp = t_1
    else if (c <= 1.55d-90) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (c <= 760000000000.0d0) then
        tmp = t_1
    else
        tmp = (c * (c * i)) * (b * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double tmp;
	if (c <= -4.7e+63) {
		tmp = (c * i) * ((b * c) * -2.0);
	} else if (c <= 1.25e-102) {
		tmp = t_1;
	} else if (c <= 1.55e-90) {
		tmp = (c * i) * (a * -2.0);
	} else if (c <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = (c * (c * i)) * (b * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	tmp = 0
	if c <= -4.7e+63:
		tmp = (c * i) * ((b * c) * -2.0)
	elif c <= 1.25e-102:
		tmp = t_1
	elif c <= 1.55e-90:
		tmp = (c * i) * (a * -2.0)
	elif c <= 760000000000.0:
		tmp = t_1
	else:
		tmp = (c * (c * i)) * (b * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	tmp = 0.0
	if (c <= -4.7e+63)
		tmp = Float64(Float64(c * i) * Float64(Float64(b * c) * -2.0));
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * Float64(c * i)) * Float64(b * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	tmp = 0.0;
	if (c <= -4.7e+63)
		tmp = (c * i) * ((b * c) * -2.0);
	elseif (c <= 1.25e-102)
		tmp = t_1;
	elseif (c <= 1.55e-90)
		tmp = (c * i) * (a * -2.0);
	elseif (c <= 760000000000.0)
		tmp = t_1;
	else
		tmp = (c * (c * i)) * (b * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[c, -4.7e+63], N[(N[(c * i), $MachinePrecision] * N[(N[(b * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-102], t$95$1, If[LessEqual[c, 1.55e-90], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 760000000000.0], t$95$1, N[(N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.7000000000000003e63

   1. Initial program 76.4%

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

   2. Taylor expanded in b around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. unpow2 65.3%

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

      5. associate-*r* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in c around 0 65.3%

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

      1. associate-*r* 65.3%

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

      2. unpow2 65.3%

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

      3. associate-*r* 66.2%

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

      4. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in c around 0 65.3%

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

   10. Simplified 69.6%

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

   if -4.7000000000000003e63 < c < 1.25000000000000006e-102 or 1.5500000000000001e-90 < c < 7.6e11

   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 78.3%

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

   if 1.25000000000000006e-102 < c < 1.5500000000000001e-90

   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 78.1%

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

      1. associate-*r* 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 67.5%

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

      4. neg-mul-1 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in a around 0 78.1%

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

      1. associate-*r* 78.1%

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

   7. Simplified 78.1%

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

   if 7.6e11 < c

   1. Initial program 82.8%

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

   2. Taylor expanded in b around inf 62.3%

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

      1. mul-1-neg 62.3%

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

      2. *-commutative 62.3%

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

      3. distribute-rgt-neg-in 62.3%

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

      4. unpow2 62.3%

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

      5. associate-*r* 63.9%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in c around 0 62.3%

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

      1. associate-*r* 62.3%

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

      2. unpow2 62.3%

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

      3. associate-*r* 63.9%

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

      4. *-commutative 63.9%

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

   7. Simplified 63.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+63}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(\left(b \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-102}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-90}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;c \leq 760000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(c \cdot i\right)\right) \cdot \left(b \cdot -2\right)\\ \end{array} \]

Alternative 12: 38.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-306}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -9.2)
     t_1
     (if (<= t 1.45e-306)
       (* -2.0 (* c (* a i)))
       (if (<= t 1.05e+40) (* (* x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 1.45e-306) {
		tmp = -2.0 * (c * (a * i));
	} else if (t <= 1.05e+40) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-9.2d0)) then
        tmp = t_1
    else if (t <= 1.45d-306) then
        tmp = (-2.0d0) * (c * (a * i))
    else if (t <= 1.05d+40) then
        tmp = (x * y) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 1.45e-306) {
		tmp = -2.0 * (c * (a * i));
	} else if (t <= 1.05e+40) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -9.2:
		tmp = t_1
	elif t <= 1.45e-306:
		tmp = -2.0 * (c * (a * i))
	elif t <= 1.05e+40:
		tmp = (x * y) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 1.45e-306)
		tmp = Float64(-2.0 * Float64(c * Float64(a * i)));
	elseif (t <= 1.05e+40)
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 1.45e-306)
		tmp = -2.0 * (c * (a * i));
	elseif (t <= 1.05e+40)
		tmp = (x * y) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2], t$95$1, If[LessEqual[t, 1.45e-306], N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+40], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999993 or 1.05000000000000005e40 < t

   1. Initial program 88.8%

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

   2. Taylor expanded in z around inf 44.9%

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

   if -9.1999999999999993 < t < 1.4499999999999999e-306

   1. Initial program 89.1%

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

   2. Taylor expanded in i around inf 50.7%

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

   3. Taylor expanded in c around 0 25.1%

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

      1. associate-*r* 20.9%

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

      2. *-commutative 20.9%

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

      3. associate-*r* 20.9%

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

   5. Simplified 20.9%

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

   if 1.4499999999999999e-306 < t < 1.05000000000000005e40

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 35.7%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-306}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 13: 39.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-306}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -9.2)
     t_1
     (if (<= t 1.42e-306)
       (* (* c i) (* a -2.0))
       (if (<= t 1.35e+46) (* (* x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 1.42e-306) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 1.35e+46) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-9.2d0)) then
        tmp = t_1
    else if (t <= 1.42d-306) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (t <= 1.35d+46) then
        tmp = (x * y) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 1.42e-306) {
		tmp = (c * i) * (a * -2.0);
	} else if (t <= 1.35e+46) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -9.2:
		tmp = t_1
	elif t <= 1.42e-306:
		tmp = (c * i) * (a * -2.0)
	elif t <= 1.35e+46:
		tmp = (x * y) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 1.42e-306)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (t <= 1.35e+46)
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 1.42e-306)
		tmp = (c * i) * (a * -2.0);
	elseif (t <= 1.35e+46)
		tmp = (x * y) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2], t$95$1, If[LessEqual[t, 1.42e-306], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+46], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999993 or 1.3500000000000001e46 < t

   1. Initial program 88.8%

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

   2. Taylor expanded in z around inf 44.9%

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

   if -9.1999999999999993 < t < 1.42000000000000005e-306

   1. Initial program 89.1%

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

   2. Taylor expanded in a around inf 25.1%

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

      1. associate-*r* 25.1%

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

      2. *-commutative 25.1%

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

      3. associate-*r* 20.9%

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

      4. neg-mul-1 20.9%

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

   4. Simplified 20.9%

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

   5. Taylor expanded in a around 0 25.1%

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

      1. associate-*r* 25.1%

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

   7. Simplified 25.1%

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

   if 1.42000000000000005e-306 < t < 1.3500000000000001e46

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 35.7%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-306}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 14: 40.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+117} \lor \neg \left(z \leq 3.3 \cdot 10^{-78}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -3.1e+117) (not (<= z 3.3e-78)))
   (* 2.0 (* z t))
   (* (* x y) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.1e+117) || !(z <= 3.3e-78)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-3.1d+117)) .or. (.not. (z <= 3.3d-78))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (x * y) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -3.1e+117) || !(z <= 3.3e-78)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -3.1e+117) or not (z <= 3.3e-78):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -3.1e+117) || !(z <= 3.3e-78))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(Float64(x * y) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -3.1e+117) || ~((z <= 3.3e-78)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -3.1e+117], N[Not[LessEqual[z, 3.3e-78]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999975e117 or 3.29999999999999982e-78 < z

   1. Initial program 89.0%

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

   2. Taylor expanded in z around inf 49.2%

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

   if -3.09999999999999975e117 < z < 3.29999999999999982e-78

   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 x around inf 34.2%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+117} \lor \neg \left(z \leq 3.3 \cdot 10^{-78}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 15: 29.0% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

2. Taylor expanded in z around inf 30.8%

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

3. Final simplification 30.8%

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

Developer target: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023290 
(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))))