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

Percentage Accurate: 89.4% → 94.5%

Time: 15.8s

Alternatives: 18

Speedup: 0.5×

• 48.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t_1 \cdot i\right)\\ t_3 := i \cdot \left(c \cdot t_1\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;-2 \cdot t_2\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - t_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* i (* c t_1))))
   (if (<= t_3 (- INFINITY))
     (* -2.0 t_2)
     (if (<= t_3 4e+283)
       (* 2.0 (- (+ (* z t) (* x y)) t_3))
       (* 2.0 (- (* z t) t_2))))))

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 t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 4e+283) {
		tmp = 2.0 * (((z * t) + (x * y)) - t_3);
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	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 t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 4e+283) {
		tmp = 2.0 * (((z * t) + (x * y)) - t_3);
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = i * (c * t_1)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = -2.0 * t_2
	elif t_3 <= 4e+283:
		tmp = 2.0 * (((z * t) + (x * y)) - t_3)
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(-2.0 * t_2);
	elseif (t_3 <= 4e+283)
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - t_3));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	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);
	t_3 = i * (c * t_1);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = -2.0 * t_2;
	elseif (t_3 <= 4e+283)
		tmp = 2.0 * (((z * t) + (x * y)) - t_3);
	else
		tmp = 2.0 * ((z * t) - t_2);
	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[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(-2.0 * t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 4e+283], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 82.4%

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

   2. Taylor expanded in i around inf 93.5%

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

   3. Taylor expanded in i around 0 93.5%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 3.99999999999999982e283

   1. Initial program 99.2%

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

   if 3.99999999999999982e283 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.5%

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

   2. Taylor expanded in x around 0 94.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 2: 94.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. associate-*l* 95.7%

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

   2. fma-def 95.7%

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

3. Simplified 95.7%

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

4. Final simplification 95.7%

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

Alternative 3: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;c \leq -4.3 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-308}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 8600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* i (* a c)))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i))))
        (t_3 (* 2.0 (- (* x y) (* c (* a i))))))
   (if (<= c -4.3e+41)
     t_2
     (if (<= c -3.4e-221)
       t_1
       (if (<= c 9e-308)
         (* 2.0 (* x y))
         (if (<= c 5.8e-159)
           t_1
           (if (<= c 7.8e-68)
             t_3
             (if (<= c 8600.0) t_1 (if (<= c 8.5e+74) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (i * (a * c)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double t_3 = 2.0 * ((x * y) - (c * (a * i)));
	double tmp;
	if (c <= -4.3e+41) {
		tmp = t_2;
	} else if (c <= -3.4e-221) {
		tmp = t_1;
	} else if (c <= 9e-308) {
		tmp = 2.0 * (x * y);
	} else if (c <= 5.8e-159) {
		tmp = t_1;
	} else if (c <= 7.8e-68) {
		tmp = t_3;
	} else if (c <= 8600.0) {
		tmp = t_1;
	} else if (c <= 8.5e+74) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (i * (a * c)))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    t_3 = 2.0d0 * ((x * y) - (c * (a * i)))
    if (c <= (-4.3d+41)) then
        tmp = t_2
    else if (c <= (-3.4d-221)) then
        tmp = t_1
    else if (c <= 9d-308) then
        tmp = 2.0d0 * (x * y)
    else if (c <= 5.8d-159) then
        tmp = t_1
    else if (c <= 7.8d-68) then
        tmp = t_3
    else if (c <= 8600.0d0) then
        tmp = t_1
    else if (c <= 8.5d+74) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (i * (a * c)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double t_3 = 2.0 * ((x * y) - (c * (a * i)));
	double tmp;
	if (c <= -4.3e+41) {
		tmp = t_2;
	} else if (c <= -3.4e-221) {
		tmp = t_1;
	} else if (c <= 9e-308) {
		tmp = 2.0 * (x * y);
	} else if (c <= 5.8e-159) {
		tmp = t_1;
	} else if (c <= 7.8e-68) {
		tmp = t_3;
	} else if (c <= 8600.0) {
		tmp = t_1;
	} else if (c <= 8.5e+74) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (i * (a * c)))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	t_3 = 2.0 * ((x * y) - (c * (a * i)))
	tmp = 0
	if c <= -4.3e+41:
		tmp = t_2
	elif c <= -3.4e-221:
		tmp = t_1
	elif c <= 9e-308:
		tmp = 2.0 * (x * y)
	elif c <= 5.8e-159:
		tmp = t_1
	elif c <= 7.8e-68:
		tmp = t_3
	elif c <= 8600.0:
		tmp = t_1
	elif c <= 8.5e+74:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))))
	tmp = 0.0
	if (c <= -4.3e+41)
		tmp = t_2;
	elseif (c <= -3.4e-221)
		tmp = t_1;
	elseif (c <= 9e-308)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (c <= 5.8e-159)
		tmp = t_1;
	elseif (c <= 7.8e-68)
		tmp = t_3;
	elseif (c <= 8600.0)
		tmp = t_1;
	elseif (c <= 8.5e+74)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (i * (a * c)));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	t_3 = 2.0 * ((x * y) - (c * (a * i)));
	tmp = 0.0;
	if (c <= -4.3e+41)
		tmp = t_2;
	elseif (c <= -3.4e-221)
		tmp = t_1;
	elseif (c <= 9e-308)
		tmp = 2.0 * (x * y);
	elseif (c <= 5.8e-159)
		tmp = t_1;
	elseif (c <= 7.8e-68)
		tmp = t_3;
	elseif (c <= 8600.0)
		tmp = t_1;
	elseif (c <= 8.5e+74)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.3e+41], t$95$2, If[LessEqual[c, -3.4e-221], t$95$1, If[LessEqual[c, 9e-308], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e-159], t$95$1, If[LessEqual[c, 7.8e-68], t$95$3, If[LessEqual[c, 8600.0], t$95$1, If[LessEqual[c, 8.5e+74], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.30000000000000024e41 or 8.50000000000000028e74 < c

   1. Initial program 83.4%

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

   2. Taylor expanded in i around inf 80.4%

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

   3. Taylor expanded in i around 0 80.4%

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

   if -4.30000000000000024e41 < c < -3.4000000000000001e-221 or 9.00000000000000017e-308 < c < 5.79999999999999981e-159 or 7.80000000000000064e-68 < c < 8600

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 71.7%

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

   3. Taylor expanded in c around 0 64.0%

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

      1. neg-mul-1 64.0%

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

      2. sub-neg 64.0%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -3.4000000000000001e-221 < c < 9.00000000000000017e-308

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.2%

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

   if 5.79999999999999981e-159 < c < 7.80000000000000064e-68 or 8600 < c < 8.50000000000000028e74

   1. Initial program 97.6%

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

   2. Taylor expanded in b around 0 97.7%

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

   3. Taylor expanded in t around 0 82.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{+41}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-308}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-159}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 8600:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{if}\;c \leq -1.46 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-306}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* i (* a c)))))
        (t_2 (* 2.0 (- (* x y) (* c (* a i))))))
   (if (<= c -1.46e-8)
     (* 2.0 (- (* z t) (* c (* c (* b i)))))
     (if (<= c -2.05e-227)
       t_1
       (if (<= c 1.75e-306)
         (* 2.0 (* x y))
         (if (<= c 6.6e-159)
           t_1
           (if (<= c 1.8e-67)
             t_2
             (if (<= c 500000000000.0)
               t_1
               (if (<= c 7.5e+75)
                 t_2
                 (* -2.0 (* c (* (+ a (* b c)) i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (i * (a * c)));
	double t_2 = 2.0 * ((x * y) - (c * (a * i)));
	double tmp;
	if (c <= -1.46e-8) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -2.05e-227) {
		tmp = t_1;
	} else if (c <= 1.75e-306) {
		tmp = 2.0 * (x * y);
	} else if (c <= 6.6e-159) {
		tmp = t_1;
	} else if (c <= 1.8e-67) {
		tmp = t_2;
	} else if (c <= 500000000000.0) {
		tmp = t_1;
	} else if (c <= 7.5e+75) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (i * (a * c)))
    t_2 = 2.0d0 * ((x * y) - (c * (a * i)))
    if (c <= (-1.46d-8)) then
        tmp = 2.0d0 * ((z * t) - (c * (c * (b * i))))
    else if (c <= (-2.05d-227)) then
        tmp = t_1
    else if (c <= 1.75d-306) then
        tmp = 2.0d0 * (x * y)
    else if (c <= 6.6d-159) then
        tmp = t_1
    else if (c <= 1.8d-67) then
        tmp = t_2
    else if (c <= 500000000000.0d0) then
        tmp = t_1
    else if (c <= 7.5d+75) then
        tmp = t_2
    else
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (i * (a * c)));
	double t_2 = 2.0 * ((x * y) - (c * (a * i)));
	double tmp;
	if (c <= -1.46e-8) {
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	} else if (c <= -2.05e-227) {
		tmp = t_1;
	} else if (c <= 1.75e-306) {
		tmp = 2.0 * (x * y);
	} else if (c <= 6.6e-159) {
		tmp = t_1;
	} else if (c <= 1.8e-67) {
		tmp = t_2;
	} else if (c <= 500000000000.0) {
		tmp = t_1;
	} else if (c <= 7.5e+75) {
		tmp = t_2;
	} else {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (i * (a * c)))
	t_2 = 2.0 * ((x * y) - (c * (a * i)))
	tmp = 0
	if c <= -1.46e-8:
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))))
	elif c <= -2.05e-227:
		tmp = t_1
	elif c <= 1.75e-306:
		tmp = 2.0 * (x * y)
	elif c <= 6.6e-159:
		tmp = t_1
	elif c <= 1.8e-67:
		tmp = t_2
	elif c <= 500000000000.0:
		tmp = t_1
	elif c <= 7.5e+75:
		tmp = t_2
	else:
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(a * i))))
	tmp = 0.0
	if (c <= -1.46e-8)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(c * Float64(b * i)))));
	elseif (c <= -2.05e-227)
		tmp = t_1;
	elseif (c <= 1.75e-306)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (c <= 6.6e-159)
		tmp = t_1;
	elseif (c <= 1.8e-67)
		tmp = t_2;
	elseif (c <= 500000000000.0)
		tmp = t_1;
	elseif (c <= 7.5e+75)
		tmp = t_2;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (i * (a * c)));
	t_2 = 2.0 * ((x * y) - (c * (a * i)));
	tmp = 0.0;
	if (c <= -1.46e-8)
		tmp = 2.0 * ((z * t) - (c * (c * (b * i))));
	elseif (c <= -2.05e-227)
		tmp = t_1;
	elseif (c <= 1.75e-306)
		tmp = 2.0 * (x * y);
	elseif (c <= 6.6e-159)
		tmp = t_1;
	elseif (c <= 1.8e-67)
		tmp = t_2;
	elseif (c <= 500000000000.0)
		tmp = t_1;
	elseif (c <= 7.5e+75)
		tmp = t_2;
	else
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.46e-8], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.05e-227], t$95$1, If[LessEqual[c, 1.75e-306], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e-159], t$95$1, If[LessEqual[c, 1.8e-67], t$95$2, If[LessEqual[c, 500000000000.0], t$95$1, If[LessEqual[c, 7.5e+75], t$95$2, N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.46e-8

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 88.3%

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

   3. Taylor expanded in c around inf 81.3%

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

   if -1.46e-8 < c < -2.05000000000000005e-227 or 1.75000000000000009e-306 < c < 6.6000000000000003e-159 or 1.8e-67 < c < 5e11

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 66.4%

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

   3. Taylor expanded in c around 0 62.9%

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

      1. neg-mul-1 62.9%

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

      2. sub-neg 62.9%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -2.05000000000000005e-227 < c < 1.75000000000000009e-306

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.2%

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

   if 6.6000000000000003e-159 < c < 1.8e-67 or 5e11 < c < 7.4999999999999995e75

   1. Initial program 97.6%

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

   2. Taylor expanded in b around 0 97.7%

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

   3. Taylor expanded in t around 0 82.9%

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

   if 7.4999999999999995e75 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in i around inf 86.1%

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

   3. Taylor expanded in i around 0 86.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.46 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.05 \cdot 10^{-227}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-306}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-159}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 500000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 47.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -6 \cdot 10^{+15}:\\ \;\;\;\;\left(i \cdot \left(c \cdot c\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(c \cdot \left(-b\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= c -6e+15)
     (* (* i (* c c)) (* b -2.0))
     (if (<= c -1.6e-224)
       t_1
       (if (<= c 1.45e-304)
         t_2
         (if (<= c 2e-197)
           t_1
           (if (<= c 1.05e-68)
             t_2
             (if (<= c 2.1e+15)
               t_1
               (if (<= c 7.2e+75) t_2 (* 2.0 (* i (* c (* c (- b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -6e+15) {
		tmp = (i * (c * c)) * (b * -2.0);
	} else if (c <= -1.6e-224) {
		tmp = t_1;
	} else if (c <= 1.45e-304) {
		tmp = t_2;
	} else if (c <= 2e-197) {
		tmp = t_1;
	} else if (c <= 1.05e-68) {
		tmp = t_2;
	} else if (c <= 2.1e+15) {
		tmp = t_1;
	} else if (c <= 7.2e+75) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (i * (c * (c * -b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-6d+15)) then
        tmp = (i * (c * c)) * (b * (-2.0d0))
    else if (c <= (-1.6d-224)) then
        tmp = t_1
    else if (c <= 1.45d-304) then
        tmp = t_2
    else if (c <= 2d-197) then
        tmp = t_1
    else if (c <= 1.05d-68) then
        tmp = t_2
    else if (c <= 2.1d+15) then
        tmp = t_1
    else if (c <= 7.2d+75) then
        tmp = t_2
    else
        tmp = 2.0d0 * (i * (c * (c * -b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -6e+15) {
		tmp = (i * (c * c)) * (b * -2.0);
	} else if (c <= -1.6e-224) {
		tmp = t_1;
	} else if (c <= 1.45e-304) {
		tmp = t_2;
	} else if (c <= 2e-197) {
		tmp = t_1;
	} else if (c <= 1.05e-68) {
		tmp = t_2;
	} else if (c <= 2.1e+15) {
		tmp = t_1;
	} else if (c <= 7.2e+75) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (i * (c * (c * -b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if c <= -6e+15:
		tmp = (i * (c * c)) * (b * -2.0)
	elif c <= -1.6e-224:
		tmp = t_1
	elif c <= 1.45e-304:
		tmp = t_2
	elif c <= 2e-197:
		tmp = t_1
	elif c <= 1.05e-68:
		tmp = t_2
	elif c <= 2.1e+15:
		tmp = t_1
	elif c <= 7.2e+75:
		tmp = t_2
	else:
		tmp = 2.0 * (i * (c * (c * -b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -6e+15)
		tmp = Float64(Float64(i * Float64(c * c)) * Float64(b * -2.0));
	elseif (c <= -1.6e-224)
		tmp = t_1;
	elseif (c <= 1.45e-304)
		tmp = t_2;
	elseif (c <= 2e-197)
		tmp = t_1;
	elseif (c <= 1.05e-68)
		tmp = t_2;
	elseif (c <= 2.1e+15)
		tmp = t_1;
	elseif (c <= 7.2e+75)
		tmp = t_2;
	else
		tmp = Float64(2.0 * Float64(i * Float64(c * Float64(c * Float64(-b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -6e+15)
		tmp = (i * (c * c)) * (b * -2.0);
	elseif (c <= -1.6e-224)
		tmp = t_1;
	elseif (c <= 1.45e-304)
		tmp = t_2;
	elseif (c <= 2e-197)
		tmp = t_1;
	elseif (c <= 1.05e-68)
		tmp = t_2;
	elseif (c <= 2.1e+15)
		tmp = t_1;
	elseif (c <= 7.2e+75)
		tmp = t_2;
	else
		tmp = 2.0 * (i * (c * (c * -b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6e+15], N[(N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.6e-224], t$95$1, If[LessEqual[c, 1.45e-304], t$95$2, If[LessEqual[c, 2e-197], t$95$1, If[LessEqual[c, 1.05e-68], t$95$2, If[LessEqual[c, 2.1e+15], t$95$1, If[LessEqual[c, 7.2e+75], t$95$2, N[(2.0 * N[(i * N[(c * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6e15

   1. Initial program 83.3%

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

   2. Taylor expanded in i around inf 72.9%

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

   3. Taylor expanded in c around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r* 71.5%

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

      3. associate-*l* 71.5%

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

      4. *-commutative 71.5%

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

      5. unpow2 71.5%

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

   5. Simplified 71.5%

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

   if -6e15 < c < -1.5999999999999999e-224 or 1.45e-304 < c < 2e-197 or 1.05000000000000004e-68 < c < 2.1e15

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 47.6%

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

   if -1.5999999999999999e-224 < c < 1.45e-304 or 2e-197 < c < 1.05000000000000004e-68 or 2.1e15 < c < 7.2e75

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 64.9%

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

   if 7.2e75 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in a around 0 67.9%

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

      1. unpow2 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in c around inf 62.1%

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

      1. unpow2 62.1%

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

      2. *-commutative 62.1%

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

      3. associate-*r* 64.1%

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

      4. associate-*r* 69.8%

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

      5. associate-*r* 69.8%

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

      6. neg-mul-1 69.8%

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

      7. *-commutative 69.8%

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

      8. distribute-lft-neg-in 69.8%

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

   7. Simplified 69.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+15}:\\ \;\;\;\;\left(i \cdot \left(c \cdot c\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-224}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot \left(c \cdot \left(-b\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 11500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* c (* (* b i) (* c -2.0))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -4.5e+47)
     t_2
     (if (<= c -7.8e-224)
       t_1
       (if (<= c -2.2e-307)
         t_3
         (if (<= c 3.4e-198)
           t_1
           (if (<= c 2.7e-66)
             t_3
             (if (<= c 11500000000000.0)
               t_1
               (if (<= c 1.12e+75) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = c * ((b * i) * (c * -2.0));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -4.5e+47) {
		tmp = t_2;
	} else if (c <= -7.8e-224) {
		tmp = t_1;
	} else if (c <= -2.2e-307) {
		tmp = t_3;
	} else if (c <= 3.4e-198) {
		tmp = t_1;
	} else if (c <= 2.7e-66) {
		tmp = t_3;
	} else if (c <= 11500000000000.0) {
		tmp = t_1;
	} else if (c <= 1.12e+75) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = c * ((b * i) * (c * (-2.0d0)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-4.5d+47)) then
        tmp = t_2
    else if (c <= (-7.8d-224)) then
        tmp = t_1
    else if (c <= (-2.2d-307)) then
        tmp = t_3
    else if (c <= 3.4d-198) then
        tmp = t_1
    else if (c <= 2.7d-66) then
        tmp = t_3
    else if (c <= 11500000000000.0d0) then
        tmp = t_1
    else if (c <= 1.12d+75) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = c * ((b * i) * (c * -2.0));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -4.5e+47) {
		tmp = t_2;
	} else if (c <= -7.8e-224) {
		tmp = t_1;
	} else if (c <= -2.2e-307) {
		tmp = t_3;
	} else if (c <= 3.4e-198) {
		tmp = t_1;
	} else if (c <= 2.7e-66) {
		tmp = t_3;
	} else if (c <= 11500000000000.0) {
		tmp = t_1;
	} else if (c <= 1.12e+75) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = c * ((b * i) * (c * -2.0))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -4.5e+47:
		tmp = t_2
	elif c <= -7.8e-224:
		tmp = t_1
	elif c <= -2.2e-307:
		tmp = t_3
	elif c <= 3.4e-198:
		tmp = t_1
	elif c <= 2.7e-66:
		tmp = t_3
	elif c <= 11500000000000.0:
		tmp = t_1
	elif c <= 1.12e+75:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(c * Float64(Float64(b * i) * Float64(c * -2.0)))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -4.5e+47)
		tmp = t_2;
	elseif (c <= -7.8e-224)
		tmp = t_1;
	elseif (c <= -2.2e-307)
		tmp = t_3;
	elseif (c <= 3.4e-198)
		tmp = t_1;
	elseif (c <= 2.7e-66)
		tmp = t_3;
	elseif (c <= 11500000000000.0)
		tmp = t_1;
	elseif (c <= 1.12e+75)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = c * ((b * i) * (c * -2.0));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -4.5e+47)
		tmp = t_2;
	elseif (c <= -7.8e-224)
		tmp = t_1;
	elseif (c <= -2.2e-307)
		tmp = t_3;
	elseif (c <= 3.4e-198)
		tmp = t_1;
	elseif (c <= 2.7e-66)
		tmp = t_3;
	elseif (c <= 11500000000000.0)
		tmp = t_1;
	elseif (c <= 1.12e+75)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(b * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e+47], t$95$2, If[LessEqual[c, -7.8e-224], t$95$1, If[LessEqual[c, -2.2e-307], t$95$3, If[LessEqual[c, 3.4e-198], t$95$1, If[LessEqual[c, 2.7e-66], t$95$3, If[LessEqual[c, 11500000000000.0], t$95$1, If[LessEqual[c, 1.12e+75], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.49999999999999979e47 or 1.12000000000000001e75 < c

   1. Initial program 83.1%

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

   2. Taylor expanded in i around inf 81.0%

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

   3. Taylor expanded in c around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. unpow2 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in c around 0 67.2%

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

      1. unpow2 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. associate-*l* 67.2%

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

      5. *-commutative 67.2%

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

      6. associate-*l* 70.8%

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

      7. *-commutative 70.8%

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

   8. Simplified 70.8%

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

   if -4.49999999999999979e47 < c < -7.7999999999999996e-224 or -2.2e-307 < c < 3.3999999999999998e-198 or 2.69999999999999996e-66 < c < 1.15e13

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 47.4%

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

   if -7.7999999999999996e-224 < c < -2.2e-307 or 3.3999999999999998e-198 < c < 2.69999999999999996e-66 or 1.15e13 < c < 1.12000000000000001e75

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 64.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-224}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-307}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-198}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 11500000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 7: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(-2 \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= c -2.2e+47)
     (* (* b i) (* -2.0 (* c c)))
     (if (<= c -2.4e-221)
       t_1
       (if (<= c 1e-306)
         t_2
         (if (<= c 8.5e-201)
           t_1
           (if (<= c 3.5e-67)
             t_2
             (if (<= c 3.1e+14)
               t_1
               (if (<= c 8.5e+74) t_2 (* c (* (* b i) (* 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.2e+47) {
		tmp = (b * i) * (-2.0 * (c * c));
	} else if (c <= -2.4e-221) {
		tmp = t_1;
	} else if (c <= 1e-306) {
		tmp = t_2;
	} else if (c <= 8.5e-201) {
		tmp = t_1;
	} else if (c <= 3.5e-67) {
		tmp = t_2;
	} else if (c <= 3.1e+14) {
		tmp = t_1;
	} else if (c <= 8.5e+74) {
		tmp = t_2;
	} else {
		tmp = c * ((b * i) * (c * -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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-2.2d+47)) then
        tmp = (b * i) * ((-2.0d0) * (c * c))
    else if (c <= (-2.4d-221)) then
        tmp = t_1
    else if (c <= 1d-306) then
        tmp = t_2
    else if (c <= 8.5d-201) then
        tmp = t_1
    else if (c <= 3.5d-67) then
        tmp = t_2
    else if (c <= 3.1d+14) then
        tmp = t_1
    else if (c <= 8.5d+74) then
        tmp = t_2
    else
        tmp = c * ((b * i) * (c * (-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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.2e+47) {
		tmp = (b * i) * (-2.0 * (c * c));
	} else if (c <= -2.4e-221) {
		tmp = t_1;
	} else if (c <= 1e-306) {
		tmp = t_2;
	} else if (c <= 8.5e-201) {
		tmp = t_1;
	} else if (c <= 3.5e-67) {
		tmp = t_2;
	} else if (c <= 3.1e+14) {
		tmp = t_1;
	} else if (c <= 8.5e+74) {
		tmp = t_2;
	} else {
		tmp = c * ((b * i) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if c <= -2.2e+47:
		tmp = (b * i) * (-2.0 * (c * c))
	elif c <= -2.4e-221:
		tmp = t_1
	elif c <= 1e-306:
		tmp = t_2
	elif c <= 8.5e-201:
		tmp = t_1
	elif c <= 3.5e-67:
		tmp = t_2
	elif c <= 3.1e+14:
		tmp = t_1
	elif c <= 8.5e+74:
		tmp = t_2
	else:
		tmp = c * ((b * i) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -2.2e+47)
		tmp = Float64(Float64(b * i) * Float64(-2.0 * Float64(c * c)));
	elseif (c <= -2.4e-221)
		tmp = t_1;
	elseif (c <= 1e-306)
		tmp = t_2;
	elseif (c <= 8.5e-201)
		tmp = t_1;
	elseif (c <= 3.5e-67)
		tmp = t_2;
	elseif (c <= 3.1e+14)
		tmp = t_1;
	elseif (c <= 8.5e+74)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(b * i) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -2.2e+47)
		tmp = (b * i) * (-2.0 * (c * c));
	elseif (c <= -2.4e-221)
		tmp = t_1;
	elseif (c <= 1e-306)
		tmp = t_2;
	elseif (c <= 8.5e-201)
		tmp = t_1;
	elseif (c <= 3.5e-67)
		tmp = t_2;
	elseif (c <= 3.1e+14)
		tmp = t_1;
	elseif (c <= 8.5e+74)
		tmp = t_2;
	else
		tmp = c * ((b * i) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+47], N[(N[(b * i), $MachinePrecision] * N[(-2.0 * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.4e-221], t$95$1, If[LessEqual[c, 1e-306], t$95$2, If[LessEqual[c, 8.5e-201], t$95$1, If[LessEqual[c, 3.5e-67], t$95$2, If[LessEqual[c, 3.1e+14], t$95$1, If[LessEqual[c, 8.5e+74], t$95$2, N[(c * N[(N[(b * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.1999999999999999e47

   1. Initial program 80.2%

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

   2. Taylor expanded in i around inf 76.0%

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

   3. Taylor expanded in c around inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. unpow2 72.4%

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

   5. Simplified 72.4%

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

   if -2.1999999999999999e47 < c < -2.40000000000000024e-221 or 1.00000000000000003e-306 < c < 8.5000000000000007e-201 or 3.5e-67 < c < 3.1e14

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 47.4%

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

   if -2.40000000000000024e-221 < c < 1.00000000000000003e-306 or 8.5000000000000007e-201 < c < 3.5e-67 or 3.1e14 < c < 8.50000000000000028e74

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 64.9%

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

   if 8.50000000000000028e74 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in i around inf 86.1%

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

   3. Taylor expanded in c around inf 62.1%

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

      1. associate-*r* 62.1%

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

      2. unpow2 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in c around 0 62.1%

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

      1. unpow2 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*l* 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-*l* 69.3%

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

      7. *-commutative 69.3%

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

   8. Simplified 69.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(-2 \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 10^{-306}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 8: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;\left(i \cdot \left(c \cdot c\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= c -1.75e+16)
     (* (* i (* c c)) (* b -2.0))
     (if (<= c -5.8e-226)
       t_1
       (if (<= c 1.4e-307)
         t_2
         (if (<= c 3.6e-196)
           t_1
           (if (<= c 5.1e-68)
             t_2
             (if (<= c 4.9e+14)
               t_1
               (if (<= c 8.4e+74) t_2 (* c (* (* b i) (* 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -1.75e+16) {
		tmp = (i * (c * c)) * (b * -2.0);
	} else if (c <= -5.8e-226) {
		tmp = t_1;
	} else if (c <= 1.4e-307) {
		tmp = t_2;
	} else if (c <= 3.6e-196) {
		tmp = t_1;
	} else if (c <= 5.1e-68) {
		tmp = t_2;
	} else if (c <= 4.9e+14) {
		tmp = t_1;
	} else if (c <= 8.4e+74) {
		tmp = t_2;
	} else {
		tmp = c * ((b * i) * (c * -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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-1.75d+16)) then
        tmp = (i * (c * c)) * (b * (-2.0d0))
    else if (c <= (-5.8d-226)) then
        tmp = t_1
    else if (c <= 1.4d-307) then
        tmp = t_2
    else if (c <= 3.6d-196) then
        tmp = t_1
    else if (c <= 5.1d-68) then
        tmp = t_2
    else if (c <= 4.9d+14) then
        tmp = t_1
    else if (c <= 8.4d+74) then
        tmp = t_2
    else
        tmp = c * ((b * i) * (c * (-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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -1.75e+16) {
		tmp = (i * (c * c)) * (b * -2.0);
	} else if (c <= -5.8e-226) {
		tmp = t_1;
	} else if (c <= 1.4e-307) {
		tmp = t_2;
	} else if (c <= 3.6e-196) {
		tmp = t_1;
	} else if (c <= 5.1e-68) {
		tmp = t_2;
	} else if (c <= 4.9e+14) {
		tmp = t_1;
	} else if (c <= 8.4e+74) {
		tmp = t_2;
	} else {
		tmp = c * ((b * i) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if c <= -1.75e+16:
		tmp = (i * (c * c)) * (b * -2.0)
	elif c <= -5.8e-226:
		tmp = t_1
	elif c <= 1.4e-307:
		tmp = t_2
	elif c <= 3.6e-196:
		tmp = t_1
	elif c <= 5.1e-68:
		tmp = t_2
	elif c <= 4.9e+14:
		tmp = t_1
	elif c <= 8.4e+74:
		tmp = t_2
	else:
		tmp = c * ((b * i) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -1.75e+16)
		tmp = Float64(Float64(i * Float64(c * c)) * Float64(b * -2.0));
	elseif (c <= -5.8e-226)
		tmp = t_1;
	elseif (c <= 1.4e-307)
		tmp = t_2;
	elseif (c <= 3.6e-196)
		tmp = t_1;
	elseif (c <= 5.1e-68)
		tmp = t_2;
	elseif (c <= 4.9e+14)
		tmp = t_1;
	elseif (c <= 8.4e+74)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(b * i) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -1.75e+16)
		tmp = (i * (c * c)) * (b * -2.0);
	elseif (c <= -5.8e-226)
		tmp = t_1;
	elseif (c <= 1.4e-307)
		tmp = t_2;
	elseif (c <= 3.6e-196)
		tmp = t_1;
	elseif (c <= 5.1e-68)
		tmp = t_2;
	elseif (c <= 4.9e+14)
		tmp = t_1;
	elseif (c <= 8.4e+74)
		tmp = t_2;
	else
		tmp = c * ((b * i) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.75e+16], N[(N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision] * N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.8e-226], t$95$1, If[LessEqual[c, 1.4e-307], t$95$2, If[LessEqual[c, 3.6e-196], t$95$1, If[LessEqual[c, 5.1e-68], t$95$2, If[LessEqual[c, 4.9e+14], t$95$1, If[LessEqual[c, 8.4e+74], t$95$2, N[(c * N[(N[(b * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.75e16

   1. Initial program 83.3%

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

   2. Taylor expanded in i around inf 72.9%

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

   3. Taylor expanded in c around inf 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-*r* 71.5%

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

      3. associate-*l* 71.5%

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

      4. *-commutative 71.5%

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

      5. unpow2 71.5%

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

   5. Simplified 71.5%

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

   if -1.75e16 < c < -5.80000000000000003e-226 or 1.4e-307 < c < 3.6000000000000001e-196 or 5.09999999999999966e-68 < c < 4.9e14

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 47.6%

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

   if -5.80000000000000003e-226 < c < 1.4e-307 or 3.6000000000000001e-196 < c < 5.09999999999999966e-68 or 4.9e14 < c < 8.3999999999999995e74

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 64.9%

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

   if 8.3999999999999995e74 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in i around inf 86.1%

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

   3. Taylor expanded in c around inf 62.1%

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

      1. associate-*r* 62.1%

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

      2. unpow2 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in c around 0 62.1%

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

      1. unpow2 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*l* 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-*l* 69.3%

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

      7. *-commutative 69.3%

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

   8. Simplified 69.3%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.75 \cdot 10^{+16}:\\ \;\;\;\;\left(i \cdot \left(c \cdot c\right)\right) \cdot \left(b \cdot -2\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-226}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+14}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 9: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{-157}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -8.5e-157)
     t_3
     (if (<= c -7e-226)
       t_2
       (if (<= c 5.4e-306)
         t_1
         (if (<= c 1.15e-199)
           t_2
           (if (<= c 6.4e-66) t_1 (if (<= c 2.35e-20) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -8.5e-157) {
		tmp = t_3;
	} else if (c <= -7e-226) {
		tmp = t_2;
	} else if (c <= 5.4e-306) {
		tmp = t_1;
	} else if (c <= 1.15e-199) {
		tmp = t_2;
	} else if (c <= 6.4e-66) {
		tmp = t_1;
	} else if (c <= 2.35e-20) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    t_3 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-8.5d-157)) then
        tmp = t_3
    else if (c <= (-7d-226)) then
        tmp = t_2
    else if (c <= 5.4d-306) then
        tmp = t_1
    else if (c <= 1.15d-199) then
        tmp = t_2
    else if (c <= 6.4d-66) then
        tmp = t_1
    else if (c <= 2.35d-20) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -8.5e-157) {
		tmp = t_3;
	} else if (c <= -7e-226) {
		tmp = t_2;
	} else if (c <= 5.4e-306) {
		tmp = t_1;
	} else if (c <= 1.15e-199) {
		tmp = t_2;
	} else if (c <= 6.4e-66) {
		tmp = t_1;
	} else if (c <= 2.35e-20) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	t_3 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -8.5e-157:
		tmp = t_3
	elif c <= -7e-226:
		tmp = t_2
	elif c <= 5.4e-306:
		tmp = t_1
	elif c <= 1.15e-199:
		tmp = t_2
	elif c <= 6.4e-66:
		tmp = t_1
	elif c <= 2.35e-20:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -8.5e-157)
		tmp = t_3;
	elseif (c <= -7e-226)
		tmp = t_2;
	elseif (c <= 5.4e-306)
		tmp = t_1;
	elseif (c <= 1.15e-199)
		tmp = t_2;
	elseif (c <= 6.4e-66)
		tmp = t_1;
	elseif (c <= 2.35e-20)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	t_3 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -8.5e-157)
		tmp = t_3;
	elseif (c <= -7e-226)
		tmp = t_2;
	elseif (c <= 5.4e-306)
		tmp = t_1;
	elseif (c <= 1.15e-199)
		tmp = t_2;
	elseif (c <= 6.4e-66)
		tmp = t_1;
	elseif (c <= 2.35e-20)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e-157], t$95$3, If[LessEqual[c, -7e-226], t$95$2, If[LessEqual[c, 5.4e-306], t$95$1, If[LessEqual[c, 1.15e-199], t$95$2, If[LessEqual[c, 6.4e-66], t$95$1, If[LessEqual[c, 2.35e-20], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.49999999999999976e-157 or 2.35000000000000007e-20 < c

   1. Initial program 89.3%

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

   2. Taylor expanded in i around inf 68.1%

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

   3. Taylor expanded in i around 0 68.1%

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

   if -8.49999999999999976e-157 < c < -7e-226 or 5.40000000000000018e-306 < c < 1.1500000000000001e-199 or 6.39999999999999963e-66 < c < 2.35000000000000007e-20

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 61.8%

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

   if -7e-226 < c < 5.40000000000000018e-306 or 1.1500000000000001e-199 < c < 6.39999999999999963e-66

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 67.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-157}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-226}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-306}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-199}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_3 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -6.9 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* 2.0 (- (* z t) (* i (* a c)))))
        (t_3 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -6.9e+39)
     t_3
     (if (<= c -1.9e-224)
       t_2
       (if (<= c 1.7e-307)
         t_1
         (if (<= c 7e-146)
           t_2
           (if (<= c 1.15e-76) t_1 (if (<= c 5.8e-18) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * ((z * t) - (i * (a * c)));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -6.9e+39) {
		tmp = t_3;
	} else if (c <= -1.9e-224) {
		tmp = t_2;
	} else if (c <= 1.7e-307) {
		tmp = t_1;
	} else if (c <= 7e-146) {
		tmp = t_2;
	} else if (c <= 1.15e-76) {
		tmp = t_1;
	} else if (c <= 5.8e-18) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * ((z * t) - (i * (a * c)))
    t_3 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-6.9d+39)) then
        tmp = t_3
    else if (c <= (-1.9d-224)) then
        tmp = t_2
    else if (c <= 1.7d-307) then
        tmp = t_1
    else if (c <= 7d-146) then
        tmp = t_2
    else if (c <= 1.15d-76) then
        tmp = t_1
    else if (c <= 5.8d-18) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * ((z * t) - (i * (a * c)));
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -6.9e+39) {
		tmp = t_3;
	} else if (c <= -1.9e-224) {
		tmp = t_2;
	} else if (c <= 1.7e-307) {
		tmp = t_1;
	} else if (c <= 7e-146) {
		tmp = t_2;
	} else if (c <= 1.15e-76) {
		tmp = t_1;
	} else if (c <= 5.8e-18) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * ((z * t) - (i * (a * c)))
	t_3 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -6.9e+39:
		tmp = t_3
	elif c <= -1.9e-224:
		tmp = t_2
	elif c <= 1.7e-307:
		tmp = t_1
	elif c <= 7e-146:
		tmp = t_2
	elif c <= 1.15e-76:
		tmp = t_1
	elif c <= 5.8e-18:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))))
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -6.9e+39)
		tmp = t_3;
	elseif (c <= -1.9e-224)
		tmp = t_2;
	elseif (c <= 1.7e-307)
		tmp = t_1;
	elseif (c <= 7e-146)
		tmp = t_2;
	elseif (c <= 1.15e-76)
		tmp = t_1;
	elseif (c <= 5.8e-18)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * ((z * t) - (i * (a * c)));
	t_3 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -6.9e+39)
		tmp = t_3;
	elseif (c <= -1.9e-224)
		tmp = t_2;
	elseif (c <= 1.7e-307)
		tmp = t_1;
	elseif (c <= 7e-146)
		tmp = t_2;
	elseif (c <= 1.15e-76)
		tmp = t_1;
	elseif (c <= 5.8e-18)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.9e+39], t$95$3, If[LessEqual[c, -1.9e-224], t$95$2, If[LessEqual[c, 1.7e-307], t$95$1, If[LessEqual[c, 7e-146], t$95$2, If[LessEqual[c, 1.15e-76], t$95$1, If[LessEqual[c, 5.8e-18], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.90000000000000005e39 or 5.8e-18 < c

   1. Initial program 85.5%

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

   2. Taylor expanded in i around inf 75.4%

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

   3. Taylor expanded in i around 0 75.4%

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

   if -6.90000000000000005e39 < c < -1.90000000000000001e-224 or 1.69999999999999994e-307 < c < 7.0000000000000003e-146 or 1.15000000000000003e-76 < c < 5.8e-18

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 69.9%

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

   3. Taylor expanded in c around 0 64.4%

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

      1. neg-mul-1 64.4%

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

      2. sub-neg 64.4%

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

      3. associate-*r* 71.6%

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

      4. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -1.90000000000000001e-224 < c < 1.69999999999999994e-307 or 7.0000000000000003e-146 < c < 1.15000000000000003e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.8%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.9 \cdot 10^{+39}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-224}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-307}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-146}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{-10} \lor \neg \left(c \leq 1.5 \cdot 10^{+75}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -9.2e-10) (not (<= c 1.5e+75)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* z t) (* x y)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.2e-10) || !(c <= 1.5e+75)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-9.2d-10)) .or. (.not. (c <= 1.5d+75))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -9.2e-10) || !(c <= 1.5e+75)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -9.2e-10) or not (c <= 1.5e+75):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -9.2e-10) || !(c <= 1.5e+75))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -9.2e-10) || ~((c <= 1.5e+75)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -9.2e-10], N[Not[LessEqual[c, 1.5e+75]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.20000000000000028e-10 or 1.5e75 < c

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 89.9%

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

   if -9.20000000000000028e-10 < c < 1.5e75

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 94.3%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{-10} \lor \neg \left(c \leq 1.5 \cdot 10^{+75}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 12: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+260}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-63}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.2e+260)
   (* 2.0 (* x y))
   (if (<= x 3e-63)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* 2.0 (- (* x y) (* 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 (x <= -7.2e+260) {
		tmp = 2.0 * (x * y);
	} else if (x <= 3e-63) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - (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 (x <= (-7.2d+260)) then
        tmp = 2.0d0 * (x * y)
    else if (x <= 3d-63) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) - (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 (x <= -7.2e+260) {
		tmp = 2.0 * (x * y);
	} else if (x <= 3e-63) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -7.2e+260:
		tmp = 2.0 * (x * y)
	elif x <= 3e-63:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) - (c * (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.2e+260)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (x <= 3e-63)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 (x <= -7.2e+260)
		tmp = 2.0 * (x * y);
	elseif (x <= 3e-63)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) - (c * (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.2e+260], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-63], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999995e260

   1. Initial program 90.9%

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

   2. Taylor expanded in x around inf 90.9%

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

   if -7.1999999999999995e260 < x < 2.99999999999999979e-63

   1. Initial program 92.1%

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

   2. Taylor expanded in x around 0 79.6%

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

   if 2.99999999999999979e-63 < x

   1. Initial program 94.5%

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

   2. Taylor expanded in b around 0 76.3%

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

   3. Taylor expanded in t around 0 58.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+260}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-63}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]

Alternative 13: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))))
   (if (<= c -5.6e-11)
     (* 2.0 (- t_1 (* c (* c (* b i)))))
     (if (<= c 1.3e+75)
       (* 2.0 (- t_1 (* i (* a c))))
       (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if (c <= -5.6e-11) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else if (c <= 1.3e+75) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) + (x * y)
    if (c <= (-5.6d-11)) then
        tmp = 2.0d0 * (t_1 - (c * (c * (b * i))))
    else if (c <= 1.3d+75) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if (c <= -5.6e-11) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else if (c <= 1.3e+75) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	tmp = 0
	if c <= -5.6e-11:
		tmp = 2.0 * (t_1 - (c * (c * (b * i))))
	elif c <= 1.3e+75:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (c <= -5.6e-11)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(b * i)))));
	elseif (c <= 1.3e+75)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	tmp = 0.0;
	if (c <= -5.6e-11)
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	elseif (c <= 1.3e+75)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.6e-11], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e+75], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.6e-11

   1. Initial program 85.5%

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

   2. Taylor expanded in a around 0 81.2%

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

      1. unpow2 81.2%

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

      2. associate-*r* 88.4%

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

   4. Simplified 88.4%

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

   if -5.6e-11 < c < 1.29999999999999992e75

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 94.3%

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

   if 1.29999999999999992e75 < c

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 92.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 14: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* 2.0 (* a (* c (- i)))))
        (t_3 (* 2.0 (* z t))))
   (if (<= t -3.9e+21)
     t_3
     (if (<= t 4.2e-199)
       t_1
       (if (<= t 1.9e-95)
         t_2
         (if (<= t 8.6e-47) t_1 (if (<= t 2e+39) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (a * (c * -i));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -3.9e+21) {
		tmp = t_3;
	} else if (t <= 4.2e-199) {
		tmp = t_1;
	} else if (t <= 1.9e-95) {
		tmp = t_2;
	} else if (t <= 8.6e-47) {
		tmp = t_1;
	} else if (t <= 2e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (a * (c * -i))
    t_3 = 2.0d0 * (z * t)
    if (t <= (-3.9d+21)) then
        tmp = t_3
    else if (t <= 4.2d-199) then
        tmp = t_1
    else if (t <= 1.9d-95) then
        tmp = t_2
    else if (t <= 8.6d-47) then
        tmp = t_1
    else if (t <= 2d+39) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (a * (c * -i));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -3.9e+21) {
		tmp = t_3;
	} else if (t <= 4.2e-199) {
		tmp = t_1;
	} else if (t <= 1.9e-95) {
		tmp = t_2;
	} else if (t <= 8.6e-47) {
		tmp = t_1;
	} else if (t <= 2e+39) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (a * (c * -i))
	t_3 = 2.0 * (z * t)
	tmp = 0
	if t <= -3.9e+21:
		tmp = t_3
	elif t <= 4.2e-199:
		tmp = t_1
	elif t <= 1.9e-95:
		tmp = t_2
	elif t <= 8.6e-47:
		tmp = t_1
	elif t <= 2e+39:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(a * Float64(c * Float64(-i))))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -3.9e+21)
		tmp = t_3;
	elseif (t <= 4.2e-199)
		tmp = t_1;
	elseif (t <= 1.9e-95)
		tmp = t_2;
	elseif (t <= 8.6e-47)
		tmp = t_1;
	elseif (t <= 2e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (a * (c * -i));
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -3.9e+21)
		tmp = t_3;
	elseif (t <= 4.2e-199)
		tmp = t_1;
	elseif (t <= 1.9e-95)
		tmp = t_2;
	elseif (t <= 8.6e-47)
		tmp = t_1;
	elseif (t <= 2e+39)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(a * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+21], t$95$3, If[LessEqual[t, 4.2e-199], t$95$1, If[LessEqual[t, 1.9e-95], t$95$2, If[LessEqual[t, 8.6e-47], t$95$1, If[LessEqual[t, 2e+39], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9e21 or 1.99999999999999988e39 < t

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 53.8%

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

   if -3.9e21 < t < 4.20000000000000004e-199 or 1.8999999999999999e-95 < t < 8.5999999999999995e-47

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 37.4%

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

   if 4.20000000000000004e-199 < t < 1.8999999999999999e-95 or 8.5999999999999995e-47 < t < 1.99999999999999988e39

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. associate-*r* 47.3%

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

      3. *-commutative 47.3%

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

      4. distribute-rgt-neg-in 47.3%

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

      5. *-commutative 47.3%

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

      6. distribute-rgt-neg-in 47.3%

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

   4. Simplified 47.3%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+21}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-199}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(a \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 15: 38.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := \left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3650:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* (* a i) (* c -2.0)))
        (t_3 (* 2.0 (* z t))))
   (if (<= t -1.4e+27)
     t_3
     (if (<= t 5e-198)
       t_1
       (if (<= t 1.95e-95)
         t_2
         (if (<= t 8.5e-47)
           t_1
           (if (<= t 3650.0) t_2 (if (<= t 1.7e+94) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (a * i) * (c * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.4e+27) {
		tmp = t_3;
	} else if (t <= 5e-198) {
		tmp = t_1;
	} else if (t <= 1.95e-95) {
		tmp = t_2;
	} else if (t <= 8.5e-47) {
		tmp = t_1;
	} else if (t <= 3650.0) {
		tmp = t_2;
	} else if (t <= 1.7e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = (a * i) * (c * (-2.0d0))
    t_3 = 2.0d0 * (z * t)
    if (t <= (-1.4d+27)) then
        tmp = t_3
    else if (t <= 5d-198) then
        tmp = t_1
    else if (t <= 1.95d-95) then
        tmp = t_2
    else if (t <= 8.5d-47) then
        tmp = t_1
    else if (t <= 3650.0d0) then
        tmp = t_2
    else if (t <= 1.7d+94) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = (a * i) * (c * -2.0);
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.4e+27) {
		tmp = t_3;
	} else if (t <= 5e-198) {
		tmp = t_1;
	} else if (t <= 1.95e-95) {
		tmp = t_2;
	} else if (t <= 8.5e-47) {
		tmp = t_1;
	} else if (t <= 3650.0) {
		tmp = t_2;
	} else if (t <= 1.7e+94) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = (a * i) * (c * -2.0)
	t_3 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.4e+27:
		tmp = t_3
	elif t <= 5e-198:
		tmp = t_1
	elif t <= 1.95e-95:
		tmp = t_2
	elif t <= 8.5e-47:
		tmp = t_1
	elif t <= 3650.0:
		tmp = t_2
	elif t <= 1.7e+94:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(Float64(a * i) * Float64(c * -2.0))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -1.4e+27)
		tmp = t_3;
	elseif (t <= 5e-198)
		tmp = t_1;
	elseif (t <= 1.95e-95)
		tmp = t_2;
	elseif (t <= 8.5e-47)
		tmp = t_1;
	elseif (t <= 3650.0)
		tmp = t_2;
	elseif (t <= 1.7e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = (a * i) * (c * -2.0);
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -1.4e+27)
		tmp = t_3;
	elseif (t <= 5e-198)
		tmp = t_1;
	elseif (t <= 1.95e-95)
		tmp = t_2;
	elseif (t <= 8.5e-47)
		tmp = t_1;
	elseif (t <= 3650.0)
		tmp = t_2;
	elseif (t <= 1.7e+94)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+27], t$95$3, If[LessEqual[t, 5e-198], t$95$1, If[LessEqual[t, 1.95e-95], t$95$2, If[LessEqual[t, 8.5e-47], t$95$1, If[LessEqual[t, 3650.0], t$95$2, If[LessEqual[t, 1.7e+94], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4e27 or 1.7000000000000001e94 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 55.0%

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

   if -1.4e27 < t < 4.9999999999999999e-198 or 1.95e-95 < t < 8.4999999999999999e-47 or 3650 < t < 1.7000000000000001e94

   1. Initial program 91.1%

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

   2. Taylor expanded in x around inf 37.3%

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

   if 4.9999999999999999e-198 < t < 1.95e-95 or 8.4999999999999999e-47 < t < 3650

   1. Initial program 90.1%

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

   2. Taylor expanded in a around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in c around 0 52.4%

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

      1. associate-*r* 52.4%

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

   7. Simplified 52.4%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-198}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-95}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3650:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+94}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 38.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := -2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* -2.0 (* i (* a c))))
        (t_3 (* 2.0 (* z t))))
   (if (<= t -2e+26)
     t_3
     (if (<= t 1.22e-198)
       t_1
       (if (<= t 2.75e-95)
         t_2
         (if (<= t 7.7e-47) t_1 (if (<= t 1.75e+41) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = -2.0 * (i * (a * c));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -2e+26) {
		tmp = t_3;
	} else if (t <= 1.22e-198) {
		tmp = t_1;
	} else if (t <= 2.75e-95) {
		tmp = t_2;
	} else if (t <= 7.7e-47) {
		tmp = t_1;
	} else if (t <= 1.75e+41) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = (-2.0d0) * (i * (a * c))
    t_3 = 2.0d0 * (z * t)
    if (t <= (-2d+26)) then
        tmp = t_3
    else if (t <= 1.22d-198) then
        tmp = t_1
    else if (t <= 2.75d-95) then
        tmp = t_2
    else if (t <= 7.7d-47) then
        tmp = t_1
    else if (t <= 1.75d+41) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = -2.0 * (i * (a * c));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (t <= -2e+26) {
		tmp = t_3;
	} else if (t <= 1.22e-198) {
		tmp = t_1;
	} else if (t <= 2.75e-95) {
		tmp = t_2;
	} else if (t <= 7.7e-47) {
		tmp = t_1;
	} else if (t <= 1.75e+41) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = -2.0 * (i * (a * c))
	t_3 = 2.0 * (z * t)
	tmp = 0
	if t <= -2e+26:
		tmp = t_3
	elif t <= 1.22e-198:
		tmp = t_1
	elif t <= 2.75e-95:
		tmp = t_2
	elif t <= 7.7e-47:
		tmp = t_1
	elif t <= 1.75e+41:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(-2.0 * Float64(i * Float64(a * c)))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (t <= -2e+26)
		tmp = t_3;
	elseif (t <= 1.22e-198)
		tmp = t_1;
	elseif (t <= 2.75e-95)
		tmp = t_2;
	elseif (t <= 7.7e-47)
		tmp = t_1;
	elseif (t <= 1.75e+41)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = -2.0 * (i * (a * c));
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (t <= -2e+26)
		tmp = t_3;
	elseif (t <= 1.22e-198)
		tmp = t_1;
	elseif (t <= 2.75e-95)
		tmp = t_2;
	elseif (t <= 7.7e-47)
		tmp = t_1;
	elseif (t <= 1.75e+41)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+26], t$95$3, If[LessEqual[t, 1.22e-198], t$95$1, If[LessEqual[t, 2.75e-95], t$95$2, If[LessEqual[t, 7.7e-47], t$95$1, If[LessEqual[t, 1.75e+41], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000001e26 or 1.75e41 < t

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 53.8%

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

   if -2.0000000000000001e26 < t < 1.22e-198 or 2.75000000000000001e-95 < t < 7.6999999999999999e-47

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 37.4%

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

   if 1.22e-198 < t < 2.75000000000000001e-95 or 7.6999999999999999e-47 < t < 1.75e41

   1. Initial program 89.9%

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

   2. Taylor expanded in a around inf 45.3%

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

      1. associate-*r* 45.3%

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

      2. neg-mul-1 45.3%

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

   4. Simplified 45.3%

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

   5. Taylor expanded in c around 0 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*r* 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-*l* 41.5%

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

   7. Simplified 41.5%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+26}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-198}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-95}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+41}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 17: 39.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+25} \lor \neg \left(t \leq 5.4 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -4.8e+25) (not (<= t 5.4e+93)))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -4.8e+25) || !(t <= 5.4e+93)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((t <= (-4.8d+25)) .or. (.not. (t <= 5.4d+93))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -4.8e+25) || !(t <= 5.4e+93)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -4.8e+25) or not (t <= 5.4e+93):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -4.8e+25) || !(t <= 5.4e+93))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -4.8e+25) || ~((t <= 5.4e+93)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -4.8e+25], N[Not[LessEqual[t, 5.4e+93]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999992e25 or 5.3999999999999999e93 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 55.0%

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

   if -4.79999999999999992e25 < t < 5.3999999999999999e93

   1. Initial program 90.9%

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

   2. Taylor expanded in x around inf 34.9%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+25} \lor \neg \left(t \leq 5.4 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 18: 29.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

2. Taylor expanded in z around inf 30.2%

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

3. Final simplification 30.2%

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

Developer target: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(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))))