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

Percentage Accurate: 90.3% → 97.1%

Time: 16.7s

Alternatives: 15

Speedup: 0.5×

• 48.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.3% 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: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. associate--l+ 89.0%

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

   2. *-commutative 89.0%

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

   3. associate--l+ 89.0%

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

   4. associate--l+ 89.0%

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

   5. *-commutative 89.0%

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

   6. associate--l+ 89.0%

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

   7. fma-def 89.0%

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

   8. associate-*l* 93.4%

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

3. Simplified 93.4%

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

   1. fma-def 93.4%

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

   2. +-commutative 93.4%

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

5. Applied egg-rr 93.4%

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

   1. associate--l+ 93.4%

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

   2. fma-def 95.4%

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

   3. fma-neg 97.7%

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

   4. distribute-rgt-neg-in 97.7%

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

   5. +-commutative 97.7%

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

   6. fma-def 97.7%

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

7. Applied egg-rr 97.7%

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

8. Final simplification 97.7%

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

Alternative 2: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(i \cdot t_1\right)\\ t_3 := i \cdot \left(c \cdot t_1\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;-2 \cdot t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* i t_1))) (t_3 (* i (* c t_1))))
   (if (<= t_3 (- INFINITY))
     (* -2.0 t_2)
     (if (<= t_3 5e+297)
       (* 2.0 (- (+ (* x y) (* z t)) 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 * (i * t_1);
	double t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 5e+297) {
		tmp = 2.0 * (((x * y) + (z * t)) - 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 * (i * t_1);
	double t_3 = i * (c * t_1);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 5e+297) {
		tmp = 2.0 * (((x * y) + (z * t)) - 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 * (i * t_1)
	t_3 = i * (c * t_1)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = -2.0 * t_2
	elif t_3 <= 5e+297:
		tmp = 2.0 * (((x * y) + (z * t)) - 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(i * t_1))
	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 <= 5e+297)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - 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 * (i * t_1);
	t_3 = i * (c * t_1);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = -2.0 * t_2;
	elseif (t_3 <= 5e+297)
		tmp = 2.0 * (((x * y) + (z * t)) - 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[(i * t$95$1), $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, 5e+297], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $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 66.4%

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

   2. Taylor expanded in z around 0 87.5%

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

   3. Taylor expanded in x around 0 91.4%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e297

   1. Initial program 98.6%

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

   if 4.9999999999999998e297 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.7%

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

   2. Taylor expanded in x around 0 94.6%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 5 \cdot 10^{+297}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 3: 96.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.3%

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

      1. associate--l+ 93.3%

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

      2. *-commutative 93.3%

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

      3. associate--l+ 93.3%

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

      4. associate--l+ 93.3%

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

      5. *-commutative 93.3%

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

      6. associate--l+ 93.3%

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

      7. fma-def 93.3%

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

      8. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

      1. fma-def 97.6%

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

      2. +-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around 0 50.0%

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

   3. Taylor expanded in x around 0 75.9%

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

4. Final simplification 96.6%

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

Alternative 4: 70.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.65 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* -2.0 (* c (* i (+ a (* b c)))))))
   (if (<= c -2.5e+185)
     t_2
     (if (<= c -3.1e+121)
       (* 2.0 (- (* x y) (* c (* b (* c i)))))
       (if (<= c -1.65e+68)
         t_2
         (if (<= c 3.65e-286)
           t_1
           (if (<= c 6.2e-118)
             (* 2.0 (- (* z t) (* a (* c i))))
             (if (<= c 1.45e-68) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (i * (a + (b * c))));
	double tmp;
	if (c <= -2.5e+185) {
		tmp = t_2;
	} else if (c <= -3.1e+121) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else if (c <= -1.65e+68) {
		tmp = t_2;
	} else if (c <= 3.65e-286) {
		tmp = t_1;
	} else if (c <= 6.2e-118) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.45e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * (i * (a + (b * c))))
    if (c <= (-2.5d+185)) then
        tmp = t_2
    else if (c <= (-3.1d+121)) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    else if (c <= (-1.65d+68)) then
        tmp = t_2
    else if (c <= 3.65d-286) then
        tmp = t_1
    else if (c <= 6.2d-118) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= 1.45d-68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (i * (a + (b * c))));
	double tmp;
	if (c <= -2.5e+185) {
		tmp = t_2;
	} else if (c <= -3.1e+121) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else if (c <= -1.65e+68) {
		tmp = t_2;
	} else if (c <= 3.65e-286) {
		tmp = t_1;
	} else if (c <= 6.2e-118) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.45e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * (i * (a + (b * c))))
	tmp = 0
	if c <= -2.5e+185:
		tmp = t_2
	elif c <= -3.1e+121:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	elif c <= -1.65e+68:
		tmp = t_2
	elif c <= 3.65e-286:
		tmp = t_1
	elif c <= 6.2e-118:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= 1.45e-68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(i * Float64(a + Float64(b * c)))))
	tmp = 0.0
	if (c <= -2.5e+185)
		tmp = t_2;
	elseif (c <= -3.1e+121)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= -1.65e+68)
		tmp = t_2;
	elseif (c <= 3.65e-286)
		tmp = t_1;
	elseif (c <= 6.2e-118)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= 1.45e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * (i * (a + (b * c))));
	tmp = 0.0;
	if (c <= -2.5e+185)
		tmp = t_2;
	elseif (c <= -3.1e+121)
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	elseif (c <= -1.65e+68)
		tmp = t_2;
	elseif (c <= 3.65e-286)
		tmp = t_1;
	elseif (c <= 6.2e-118)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= 1.45e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+185], t$95$2, If[LessEqual[c, -3.1e+121], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.65e+68], t$95$2, If[LessEqual[c, 3.65e-286], t$95$1, If[LessEqual[c, 6.2e-118], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-68], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.49999999999999995e185 or -3.10000000000000008e121 < c < -1.65e68 or 1.45e-68 < c

   1. Initial program 81.4%

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

   2. Taylor expanded in z around 0 85.0%

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

   3. Taylor expanded in x around 0 78.5%

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

   if -2.49999999999999995e185 < c < -3.10000000000000008e121

   1. Initial program 71.1%

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

   2. Taylor expanded in z around 0 73.7%

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

   3. Taylor expanded in a around 0 83.3%

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

   if -1.65e68 < c < 3.64999999999999979e-286 or 6.2000000000000002e-118 < c < 1.45e-68

   1. Initial program 98.9%

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

   2. Taylor expanded in c around 0 78.9%

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

   if 3.64999999999999979e-286 < c < 6.2000000000000002e-118

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 96.9%

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

      1. *-commutative 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in x around 0 77.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+185}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+68}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.65 \cdot 10^{-286}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 5: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-106} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (+ a (* b c))))))
   (if (or (<= (* x y) -4e-106) (not (<= (* x y) 2e+16)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * (a + (b * c)));
	double tmp;
	if (((x * y) <= -4e-106) || !((x * y) <= 2e+16)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * (a + (b * c)))
    if (((x * y) <= (-4d-106)) .or. (.not. ((x * y) <= 2d+16))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * (a + (b * c)));
	double tmp;
	if (((x * y) <= -4e-106) || !((x * y) <= 2e+16)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * (a + (b * c)))
	tmp = 0
	if ((x * y) <= -4e-106) or not ((x * y) <= 2e+16):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(a + Float64(b * c))))
	tmp = 0.0
	if ((Float64(x * y) <= -4e-106) || !(Float64(x * y) <= 2e+16))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * (a + (b * c)));
	tmp = 0.0;
	if (((x * y) <= -4e-106) || ~(((x * y) <= 2e+16)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e-106], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+16]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.99999999999999976e-106 or 2e16 < (*.f64 x y)

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 76.5%

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

   if -3.99999999999999976e-106 < (*.f64 x y) < 2e16

   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 0 85.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-106} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 6: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := -2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.65 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-116}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* -2.0 (* c (* i (+ a (* b c)))))))
   (if (<= c -1.5e+68)
     t_2
     (if (<= c 3.65e-286)
       t_1
       (if (<= c 2.3e-116)
         (* 2.0 (- (* z t) (* a (* c i))))
         (if (<= c 1.25e-68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (i * (a + (b * c))));
	double tmp;
	if (c <= -1.5e+68) {
		tmp = t_2;
	} else if (c <= 3.65e-286) {
		tmp = t_1;
	} else if (c <= 2.3e-116) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.25e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = (-2.0d0) * (c * (i * (a + (b * c))))
    if (c <= (-1.5d+68)) then
        tmp = t_2
    else if (c <= 3.65d-286) then
        tmp = t_1
    else if (c <= 2.3d-116) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= 1.25d-68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = -2.0 * (c * (i * (a + (b * c))));
	double tmp;
	if (c <= -1.5e+68) {
		tmp = t_2;
	} else if (c <= 3.65e-286) {
		tmp = t_1;
	} else if (c <= 2.3e-116) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.25e-68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = -2.0 * (c * (i * (a + (b * c))))
	tmp = 0
	if c <= -1.5e+68:
		tmp = t_2
	elif c <= 3.65e-286:
		tmp = t_1
	elif c <= 2.3e-116:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= 1.25e-68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(-2.0 * Float64(c * Float64(i * Float64(a + Float64(b * c)))))
	tmp = 0.0
	if (c <= -1.5e+68)
		tmp = t_2;
	elseif (c <= 3.65e-286)
		tmp = t_1;
	elseif (c <= 2.3e-116)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= 1.25e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = -2.0 * (c * (i * (a + (b * c))));
	tmp = 0.0;
	if (c <= -1.5e+68)
		tmp = t_2;
	elseif (c <= 3.65e-286)
		tmp = t_1;
	elseif (c <= 2.3e-116)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= 1.25e-68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+68], t$95$2, If[LessEqual[c, 3.65e-286], t$95$1, If[LessEqual[c, 2.3e-116], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5000000000000001e68 or 1.24999999999999993e-68 < c

   1. Initial program 79.9%

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

   2. Taylor expanded in z around 0 83.4%

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

   3. Taylor expanded in x around 0 76.0%

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

   if -1.5000000000000001e68 < c < 3.64999999999999979e-286 or 2.30000000000000002e-116 < c < 1.24999999999999993e-68

   1. Initial program 98.9%

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

   2. Taylor expanded in c around 0 78.9%

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

   if 3.64999999999999979e-286 < c < 2.30000000000000002e-116

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 96.9%

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

      1. *-commutative 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in x around 0 77.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.65 \cdot 10^{-286}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-116}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 7: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.08e+23)
   (* 2.0 (+ (* x y) (* z t)))
   (if (<= y 4.2e+139)
     (* 2.0 (- (* z t) (* c (* i (+ a (* b c))))))
     (* 2.0 (- (* x y) (* c (* c (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.08e+23) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (y <= 4.2e+139) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * ((x * y) - (c * (c * (b * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.08d+23)) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (y <= 4.2d+139) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (b * c)))))
    else
        tmp = 2.0d0 * ((x * y) - (c * (c * (b * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.08e+23) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (y <= 4.2e+139) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	} else {
		tmp = 2.0 * ((x * y) - (c * (c * (b * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.08e+23:
		tmp = 2.0 * ((x * y) + (z * t))
	elif y <= 4.2e+139:
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))))
	else:
		tmp = 2.0 * ((x * y) - (c * (c * (b * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.08e+23)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (y <= 4.2e+139)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(b * c))))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(c * Float64(b * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.08e+23)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (y <= 4.2e+139)
		tmp = 2.0 * ((z * t) - (c * (i * (a + (b * c)))));
	else
		tmp = 2.0 * ((x * y) - (c * (c * (b * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.08e+23], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+139], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0800000000000001e23

   1. Initial program 86.4%

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

   2. Taylor expanded in c around 0 59.3%

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

   if -1.0800000000000001e23 < y < 4.1999999999999997e139

   1. Initial program 89.0%

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

   2. Taylor expanded in x around 0 79.6%

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

   if 4.1999999999999997e139 < y

   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 z around 0 79.2%

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

   3. Taylor expanded in a around 0 71.6%

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

      1. expm1-log1p-u 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)\right)}\right) \]

      2. expm1-udef 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \left(c \cdot i\right)\right)} - 1\right)}\right) \]

      3. *-commutative 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(c \cdot i\right) \cdot b}\right)} - 1\right)\right) \]

      4. *-commutative 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(i \cdot c\right)} \cdot b\right)} - 1\right)\right) \]

      5. associate-*r* 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{i \cdot \left(c \cdot b\right)}\right)} - 1\right)\right) \]

      6. *-commutative 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(e^{\mathsf{log1p}\left(i \cdot \color{blue}{\left(b \cdot c\right)}\right)} - 1\right)\right) \]

      7. associate-*r* 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(i \cdot b\right) \cdot c}\right)} - 1\right)\right) \]

   5. Applied egg-rr 50.3%

      \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(i \cdot b\right) \cdot c\right)} - 1\right)}\right) \]
   6. Step-by-step derivation

      1. expm1-def 50.3%

         \[\leadsto 2 \cdot \left(x \cdot y - c \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(i \cdot b\right) \cdot c\right)\right)}\right) \]

      2. expm1-log1p 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+139}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 8: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* i (+ a (* b c))))))
   (if (<= c -1.12e-9)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 1.3e-51)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a))))
       (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * (a + (b * c)));
	double tmp;
	if (c <= -1.12e-9) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 1.3e-51) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * (a + (b * c)))
    if (c <= (-1.12d-9)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 1.3d-51) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * (i * (a + (b * c)));
	double tmp;
	if (c <= -1.12e-9) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 1.3e-51) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * (i * (a + (b * c)))
	tmp = 0
	if c <= -1.12e-9:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 1.3e-51:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(i * Float64(a + Float64(b * c))))
	tmp = 0.0
	if (c <= -1.12e-9)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 1.3e-51)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * (i * (a + (b * c)));
	tmp = 0.0;
	if (c <= -1.12e-9)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 1.3e-51)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.12e-9], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-51], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.12000000000000006e-9

   1. Initial program 76.7%

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

   2. Taylor expanded in x around 0 83.4%

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

   if -1.12000000000000006e-9 < c < 1.3e-51

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 96.1%

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

      1. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   if 1.3e-51 < c

   1. Initial program 85.8%

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

   2. Taylor expanded in z around 0 86.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 9: 35.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;i \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-162}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+273}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot \left(2 \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* -2.0 (* a (* c i)))))
   (if (<= i -1.8e-107)
     t_2
     (if (<= i 5e-273)
       t_1
       (if (<= i 3e-162)
         (* 2.0 (* x y))
         (if (<= i 6.6e+49)
           t_1
           (if (<= i 3.8e+273) t_2 (* i (* a (* 2.0 c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -1.8e-107) {
		tmp = t_2;
	} else if (i <= 5e-273) {
		tmp = t_1;
	} else if (i <= 3e-162) {
		tmp = 2.0 * (x * y);
	} else if (i <= 6.6e+49) {
		tmp = t_1;
	} else if (i <= 3.8e+273) {
		tmp = t_2;
	} else {
		tmp = i * (a * (2.0 * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    if (i <= (-1.8d-107)) then
        tmp = t_2
    else if (i <= 5d-273) then
        tmp = t_1
    else if (i <= 3d-162) then
        tmp = 2.0d0 * (x * y)
    else if (i <= 6.6d+49) then
        tmp = t_1
    else if (i <= 3.8d+273) then
        tmp = t_2
    else
        tmp = i * (a * (2.0d0 * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -1.8e-107) {
		tmp = t_2;
	} else if (i <= 5e-273) {
		tmp = t_1;
	} else if (i <= 3e-162) {
		tmp = 2.0 * (x * y);
	} else if (i <= 6.6e+49) {
		tmp = t_1;
	} else if (i <= 3.8e+273) {
		tmp = t_2;
	} else {
		tmp = i * (a * (2.0 * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	tmp = 0
	if i <= -1.8e-107:
		tmp = t_2
	elif i <= 5e-273:
		tmp = t_1
	elif i <= 3e-162:
		tmp = 2.0 * (x * y)
	elif i <= 6.6e+49:
		tmp = t_1
	elif i <= 3.8e+273:
		tmp = t_2
	else:
		tmp = i * (a * (2.0 * c))
	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(a * Float64(c * i)))
	tmp = 0.0
	if (i <= -1.8e-107)
		tmp = t_2;
	elseif (i <= 5e-273)
		tmp = t_1;
	elseif (i <= 3e-162)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (i <= 6.6e+49)
		tmp = t_1;
	elseif (i <= 3.8e+273)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(a * Float64(2.0 * c)));
	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 * (a * (c * i));
	tmp = 0.0;
	if (i <= -1.8e-107)
		tmp = t_2;
	elseif (i <= 5e-273)
		tmp = t_1;
	elseif (i <= 3e-162)
		tmp = 2.0 * (x * y);
	elseif (i <= 6.6e+49)
		tmp = t_1;
	elseif (i <= 3.8e+273)
		tmp = t_2;
	else
		tmp = i * (a * (2.0 * c));
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.8e-107], t$95$2, If[LessEqual[i, 5e-273], t$95$1, If[LessEqual[i, 3e-162], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.6e+49], t$95$1, If[LessEqual[i, 3.8e+273], t$95$2, N[(i * N[(a * N[(2.0 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.79999999999999988e-107 or 6.5999999999999997e49 < i < 3.8e273

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 76.1%

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

   3. Taylor expanded in a around inf 44.5%

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

   if -1.79999999999999988e-107 < i < 4.99999999999999965e-273 or 2.99999999999999999e-162 < i < 6.5999999999999997e49

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 44.8%

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

   if 4.99999999999999965e-273 < i < 2.99999999999999999e-162

   1. Initial program 80.0%

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

   2. Taylor expanded in x around inf 57.9%

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

   if 3.8e273 < i

   1. Initial program 87.5%

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

      1. associate--l+ 87.5%

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

      2. *-commutative 87.5%

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

      3. associate--l+ 87.5%

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

      4. associate--l+ 87.5%

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

      5. *-commutative 87.5%

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

      6. associate--l+ 87.5%

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

      7. fma-def 87.5%

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

      8. associate-*l* 75.8%

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

   3. Simplified 75.8%

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

      1. fma-def 75.8%

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

      2. +-commutative 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in a around inf 0.9%

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

      1. mul-1-neg 0.9%

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

      2. associate-*r* 1.5%

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

      3. distribute-rgt-neg-out 1.5%

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

      4. *-commutative 1.5%

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

      5. *-commutative 1.5%

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

   8. Simplified 1.5%

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

      1. expm1-log1p-u 1.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(-i\right) \cdot \left(c \cdot a\right)\right)\right)\right)} \]

      2. expm1-udef 1.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(-i\right) \cdot \left(c \cdot a\right)\right)\right)} - 1} \]

      3. *-commutative 1.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(-i\right) \cdot \left(c \cdot a\right)\right) \cdot 2}\right)} - 1 \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\left(\sqrt{-i} \cdot \sqrt{-i}\right)} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      5. sqrt-unprod 37.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\sqrt{\left(-i\right) \cdot \left(-i\right)}} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      6. sqr-neg 37.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\sqrt{\color{blue}{i \cdot i}} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      7. sqrt-unprod 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      8. add-sqr-sqrt 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{i} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      9. *-commutative 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(i \cdot \color{blue}{\left(a \cdot c\right)}\right) \cdot 2\right)} - 1 \]

      10. associate-*r* 26.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot a\right) \cdot c\right)} \cdot 2\right)} - 1 \]

   10. Applied egg-rr 26.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot a\right) \cdot c\right) \cdot 2\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 26.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot a\right) \cdot c\right) \cdot 2\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. associate-*l* 51.8%

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

       4. associate-*l* 51.7%

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

   12. Simplified 51.7%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-162}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+273}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot \left(2 \cdot c\right)\right)\\ \end{array} \]

Alternative 10: 35.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-164}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+273}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(2 \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* -2.0 (* a (* c i)))))
   (if (<= i -4.8e-119)
     t_2
     (if (<= i 1.9e-276)
       t_1
       (if (<= i 1.12e-164)
         (* 2.0 (* x y))
         (if (<= i 1.5e+49)
           t_1
           (if (<= i 3.8e+273) t_2 (* (* a i) (* 2.0 c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -4.8e-119) {
		tmp = t_2;
	} else if (i <= 1.9e-276) {
		tmp = t_1;
	} else if (i <= 1.12e-164) {
		tmp = 2.0 * (x * y);
	} else if (i <= 1.5e+49) {
		tmp = t_1;
	} else if (i <= 3.8e+273) {
		tmp = t_2;
	} else {
		tmp = (a * i) * (2.0 * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    if (i <= (-4.8d-119)) then
        tmp = t_2
    else if (i <= 1.9d-276) then
        tmp = t_1
    else if (i <= 1.12d-164) then
        tmp = 2.0d0 * (x * y)
    else if (i <= 1.5d+49) then
        tmp = t_1
    else if (i <= 3.8d+273) then
        tmp = t_2
    else
        tmp = (a * i) * (2.0d0 * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -4.8e-119) {
		tmp = t_2;
	} else if (i <= 1.9e-276) {
		tmp = t_1;
	} else if (i <= 1.12e-164) {
		tmp = 2.0 * (x * y);
	} else if (i <= 1.5e+49) {
		tmp = t_1;
	} else if (i <= 3.8e+273) {
		tmp = t_2;
	} else {
		tmp = (a * i) * (2.0 * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	tmp = 0
	if i <= -4.8e-119:
		tmp = t_2
	elif i <= 1.9e-276:
		tmp = t_1
	elif i <= 1.12e-164:
		tmp = 2.0 * (x * y)
	elif i <= 1.5e+49:
		tmp = t_1
	elif i <= 3.8e+273:
		tmp = t_2
	else:
		tmp = (a * i) * (2.0 * c)
	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(a * Float64(c * i)))
	tmp = 0.0
	if (i <= -4.8e-119)
		tmp = t_2;
	elseif (i <= 1.9e-276)
		tmp = t_1;
	elseif (i <= 1.12e-164)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (i <= 1.5e+49)
		tmp = t_1;
	elseif (i <= 3.8e+273)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * i) * Float64(2.0 * c));
	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 * (a * (c * i));
	tmp = 0.0;
	if (i <= -4.8e-119)
		tmp = t_2;
	elseif (i <= 1.9e-276)
		tmp = t_1;
	elseif (i <= 1.12e-164)
		tmp = 2.0 * (x * y);
	elseif (i <= 1.5e+49)
		tmp = t_1;
	elseif (i <= 3.8e+273)
		tmp = t_2;
	else
		tmp = (a * i) * (2.0 * c);
	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[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e-119], t$95$2, If[LessEqual[i, 1.9e-276], t$95$1, If[LessEqual[i, 1.12e-164], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+49], t$95$1, If[LessEqual[i, 3.8e+273], t$95$2, N[(N[(a * i), $MachinePrecision] * N[(2.0 * c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.80000000000000017e-119 or 1.5000000000000001e49 < i < 3.8e273

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 76.1%

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

   3. Taylor expanded in a around inf 44.5%

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

   if -4.80000000000000017e-119 < i < 1.9e-276 or 1.12e-164 < i < 1.5000000000000001e49

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 44.8%

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

   if 1.9e-276 < i < 1.12e-164

   1. Initial program 80.0%

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

   2. Taylor expanded in x around inf 57.9%

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

   if 3.8e273 < i

   1. Initial program 87.5%

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

      1. associate--l+ 87.5%

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

      2. *-commutative 87.5%

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

      3. associate--l+ 87.5%

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

      4. associate--l+ 87.5%

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

      5. *-commutative 87.5%

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

      6. associate--l+ 87.5%

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

      7. fma-def 87.5%

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

      8. associate-*l* 75.8%

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

   3. Simplified 75.8%

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

      1. fma-def 75.8%

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

      2. +-commutative 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in a around inf 0.9%

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

      1. mul-1-neg 0.9%

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

      2. associate-*r* 1.5%

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

      3. distribute-rgt-neg-out 1.5%

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

      4. *-commutative 1.5%

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

      5. *-commutative 1.5%

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

   8. Simplified 1.5%

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

      1. expm1-log1p-u 1.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(-i\right) \cdot \left(c \cdot a\right)\right)\right)\right)} \]

      2. expm1-udef 1.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(-i\right) \cdot \left(c \cdot a\right)\right)\right)} - 1} \]

      3. *-commutative 1.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(-i\right) \cdot \left(c \cdot a\right)\right) \cdot 2}\right)} - 1 \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\left(\sqrt{-i} \cdot \sqrt{-i}\right)} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      5. sqrt-unprod 37.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\sqrt{\left(-i\right) \cdot \left(-i\right)}} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      6. sqr-neg 37.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\sqrt{\color{blue}{i \cdot i}} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      7. sqrt-unprod 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      8. add-sqr-sqrt 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{i} \cdot \left(c \cdot a\right)\right) \cdot 2\right)} - 1 \]

      9. *-commutative 26.1%

         \[\leadsto e^{\mathsf{log1p}\left(\left(i \cdot \color{blue}{\left(a \cdot c\right)}\right) \cdot 2\right)} - 1 \]

      10. associate-*r* 26.1%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot a\right) \cdot c\right)} \cdot 2\right)} - 1 \]

   10. Applied egg-rr 26.1%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot a\right) \cdot c\right) \cdot 2\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 26.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot a\right) \cdot c\right) \cdot 2\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. associate-*l* 51.8%

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

   12. Simplified 51.8%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{-119}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-276}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-164}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+273}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(2 \cdot c\right)\\ \end{array} \]

Alternative 11: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* -2.0 (* a (* c i)))))
   (if (<= i -9.5e-104)
     t_2
     (if (<= i 4.5e-275)
       t_1
       (if (<= i 7.2e-163) (* 2.0 (* x y)) (if (<= i 4.8e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -9.5e-104) {
		tmp = t_2;
	} else if (i <= 4.5e-275) {
		tmp = t_1;
	} else if (i <= 7.2e-163) {
		tmp = 2.0 * (x * y);
	} else if (i <= 4.8e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (-2.0d0) * (a * (c * i))
    if (i <= (-9.5d-104)) then
        tmp = t_2
    else if (i <= 4.5d-275) then
        tmp = t_1
    else if (i <= 7.2d-163) then
        tmp = 2.0d0 * (x * y)
    else if (i <= 4.8d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (i <= -9.5e-104) {
		tmp = t_2;
	} else if (i <= 4.5e-275) {
		tmp = t_1;
	} else if (i <= 7.2e-163) {
		tmp = 2.0 * (x * y);
	} else if (i <= 4.8e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = -2.0 * (a * (c * i))
	tmp = 0
	if i <= -9.5e-104:
		tmp = t_2
	elif i <= 4.5e-275:
		tmp = t_1
	elif i <= 7.2e-163:
		tmp = 2.0 * (x * y)
	elif i <= 4.8e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(-2.0 * Float64(a * Float64(c * i)))
	tmp = 0.0
	if (i <= -9.5e-104)
		tmp = t_2;
	elseif (i <= 4.5e-275)
		tmp = t_1;
	elseif (i <= 7.2e-163)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (i <= 4.8e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = -2.0 * (a * (c * i));
	tmp = 0.0;
	if (i <= -9.5e-104)
		tmp = t_2;
	elseif (i <= 4.5e-275)
		tmp = t_1;
	elseif (i <= 7.2e-163)
		tmp = 2.0 * (x * y);
	elseif (i <= 4.8e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e-104], t$95$2, If[LessEqual[i, 4.5e-275], t$95$1, If[LessEqual[i, 7.2e-163], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.5000000000000002e-104 or 4.8e49 < i

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 76.1%

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

   3. Taylor expanded in a around inf 42.2%

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

   if -9.5000000000000002e-104 < i < 4.49999999999999978e-275 or 7.1999999999999996e-163 < i < 4.8e49

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 44.8%

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

   if 4.49999999999999978e-275 < i < 7.1999999999999996e-163

   1. Initial program 80.0%

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

   2. Taylor expanded in x around inf 57.9%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{-104}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-275}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-163}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 12: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+67} \lor \neg \left(c \leq 1.45 \cdot 10^{-68}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.8e+67) (not (<= c 1.45e-68)))
   (* -2.0 (* c (* i (+ a (* b c)))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.8e+67) || !(c <= 1.45e-68)) {
		tmp = -2.0 * (c * (i * (a + (b * c))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.8d+67)) .or. (.not. (c <= 1.45d-68))) then
        tmp = (-2.0d0) * (c * (i * (a + (b * c))))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.8e+67) || !(c <= 1.45e-68)) {
		tmp = -2.0 * (c * (i * (a + (b * c))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.8e+67) or not (c <= 1.45e-68):
		tmp = -2.0 * (c * (i * (a + (b * c))))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.8e+67) || !(c <= 1.45e-68))
		tmp = Float64(-2.0 * Float64(c * Float64(i * Float64(a + Float64(b * c)))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.8e+67) || ~((c <= 1.45e-68)))
		tmp = -2.0 * (c * (i * (a + (b * c))));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.8e+67], N[Not[LessEqual[c, 1.45e-68]], $MachinePrecision]], N[(-2.0 * N[(c * N[(i * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.80000000000000004e67 or 1.45e-68 < c

   1. Initial program 79.9%

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

   2. Taylor expanded in z around 0 83.4%

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

   3. Taylor expanded in x around 0 76.0%

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

   if -4.80000000000000004e67 < c < 1.45e-68

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 74.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+67} \lor \neg \left(c \leq 1.45 \cdot 10^{-68}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 13: 44.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+39} \lor \neg \left(x \cdot y \leq 10^{+60}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+39) (not (<= (* x y) 1e+60)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -5e+39) || !((x * y) <= 1e+60)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-5d+39)) .or. (.not. ((x * y) <= 1d+60))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -5e+39) || !((x * y) <= 1e+60)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -5e+39) or not ((x * y) <= 1e+60):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+39) || !(Float64(x * y) <= 1e+60))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -5e+39) || ~(((x * y) <= 1e+60)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+39], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+60]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.00000000000000015e39 or 9.9999999999999995e59 < (*.f64 x y)

   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 inf 50.7%

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

   if -5.00000000000000015e39 < (*.f64 x y) < 9.9999999999999995e59

   1. Initial program 91.2%

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

   2. Taylor expanded in z around inf 33.0%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+39} \lor \neg \left(x \cdot y \leq 10^{+60}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 14: 57.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+182} \lor \neg \left(c \leq 8.6 \cdot 10^{+51}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.1e+182) (not (<= c 8.6e+51)))
   (* -2.0 (* a (* c i)))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.1e+182) || !(c <= 8.6e+51)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.1d+182)) .or. (.not. (c <= 8.6d+51))) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.1e+182) || !(c <= 8.6e+51)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.1e+182) or not (c <= 8.6e+51):
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.1e+182) || !(c <= 8.6e+51))
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.1e+182) || ~((c <= 8.6e+51)))
		tmp = -2.0 * (a * (c * i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.1e+182], N[Not[LessEqual[c, 8.6e+51]], $MachinePrecision]], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.09999999999999996e182 or 8.5999999999999994e51 < c

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0 89.9%

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

   3. Taylor expanded in a around inf 39.8%

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

   if -3.09999999999999996e182 < c < 8.5999999999999994e51

   1. Initial program 92.9%

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

   2. Taylor expanded in c around 0 61.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+182} \lor \neg \left(c \leq 8.6 \cdot 10^{+51}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 15: 29.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

2. Taylor expanded in z around inf 25.6%

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

3. Final simplification 25.6%

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

Developer target: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023326 
(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))))