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

Percentage Accurate: 90.2% → 96.3%

Time: 15.9s

Alternatives: 14

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.9%

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

      1. associate--l+ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate--l+ 95.9%

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

      4. associate--l+ 95.9%

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

      5. *-commutative 95.9%

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

      6. associate--l+ 95.9%

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

      7. fma-def 95.9%

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

      8. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 71.5%

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

   3. Taylor expanded in i around 0 71.5%

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

4. Final simplification 97.3%

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

Alternative 2: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+269}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot i\right) \cdot \mathsf{fma}\left(b, c, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* -2.0 (* c (* t_1 i)))
     (if (<= t_2 1e+269)
       (* 2.0 (- (+ (* x y) (* z t)) (+ (* (* b c) (* c i)) (* a (* c i)))))
       (* 2.0 (- (* z t) (* (* c i) (fma b c a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -2.0 * (c * (t_1 * i));
	} else if (t_2 <= 1e+269) {
		tmp = 2.0 * (((x * y) + (z * t)) - (((b * c) * (c * i)) + (a * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - ((c * i) * fma(b, c, a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	elseif (t_2 <= 1e+269)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(b * c) * Float64(c * i)) + Float64(a * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(Float64(c * i) * fma(b, c, a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+269], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(N[(c * i), $MachinePrecision] * N[(b * c + a), $MachinePrecision]), $MachinePrecision]), $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 72.9%

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

   2. Taylor expanded in i around inf 89.7%

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

   3. Taylor expanded in i around 0 89.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1e269

   1. Initial program 99.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   if 1e269 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 79.2%

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

   2. 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. Step-by-step derivation

      1. associate-*r* 91.7%

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

      2. +-commutative 91.7%

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

      3. fma-udef 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+269}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - \left(c \cdot i\right) \cdot \mathsf{fma}\left(b, c, a\right)\right)\\ \end{array} \]

Alternative 3: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t_1 \cdot i\right)\\ t_3 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;-2 \cdot t_2\\ \mathbf{elif}\;t_3 \leq 8 \cdot 10^{+292}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* (* c t_1) i)))
   (if (<= t_3 (- INFINITY))
     (* -2.0 t_2)
     (if (<= t_3 8e+292)
       (* 2.0 (- (+ (* x y) (* z t)) (+ (* (* b c) (* c i)) (* a (* c i)))))
       (* 2.0 (- (* z t) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 8e+292) {
		tmp = 2.0 * (((x * y) + (z * t)) - (((b * c) * (c * i)) + (a * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = -2.0 * t_2;
	} else if (t_3 <= 8e+292) {
		tmp = 2.0 * (((x * y) + (z * t)) - (((b * c) * (c * i)) + (a * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = (c * t_1) * i
	tmp = 0
	if t_3 <= -math.inf:
		tmp = -2.0 * t_2
	elif t_3 <= 8e+292:
		tmp = 2.0 * (((x * y) + (z * t)) - (((b * c) * (c * i)) + (a * (c * i))))
	else:
		tmp = 2.0 * ((z * t) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(-2.0 * t_2);
	elseif (t_3 <= 8e+292)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(b * c) * Float64(c * i)) + Float64(a * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	t_3 = (c * t_1) * i;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = -2.0 * t_2;
	elseif (t_3 <= 8e+292)
		tmp = 2.0 * (((x * y) + (z * t)) - (((b * c) * (c * i)) + (a * (c * i))));
	else
		tmp = 2.0 * ((z * t) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(-2.0 * t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 8e+292], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 72.9%

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

   2. Taylor expanded in i around inf 89.7%

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

   3. Taylor expanded in i around 0 89.7%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 8.0000000000000001e292

   1. Initial program 99.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-lft-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   if 8.0000000000000001e292 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 91.1%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 8 \cdot 10^{+292}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(b \cdot c\right) \cdot \left(c \cdot i\right) + a \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* (+ a (* b c)) i))))
        (t_2 (* 2.0 (- (* z t) (* i (* a c)))))
        (t_3 (* 2.0 (- (* x y) (* c (* b (* c i)))))))
   (if (<= (* x y) -2e+90)
     t_3
     (if (<= (* x y) -5e+20)
       t_2
       (if (<= (* x y) -5e-45)
         t_3
         (if (<= (* x y) -1e-112)
           t_1
           (if (<= (* x y) 5e-281)
             t_2
             (if (<= (* x y) 5e-88)
               t_1
               (if (<= (* x y) 5000000000.0) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * ((a + (b * c)) * i));
	double t_2 = 2.0 * ((z * t) - (i * (a * c)));
	double t_3 = 2.0 * ((x * y) - (c * (b * (c * i))));
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -5e+20) {
		tmp = t_2;
	} else if ((x * y) <= -5e-45) {
		tmp = t_3;
	} else if ((x * y) <= -1e-112) {
		tmp = t_1;
	} else if ((x * y) <= 5e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-88) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * ((a + (b * c)) * i))
    t_2 = 2.0d0 * ((z * t) - (i * (a * c)))
    t_3 = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    if ((x * y) <= (-2d+90)) then
        tmp = t_3
    else if ((x * y) <= (-5d+20)) then
        tmp = t_2
    else if ((x * y) <= (-5d-45)) then
        tmp = t_3
    else if ((x * y) <= (-1d-112)) then
        tmp = t_1
    else if ((x * y) <= 5d-281) then
        tmp = t_2
    else if ((x * y) <= 5d-88) then
        tmp = t_1
    else if ((x * y) <= 5000000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * ((a + (b * c)) * i));
	double t_2 = 2.0 * ((z * t) - (i * (a * c)));
	double t_3 = 2.0 * ((x * y) - (c * (b * (c * i))));
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -5e+20) {
		tmp = t_2;
	} else if ((x * y) <= -5e-45) {
		tmp = t_3;
	} else if ((x * y) <= -1e-112) {
		tmp = t_1;
	} else if ((x * y) <= 5e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-88) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * ((a + (b * c)) * i))
	t_2 = 2.0 * ((z * t) - (i * (a * c)))
	t_3 = 2.0 * ((x * y) - (c * (b * (c * i))))
	tmp = 0
	if (x * y) <= -2e+90:
		tmp = t_3
	elif (x * y) <= -5e+20:
		tmp = t_2
	elif (x * y) <= -5e-45:
		tmp = t_3
	elif (x * y) <= -1e-112:
		tmp = t_1
	elif (x * y) <= 5e-281:
		tmp = t_2
	elif (x * y) <= 5e-88:
		tmp = t_1
	elif (x * y) <= 5000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	t_2 = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))))
	tmp = 0.0
	if (Float64(x * y) <= -2e+90)
		tmp = t_3;
	elseif (Float64(x * y) <= -5e+20)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e-45)
		tmp = t_3;
	elseif (Float64(x * y) <= -1e-112)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-281)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-88)
		tmp = t_1;
	elseif (Float64(x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * ((a + (b * c)) * i));
	t_2 = 2.0 * ((z * t) - (i * (a * c)));
	t_3 = 2.0 * ((x * y) - (c * (b * (c * i))));
	tmp = 0.0;
	if ((x * y) <= -2e+90)
		tmp = t_3;
	elseif ((x * y) <= -5e+20)
		tmp = t_2;
	elseif ((x * y) <= -5e-45)
		tmp = t_3;
	elseif ((x * y) <= -1e-112)
		tmp = t_1;
	elseif ((x * y) <= 5e-281)
		tmp = t_2;
	elseif ((x * y) <= 5e-88)
		tmp = t_1;
	elseif ((x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+90], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5e+20], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e-45], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1e-112], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-281], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-88], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5000000000.0], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or -5e20 < (*.f64 x y) < -4.99999999999999976e-45 or 5e9 < (*.f64 x y)

   1. Initial program 87.6%

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

   2. Taylor expanded in z around 0 77.7%

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

   3. Taylor expanded in a around 0 73.0%

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

   if -1.99999999999999993e90 < (*.f64 x y) < -5e20 or -9.9999999999999995e-113 < (*.f64 x y) < 4.9999999999999998e-281 or 5.00000000000000009e-88 < (*.f64 x y) < 5e9

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 77.4%

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

      1. *-commutative 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   if -4.99999999999999976e-45 < (*.f64 x y) < -9.9999999999999995e-113 or 4.9999999999999998e-281 < (*.f64 x y) < 5.00000000000000009e-88

   1. Initial program 86.9%

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

   2. Taylor expanded in i around inf 81.1%

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

   3. Taylor expanded in i around 0 81.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-45}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-112}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-88}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5: 92.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 71.5%

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

   3. Taylor expanded in i around 0 71.5%

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

4. Final simplification 94.5%

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

Alternative 6: 41.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(c \cdot \left(a \cdot -2\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* i (* c (* a -2.0))))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -2e+90)
     t_3
     (if (<= (* x y) -2e-134)
       t_1
       (if (<= (* x y) 2e-281)
         t_2
         (if (<= (* x y) 5e-99)
           t_1
           (if (<= (* x y) 5000000000.0) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (c * (a * -2.0));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -2e-134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-99) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (c * (a * (-2.0d0)))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-2d+90)) then
        tmp = t_3
    else if ((x * y) <= (-2d-134)) then
        tmp = t_1
    else if ((x * y) <= 2d-281) then
        tmp = t_2
    else if ((x * y) <= 5d-99) then
        tmp = t_1
    else if ((x * y) <= 5000000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i * (c * (a * -2.0));
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -2e-134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-99) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = i * (c * (a * -2.0))
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2e+90:
		tmp = t_3
	elif (x * y) <= -2e-134:
		tmp = t_1
	elif (x * y) <= 2e-281:
		tmp = t_2
	elif (x * y) <= 5e-99:
		tmp = t_1
	elif (x * y) <= 5000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i * Float64(c * Float64(a * -2.0)))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2e+90)
		tmp = t_3;
	elseif (Float64(x * y) <= -2e-134)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-281)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-99)
		tmp = t_1;
	elseif (Float64(x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = i * (c * (a * -2.0));
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2e+90)
		tmp = t_3;
	elseif ((x * y) <= -2e-134)
		tmp = t_1;
	elseif ((x * y) <= 2e-281)
		tmp = t_2;
	elseif ((x * y) <= 5e-99)
		tmp = t_1;
	elseif ((x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * N[(c * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+90], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2e-134], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-281], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-99], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5000000000.0], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or 5e9 < (*.f64 x y)

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf 57.1%

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

   if -1.99999999999999993e90 < (*.f64 x y) < -2.00000000000000008e-134 or 2e-281 < (*.f64 x y) < 4.99999999999999969e-99

   1. Initial program 90.3%

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

   2. Taylor expanded in a around inf 46.7%

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

      1. mul-1-neg 46.7%

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

      2. *-commutative 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in c around 0 46.7%

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

      1. associate-*r* 46.7%

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

   7. Simplified 46.7%

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

   8. Taylor expanded in a around 0 46.7%

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

      1. associate-*l* 46.7%

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

      2. *-commutative 46.7%

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

      3. associate-*r* 40.0%

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

      4. *-commutative 40.0%

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

      5. associate-*l* 40.1%

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

   10. Simplified 40.1%

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

   if -2.00000000000000008e-134 < (*.f64 x y) < 2e-281 or 4.99999999999999969e-99 < (*.f64 x y) < 5e9

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 47.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(c \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(c \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 7: 42.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c i) (* a -2.0)))
        (t_2 (* 2.0 (* z t)))
        (t_3 (* (* x y) 2.0)))
   (if (<= (* x y) -2e+90)
     t_3
     (if (<= (* x y) -2e-134)
       t_1
       (if (<= (* x y) 2e-281)
         t_2
         (if (<= (* x y) 5e-88)
           t_1
           (if (<= (* x y) 5000000000.0) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -2e-134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-88) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * i) * (a * (-2.0d0))
    t_2 = 2.0d0 * (z * t)
    t_3 = (x * y) * 2.0d0
    if ((x * y) <= (-2d+90)) then
        tmp = t_3
    else if ((x * y) <= (-2d-134)) then
        tmp = t_1
    else if ((x * y) <= 2d-281) then
        tmp = t_2
    else if ((x * y) <= 5d-88) then
        tmp = t_1
    else if ((x * y) <= 5000000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) * (a * -2.0);
	double t_2 = 2.0 * (z * t);
	double t_3 = (x * y) * 2.0;
	double tmp;
	if ((x * y) <= -2e+90) {
		tmp = t_3;
	} else if ((x * y) <= -2e-134) {
		tmp = t_1;
	} else if ((x * y) <= 2e-281) {
		tmp = t_2;
	} else if ((x * y) <= 5e-88) {
		tmp = t_1;
	} else if ((x * y) <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) * (a * -2.0)
	t_2 = 2.0 * (z * t)
	t_3 = (x * y) * 2.0
	tmp = 0
	if (x * y) <= -2e+90:
		tmp = t_3
	elif (x * y) <= -2e-134:
		tmp = t_1
	elif (x * y) <= 2e-281:
		tmp = t_2
	elif (x * y) <= 5e-88:
		tmp = t_1
	elif (x * y) <= 5000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) * Float64(a * -2.0))
	t_2 = Float64(2.0 * Float64(z * t))
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2e+90)
		tmp = t_3;
	elseif (Float64(x * y) <= -2e-134)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-281)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-88)
		tmp = t_1;
	elseif (Float64(x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) * (a * -2.0);
	t_2 = 2.0 * (z * t);
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if ((x * y) <= -2e+90)
		tmp = t_3;
	elseif ((x * y) <= -2e-134)
		tmp = t_1;
	elseif ((x * y) <= 2e-281)
		tmp = t_2;
	elseif ((x * y) <= 5e-88)
		tmp = t_1;
	elseif ((x * y) <= 5000000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+90], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2e-134], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-281], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-88], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5000000000.0], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or 5e9 < (*.f64 x y)

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf 57.1%

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

   if -1.99999999999999993e90 < (*.f64 x y) < -2.00000000000000008e-134 or 2e-281 < (*.f64 x y) < 5.00000000000000009e-88

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. *-commutative 46.8%

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

      3. distribute-rgt-neg-in 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in c around 0 46.8%

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

      1. associate-*r* 46.8%

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

   7. Simplified 46.8%

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

   if -2.00000000000000008e-134 < (*.f64 x y) < 2e-281 or 5.00000000000000009e-88 < (*.f64 x y) < 5e9

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 48.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-134}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-88}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;x \cdot y \leq 5000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 8: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(x \cdot y\right) \cdot 2\\ t_3 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* (* x y) 2.0))
        (t_3 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -4e-104)
     t_3
     (if (<= c 1.02e-245)
       t_2
       (if (<= c 8e-204)
         t_1
         (if (<= c 2.7e-119)
           t_2
           (if (<= c 5.8e-94) t_1 (if (<= c 4.5e-60) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -4e-104) {
		tmp = t_3;
	} else if (c <= 1.02e-245) {
		tmp = t_2;
	} else if (c <= 8e-204) {
		tmp = t_1;
	} else if (c <= 2.7e-119) {
		tmp = t_2;
	} else if (c <= 5.8e-94) {
		tmp = t_1;
	} else if (c <= 4.5e-60) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = (x * y) * 2.0d0
    t_3 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-4d-104)) then
        tmp = t_3
    else if (c <= 1.02d-245) then
        tmp = t_2
    else if (c <= 8d-204) then
        tmp = t_1
    else if (c <= 2.7d-119) then
        tmp = t_2
    else if (c <= 5.8d-94) then
        tmp = t_1
    else if (c <= 4.5d-60) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = (x * y) * 2.0;
	double t_3 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -4e-104) {
		tmp = t_3;
	} else if (c <= 1.02e-245) {
		tmp = t_2;
	} else if (c <= 8e-204) {
		tmp = t_1;
	} else if (c <= 2.7e-119) {
		tmp = t_2;
	} else if (c <= 5.8e-94) {
		tmp = t_1;
	} else if (c <= 4.5e-60) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = (x * y) * 2.0
	t_3 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -4e-104:
		tmp = t_3
	elif c <= 1.02e-245:
		tmp = t_2
	elif c <= 8e-204:
		tmp = t_1
	elif c <= 2.7e-119:
		tmp = t_2
	elif c <= 5.8e-94:
		tmp = t_1
	elif c <= 4.5e-60:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(Float64(x * y) * 2.0)
	t_3 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -4e-104)
		tmp = t_3;
	elseif (c <= 1.02e-245)
		tmp = t_2;
	elseif (c <= 8e-204)
		tmp = t_1;
	elseif (c <= 2.7e-119)
		tmp = t_2;
	elseif (c <= 5.8e-94)
		tmp = t_1;
	elseif (c <= 4.5e-60)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = (x * y) * 2.0;
	t_3 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -4e-104)
		tmp = t_3;
	elseif (c <= 1.02e-245)
		tmp = t_2;
	elseif (c <= 8e-204)
		tmp = t_1;
	elseif (c <= 2.7e-119)
		tmp = t_2;
	elseif (c <= 5.8e-94)
		tmp = t_1;
	elseif (c <= 4.5e-60)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e-104], t$95$3, If[LessEqual[c, 1.02e-245], t$95$2, If[LessEqual[c, 8e-204], t$95$1, If[LessEqual[c, 2.7e-119], t$95$2, If[LessEqual[c, 5.8e-94], t$95$1, If[LessEqual[c, 4.5e-60], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.99999999999999971e-104 or 4.50000000000000001e-60 < c

   1. Initial program 85.7%

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

   2. Taylor expanded in i around inf 70.7%

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

   3. Taylor expanded in i around 0 70.7%

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

   if -3.99999999999999971e-104 < c < 1.01999999999999994e-245 or 8.00000000000000001e-204 < c < 2.70000000000000027e-119 or 5.79999999999999991e-94 < c < 4.50000000000000001e-60

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 53.1%

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

   if 1.01999999999999994e-245 < c < 8.00000000000000001e-204 or 2.70000000000000027e-119 < c < 5.79999999999999991e-94

   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 z around inf 65.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-104}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-245}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-94}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-78} \lor \neg \left(c \leq 6.2 \cdot 10^{-60}\right) \land \left(c \leq 6.2 \cdot 10^{+75} \lor \neg \left(c \leq 1.6 \cdot 10^{+145}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -5.5e-78)
         (and (not (<= c 6.2e-60)) (or (<= c 6.2e+75) (not (<= c 1.6e+145)))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.5e-78) || (!(c <= 6.2e-60) && ((c <= 6.2e+75) || !(c <= 1.6e+145)))) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-5.5d-78)) .or. (.not. (c <= 6.2d-60)) .and. (c <= 6.2d+75) .or. (.not. (c <= 1.6d+145))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -5.5e-78) || (!(c <= 6.2e-60) && ((c <= 6.2e+75) || !(c <= 1.6e+145)))) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -5.5e-78) or (not (c <= 6.2e-60) and ((c <= 6.2e+75) or not (c <= 1.6e+145))):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -5.5e-78) || (!(c <= 6.2e-60) && ((c <= 6.2e+75) || !(c <= 1.6e+145))))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -5.5e-78) || (~((c <= 6.2e-60)) && ((c <= 6.2e+75) || ~((c <= 1.6e+145)))))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -5.5e-78], And[N[Not[LessEqual[c, 6.2e-60]], $MachinePrecision], Or[LessEqual[c, 6.2e+75], N[Not[LessEqual[c, 1.6e+145]], $MachinePrecision]]]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.50000000000000017e-78 or 6.19999999999999976e-60 < c < 6.2000000000000002e75 or 1.60000000000000004e145 < c

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0 88.5%

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

   if -5.50000000000000017e-78 < c < 6.19999999999999976e-60 or 6.2000000000000002e75 < c < 1.60000000000000004e145

   1. Initial program 94.6%

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

   2. Taylor expanded in a around inf 90.8%

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

      1. *-commutative 90.8%

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

   4. Simplified 90.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{-78} \lor \neg \left(c \leq 6.2 \cdot 10^{-60}\right) \land \left(c \leq 6.2 \cdot 10^{+75} \lor \neg \left(c \leq 1.6 \cdot 10^{+145}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 10: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 500000000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+90) (not (<= (* x y) 500000000.0)))
   (* 2.0 (- (* x y) (* c (* b (* c i)))))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 500000000.0)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2d+90)) .or. (.not. ((x * y) <= 500000000.0d0))) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    else
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 500000000.0)) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+90) or not ((x * y) <= 500000000.0):
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	else:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+90) || !(Float64(x * y) <= 500000000.0))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2e+90) || ~(((x * y) <= 500000000.0)))
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	else
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 500000000.0]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or 5e8 < (*.f64 x y)

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 77.6%

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

   3. Taylor expanded in a around 0 74.0%

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

   if -1.99999999999999993e90 < (*.f64 x y) < 5e8

   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 x around 0 87.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 500000000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 11: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 500000000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* x y) -2e+90) (not (<= (* x y) 500000000.0)))
     (* 2.0 (- (* x y) t_1))
     (* 2.0 (- (* z t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 500000000.0)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (((x * y) <= (-2d+90)) .or. (.not. ((x * y) <= 500000000.0d0))) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((x * y) <= -2e+90) || !((x * y) <= 500000000.0)) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if ((x * y) <= -2e+90) or not ((x * y) <= 500000000.0):
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if ((Float64(x * y) <= -2e+90) || !(Float64(x * y) <= 500000000.0))
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (((x * y) <= -2e+90) || ~(((x * y) <= 500000000.0)))
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 500000000.0]], $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) < -1.99999999999999993e90 or 5e8 < (*.f64 x y)

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 77.6%

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

   if -1.99999999999999993e90 < (*.f64 x y) < 5e8

   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 x around 0 87.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 500000000\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 12: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ t_2 := -2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -650000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.06 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-245}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* i (* a c)))))
        (t_2 (* -2.0 (* c (* (+ a (* b c)) i)))))
   (if (<= c -650000000000.0)
     t_2
     (if (<= c -2.06e-193)
       t_1
       (if (<= c 1.85e-245) (* (* x y) 2.0) (if (<= c 1.25e-64) 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) - (i * (a * c)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -650000000000.0) {
		tmp = t_2;
	} else if (c <= -2.06e-193) {
		tmp = t_1;
	} else if (c <= 1.85e-245) {
		tmp = (x * y) * 2.0;
	} else if (c <= 1.25e-64) {
		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) - (i * (a * c)))
    t_2 = (-2.0d0) * (c * ((a + (b * c)) * i))
    if (c <= (-650000000000.0d0)) then
        tmp = t_2
    else if (c <= (-2.06d-193)) then
        tmp = t_1
    else if (c <= 1.85d-245) then
        tmp = (x * y) * 2.0d0
    else if (c <= 1.25d-64) 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) - (i * (a * c)));
	double t_2 = -2.0 * (c * ((a + (b * c)) * i));
	double tmp;
	if (c <= -650000000000.0) {
		tmp = t_2;
	} else if (c <= -2.06e-193) {
		tmp = t_1;
	} else if (c <= 1.85e-245) {
		tmp = (x * y) * 2.0;
	} else if (c <= 1.25e-64) {
		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) - (i * (a * c)))
	t_2 = -2.0 * (c * ((a + (b * c)) * i))
	tmp = 0
	if c <= -650000000000.0:
		tmp = t_2
	elif c <= -2.06e-193:
		tmp = t_1
	elif c <= 1.85e-245:
		tmp = (x * y) * 2.0
	elif c <= 1.25e-64:
		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(z * t) - Float64(i * Float64(a * c))))
	t_2 = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)))
	tmp = 0.0
	if (c <= -650000000000.0)
		tmp = t_2;
	elseif (c <= -2.06e-193)
		tmp = t_1;
	elseif (c <= 1.85e-245)
		tmp = Float64(Float64(x * y) * 2.0);
	elseif (c <= 1.25e-64)
		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) - (i * (a * c)));
	t_2 = -2.0 * (c * ((a + (b * c)) * i));
	tmp = 0.0;
	if (c <= -650000000000.0)
		tmp = t_2;
	elseif (c <= -2.06e-193)
		tmp = t_1;
	elseif (c <= 1.85e-245)
		tmp = (x * y) * 2.0;
	elseif (c <= 1.25e-64)
		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[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -650000000000.0], t$95$2, If[LessEqual[c, -2.06e-193], t$95$1, If[LessEqual[c, 1.85e-245], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 1.25e-64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.5e11 or 1.25000000000000008e-64 < c

   1. Initial program 83.7%

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

   2. Taylor expanded in i around inf 72.5%

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

   3. Taylor expanded in i around 0 72.5%

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

   if -6.5e11 < c < -2.0600000000000001e-193 or 1.8500000000000001e-245 < c < 1.25000000000000008e-64

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 86.3%

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

      1. *-commutative 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in x around 0 58.1%

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

      1. associate-*r* 58.1%

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

      2. *-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -2.0600000000000001e-193 < c < 1.8500000000000001e-245

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -650000000000:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.06 \cdot 10^{-193}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-245}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 13: 43.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 5000000000\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2e+90) (not (<= (* x y) 5000000000.0)))
   (* (* x y) 2.0)
   (* 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) <= -2e+90) || !((x * y) <= 5000000000.0)) {
		tmp = (x * y) * 2.0;
	} 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) <= (-2d+90)) .or. (.not. ((x * y) <= 5000000000.0d0))) then
        tmp = (x * y) * 2.0d0
    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) <= -2e+90) || !((x * y) <= 5000000000.0)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2e+90) or not ((x * y) <= 5000000000.0):
		tmp = (x * y) * 2.0
	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) <= -2e+90) || !(Float64(x * y) <= 5000000000.0))
		tmp = Float64(Float64(x * y) * 2.0);
	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) <= -2e+90) || ~(((x * y) <= 5000000000.0)))
		tmp = (x * y) * 2.0;
	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], -2e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5000000000.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999993e90 or 5e9 < (*.f64 x y)

   1. Initial program 87.6%

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

   2. Taylor expanded in x around inf 57.1%

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

   if -1.99999999999999993e90 < (*.f64 x y) < 5e9

   1. Initial program 93.0%

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

   2. Taylor expanded in z around inf 36.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 5000000000\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 14: 28.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

2. Taylor expanded in z around inf 27.8%

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

3. Final simplification 27.8%

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

Developer target: 94.3% 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 2023320 
(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))))