Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.4% → 97.9%

Time: 18.8s

Alternatives: 25

Speedup: 0.5×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (- x (* z (+ y -1.0))) (* a (- 1.0 t))) (* b (- (+ y t) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (z * (y + -1.0))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (z * (y + -1.0))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - (z * (y + -1.0))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(z * Float64(y + -1.0))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - (z * (y + -1.0))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.7%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 93.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   2. fma-define 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   3. associate--l+ 96.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y + \left(t - 2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   4. sub-neg 96.1%

      \[\leadsto \mathsf{fma}\left(y + \color{blue}{\left(t + \left(-2\right)\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   5. metadata-eval 96.1%

      \[\leadsto \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   6. sub-neg 96.1%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]

   7. associate-+l- 96.1%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   8. fma-neg 97.2%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   9. sub-neg 97.2%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   10. metadata-eval 97.2%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   11. remove-double-neg 97.2%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right) \cdot a}\right)\right) \]

   12. sub-neg 97.2%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]

   13. metadata-eval 97.2%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]
4. Add Preprocessing

5. Final simplification 97.2%

   \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-10}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+104}:\\ \;\;\;\;a + \left(x + \left(-2 \cdot b + y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -3e+17)
     t_1
     (if (<= y 6.2e-165)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= y 4.5e-10)
         (+ z (+ x (* b (- t 2.0))))
         (if (<= y 2.1e+104) (+ a (+ x (+ (* -2.0 b) (* y b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3e+17) {
		tmp = t_1;
	} else if (y <= 6.2e-165) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 4.5e-10) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 2.1e+104) {
		tmp = a + (x + ((-2.0 * b) + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3d+17)) then
        tmp = t_1
    else if (y <= 6.2d-165) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (y <= 4.5d-10) then
        tmp = z + (x + (b * (t - 2.0d0)))
    else if (y <= 2.1d+104) then
        tmp = a + (x + (((-2.0d0) * b) + (y * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3e+17) {
		tmp = t_1;
	} else if (y <= 6.2e-165) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 4.5e-10) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 2.1e+104) {
		tmp = a + (x + ((-2.0 * b) + (y * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3e+17:
		tmp = t_1
	elif y <= 6.2e-165:
		tmp = x + (z + (a * (1.0 - t)))
	elif y <= 4.5e-10:
		tmp = z + (x + (b * (t - 2.0)))
	elif y <= 2.1e+104:
		tmp = a + (x + ((-2.0 * b) + (y * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3e+17)
		tmp = t_1;
	elseif (y <= 6.2e-165)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (y <= 4.5e-10)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t - 2.0))));
	elseif (y <= 2.1e+104)
		tmp = Float64(a + Float64(x + Float64(Float64(-2.0 * b) + Float64(y * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3e+17)
		tmp = t_1;
	elseif (y <= 6.2e-165)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (y <= 4.5e-10)
		tmp = z + (x + (b * (t - 2.0)));
	elseif (y <= 2.1e+104)
		tmp = a + (x + ((-2.0 * b) + (y * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+17], t$95$1, If[LessEqual[y, 6.2e-165], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-10], N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+104], N[(a + N[(x + N[(N[(-2.0 * b), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e17 or 2.0999999999999998e104 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -3e17 < y < 6.19999999999999992e-165

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 82.1%

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

      1. +-commutative 82.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 82.1%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 82.1%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. neg-mul-1 82.1%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 82.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 82.1%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   if 6.19999999999999992e-165 < y < 4.5e-10

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.4%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in z around inf 79.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{-1 \cdot z} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around 0 79.7%

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

   if 4.5e-10 < y < 2.0999999999999998e104

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 72.1%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - -1 \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 72.1%

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

      2. metadata-eval 72.1%

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

      3. neg-mul-1 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 72.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-10}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+104}:\\ \;\;\;\;a + \left(x + \left(-2 \cdot b + y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-11}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+108}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.6e+35)
     t_1
     (if (<= y 6.2e-165)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= y 1.3e-11)
         (+ z (+ x (* b (- t 2.0))))
         (if (<= y 5.2e+108) (+ a (+ x (* b (+ y -2.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.6e+35) {
		tmp = t_1;
	} else if (y <= 6.2e-165) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 1.3e-11) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 5.2e+108) {
		tmp = a + (x + (b * (y + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.6d+35)) then
        tmp = t_1
    else if (y <= 6.2d-165) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (y <= 1.3d-11) then
        tmp = z + (x + (b * (t - 2.0d0)))
    else if (y <= 5.2d+108) then
        tmp = a + (x + (b * (y + (-2.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.6e+35) {
		tmp = t_1;
	} else if (y <= 6.2e-165) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 1.3e-11) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 5.2e+108) {
		tmp = a + (x + (b * (y + -2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.6e+35:
		tmp = t_1
	elif y <= 6.2e-165:
		tmp = x + (z + (a * (1.0 - t)))
	elif y <= 1.3e-11:
		tmp = z + (x + (b * (t - 2.0)))
	elif y <= 5.2e+108:
		tmp = a + (x + (b * (y + -2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.6e+35)
		tmp = t_1;
	elseif (y <= 6.2e-165)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (y <= 1.3e-11)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t - 2.0))));
	elseif (y <= 5.2e+108)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.6e+35)
		tmp = t_1;
	elseif (y <= 6.2e-165)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (y <= 1.3e-11)
		tmp = z + (x + (b * (t - 2.0)));
	elseif (y <= 5.2e+108)
		tmp = a + (x + (b * (y + -2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+35], t$95$1, If[LessEqual[y, 6.2e-165], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-11], N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+108], N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999996e35 or 5.2000000000000005e108 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -4.5999999999999996e35 < y < 6.19999999999999992e-165

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 82.1%

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

      1. +-commutative 82.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 82.1%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 82.1%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. neg-mul-1 82.1%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 82.1%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 82.1%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   if 6.19999999999999992e-165 < y < 1.3e-11

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.4%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in z around inf 79.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{-1 \cdot z} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around 0 79.7%

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

   if 1.3e-11 < y < 5.2000000000000005e108

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 72.1%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - -1 \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 72.1%

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

      2. metadata-eval 72.1%

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

      3. neg-mul-1 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-11}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+108}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-139}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 430000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -5.3e+16)
     t_1
     (if (<= y 1.85e-215)
       (* a (- 1.0 t))
       (if (<= y 8.5e-139)
         (+ x a)
         (if (<= y 430000000.0) (* b (- (+ y t) 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5.3e+16) {
		tmp = t_1;
	} else if (y <= 1.85e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.5e-139) {
		tmp = x + a;
	} else if (y <= 430000000.0) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-5.3d+16)) then
        tmp = t_1
    else if (y <= 1.85d-215) then
        tmp = a * (1.0d0 - t)
    else if (y <= 8.5d-139) then
        tmp = x + a
    else if (y <= 430000000.0d0) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5.3e+16) {
		tmp = t_1;
	} else if (y <= 1.85e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.5e-139) {
		tmp = x + a;
	} else if (y <= 430000000.0) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -5.3e+16:
		tmp = t_1
	elif y <= 1.85e-215:
		tmp = a * (1.0 - t)
	elif y <= 8.5e-139:
		tmp = x + a
	elif y <= 430000000.0:
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5.3e+16)
		tmp = t_1;
	elseif (y <= 1.85e-215)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 8.5e-139)
		tmp = Float64(x + a);
	elseif (y <= 430000000.0)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -5.3e+16)
		tmp = t_1;
	elseif (y <= 1.85e-215)
		tmp = a * (1.0 - t);
	elseif (y <= 8.5e-139)
		tmp = x + a;
	elseif (y <= 430000000.0)
		tmp = b * ((y + t) - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.3e+16], t$95$1, If[LessEqual[y, 1.85e-215], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-139], N[(x + a), $MachinePrecision], If[LessEqual[y, 430000000.0], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3e16 or 4.3e8 < y

   1. Initial program 88.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -5.3e16 < y < 1.85000000000000005e-215

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.0%

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

   if 1.85000000000000005e-215 < y < 8.5000000000000003e-139

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 94.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 65.2%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 66.1%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 66.1%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 66.1%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 66.1%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 66.1%

      \[\leadsto \color{blue}{x + a} \]

   if 8.5000000000000003e-139 < y < 4.3e8

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 49.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-139}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 430000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot a\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -95000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-57}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t a))) (t_2 (* z (- 1.0 y))))
   (if (<= z -9.5e+113)
     t_2
     (if (<= z -95000000.0)
       t_1
       (if (<= z 8e-57) (+ a (* b (- y 2.0))) (if (<= z 1.3e+79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -9.5e+113) {
		tmp = t_2;
	} else if (z <= -95000000.0) {
		tmp = t_1;
	} else if (z <= 8e-57) {
		tmp = a + (b * (y - 2.0));
	} else if (z <= 1.3e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (t * a)
    t_2 = z * (1.0d0 - y)
    if (z <= (-9.5d+113)) then
        tmp = t_2
    else if (z <= (-95000000.0d0)) then
        tmp = t_1
    else if (z <= 8d-57) then
        tmp = a + (b * (y - 2.0d0))
    else if (z <= 1.3d+79) 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 t_1 = x - (t * a);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -9.5e+113) {
		tmp = t_2;
	} else if (z <= -95000000.0) {
		tmp = t_1;
	} else if (z <= 8e-57) {
		tmp = a + (b * (y - 2.0));
	} else if (z <= 1.3e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * a)
	t_2 = z * (1.0 - y)
	tmp = 0
	if z <= -9.5e+113:
		tmp = t_2
	elif z <= -95000000.0:
		tmp = t_1
	elif z <= 8e-57:
		tmp = a + (b * (y - 2.0))
	elif z <= 1.3e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * a))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -9.5e+113)
		tmp = t_2;
	elseif (z <= -95000000.0)
		tmp = t_1;
	elseif (z <= 8e-57)
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	elseif (z <= 1.3e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (t * a);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -9.5e+113)
		tmp = t_2;
	elseif (z <= -95000000.0)
		tmp = t_1;
	elseif (z <= 8e-57)
		tmp = a + (b * (y - 2.0));
	elseif (z <= 1.3e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+113], t$95$2, If[LessEqual[z, -95000000.0], t$95$1, If[LessEqual[z, 8e-57], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000001e113 or 1.30000000000000007e79 < z

   1. Initial program 87.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -9.5000000000000001e113 < z < -9.5e7 or 7.99999999999999964e-57 < z < 1.30000000000000007e79

   1. Initial program 92.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 64.2%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around -inf 56.9%

      \[\leadsto x - \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.9%

         \[\leadsto x - \color{blue}{\left(-y \cdot \left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right)\right)} \]

      2. *-commutative 56.9%

         \[\leadsto x - \left(-\color{blue}{\left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right) \cdot y}\right) \]

      3. distribute-rgt-neg-in 56.9%

         \[\leadsto x - \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right) \cdot \left(-y\right)} \]

   6. Simplified 56.9%

      \[\leadsto x - \color{blue}{\left(\frac{z - a \cdot \left(t + -1\right)}{y} - z\right) \cdot \left(-y\right)} \]

   7. Taylor expanded in t around inf 54.9%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   8. Step-by-step derivation

      1. *-commutative 54.9%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   9. Simplified 54.9%

      \[\leadsto x - \color{blue}{t \cdot a} \]

   if -9.5e7 < z < 7.99999999999999964e-57

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 96.7%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 73.7%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - -1 \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 73.7%

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

      2. metadata-eval 73.7%

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

      3. neg-mul-1 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in x around 0 57.9%

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

Alternative 7: 49.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-70}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 350000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.9e+31)
     t_1
     (if (<= y 2.15e-215)
       (* a (- 1.0 t))
       (if (<= y 2.9e-70)
         (+ x a)
         (if (<= y 350000000000.0) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.9e+31) {
		tmp = t_1;
	} else if (y <= 2.15e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.9e-70) {
		tmp = x + a;
	} else if (y <= 350000000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.9d+31)) then
        tmp = t_1
    else if (y <= 2.15d-215) then
        tmp = a * (1.0d0 - t)
    else if (y <= 2.9d-70) then
        tmp = x + a
    else if (y <= 350000000000.0d0) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.9e+31) {
		tmp = t_1;
	} else if (y <= 2.15e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 2.9e-70) {
		tmp = x + a;
	} else if (y <= 350000000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.9e+31:
		tmp = t_1
	elif y <= 2.15e-215:
		tmp = a * (1.0 - t)
	elif y <= 2.9e-70:
		tmp = x + a
	elif y <= 350000000000.0:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.9e+31)
		tmp = t_1;
	elseif (y <= 2.15e-215)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 2.9e-70)
		tmp = Float64(x + a);
	elseif (y <= 350000000000.0)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.9e+31)
		tmp = t_1;
	elseif (y <= 2.15e-215)
		tmp = a * (1.0 - t);
	elseif (y <= 2.9e-70)
		tmp = x + a;
	elseif (y <= 350000000000.0)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+31], t$95$1, If[LessEqual[y, 2.15e-215], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-70], N[(x + a), $MachinePrecision], If[LessEqual[y, 350000000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000001e31 or 3.5e11 < y

   1. Initial program 88.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.8%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -1.9000000000000001e31 < y < 2.15000000000000012e-215

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.0%

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

   if 2.15000000000000012e-215 < y < 2.89999999999999971e-70

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 68.4%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 51.1%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 48.7%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 48.7%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 48.7%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 48.7%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 48.7%

      \[\leadsto \color{blue}{x + a} \]

   if 2.89999999999999971e-70 < y < 3.5e11

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.5%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+113} \lor \neg \left(z \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.7e+113) (not (<= z 4.5e+55)))
   (+ z (+ x (+ (* b (- t 2.0)) (* y (- b z)))))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.7e+113) || !(z <= 4.5e+55)) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((z <= (-5.7d+113)) .or. (.not. (z <= 4.5d+55))) then
        tmp = z + (x + ((b * (t - 2.0d0)) + (y * (b - z))))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - 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 tmp;
	if ((z <= -5.7e+113) || !(z <= 4.5e+55)) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.7e+113) or not (z <= 4.5e+55):
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.7e+113) || !(z <= 4.5e+55))
		tmp = Float64(z + Float64(x + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * Float64(b - z)))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.7e+113) || ~((z <= 4.5e+55)))
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.7e+113], N[Not[LessEqual[z, 4.5e+55]], $MachinePrecision]], N[(z + N[(x + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6999999999999998e113 or 4.49999999999999998e55 < z

   1. Initial program 88.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.4%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{-1 \cdot z} \]
   5. Step-by-step derivation

      1. neg-mul-1 88.8%

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

   6. Simplified 88.8%

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

   if -5.6999999999999998e113 < z < 4.49999999999999998e55

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+113} \lor \neg \left(z \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+113}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= z -4.9e+113)
     (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))
     (if (<= z 1.15e-16) (+ t_1 (* a (- 1.0 t))) (+ t_1 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -4.9e+113) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else if (z <= 1.15e-16) {
		tmp = t_1 + (a * (1.0 - t));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (z <= (-4.9d+113)) then
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    else if (z <= 1.15d-16) then
        tmp = t_1 + (a * (1.0d0 - t))
    else
        tmp = t_1 + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -4.9e+113) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else if (z <= 1.15e-16) {
		tmp = t_1 + (a * (1.0 - t));
	} else {
		tmp = t_1 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if z <= -4.9e+113:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	elif z <= 1.15e-16:
		tmp = t_1 + (a * (1.0 - t))
	else:
		tmp = t_1 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (z <= -4.9e+113)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	elseif (z <= 1.15e-16)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (z <= -4.9e+113)
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	elseif (z <= 1.15e-16)
		tmp = t_1 + (a * (1.0 - t));
	else
		tmp = t_1 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+113], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-16], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.90000000000000021e113

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.3%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if -4.90000000000000021e113 < z < 1.15e-16

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.6%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   if 1.15e-16 < z

   1. Initial program 84.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 85.5%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+113}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+67}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e+113)
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))
   (if (<= z 4.1e+67)
     (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
     (+ x (- (* z (- 1.0 y)) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e+113) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else if (z <= 4.1e+67) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-3.5d+113)) then
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    else if (z <= 4.1d+67) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = x + ((z * (1.0d0 - y)) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e+113) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else if (z <= 4.1e+67) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.5e+113:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	elif z <= 4.1e+67:
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = x + ((z * (1.0 - y)) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.5e+113)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	elseif (z <= 4.1e+67)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.5e+113)
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	elseif (z <= 4.1e+67)
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = x + ((z * (1.0 - y)) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.5e+113], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+67], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e113

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 87.3%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if -3.5000000000000001e113 < z < 4.09999999999999979e67

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.8%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   if 4.09999999999999979e67 < z

   1. Initial program 83.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.7%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 83.7%

      \[\leadsto x - \left(\color{blue}{a \cdot t} + z \cdot \left(y - 1\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto x - \left(\color{blue}{t \cdot a} + z \cdot \left(y - 1\right)\right) \]

   6. Simplified 83.7%

      \[\leadsto x - \left(\color{blue}{t \cdot a} + z \cdot \left(y - 1\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+67}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.1e+32)
     t_1
     (if (<= y 1.9e-138)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= y 1.65e+103) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.1e+32) {
		tmp = t_1;
	} else if (y <= 1.9e-138) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 1.65e+103) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.1d+32)) then
        tmp = t_1
    else if (y <= 1.9d-138) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (y <= 1.65d+103) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.1e+32) {
		tmp = t_1;
	} else if (y <= 1.9e-138) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 1.65e+103) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.1e+32:
		tmp = t_1
	elif y <= 1.9e-138:
		tmp = x + (z + (a * (1.0 - t)))
	elif y <= 1.65e+103:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.1e+32)
		tmp = t_1;
	elseif (y <= 1.9e-138)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (y <= 1.65e+103)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.1e+32)
		tmp = t_1;
	elseif (y <= 1.9e-138)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (y <= 1.65e+103)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+32], t$95$1, If[LessEqual[y, 1.9e-138], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+103], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999981e32 or 1.65000000000000004e103 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -4.09999999999999981e32 < y < 1.9000000000000001e-138

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.1%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around 0 82.3%

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

      1. +-commutative 82.3%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)} \]

      2. sub-neg 82.3%

         \[\leadsto x - \left(a \cdot \color{blue}{\left(t + \left(-1\right)\right)} + -1 \cdot z\right) \]

      3. metadata-eval 82.3%

         \[\leadsto x - \left(a \cdot \left(t + \color{blue}{-1}\right) + -1 \cdot z\right) \]

      4. neg-mul-1 82.3%

         \[\leadsto x - \left(a \cdot \left(t + -1\right) + \color{blue}{\left(-z\right)}\right) \]

      5. unsub-neg 82.3%

         \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   6. Simplified 82.3%

      \[\leadsto x - \color{blue}{\left(a \cdot \left(t + -1\right) - z\right)} \]

   if 1.9000000000000001e-138 < y < 1.65000000000000004e103

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.2%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 64.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+103}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.1e+32)
     t_1
     (if (<= y 2.6e-164)
       (+ x (* a (- 1.0 t)))
       (if (<= y 2.7e+103) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.1e+32) {
		tmp = t_1;
	} else if (y <= 2.6e-164) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 2.7e+103) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.1d+32)) then
        tmp = t_1
    else if (y <= 2.6d-164) then
        tmp = x + (a * (1.0d0 - t))
    else if (y <= 2.7d+103) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.1e+32) {
		tmp = t_1;
	} else if (y <= 2.6e-164) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 2.7e+103) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.1e+32:
		tmp = t_1
	elif y <= 2.6e-164:
		tmp = x + (a * (1.0 - t))
	elif y <= 2.7e+103:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.1e+32)
		tmp = t_1;
	elseif (y <= 2.6e-164)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (y <= 2.7e+103)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.1e+32)
		tmp = t_1;
	elseif (y <= 2.6e-164)
		tmp = x + (a * (1.0 - t));
	elseif (y <= 2.7e+103)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+32], t$95$1, If[LessEqual[y, 2.6e-164], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+103], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999981e32 or 2.69999999999999993e103 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -4.09999999999999981e32 < y < 2.6000000000000002e-164

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 83.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 64.3%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   if 2.6000000000000002e-164 < y < 2.69999999999999993e103

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 85.5%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in a around 0 63.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+103}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+36}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e+260)
   (* y b)
   (if (<= y -7e+36)
     (- (* y z))
     (if (<= y 1.65e-215)
       (* a (- 1.0 t))
       (if (<= y 1.3e+105) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+260) {
		tmp = y * b;
	} else if (y <= -7e+36) {
		tmp = -(y * z);
	} else if (y <= 1.65e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.3e+105) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= (-1.5d+260)) then
        tmp = y * b
    else if (y <= (-7d+36)) then
        tmp = -(y * z)
    else if (y <= 1.65d-215) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.3d+105) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+260) {
		tmp = y * b;
	} else if (y <= -7e+36) {
		tmp = -(y * z);
	} else if (y <= 1.65e-215) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.3e+105) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.5e+260:
		tmp = y * b
	elif y <= -7e+36:
		tmp = -(y * z)
	elif y <= 1.65e-215:
		tmp = a * (1.0 - t)
	elif y <= 1.3e+105:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e+260)
		tmp = Float64(y * b);
	elseif (y <= -7e+36)
		tmp = Float64(-Float64(y * z));
	elseif (y <= 1.65e-215)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.3e+105)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.5e+260)
		tmp = y * b;
	elseif (y <= -7e+36)
		tmp = -(y * z);
	elseif (y <= 1.65e-215)
		tmp = a * (1.0 - t);
	elseif (y <= 1.3e+105)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e+260], N[(y * b), $MachinePrecision], If[LessEqual[y, -7e+36], (-N[(y * z), $MachinePrecision]), If[LessEqual[y, 1.65e-215], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+105], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4999999999999999e260 or 1.3000000000000001e105 < y

   1. Initial program 84.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 65.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 53.3%

      \[\leadsto \color{blue}{b \cdot y} \]

   if -1.4999999999999999e260 < y < -6.9999999999999996e36

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around inf 54.2%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 54.2%

         \[\leadsto z \cdot \color{blue}{\left(-y\right)} \]

   6. Simplified 54.2%

      \[\leadsto z \cdot \color{blue}{\left(-y\right)} \]

   if -6.9999999999999996e36 < y < 1.6499999999999999e-215

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.0%

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

   if 1.6499999999999999e-215 < y < 1.3000000000000001e105

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 64.6%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 52.1%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 38.3%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 38.3%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 38.3%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 38.3%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 38.3%

      \[\leadsto \color{blue}{x + a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+36}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+114} \lor \neg \left(b \leq 1600000000000\right):\\ \;\;\;\;a + \left(x + b \cdot \left(\left(y + t\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+114) (not (<= b 1600000000000.0)))
   (+ a (+ x (* b (- (+ y t) 2.0))))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+114) || !(b <= 1600000000000.0)) {
		tmp = a + (x + (b * ((y + t) - 2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((b <= (-7.5d+114)) .or. (.not. (b <= 1600000000000.0d0))) then
        tmp = a + (x + (b * ((y + t) - 2.0d0)))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+114) || !(b <= 1600000000000.0)) {
		tmp = a + (x + (b * ((y + t) - 2.0)));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+114) or not (b <= 1600000000000.0):
		tmp = a + (x + (b * ((y + t) - 2.0)))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+114) || !(b <= 1600000000000.0))
		tmp = Float64(a + Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+114) || ~((b <= 1600000000000.0)))
		tmp = a + (x + (b * ((y + t) - 2.0)));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+114], N[Not[LessEqual[b, 1600000000000.0]], $MachinePrecision]], N[(a + N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5000000000000001e114 or 1.6e12 < b

   1. Initial program 87.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 85.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 85.2%

      \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \color{blue}{-1 \cdot a} \]
   5. Step-by-step derivation

      1. neg-mul-1 85.2%

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

   6. Simplified 85.2%

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

   if -7.5000000000000001e114 < b < 1.6e12

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 89.5%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+114} \lor \neg \left(b \leq 1600000000000\right):\\ \;\;\;\;a + \left(x + b \cdot \left(\left(y + t\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.7e+18)
     t_1
     (if (<= y -1.05e-178)
       (* a (- 1.0 t))
       (if (<= y 21000000.0) (+ a (+ x (* -2.0 b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.7e+18) {
		tmp = t_1;
	} else if (y <= -1.05e-178) {
		tmp = a * (1.0 - t);
	} else if (y <= 21000000.0) {
		tmp = a + (x + (-2.0 * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.7d+18)) then
        tmp = t_1
    else if (y <= (-1.05d-178)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 21000000.0d0) then
        tmp = a + (x + ((-2.0d0) * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.7e+18) {
		tmp = t_1;
	} else if (y <= -1.05e-178) {
		tmp = a * (1.0 - t);
	} else if (y <= 21000000.0) {
		tmp = a + (x + (-2.0 * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.7e+18:
		tmp = t_1
	elif y <= -1.05e-178:
		tmp = a * (1.0 - t)
	elif y <= 21000000.0:
		tmp = a + (x + (-2.0 * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.7e+18)
		tmp = t_1;
	elseif (y <= -1.05e-178)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 21000000.0)
		tmp = Float64(a + Float64(x + Float64(-2.0 * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.7e+18)
		tmp = t_1;
	elseif (y <= -1.05e-178)
		tmp = a * (1.0 - t);
	elseif (y <= 21000000.0)
		tmp = a + (x + (-2.0 * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+18], t$95$1, If[LessEqual[y, -1.05e-178], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 21000000.0], N[(a + N[(x + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e18 or 2.1e7 < y

   1. Initial program 88.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.1%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -1.7e18 < y < -1.05e-178

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 59.4%

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

   if -1.05e-178 < y < 2.1e7

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.5%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 55.2%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - -1 \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 55.2%

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

      2. metadata-eval 55.2%

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

      3. neg-mul-1 55.2%

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

   6. Simplified 55.2%

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

   7. Taylor expanded in y around 0 54.4%

      \[\leadsto \color{blue}{a + \left(x + -2 \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.4%

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

   9. Simplified 54.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+43} \lor \neg \left(z \leq 3 \cdot 10^{+66}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + b \cdot \left(\left(y + t\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.75e+43) (not (<= z 3e+66)))
   (+ x (- (* z (- 1.0 y)) (* t a)))
   (+ a (+ x (* b (- (+ y t) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.75e+43) || !(z <= 3e+66)) {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	} else {
		tmp = a + (x + (b * ((y + t) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((z <= (-1.75d+43)) .or. (.not. (z <= 3d+66))) then
        tmp = x + ((z * (1.0d0 - y)) - (t * a))
    else
        tmp = a + (x + (b * ((y + t) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.75e+43) || !(z <= 3e+66)) {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	} else {
		tmp = a + (x + (b * ((y + t) - 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.75e+43) or not (z <= 3e+66):
		tmp = x + ((z * (1.0 - y)) - (t * a))
	else:
		tmp = a + (x + (b * ((y + t) - 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.75e+43) || !(z <= 3e+66))
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	else
		tmp = Float64(a + Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.75e+43) || ~((z <= 3e+66)))
		tmp = x + ((z * (1.0 - y)) - (t * a));
	else
		tmp = a + (x + (b * ((y + t) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.75e+43], N[Not[LessEqual[z, 3e+66]], $MachinePrecision]], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e43 or 3.00000000000000002e66 < z

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 82.1%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in t around inf 79.7%

      \[\leadsto x - \left(\color{blue}{a \cdot t} + z \cdot \left(y - 1\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto x - \left(\color{blue}{t \cdot a} + z \cdot \left(y - 1\right)\right) \]

   6. Simplified 79.7%

      \[\leadsto x - \left(\color{blue}{t \cdot a} + z \cdot \left(y - 1\right)\right) \]

   if -1.7500000000000001e43 < z < 3.00000000000000002e66

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in t around 0 82.5%

      \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \color{blue}{-1 \cdot a} \]
   5. Step-by-step derivation

      1. neg-mul-1 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+43} \lor \neg \left(z \leq 3 \cdot 10^{+66}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + b \cdot \left(\left(y + t\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6e+30)
     t_1
     (if (<= y 2.2e-218)
       (* a (- 1.0 t))
       (if (<= y 1.65e+50) (- x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6e+30) {
		tmp = t_1;
	} else if (y <= 2.2e-218) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.65e+50) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-6d+30)) then
        tmp = t_1
    else if (y <= 2.2d-218) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.65d+50) then
        tmp = x - (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6e+30) {
		tmp = t_1;
	} else if (y <= 2.2e-218) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.65e+50) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6e+30:
		tmp = t_1
	elif y <= 2.2e-218:
		tmp = a * (1.0 - t)
	elif y <= 1.65e+50:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6e+30)
		tmp = t_1;
	elseif (y <= 2.2e-218)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.65e+50)
		tmp = Float64(x - Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -6e+30)
		tmp = t_1;
	elseif (y <= 2.2e-218)
		tmp = a * (1.0 - t);
	elseif (y <= 1.65e+50)
		tmp = x - (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+30], t$95$1, If[LessEqual[y, 2.2e-218], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+50], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999956e30 or 1.65e50 < y

   1. Initial program 87.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.5%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -5.99999999999999956e30 < y < 2.20000000000000007e-218

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.4%

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

   if 2.20000000000000007e-218 < y < 1.65e50

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 67.6%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in y around -inf 61.1%

      \[\leadsto x - \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 61.1%

         \[\leadsto x - \color{blue}{\left(-y \cdot \left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right)\right)} \]

      2. *-commutative 61.1%

         \[\leadsto x - \left(-\color{blue}{\left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right) \cdot y}\right) \]

      3. distribute-rgt-neg-in 61.1%

         \[\leadsto x - \color{blue}{\left(-1 \cdot z + -1 \cdot \frac{-1 \cdot z + a \cdot \left(t - 1\right)}{y}\right) \cdot \left(-y\right)} \]

   6. Simplified 61.1%

      \[\leadsto x - \color{blue}{\left(\frac{z - a \cdot \left(t + -1\right)}{y} - z\right) \cdot \left(-y\right)} \]

   7. Taylor expanded in t around inf 46.4%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   8. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   9. Simplified 46.4%

      \[\leadsto x - \color{blue}{t \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+35}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+104}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.5e+260)
   (* y b)
   (if (<= y -4.6e+35) (- (* y z)) (if (<= y 3.7e+104) (+ x a) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+260) {
		tmp = y * b;
	} else if (y <= -4.6e+35) {
		tmp = -(y * z);
	} else if (y <= 3.7e+104) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= (-1.5d+260)) then
        tmp = y * b
    else if (y <= (-4.6d+35)) then
        tmp = -(y * z)
    else if (y <= 3.7d+104) then
        tmp = x + a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.5e+260) {
		tmp = y * b;
	} else if (y <= -4.6e+35) {
		tmp = -(y * z);
	} else if (y <= 3.7e+104) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.5e+260:
		tmp = y * b
	elif y <= -4.6e+35:
		tmp = -(y * z)
	elif y <= 3.7e+104:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.5e+260)
		tmp = Float64(y * b);
	elseif (y <= -4.6e+35)
		tmp = Float64(-Float64(y * z));
	elseif (y <= 3.7e+104)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.5e+260)
		tmp = y * b;
	elseif (y <= -4.6e+35)
		tmp = -(y * z);
	elseif (y <= 3.7e+104)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.5e+260], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.6e+35], (-N[(y * z), $MachinePrecision]), If[LessEqual[y, 3.7e+104], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4999999999999999e260 or 3.6999999999999998e104 < y

   1. Initial program 84.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 65.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 53.3%

      \[\leadsto \color{blue}{b \cdot y} \]

   if -1.4999999999999999e260 < y < -4.5999999999999996e35

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around inf 54.2%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 54.2%

         \[\leadsto z \cdot \color{blue}{\left(-y\right)} \]

   6. Simplified 54.2%

      \[\leadsto z \cdot \color{blue}{\left(-y\right)} \]

   if -4.5999999999999996e35 < y < 3.6999999999999998e104

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 73.9%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 58.0%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 38.2%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 38.2%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 38.2%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 38.2%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{x + a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+35}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+104}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-233}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 220000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e+29)
   (* y b)
   (if (<= y 1.1e-233) a (if (<= y 220000000000.0) x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+29) {
		tmp = y * b;
	} else if (y <= 1.1e-233) {
		tmp = a;
	} else if (y <= 220000000000.0) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= (-6.2d+29)) then
        tmp = y * b
    else if (y <= 1.1d-233) then
        tmp = a
    else if (y <= 220000000000.0d0) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+29) {
		tmp = y * b;
	} else if (y <= 1.1e-233) {
		tmp = a;
	} else if (y <= 220000000000.0) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e+29:
		tmp = y * b
	elif y <= 1.1e-233:
		tmp = a
	elif y <= 220000000000.0:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e+29)
		tmp = Float64(y * b);
	elseif (y <= 1.1e-233)
		tmp = a;
	elseif (y <= 220000000000.0)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e+29)
		tmp = y * b;
	elseif (y <= 1.1e-233)
		tmp = a;
	elseif (y <= 220000000000.0)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e+29], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.1e-233], a, If[LessEqual[y, 220000000000.0], x, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999998e29 or 2.2e11 < y

   1. Initial program 88.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 64.7%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{b \cdot y} \]

   if -6.1999999999999998e29 < y < 1.1e-233

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.4%

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

   4. Taylor expanded in t around 0 26.2%

      \[\leadsto \color{blue}{a} \]

   if 1.1e-233 < y < 2.2e11

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 29.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-233}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 220000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+26} \lor \neg \left(y \leq 1.4 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+26) (not (<= y 1.4e+104)))
   (* y (- b z))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+26) || !(y <= 1.4e+104)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-1.25d+26)) .or. (.not. (y <= 1.4d+104))) then
        tmp = y * (b - z)
    else
        tmp = x + (a * (1.0d0 - 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 tmp;
	if ((y <= -1.25e+26) || !(y <= 1.4e+104)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+26) or not (y <= 1.4e+104):
		tmp = y * (b - z)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+26) || !(y <= 1.4e+104))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+26) || ~((y <= 1.4e+104)))
		tmp = y * (b - z);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+26], N[Not[LessEqual[y, 1.4e+104]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e26 or 1.4e104 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -1.25e26 < y < 1.4e104

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 73.9%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 58.0%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+26} \lor \neg \left(y \leq 1.4 \cdot 10^{+104}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 19.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-182}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e+75) z (if (<= z 1.02e-182) a (if (<= z 3e+183) x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+75) {
		tmp = z;
	} else if (z <= 1.02e-182) {
		tmp = a;
	} else if (z <= 3e+183) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-1.65d+75)) then
        tmp = z
    else if (z <= 1.02d-182) then
        tmp = a
    else if (z <= 3d+183) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+75) {
		tmp = z;
	} else if (z <= 1.02e-182) {
		tmp = a;
	} else if (z <= 3e+183) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e+75:
		tmp = z
	elif z <= 1.02e-182:
		tmp = a
	elif z <= 3e+183:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e+75)
		tmp = z;
	elseif (z <= 1.02e-182)
		tmp = a;
	elseif (z <= 3e+183)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.65e+75)
		tmp = z;
	elseif (z <= 1.02e-182)
		tmp = a;
	elseif (z <= 3e+183)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e+75], z, If[LessEqual[z, 1.02e-182], a, If[LessEqual[z, 3e+183], x, z]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999999e75 or 2.99999999999999996e183 < z

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   4. Taylor expanded in y around 0 30.7%

      \[\leadsto \color{blue}{z} \]

   if -1.64999999999999999e75 < z < 1.02e-182

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.9%

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

   4. Taylor expanded in t around 0 23.3%

      \[\leadsto \color{blue}{a} \]

   if 1.02e-182 < z < 2.99999999999999996e183

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 27.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 49.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+53} \lor \neg \left(t \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.5e+53) (not (<= t 2e+22))) (* t (- b a)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e+53) || !(t <= 2e+22)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((t <= (-7.5d+53)) .or. (.not. (t <= 2d+22))) then
        tmp = t * (b - a)
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e+53) || !(t <= 2e+22)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.5e+53) or not (t <= 2e+22):
		tmp = t * (b - a)
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.5e+53) || !(t <= 2e+22))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.5e+53) || ~((t <= 2e+22)))
		tmp = t * (b - a);
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.5e+53], N[Not[LessEqual[t, 2e+22]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4999999999999997e53 or 2e22 < t

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -7.4999999999999997e53 < t < 2e22

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 66.4%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 37.9%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 37.4%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 37.4%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 37.4%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 37.4%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 37.4%

      \[\leadsto \color{blue}{x + a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+53} \lor \neg \left(t \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 34.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+33} \lor \neg \left(y \leq 4.8 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e+33) (not (<= y 4.8e+106))) (* y b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+33) || !(y <= 4.8e+106)) {
		tmp = y * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-8.5d+33)) .or. (.not. (y <= 4.8d+106))) then
        tmp = y * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+33) || !(y <= 4.8e+106)) {
		tmp = y * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e+33) or not (y <= 4.8e+106):
		tmp = y * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e+33) || !(y <= 4.8e+106))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e+33) || ~((y <= 4.8e+106)))
		tmp = y * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e+33], N[Not[LessEqual[y, 4.8e+106]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999998e33 or 4.8000000000000001e106 < y

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 59.1%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   4. Taylor expanded in y around inf 41.9%

      \[\leadsto \color{blue}{b \cdot y} \]

   if -8.4999999999999998e33 < y < 4.8000000000000001e106

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 73.9%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in z around 0 58.0%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]

   5. Taylor expanded in t around 0 38.2%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 38.2%

         \[\leadsto \color{blue}{x + \left(--1\right) \cdot a} \]

      2. metadata-eval 38.2%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 38.2%

         \[\leadsto x + \color{blue}{a} \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{x + a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+33} \lor \neg \left(y \leq 4.8 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+50}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.6e+124) x (if (<= x 5.8e+50) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.6e+124) {
		tmp = x;
	} else if (x <= 5.8e+50) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (x <= (-2.6d+124)) then
        tmp = x
    else if (x <= 5.8d+50) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.6e+124) {
		tmp = x;
	} else if (x <= 5.8e+50) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.6e+124:
		tmp = x
	elif x <= 5.8e+50:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.6e+124)
		tmp = x;
	elseif (x <= 5.8e+50)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.6e+124)
		tmp = x;
	elseif (x <= 5.8e+50)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.6e+124], x, If[LessEqual[x, 5.8e+50], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e124 or 5.8e50 < x

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 31.5%

      \[\leadsto \color{blue}{x} \]

   if -2.6e124 < x < 5.8e50

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 32.0%

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

   4. Taylor expanded in t around 0 20.3%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 11.7% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = a
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 93.7%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around inf 29.5%

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

4. Taylor expanded in t around 0 13.5%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))