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

Percentage Accurate: 95.2% → 97.7%

Time: 13.2s

Alternatives: 21

Speedup: 0.5×

• 36.4% 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: 95.2% 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: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + 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(y * Float64(b - z));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $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[(y * N[(b - z), $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 y around inf 56.6%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
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 96.5%

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

   3. associate--l+ 96.5%

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

   4. sub-neg 96.5%

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

   5. metadata-eval 96.5%

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

   6. sub-neg 96.5%

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

   7. associate-+l- 96.5%

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

   8. fma-neg 97.3%

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

   9. sub-neg 97.3%

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

   10. metadata-eval 97.3%

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

   11. remove-double-neg 97.3%

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

   12. sub-neg 97.3%

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

   13. metadata-eval 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 3: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (* y (- b z))))
   (if (<= y -2.6e+55)
     t_2
     (if (<= y -4.6e-168)
       t_1
       (if (<= y 1.25e-150)
         (+ x (+ z (* (+ t -2.0) b)))
         (if (<= y 6.5e+26)
           t_1
           (if (<= y 4.7e+86) (+ x (* b (- (+ y t) 2.0))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.6e+55) {
		tmp = t_2;
	} else if (y <= -4.6e-168) {
		tmp = t_1;
	} else if (y <= 1.25e-150) {
		tmp = x + (z + ((t + -2.0) * b));
	} else if (y <= 6.5e+26) {
		tmp = t_1;
	} else if (y <= 4.7e+86) {
		tmp = x + (b * ((y + t) - 2.0));
	} 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 + (z + (a * (1.0d0 - t)))
    t_2 = y * (b - z)
    if (y <= (-2.6d+55)) then
        tmp = t_2
    else if (y <= (-4.6d-168)) then
        tmp = t_1
    else if (y <= 1.25d-150) then
        tmp = x + (z + ((t + (-2.0d0)) * b))
    else if (y <= 6.5d+26) then
        tmp = t_1
    else if (y <= 4.7d+86) then
        tmp = x + (b * ((y + t) - 2.0d0))
    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 + (z + (a * (1.0 - t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.6e+55) {
		tmp = t_2;
	} else if (y <= -4.6e-168) {
		tmp = t_1;
	} else if (y <= 1.25e-150) {
		tmp = x + (z + ((t + -2.0) * b));
	} else if (y <= 6.5e+26) {
		tmp = t_1;
	} else if (y <= 4.7e+86) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.6e+55:
		tmp = t_2
	elif y <= -4.6e-168:
		tmp = t_1
	elif y <= 1.25e-150:
		tmp = x + (z + ((t + -2.0) * b))
	elif y <= 6.5e+26:
		tmp = t_1
	elif y <= 4.7e+86:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.6e+55)
		tmp = t_2;
	elseif (y <= -4.6e-168)
		tmp = t_1;
	elseif (y <= 1.25e-150)
		tmp = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)));
	elseif (y <= 6.5e+26)
		tmp = t_1;
	elseif (y <= 4.7e+86)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.6e+55)
		tmp = t_2;
	elseif (y <= -4.6e-168)
		tmp = t_1;
	elseif (y <= 1.25e-150)
		tmp = x + (z + ((t + -2.0) * b));
	elseif (y <= 6.5e+26)
		tmp = t_1;
	elseif (y <= 4.7e+86)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+55], t$95$2, If[LessEqual[y, -4.6e-168], t$95$1, If[LessEqual[y, 1.25e-150], N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+26], t$95$1, If[LessEqual[y, 4.7e+86], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6e55 or 4.7000000000000002e86 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 73.7%

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

   if -2.6e55 < y < -4.59999999999999971e-168 or 1.24999999999999997e-150 < y < 6.50000000000000022e26

   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 b around 0 82.9%

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

   4. Taylor expanded in y around 0 79.0%

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

      1. +-commutative 79.0%

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

      2. sub-neg 79.0%

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

      3. metadata-eval 79.0%

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

      4. neg-mul-1 79.0%

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

      5. unsub-neg 79.0%

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

   6. Simplified 79.0%

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

   if -4.59999999999999971e-168 < y < 1.24999999999999997e-150

   1. Initial program 96.3%

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

   3. Taylor expanded in a around 0 77.4%

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

   4. Taylor expanded in y around 0 77.4%

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

      1. associate--l+ 77.4%

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

      2. sub-neg 77.4%

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

      3. metadata-eval 77.4%

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

      4. neg-mul-1 77.4%

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

   6. Simplified 77.4%

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

   if 6.50000000000000022e26 < y < 4.7000000000000002e86

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0 86.8%

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

   4. Taylor expanded in z around 0 73.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-168}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t \cdot b\right) + z \cdot \left(1 - y\right)\\ t_2 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x (* t b)) (* z (- 1.0 y))))
        (t_2 (+ x (+ z (* a (- 1.0 t))))))
   (if (<= a -3.4e+50)
     t_2
     (if (<= a 8.6e+64)
       t_1
       (if (<= a 1.1e+110)
         (- (* b (- (+ y t) 2.0)) (* t a))
         (if (<= a 1.3e+115) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (t * b)) + (z * (1.0 - y));
	double t_2 = x + (z + (a * (1.0 - t)));
	double tmp;
	if (a <= -3.4e+50) {
		tmp = t_2;
	} else if (a <= 8.6e+64) {
		tmp = t_1;
	} else if (a <= 1.1e+110) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (a <= 1.3e+115) {
		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 * b)) + (z * (1.0d0 - y))
    t_2 = x + (z + (a * (1.0d0 - t)))
    if (a <= (-3.4d+50)) then
        tmp = t_2
    else if (a <= 8.6d+64) then
        tmp = t_1
    else if (a <= 1.1d+110) then
        tmp = (b * ((y + t) - 2.0d0)) - (t * a)
    else if (a <= 1.3d+115) 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 * b)) + (z * (1.0 - y));
	double t_2 = x + (z + (a * (1.0 - t)));
	double tmp;
	if (a <= -3.4e+50) {
		tmp = t_2;
	} else if (a <= 8.6e+64) {
		tmp = t_1;
	} else if (a <= 1.1e+110) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (a <= 1.3e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (t * b)) + (z * (1.0 - y))
	t_2 = x + (z + (a * (1.0 - t)))
	tmp = 0
	if a <= -3.4e+50:
		tmp = t_2
	elif a <= 8.6e+64:
		tmp = t_1
	elif a <= 1.1e+110:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	elif a <= 1.3e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(t * b)) + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	tmp = 0.0
	if (a <= -3.4e+50)
		tmp = t_2;
	elseif (a <= 8.6e+64)
		tmp = t_1;
	elseif (a <= 1.1e+110)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	elseif (a <= 1.3e+115)
		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 * b)) + (z * (1.0 - y));
	t_2 = x + (z + (a * (1.0 - t)));
	tmp = 0.0;
	if (a <= -3.4e+50)
		tmp = t_2;
	elseif (a <= 8.6e+64)
		tmp = t_1;
	elseif (a <= 1.1e+110)
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	elseif (a <= 1.3e+115)
		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[(N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+50], t$95$2, If[LessEqual[a, 8.6e+64], t$95$1, If[LessEqual[a, 1.1e+110], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+115], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3999999999999998e50 or 1.3e115 < a

   1. Initial program 91.5%

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

   3. Taylor expanded in b around 0 81.9%

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

   4. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. neg-mul-1 76.5%

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

      5. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -3.3999999999999998e50 < a < 8.5999999999999995e64 or 1.09999999999999996e110 < a < 1.3e115

   1. Initial program 95.5%

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

   3. Taylor expanded in a around 0 88.4%

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

   4. Taylor expanded in t around inf 75.4%

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

   if 8.5999999999999995e64 < a < 1.09999999999999996e110

   1. Initial program 89.5%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. distribute-rgt-neg-in 69.0%

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

   5. Simplified 69.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+50}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+64}:\\ \;\;\;\;\left(x + t \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+115}:\\ \;\;\;\;\left(x + t \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -2.3e+55)
     t_2
     (if (<= y -4.9e-132)
       (* a (- 1.0 t))
       (if (<= y 1.2e-66)
         t_1
         (if (<= y 1.2e-7) (* z (- 1.0 y)) (if (<= y 5e+19) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.3e+55) {
		tmp = t_2;
	} else if (y <= -4.9e-132) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.2e-66) {
		tmp = t_1;
	} else if (y <= 1.2e-7) {
		tmp = z * (1.0 - y);
	} else if (y <= 5e+19) {
		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 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-2.3d+55)) then
        tmp = t_2
    else if (y <= (-4.9d-132)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.2d-66) then
        tmp = t_1
    else if (y <= 1.2d-7) then
        tmp = z * (1.0d0 - y)
    else if (y <= 5d+19) 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 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.3e+55) {
		tmp = t_2;
	} else if (y <= -4.9e-132) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.2e-66) {
		tmp = t_1;
	} else if (y <= 1.2e-7) {
		tmp = z * (1.0 - y);
	} else if (y <= 5e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.3e+55:
		tmp = t_2
	elif y <= -4.9e-132:
		tmp = a * (1.0 - t)
	elif y <= 1.2e-66:
		tmp = t_1
	elif y <= 1.2e-7:
		tmp = z * (1.0 - y)
	elif y <= 5e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.3e+55)
		tmp = t_2;
	elseif (y <= -4.9e-132)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.2e-66)
		tmp = t_1;
	elseif (y <= 1.2e-7)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 5e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.3e+55)
		tmp = t_2;
	elseif (y <= -4.9e-132)
		tmp = a * (1.0 - t);
	elseif (y <= 1.2e-66)
		tmp = t_1;
	elseif (y <= 1.2e-7)
		tmp = z * (1.0 - y);
	elseif (y <= 5e+19)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+55], t$95$2, If[LessEqual[y, -4.9e-132], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-66], t$95$1, If[LessEqual[y, 1.2e-7], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+19], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.29999999999999987e55 or 5e19 < y

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 68.7%

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

   if -2.29999999999999987e55 < y < -4.89999999999999981e-132

   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 45.8%

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

   if -4.89999999999999981e-132 < y < 1.20000000000000013e-66 or 1.19999999999999989e-7 < y < 5e19

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf 51.9%

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

   if 1.20000000000000013e-66 < y < 1.19999999999999989e-7

   1. Initial program 89.8%

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

   3. Taylor expanded in z around inf 55.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= z -6.2e+97)
     (- z (* y z))
     (if (<= z -1.2e-35)
       t_1
       (if (<= z -1.9e-231)
         (* a (- 1.0 t))
         (if (<= z 4.5e+221) 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 <= -6.2e+97) {
		tmp = z - (y * z);
	} else if (z <= -1.2e-35) {
		tmp = t_1;
	} else if (z <= -1.9e-231) {
		tmp = a * (1.0 - t);
	} else if (z <= 4.5e+221) {
		tmp = t_1;
	} else {
		tmp = 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 <= (-6.2d+97)) then
        tmp = z - (y * z)
    else if (z <= (-1.2d-35)) then
        tmp = t_1
    else if (z <= (-1.9d-231)) then
        tmp = a * (1.0d0 - t)
    else if (z <= 4.5d+221) then
        tmp = t_1
    else
        tmp = 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 <= -6.2e+97) {
		tmp = z - (y * z);
	} else if (z <= -1.2e-35) {
		tmp = t_1;
	} else if (z <= -1.9e-231) {
		tmp = a * (1.0 - t);
	} else if (z <= 4.5e+221) {
		tmp = t_1;
	} else {
		tmp = 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 <= -6.2e+97:
		tmp = z - (y * z)
	elif z <= -1.2e-35:
		tmp = t_1
	elif z <= -1.9e-231:
		tmp = a * (1.0 - t)
	elif z <= 4.5e+221:
		tmp = t_1
	else:
		tmp = 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 <= -6.2e+97)
		tmp = Float64(z - Float64(y * z));
	elseif (z <= -1.2e-35)
		tmp = t_1;
	elseif (z <= -1.9e-231)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (z <= 4.5e+221)
		tmp = t_1;
	else
		tmp = 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 <= -6.2e+97)
		tmp = z - (y * z);
	elseif (z <= -1.2e-35)
		tmp = t_1;
	elseif (z <= -1.9e-231)
		tmp = a * (1.0 - t);
	elseif (z <= 4.5e+221)
		tmp = t_1;
	else
		tmp = 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, -6.2e+97], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-35], t$95$1, If[LessEqual[z, -1.9e-231], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+221], t$95$1, N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.19999999999999962e97

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 73.7%

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

   4. Taylor expanded in y around 0 73.7%

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

   if -6.19999999999999962e97 < z < -1.2000000000000001e-35 or -1.90000000000000007e-231 < z < 4.5000000000000002e221

   1. Initial program 95.2%

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

   3. Taylor expanded in a around 0 74.8%

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

   4. Taylor expanded in z around 0 65.0%

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

   if -1.2000000000000001e-35 < z < -1.90000000000000007e-231

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 66.3%

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

   if 4.5000000000000002e221 < z

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 85.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+221}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -2.1e+133)
     t_2
     (if (<= b -3.6e-280)
       t_1
       (if (<= b -2e-302) (* z (- 1.0 y)) (if (<= b 8e+55) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.1e+133) {
		tmp = t_2;
	} else if (b <= -3.6e-280) {
		tmp = t_1;
	} else if (b <= -2e-302) {
		tmp = z * (1.0 - y);
	} else if (b <= 8e+55) {
		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 + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-2.1d+133)) then
        tmp = t_2
    else if (b <= (-3.6d-280)) then
        tmp = t_1
    else if (b <= (-2d-302)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 8d+55) 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 + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.1e+133) {
		tmp = t_2;
	} else if (b <= -3.6e-280) {
		tmp = t_1;
	} else if (b <= -2e-302) {
		tmp = z * (1.0 - y);
	} else if (b <= 8e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -2.1e+133:
		tmp = t_2
	elif b <= -3.6e-280:
		tmp = t_1
	elif b <= -2e-302:
		tmp = z * (1.0 - y)
	elif b <= 8e+55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -2.1e+133)
		tmp = t_2;
	elseif (b <= -3.6e-280)
		tmp = t_1;
	elseif (b <= -2e-302)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 8e+55)
		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 + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -2.1e+133)
		tmp = t_2;
	elseif (b <= -3.6e-280)
		tmp = t_1;
	elseif (b <= -2e-302)
		tmp = z * (1.0 - y);
	elseif (b <= 8e+55)
		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[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+133], t$95$2, If[LessEqual[b, -3.6e-280], t$95$1, If[LessEqual[b, -2e-302], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1e133 or 8.00000000000000008e55 < b

   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 a around 0 82.8%

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

   4. Taylor expanded in z around 0 79.9%

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

   if -2.1e133 < b < -3.59999999999999994e-280 or -1.9999999999999999e-302 < b < 8.00000000000000008e55

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 90.8%

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

   4. Taylor expanded in y around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. sub-neg 71.4%

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

      3. metadata-eval 71.4%

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

      4. neg-mul-1 71.4%

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

      5. unsub-neg 71.4%

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

   6. Simplified 71.4%

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

   if -3.59999999999999994e-280 < b < -1.9999999999999999e-302

   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 z around inf 87.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+133}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-280}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+55}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -7e+169)
     t_2
     (if (<= b -1.55e-178)
       t_1
       (if (<= b -1.06e-224) (* a (- 1.0 t)) (if (<= b 3.4e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+169) {
		tmp = t_2;
	} else if (b <= -1.55e-178) {
		tmp = t_1;
	} else if (b <= -1.06e-224) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.4e+52) {
		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 - (y * z)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-7d+169)) then
        tmp = t_2
    else if (b <= (-1.55d-178)) then
        tmp = t_1
    else if (b <= (-1.06d-224)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 3.4d+52) 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 - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+169) {
		tmp = t_2;
	} else if (b <= -1.55e-178) {
		tmp = t_1;
	} else if (b <= -1.06e-224) {
		tmp = a * (1.0 - t);
	} else if (b <= 3.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -7e+169:
		tmp = t_2
	elif b <= -1.55e-178:
		tmp = t_1
	elif b <= -1.06e-224:
		tmp = a * (1.0 - t)
	elif b <= 3.4e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -7e+169)
		tmp = t_2;
	elseif (b <= -1.55e-178)
		tmp = t_1;
	elseif (b <= -1.06e-224)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 3.4e+52)
		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 - (y * z);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -7e+169)
		tmp = t_2;
	elseif (b <= -1.55e-178)
		tmp = t_1;
	elseif (b <= -1.06e-224)
		tmp = a * (1.0 - t);
	elseif (b <= 3.4e+52)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+169], t$95$2, If[LessEqual[b, -1.55e-178], t$95$1, If[LessEqual[b, -1.06e-224], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000038e169 or 3.4e52 < b

   1. Initial program 88.1%

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

   3. Taylor expanded in b around inf 78.3%

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

   if -7.00000000000000038e169 < b < -1.55e-178 or -1.06000000000000001e-224 < b < 3.4e52

   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 0 91.0%

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

   4. Taylor expanded in y around inf 51.1%

      \[\leadsto x - \color{blue}{y \cdot z} \]

   if -1.55e-178 < b < -1.06000000000000001e-224

   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 a around inf 71.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-178}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- t 2.0))))
   (if (<= b -2.3e+103)
     t_2
     (if (<= b 1.22e-226)
       t_1
       (if (<= b 1.42e-178) x (if (<= b 1.95e+56) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.3e+103) {
		tmp = t_2;
	} else if (b <= 1.22e-226) {
		tmp = t_1;
	} else if (b <= 1.42e-178) {
		tmp = x;
	} else if (b <= 1.95e+56) {
		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 = a * (1.0d0 - t)
    t_2 = b * (t - 2.0d0)
    if (b <= (-2.3d+103)) then
        tmp = t_2
    else if (b <= 1.22d-226) then
        tmp = t_1
    else if (b <= 1.42d-178) then
        tmp = x
    else if (b <= 1.95d+56) 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 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.3e+103) {
		tmp = t_2;
	} else if (b <= 1.22e-226) {
		tmp = t_1;
	} else if (b <= 1.42e-178) {
		tmp = x;
	} else if (b <= 1.95e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (t - 2.0)
	tmp = 0
	if b <= -2.3e+103:
		tmp = t_2
	elif b <= 1.22e-226:
		tmp = t_1
	elif b <= 1.42e-178:
		tmp = x
	elif b <= 1.95e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -2.3e+103)
		tmp = t_2;
	elseif (b <= 1.22e-226)
		tmp = t_1;
	elseif (b <= 1.42e-178)
		tmp = x;
	elseif (b <= 1.95e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+103)
		tmp = t_2;
	elseif (b <= 1.22e-226)
		tmp = t_1;
	elseif (b <= 1.42e-178)
		tmp = x;
	elseif (b <= 1.95e+56)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+103], t$95$2, If[LessEqual[b, 1.22e-226], t$95$1, If[LessEqual[b, 1.42e-178], x, If[LessEqual[b, 1.95e+56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.30000000000000008e103 or 1.94999999999999997e56 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf 73.5%

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

   4. Taylor expanded in y around 0 49.9%

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

   if -2.30000000000000008e103 < b < 1.22e-226 or 1.4200000000000001e-178 < b < 1.94999999999999997e56

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 40.1%

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

   if 1.22e-226 < b < 1.4200000000000001e-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 x around inf 38.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -650000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* t (- b a))))
   (if (<= t -650000.0)
     t_2
     (if (<= t 1.02e-116)
       t_1
       (if (<= t 4.2e+22) (* y (- b z)) (if (<= t 7.8e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -650000.0) {
		tmp = t_2;
	} else if (t <= 1.02e-116) {
		tmp = t_1;
	} else if (t <= 4.2e+22) {
		tmp = y * (b - z);
	} else if (t <= 7.8e+75) {
		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 - (y * z)
    t_2 = t * (b - a)
    if (t <= (-650000.0d0)) then
        tmp = t_2
    else if (t <= 1.02d-116) then
        tmp = t_1
    else if (t <= 4.2d+22) then
        tmp = y * (b - z)
    else if (t <= 7.8d+75) 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 - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -650000.0) {
		tmp = t_2;
	} else if (t <= 1.02e-116) {
		tmp = t_1;
	} else if (t <= 4.2e+22) {
		tmp = y * (b - z);
	} else if (t <= 7.8e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -650000.0:
		tmp = t_2
	elif t <= 1.02e-116:
		tmp = t_1
	elif t <= 4.2e+22:
		tmp = y * (b - z)
	elif t <= 7.8e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -650000.0)
		tmp = t_2;
	elseif (t <= 1.02e-116)
		tmp = t_1;
	elseif (t <= 4.2e+22)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 7.8e+75)
		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 - (y * z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -650000.0)
		tmp = t_2;
	elseif (t <= 1.02e-116)
		tmp = t_1;
	elseif (t <= 4.2e+22)
		tmp = y * (b - z);
	elseif (t <= 7.8e+75)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -650000.0], t$95$2, If[LessEqual[t, 1.02e-116], t$95$1, If[LessEqual[t, 4.2e+22], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5e5 or 7.80000000000000075e75 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 68.8%

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

   if -6.5e5 < t < 1.02e-116 or 4.1999999999999996e22 < t < 7.80000000000000075e75

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 79.9%

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

   4. Taylor expanded in y around inf 52.7%

      \[\leadsto x - \color{blue}{y \cdot z} \]

   if 1.02e-116 < t < 4.1999999999999996e22

   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 y around inf 54.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -650000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-116}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+75}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.6 \cdot 10^{+181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t\_2\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -9.6e+181)
     t_2
     (if (<= b 3.3e-9) (+ x (- t_1 (* z (+ y -1.0)))) (+ (+ x t_2) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.6e+181) {
		tmp = t_2;
	} else if (b <= 3.3e-9) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = (x + t_2) + 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) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-9.6d+181)) then
        tmp = t_2
    else if (b <= 3.3d-9) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else
        tmp = (x + t_2) + 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 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.6e+181) {
		tmp = t_2;
	} else if (b <= 3.3e-9) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = (x + t_2) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9.6e+181:
		tmp = t_2
	elif b <= 3.3e-9:
		tmp = x + (t_1 - (z * (y + -1.0)))
	else:
		tmp = (x + t_2) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9.6e+181)
		tmp = t_2;
	elseif (b <= 3.3e-9)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x + t_2) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9.6e+181)
		tmp = t_2;
	elseif (b <= 3.3e-9)
		tmp = x + (t_1 - (z * (y + -1.0)));
	else
		tmp = (x + t_2) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.6e+181], t$95$2, If[LessEqual[b, 3.3e-9], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.60000000000000009e181

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf 93.3%

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

   if -9.60000000000000009e181 < b < 3.30000000000000018e-9

   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 0 91.8%

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

   if 3.30000000000000018e-9 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 87.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -7e+181)
     t_1
     (if (<= b 5.5e+56)
       (+ x (- (* a (- 1.0 t)) (* z (+ y -1.0))))
       (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+181) {
		tmp = t_1;
	} else if (b <= 5.5e+56) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else {
		tmp = x + 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 = b * ((y + t) - 2.0d0)
    if (b <= (-7d+181)) then
        tmp = t_1
    else if (b <= 5.5d+56) then
        tmp = x + ((a * (1.0d0 - t)) - (z * (y + (-1.0d0))))
    else
        tmp = x + 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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+181) {
		tmp = t_1;
	} else if (b <= 5.5e+56) {
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -7e+181:
		tmp = t_1
	elif b <= 5.5e+56:
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -7e+181)
		tmp = t_1;
	elseif (b <= 5.5e+56)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -7e+181)
		tmp = t_1;
	elseif (b <= 5.5e+56)
		tmp = x + ((a * (1.0 - t)) - (z * (y + -1.0)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+181], t$95$1, If[LessEqual[b, 5.5e+56], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000016e181

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf 93.3%

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

   if -7.00000000000000016e181 < b < 5.5000000000000002e56

   1. Initial program 96.5%

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

   3. Taylor expanded in b around 0 90.5%

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

   if 5.5000000000000002e56 < b

   1. Initial program 91.2%

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

   3. Taylor expanded in a around 0 82.9%

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

   4. Taylor expanded in z around 0 78.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 20.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-149}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+171}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.05e+56)
   x
   (if (<= x 2.8e-149) z (if (<= x 0.65) a (if (<= x 3e+171) z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+56) {
		tmp = x;
	} else if (x <= 2.8e-149) {
		tmp = z;
	} else if (x <= 0.65) {
		tmp = a;
	} else if (x <= 3e+171) {
		tmp = z;
	} 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 <= (-1.05d+56)) then
        tmp = x
    else if (x <= 2.8d-149) then
        tmp = z
    else if (x <= 0.65d0) then
        tmp = a
    else if (x <= 3d+171) then
        tmp = z
    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 <= -1.05e+56) {
		tmp = x;
	} else if (x <= 2.8e-149) {
		tmp = z;
	} else if (x <= 0.65) {
		tmp = a;
	} else if (x <= 3e+171) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.05e+56:
		tmp = x
	elif x <= 2.8e-149:
		tmp = z
	elif x <= 0.65:
		tmp = a
	elif x <= 3e+171:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.05e+56)
		tmp = x;
	elseif (x <= 2.8e-149)
		tmp = z;
	elseif (x <= 0.65)
		tmp = a;
	elseif (x <= 3e+171)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.05e+56)
		tmp = x;
	elseif (x <= 2.8e-149)
		tmp = z;
	elseif (x <= 0.65)
		tmp = a;
	elseif (x <= 3e+171)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.05e+56], x, If[LessEqual[x, 2.8e-149], z, If[LessEqual[x, 0.65], a, If[LessEqual[x, 3e+171], z, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05000000000000009e56 or 3.0000000000000001e171 < x

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 40.9%

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

   if -1.05000000000000009e56 < x < 2.7999999999999999e-149 or 0.650000000000000022 < x < 3.0000000000000001e171

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 36.6%

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

   4. Taylor expanded in y around 0 19.7%

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

   if 2.7999999999999999e-149 < x < 0.650000000000000022

   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 a around inf 39.0%

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

   4. Taylor expanded in t around 0 21.4%

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

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-149}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+171}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+51} \lor \neg \left(a \leq 10^{+52}\right):\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.2e+51) (not (<= a 1e+52)))
   (+ x (+ z (* a (- 1.0 t))))
   (+ (+ x (* t b)) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.2e+51) || !(a <= 1e+52)) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = (x + (t * b)) + (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) :: tmp
    if ((a <= (-1.2d+51)) .or. (.not. (a <= 1d+52))) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else
        tmp = (x + (t * b)) + (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 tmp;
	if ((a <= -1.2e+51) || !(a <= 1e+52)) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = (x + (t * b)) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.2e+51) or not (a <= 1e+52):
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = (x + (t * b)) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.2e+51) || !(a <= 1e+52))
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(Float64(x + Float64(t * b)) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.2e+51) || ~((a <= 1e+52)))
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = (x + (t * b)) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.2e+51], N[Not[LessEqual[a, 1e+52]], $MachinePrecision]], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1999999999999999e51 or 9.9999999999999999e51 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in b around 0 75.7%

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

   4. Taylor expanded in y around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. neg-mul-1 69.6%

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

      5. unsub-neg 69.6%

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

   6. Simplified 69.6%

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

   if -1.1999999999999999e51 < a < 9.9999999999999999e51

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0 89.1%

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

   4. Taylor expanded in t around inf 76.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+51} \lor \neg \left(a \leq 10^{+52}\right):\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8000000.0)
     t_1
     (if (<= t 5.5e-270) x (if (<= t 7.6e+28) (* b (- y 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8000000.0) {
		tmp = t_1;
	} else if (t <= 5.5e-270) {
		tmp = x;
	} else if (t <= 7.6e+28) {
		tmp = 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 = t * (b - a)
    if (t <= (-8000000.0d0)) then
        tmp = t_1
    else if (t <= 5.5d-270) then
        tmp = x
    else if (t <= 7.6d+28) then
        tmp = 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 = t * (b - a);
	double tmp;
	if (t <= -8000000.0) {
		tmp = t_1;
	} else if (t <= 5.5e-270) {
		tmp = x;
	} else if (t <= 7.6e+28) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -8000000.0:
		tmp = t_1
	elif t <= 5.5e-270:
		tmp = x
	elif t <= 7.6e+28:
		tmp = b * (y - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8000000.0)
		tmp = t_1;
	elseif (t <= 5.5e-270)
		tmp = x;
	elseif (t <= 7.6e+28)
		tmp = 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 = t * (b - a);
	tmp = 0.0;
	if (t <= -8000000.0)
		tmp = t_1;
	elseif (t <= 5.5e-270)
		tmp = x;
	elseif (t <= 7.6e+28)
		tmp = 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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8000000.0], t$95$1, If[LessEqual[t, 5.5e-270], x, If[LessEqual[t, 7.6e+28], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8e6 or 7.5999999999999998e28 < t

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf 65.6%

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

   if -8e6 < t < 5.4999999999999996e-270

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 31.4%

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

   if 5.4999999999999996e-270 < t < 7.5999999999999998e28

   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 t around inf 33.6%

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

      1. mul-1-neg 33.6%

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

      2. distribute-rgt-neg-in 33.6%

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

   5. Simplified 33.6%

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

   6. Taylor expanded in t around 0 32.2%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.3e+55)
     t_1
     (if (<= y -1.7e-131)
       (* a (- 1.0 t))
       (if (<= y 7e+16) (* 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 <= -2.3e+55) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = a * (1.0 - t);
	} else if (y <= 7e+16) {
		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 <= (-2.3d+55)) then
        tmp = t_1
    else if (y <= (-1.7d-131)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 7d+16) 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 <= -2.3e+55) {
		tmp = t_1;
	} else if (y <= -1.7e-131) {
		tmp = a * (1.0 - t);
	} else if (y <= 7e+16) {
		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 <= -2.3e+55:
		tmp = t_1
	elif y <= -1.7e-131:
		tmp = a * (1.0 - t)
	elif y <= 7e+16:
		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 <= -2.3e+55)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 7e+16)
		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 <= -2.3e+55)
		tmp = t_1;
	elseif (y <= -1.7e-131)
		tmp = a * (1.0 - t);
	elseif (y <= 7e+16)
		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, -2.3e+55], t$95$1, If[LessEqual[y, -1.7e-131], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+16], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999987e55 or 7e16 < y

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 68.7%

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

   if -2.29999999999999987e55 < y < -1.69999999999999998e-131

   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 45.8%

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

   if -1.69999999999999998e-131 < y < 7e16

   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 t around inf 47.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-11} \lor \neg \left(a \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.7e-11) (not (<= a 1.6e+43))) (* a (- 1.0 t)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.7e-11) || !(a <= 1.6e+43)) {
		tmp = a * (1.0 - t);
	} 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 ((a <= (-5.7d-11)) .or. (.not. (a <= 1.6d+43))) then
        tmp = a * (1.0d0 - t)
    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 ((a <= -5.7e-11) || !(a <= 1.6e+43)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.7e-11) or not (a <= 1.6e+43):
		tmp = a * (1.0 - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.7e-11) || !(a <= 1.6e+43))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5.7e-11) || ~((a <= 1.6e+43)))
		tmp = a * (1.0 - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.7e-11], N[Not[LessEqual[a, 1.6e+43]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.6999999999999997e-11 or 1.60000000000000007e43 < a

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 50.9%

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

   if -5.6999999999999997e-11 < a < 1.60000000000000007e43

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 24.8%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-11} \lor \neg \left(a \leq 1.6 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 27.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1800000 \lor \neg \left(t \leq 1.1 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1800000.0) (not (<= t 1.1e+75))) (* a (- t)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1800000.0) || !(t <= 1.1e+75)) {
		tmp = a * -t;
	} 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 ((t <= (-1800000.0d0)) .or. (.not. (t <= 1.1d+75))) then
        tmp = a * -t
    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 ((t <= -1800000.0) || !(t <= 1.1e+75)) {
		tmp = a * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1800000.0) or not (t <= 1.1e+75):
		tmp = a * -t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1800000.0) || !(t <= 1.1e+75))
		tmp = Float64(a * Float64(-t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1800000.0) || ~((t <= 1.1e+75)))
		tmp = a * -t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1800000.0], N[Not[LessEqual[t, 1.1e+75]], $MachinePrecision]], N[(a * (-t)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e6 or 1.10000000000000006e75 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 69.4%

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

   4. Taylor expanded in b around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. mul-1-neg 40.0%

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

   6. Simplified 40.0%

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

   if -1.8e6 < t < 1.10000000000000006e75

   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 x around inf 26.6%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1800000 \lor \neg \left(t \leq 1.1 \cdot 10^{+75}\right):\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -210000000000 \lor \neg \left(t \leq 3.7 \cdot 10^{+112}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -210000000000.0) (not (<= t 3.7e+112))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -210000000000.0) || !(t <= 3.7e+112)) {
		tmp = t * b;
	} 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 ((t <= (-210000000000.0d0)) .or. (.not. (t <= 3.7d+112))) then
        tmp = t * b
    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 ((t <= -210000000000.0) || !(t <= 3.7e+112)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -210000000000.0) or not (t <= 3.7e+112):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -210000000000.0) || !(t <= 3.7e+112))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -210000000000.0) || ~((t <= 3.7e+112)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -210000000000.0], N[Not[LessEqual[t, 3.7e+112]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e11 or 3.70000000000000004e112 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in b around inf 39.9%

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

   4. Taylor expanded in t around inf 36.4%

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

   if -2.1e11 < t < 3.70000000000000004e112

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 25.9%

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

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -210000000000 \lor \neg \left(t \leq 3.7 \cdot 10^{+112}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+184}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.2e+184) a (if (<= a 1.9e+43) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.2e+184) {
		tmp = a;
	} else if (a <= 1.9e+43) {
		tmp = x;
	} else {
		tmp = 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 (a <= (-8.2d+184)) then
        tmp = a
    else if (a <= 1.9d+43) then
        tmp = x
    else
        tmp = 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 (a <= -8.2e+184) {
		tmp = a;
	} else if (a <= 1.9e+43) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.2e+184:
		tmp = a
	elif a <= 1.9e+43:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.2e+184)
		tmp = a;
	elseif (a <= 1.9e+43)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8.2e+184)
		tmp = a;
	elseif (a <= 1.9e+43)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.2e+184], a, If[LessEqual[a, 1.9e+43], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -8.1999999999999993e184 or 1.90000000000000004e43 < a

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 57.9%

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

   4. Taylor expanded in t around 0 22.3%

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

   if -8.1999999999999993e184 < a < 1.90000000000000004e43

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf 23.7%

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

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+184}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 11.2% 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 28.3%

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

4. Taylor expanded in t around 0 10.3%

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

5. Final simplification 10.3%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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)))