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

Percentage Accurate: 95.4% → 97.1%

Time: 12.8s

Alternatives: 16

Speedup: 0.5×

• 36.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.56e+192)
   (* b (- (+ t y) 2.0))
   (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) {
	double tmp;
	if (b <= -1.56e+192) {
		tmp = b * ((t + y) - 2.0);
	} else {
		tmp = fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.56e+192)
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	else
		tmp = fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.56e+192], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if b < -1.56e192

   1. Initial program 70.8%

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

   3. Taylor expanded in b around inf 95.8%

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

   if -1.56e192 < b

   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. Step-by-step derivation

      1. +-commutative 95.7%

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

      2. fma-def 98.7%

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

      3. associate--l+ 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

      6. sub-neg 98.7%

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

      7. associate-+l- 98.7%

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

      8. fma-neg 99.1%

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

      9. sub-neg 99.1%

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

      10. metadata-eval 99.1%

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

      11. remove-double-neg 99.1%

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

      12. sub-neg 99.1%

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

      13. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 77.0%

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

4. Final simplification 98.5%

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

Alternative 3: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -3e+29)
     t_2
     (if (<= b -1.5e-68)
       t_1
       (if (<= b -6.8e-166) (* a (- 1.0 t)) (if (<= b 1.62e+47) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -3e+29) {
		tmp = t_2;
	} else if (b <= -1.5e-68) {
		tmp = t_1;
	} else if (b <= -6.8e-166) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.62e+47) {
		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 * (1.0d0 - y))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-3d+29)) then
        tmp = t_2
    else if (b <= (-1.5d-68)) then
        tmp = t_1
    else if (b <= (-6.8d-166)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.62d+47) 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 * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -3e+29) {
		tmp = t_2;
	} else if (b <= -1.5e-68) {
		tmp = t_1;
	} else if (b <= -6.8e-166) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.62e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -3e+29:
		tmp = t_2
	elif b <= -1.5e-68:
		tmp = t_1
	elif b <= -6.8e-166:
		tmp = a * (1.0 - t)
	elif b <= 1.62e+47:
		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(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -3e+29)
		tmp = t_2;
	elseif (b <= -1.5e-68)
		tmp = t_1;
	elseif (b <= -6.8e-166)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.62e+47)
		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 * (1.0 - y));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -3e+29)
		tmp = t_2;
	elseif (b <= -1.5e-68)
		tmp = t_1;
	elseif (b <= -6.8e-166)
		tmp = a * (1.0 - t);
	elseif (b <= 1.62e+47)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+29], t$95$2, If[LessEqual[b, -1.5e-68], t$95$1, If[LessEqual[b, -6.8e-166], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.62e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9999999999999999e29 or 1.6200000000000001e47 < b

   1. Initial program 86.9%

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

   3. Taylor expanded in b around inf 77.1%

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

   if -2.9999999999999999e29 < b < -1.5e-68 or -6.7999999999999995e-166 < b < 1.6200000000000001e47

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 98.3%

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

   4. Taylor expanded in a around 0 73.6%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in b around 0 67.3%

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

      1. +-commutative 67.3%

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

   9. Simplified 67.3%

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

   if -1.5e-68 < b < -6.7999999999999995e-166

   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 70.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.62 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-151}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -7.6e+56)
     t_2
     (if (<= y 2.35e-204)
       t_1
       (if (<= y 4.4e-151) (* b t) (if (<= y 7.2e+64) 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 = z * -y;
	double tmp;
	if (y <= -7.6e+56) {
		tmp = t_2;
	} else if (y <= 2.35e-204) {
		tmp = t_1;
	} else if (y <= 4.4e-151) {
		tmp = b * t;
	} else if (y <= 7.2e+64) {
		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 = z * -y
    if (y <= (-7.6d+56)) then
        tmp = t_2
    else if (y <= 2.35d-204) then
        tmp = t_1
    else if (y <= 4.4d-151) then
        tmp = b * t
    else if (y <= 7.2d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -7.6e+56) {
		tmp = t_2;
	} else if (y <= 2.35e-204) {
		tmp = t_1;
	} else if (y <= 4.4e-151) {
		tmp = b * t;
	} else if (y <= 7.2e+64) {
		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 = z * -y
	tmp = 0
	if y <= -7.6e+56:
		tmp = t_2
	elif y <= 2.35e-204:
		tmp = t_1
	elif y <= 4.4e-151:
		tmp = b * t
	elif y <= 7.2e+64:
		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(z * Float64(-y))
	tmp = 0.0
	if (y <= -7.6e+56)
		tmp = t_2;
	elseif (y <= 2.35e-204)
		tmp = t_1;
	elseif (y <= 4.4e-151)
		tmp = Float64(b * t);
	elseif (y <= 7.2e+64)
		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 = z * -y;
	tmp = 0.0;
	if (y <= -7.6e+56)
		tmp = t_2;
	elseif (y <= 2.35e-204)
		tmp = t_1;
	elseif (y <= 4.4e-151)
		tmp = b * t;
	elseif (y <= 7.2e+64)
		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[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -7.6e+56], t$95$2, If[LessEqual[y, 2.35e-204], t$95$1, If[LessEqual[y, 4.4e-151], N[(b * t), $MachinePrecision], If[LessEqual[y, 7.2e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.59999999999999991e56 or 7.20000000000000027e64 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 79.2%

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

   4. Taylor expanded in b around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. *-commutative 48.1%

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

      3. distribute-rgt-neg-in 48.1%

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

   6. Simplified 48.1%

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

   if -7.59999999999999991e56 < y < 2.34999999999999996e-204 or 4.3999999999999999e-151 < y < 7.20000000000000027e64

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 40.9%

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

   if 2.34999999999999996e-204 < y < 4.3999999999999999e-151

   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 t around inf 55.4%

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

   4. Taylor expanded in b around inf 55.4%

      \[\leadsto \color{blue}{b \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-151}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -2.8e+50)
     t_2
     (if (<= y -1.85e-300)
       t_1
       (if (<= y 1.3e-147) (* b (- t 2.0)) (if (<= y 5e+62) 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 = z * -y;
	double tmp;
	if (y <= -2.8e+50) {
		tmp = t_2;
	} else if (y <= -1.85e-300) {
		tmp = t_1;
	} else if (y <= 1.3e-147) {
		tmp = b * (t - 2.0);
	} else if (y <= 5e+62) {
		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 = z * -y
    if (y <= (-2.8d+50)) then
        tmp = t_2
    else if (y <= (-1.85d-300)) then
        tmp = t_1
    else if (y <= 1.3d-147) then
        tmp = b * (t - 2.0d0)
    else if (y <= 5d+62) 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 = z * -y;
	double tmp;
	if (y <= -2.8e+50) {
		tmp = t_2;
	} else if (y <= -1.85e-300) {
		tmp = t_1;
	} else if (y <= 1.3e-147) {
		tmp = b * (t - 2.0);
	} else if (y <= 5e+62) {
		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 = z * -y
	tmp = 0
	if y <= -2.8e+50:
		tmp = t_2
	elif y <= -1.85e-300:
		tmp = t_1
	elif y <= 1.3e-147:
		tmp = b * (t - 2.0)
	elif y <= 5e+62:
		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(z * Float64(-y))
	tmp = 0.0
	if (y <= -2.8e+50)
		tmp = t_2;
	elseif (y <= -1.85e-300)
		tmp = t_1;
	elseif (y <= 1.3e-147)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 5e+62)
		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 = z * -y;
	tmp = 0.0;
	if (y <= -2.8e+50)
		tmp = t_2;
	elseif (y <= -1.85e-300)
		tmp = t_1;
	elseif (y <= 1.3e-147)
		tmp = b * (t - 2.0);
	elseif (y <= 5e+62)
		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[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -2.8e+50], t$95$2, If[LessEqual[y, -1.85e-300], t$95$1, If[LessEqual[y, 1.3e-147], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e50 or 5.00000000000000029e62 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 79.2%

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

   4. Taylor expanded in b around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. *-commutative 48.1%

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

      3. distribute-rgt-neg-in 48.1%

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

   6. Simplified 48.1%

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

   if -2.7999999999999998e50 < y < -1.8500000000000001e-300 or 1.2999999999999999e-147 < y < 5.00000000000000029e62

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 41.2%

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

   if -1.8500000000000001e-300 < y < 1.2999999999999999e-147

   1. Initial program 96.0%

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

   3. Taylor expanded in b around inf 56.9%

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

   4. Taylor expanded in y around 0 56.9%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+28} \lor \neg \left(b \leq 2.4 \cdot 10^{+34}\right):\\ \;\;\;\;\left(b \cdot \left(\left(t + y\right) - 2\right) + x\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -2.6e+28) (not (<= b 2.4e+34)))
     (+ (+ (* b (- (+ t y) 2.0)) x) t_1)
     (+ x (+ (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.6e+28) || !(b <= 2.4e+34)) {
		tmp = ((b * ((t + y) - 2.0)) + x) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + 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 = z * (1.0d0 - y)
    if ((b <= (-2.6d+28)) .or. (.not. (b <= 2.4d+34))) then
        tmp = ((b * ((t + y) - 2.0d0)) + x) + t_1
    else
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.6e+28) || !(b <= 2.4e+34)) {
		tmp = ((b * ((t + y) - 2.0)) + x) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -2.6e+28) or not (b <= 2.4e+34):
		tmp = ((b * ((t + y) - 2.0)) + x) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -2.6e+28) || !(b <= 2.4e+34))
		tmp = Float64(Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + x) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -2.6e+28) || ~((b <= 2.4e+34)))
		tmp = ((b * ((t + y) - 2.0)) + x) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.6e+28], N[Not[LessEqual[b, 2.4e+34]], $MachinePrecision]], N[(N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6000000000000002e28 or 2.39999999999999987e34 < b

   1. Initial program 87.5%

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

   3. Taylor expanded in a around 0 86.0%

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

   if -2.6000000000000002e28 < b < 2.39999999999999987e34

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 93.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+28} \lor \neg \left(b \leq 2.4 \cdot 10^{+34}\right):\\ \;\;\;\;\left(b \cdot \left(\left(t + y\right) - 2\right) + x\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.22 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+123}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -2.22e+30)
     t_1
     (if (<= b 6.5e+123)
       (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))
       (- t_1 (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.22e+30) {
		tmp = t_1;
	} else if (b <= 6.5e+123) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t + y) - 2.0d0)
    if (b <= (-2.22d+30)) then
        tmp = t_1
    else if (b <= 6.5d+123) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    else
        tmp = t_1 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.22e+30) {
		tmp = t_1;
	} else if (b <= 6.5e+123) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.22e+30:
		tmp = t_1
	elif b <= 6.5e+123:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	else:
		tmp = t_1 - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.22e+30)
		tmp = t_1;
	elseif (b <= 6.5e+123)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(t_1 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.22e+30)
		tmp = t_1;
	elseif (b <= 6.5e+123)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	else
		tmp = t_1 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.22e+30], t$95$1, If[LessEqual[b, 6.5e+123], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.22e30

   1. Initial program 87.7%

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

   3. Taylor expanded in b around inf 83.3%

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

   if -2.22e30 < b < 6.5000000000000001e123

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 89.6%

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

   if 6.5000000000000001e123 < b

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. *-commutative 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.22 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+123}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.8e+38)
     t_1
     (if (<= t 5.6e-122)
       (* y (- b z))
       (if (<= t 4.2e+26) (* z (- 1.0 y)) 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 <= -4.8e+38) {
		tmp = t_1;
	} else if (t <= 5.6e-122) {
		tmp = y * (b - z);
	} else if (t <= 4.2e+26) {
		tmp = z * (1.0 - y);
	} 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 <= (-4.8d+38)) then
        tmp = t_1
    else if (t <= 5.6d-122) then
        tmp = y * (b - z)
    else if (t <= 4.2d+26) then
        tmp = z * (1.0d0 - y)
    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 <= -4.8e+38) {
		tmp = t_1;
	} else if (t <= 5.6e-122) {
		tmp = y * (b - z);
	} else if (t <= 4.2e+26) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.8e+38:
		tmp = t_1
	elif t <= 5.6e-122:
		tmp = y * (b - z)
	elif t <= 4.2e+26:
		tmp = z * (1.0 - y)
	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 <= -4.8e+38)
		tmp = t_1;
	elseif (t <= 5.6e-122)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 4.2e+26)
		tmp = Float64(z * Float64(1.0 - y));
	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 <= -4.8e+38)
		tmp = t_1;
	elseif (t <= 5.6e-122)
		tmp = y * (b - z);
	elseif (t <= 4.2e+26)
		tmp = z * (1.0 - y);
	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, -4.8e+38], t$95$1, If[LessEqual[t, 5.6e-122], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+26], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000035e38 or 4.2000000000000002e26 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 72.7%

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

   if -4.80000000000000035e38 < t < 5.5999999999999998e-122

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 51.8%

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

   if 5.5999999999999998e-122 < t < 4.2000000000000002e26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 61.5%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+144} \lor \neg \left(y \leq 6.5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+144) (not (<= y 6.5e+53)))
   (* y (- b z))
   (+ x (+ z (* b (+ t -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+144) || !(y <= 6.5e+53)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (b * (t + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d+144)) .or. (.not. (y <= 6.5d+53))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + (b * (t + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+144) || !(y <= 6.5e+53)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (b * (t + -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+144) or not (y <= 6.5e+53):
		tmp = y * (b - z)
	else:
		tmp = x + (z + (b * (t + -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+144) || !(y <= 6.5e+53))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(b * Float64(t + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+144) || ~((y <= 6.5e+53)))
		tmp = y * (b - z);
	else
		tmp = x + (z + (b * (t + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+144], N[Not[LessEqual[y, 6.5e+53]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999935e144 or 6.50000000000000017e53 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 84.3%

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

   if -8.99999999999999935e144 < y < 6.50000000000000017e53

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 97.4%

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

   4. Taylor expanded in a around 0 67.2%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in y around 0 63.6%

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

      1. +-commutative 63.6%

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

      2. sub-neg 63.6%

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

      3. metadata-eval 63.6%

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

   9. Simplified 63.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+144} \lor \neg \left(y \leq 6.5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 25.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+47}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-166}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.3e+47)
   (* b t)
   (if (<= b -7e-166) a (if (<= b 1e+30) x (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.3e+47) {
		tmp = b * t;
	} else if (b <= -7e-166) {
		tmp = a;
	} else if (b <= 1e+30) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.3d+47)) then
        tmp = b * t
    else if (b <= (-7d-166)) then
        tmp = a
    else if (b <= 1d+30) then
        tmp = x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.3e+47) {
		tmp = b * t;
	} else if (b <= -7e-166) {
		tmp = a;
	} else if (b <= 1e+30) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.3e+47:
		tmp = b * t
	elif b <= -7e-166:
		tmp = a
	elif b <= 1e+30:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.3e+47)
		tmp = Float64(b * t);
	elseif (b <= -7e-166)
		tmp = a;
	elseif (b <= 1e+30)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.3e+47)
		tmp = b * t;
	elseif (b <= -7e-166)
		tmp = a;
	elseif (b <= 1e+30)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.3e+47], N[(b * t), $MachinePrecision], If[LessEqual[b, -7e-166], a, If[LessEqual[b, 1e+30], x, N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.30000000000000003e47 or 1e30 < b

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 43.2%

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

   4. Taylor expanded in b around inf 34.0%

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

   if -6.30000000000000003e47 < b < -6.9999999999999998e-166

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 48.4%

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

   4. Taylor expanded in t around 0 23.9%

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

   if -6.9999999999999998e-166 < b < 1e30

   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 x around inf 24.4%

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

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+47}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-166}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+38} \lor \neg \left(t \leq 1.05 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.3e+38) (not (<= t 1.05e+26))) (* t (- b a)) (* z (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.3e+38) || !(t <= 1.05e+26)) {
		tmp = t * (b - a);
	} else {
		tmp = z * -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 ((t <= (-1.3d+38)) .or. (.not. (t <= 1.05d+26))) then
        tmp = t * (b - a)
    else
        tmp = z * -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 ((t <= -1.3e+38) || !(t <= 1.05e+26)) {
		tmp = t * (b - a);
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.3e+38) or not (t <= 1.05e+26):
		tmp = t * (b - a)
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.3e+38) || !(t <= 1.05e+26))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.3e+38) || ~((t <= 1.05e+26)))
		tmp = t * (b - a);
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.3e+38], N[Not[LessEqual[t, 1.05e+26]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e38 or 1.05e26 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 72.7%

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

   if -1.3e38 < t < 1.05e26

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 50.2%

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

   4. Taylor expanded in b around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

      3. distribute-rgt-neg-in 29.0%

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

   6. Simplified 29.0%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+38} \lor \neg \left(t \leq 1.05 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+63} \lor \neg \left(y \leq 1.6 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.2e+63) (not (<= y 1.6e+57))) (* y (- b z)) (* t (- b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+63) || !(y <= 1.6e+57)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.2d+63)) .or. (.not. (y <= 1.6d+57))) then
        tmp = y * (b - z)
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.2e+63) || !(y <= 1.6e+57)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.2e+63) or not (y <= 1.6e+57):
		tmp = y * (b - z)
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.2e+63) || !(y <= 1.6e+57))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.2e+63) || ~((y <= 1.6e+57)))
		tmp = y * (b - z);
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.2e+63], N[Not[LessEqual[y, 1.6e+57]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999985e63 or 1.60000000000000015e57 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 80.1%

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

   if -8.19999999999999985e63 < y < 1.60000000000000015e57

   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 t around inf 44.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+63} \lor \neg \left(y \leq 1.6 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+116} \lor \neg \left(t \leq 2.05 \cdot 10^{+26}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.4e+116) (not (<= t 2.05e+26))) (* b t) (* z (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.4e+116) || !(t <= 2.05e+26)) {
		tmp = b * t;
	} else {
		tmp = z * -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 ((t <= (-9.4d+116)) .or. (.not. (t <= 2.05d+26))) then
        tmp = b * t
    else
        tmp = z * -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 ((t <= -9.4e+116) || !(t <= 2.05e+26)) {
		tmp = b * t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.4e+116) or not (t <= 2.05e+26):
		tmp = b * t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.4e+116) || !(t <= 2.05e+26))
		tmp = Float64(b * t);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.4e+116) || ~((t <= 2.05e+26)))
		tmp = b * t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.4e+116], N[Not[LessEqual[t, 2.05e+26]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4000000000000007e116 or 2.04999999999999992e26 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 77.8%

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

   4. Taylor expanded in b around inf 41.2%

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

   if -9.4000000000000007e116 < t < 2.04999999999999992e26

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 49.1%

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

   4. Taylor expanded in b around 0 29.7%

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

      1. mul-1-neg 29.7%

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

      2. *-commutative 29.7%

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

      3. distribute-rgt-neg-in 29.7%

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

   6. Simplified 29.7%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+116} \lor \neg \left(t \leq 2.05 \cdot 10^{+26}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+117} \lor \neg \left(t \leq 4.4 \cdot 10^{+32}\right):\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e+117) (not (<= t 4.4e+32))) (* t (- a)) (* z (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e+117) || !(t <= 4.4e+32)) {
		tmp = t * -a;
	} else {
		tmp = z * -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 ((t <= (-2.2d+117)) .or. (.not. (t <= 4.4d+32))) then
        tmp = t * -a
    else
        tmp = z * -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 ((t <= -2.2e+117) || !(t <= 4.4e+32)) {
		tmp = t * -a;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e+117) or not (t <= 4.4e+32):
		tmp = t * -a
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e+117) || !(t <= 4.4e+32))
		tmp = Float64(t * Float64(-a));
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e+117) || ~((t <= 4.4e+32)))
		tmp = t * -a;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e+117], N[Not[LessEqual[t, 4.4e+32]], $MachinePrecision]], N[(t * (-a)), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000014e117 or 4.40000000000000002e32 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 47.7%

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

   4. Taylor expanded in t around 0 47.7%

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

   5. Taylor expanded in t around inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. mul-1-neg 47.7%

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

   7. Simplified 47.7%

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

   if -2.20000000000000014e117 < t < 4.40000000000000002e32

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf 48.3%

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

   4. Taylor expanded in b around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. *-commutative 29.2%

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

      3. distribute-rgt-neg-in 29.2%

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

   6. Simplified 29.2%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+117} \lor \neg \left(t \leq 4.4 \cdot 10^{+32}\right):\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 21.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+116}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.6e+91) x (if (<= x 8.8e+116) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+91) {
		tmp = x;
	} else if (x <= 8.8e+116) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.6d+91)) then
        tmp = x
    else if (x <= 8.8d+116) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+91) {
		tmp = x;
	} else if (x <= 8.8e+116) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.6e+91:
		tmp = x
	elif x <= 8.8e+116:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.6e+91)
		tmp = x;
	elseif (x <= 8.8e+116)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.6e+91)
		tmp = x;
	elseif (x <= 8.8e+116)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.6e+91], x, If[LessEqual[x, 8.8e+116], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.59999999999999932e91 or 8.799999999999999e116 < x

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 35.7%

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

   if -9.59999999999999932e91 < x < 8.799999999999999e116

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 31.6%

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

   4. Taylor expanded in t around 0 12.8%

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

4. Final simplification 20.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+116}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 93.3%

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

3. Taylor expanded in a around inf 27.2%

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

4. Taylor expanded in t around 0 9.6%

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

5. Final simplification 9.6%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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)))