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

Percentage Accurate: 95.2% → 97.5%

Time: 19.2s

Alternatives: 23

Speedup: 0.5×

• 35.9% 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: 95.2% 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: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.95e+183)
   (+ x (* b (- (+ y t) 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 <= -1.95e+183) {
		tmp = x + (b * ((y + t) - 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 <= -1.95e+183)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 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, -1.95e+183], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $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 < -1.9499999999999999e183

   1. Initial program 81.5%

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

   3. Taylor expanded in y around -inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. distribute-lft-out-- 67.6%

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

      3. associate-*r* 67.6%

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

      4. neg-mul-1 67.6%

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

      5. distribute-lft-neg-in 67.6%

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

      6. *-commutative 67.6%

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

      7. distribute-lft-neg-in 67.6%

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

      8. metadata-eval 67.6%

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

      9. *-lft-identity 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in x around inf 96.5%

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

   if -1.9499999999999999e183 < b

   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. Step-by-step derivation

      1. +-commutative 96.5%

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

      2. fma-define 98.2%

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

      3. associate--l+ 98.2%

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

      4. sub-neg 98.2%

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

      5. metadata-eval 98.2%

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

      6. sub-neg 98.2%

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

      7. associate-+l- 98.2%

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

      8. fma-neg 98.7%

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

      9. sub-neg 98.7%

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

      10. metadata-eval 98.7%

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

      11. remove-double-neg 98.7%

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

      12. sub-neg 98.7%

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

      13. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 34.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+179}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-95}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-104}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* y (- z))))
   (if (<= y -2.35e+179)
     (* b y)
     (if (<= y -1.05e+94)
       t_2
       (if (<= y -3.7e+33)
         t_1
         (if (<= y -2.2)
           t_2
           (if (<= y -3e-46)
             t_1
             (if (<= y -8.5e-95)
               (+ x a)
               (if (<= y -9e-104)
                 (- (* t a))
                 (if (<= y -2.65e-188)
                   t_1
                   (if (<= y 1.56e+38) (* a (- 1.0 t)) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = y * -z;
	double tmp;
	if (y <= -2.35e+179) {
		tmp = b * y;
	} else if (y <= -1.05e+94) {
		tmp = t_2;
	} else if (y <= -3.7e+33) {
		tmp = t_1;
	} else if (y <= -2.2) {
		tmp = t_2;
	} else if (y <= -3e-46) {
		tmp = t_1;
	} else if (y <= -8.5e-95) {
		tmp = x + a;
	} else if (y <= -9e-104) {
		tmp = -(t * a);
	} else if (y <= -2.65e-188) {
		tmp = t_1;
	} else if (y <= 1.56e+38) {
		tmp = a * (1.0 - t);
	} 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 = b * (t - 2.0d0)
    t_2 = y * -z
    if (y <= (-2.35d+179)) then
        tmp = b * y
    else if (y <= (-1.05d+94)) then
        tmp = t_2
    else if (y <= (-3.7d+33)) then
        tmp = t_1
    else if (y <= (-2.2d0)) then
        tmp = t_2
    else if (y <= (-3d-46)) then
        tmp = t_1
    else if (y <= (-8.5d-95)) then
        tmp = x + a
    else if (y <= (-9d-104)) then
        tmp = -(t * a)
    else if (y <= (-2.65d-188)) then
        tmp = t_1
    else if (y <= 1.56d+38) then
        tmp = a * (1.0d0 - t)
    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 = b * (t - 2.0);
	double t_2 = y * -z;
	double tmp;
	if (y <= -2.35e+179) {
		tmp = b * y;
	} else if (y <= -1.05e+94) {
		tmp = t_2;
	} else if (y <= -3.7e+33) {
		tmp = t_1;
	} else if (y <= -2.2) {
		tmp = t_2;
	} else if (y <= -3e-46) {
		tmp = t_1;
	} else if (y <= -8.5e-95) {
		tmp = x + a;
	} else if (y <= -9e-104) {
		tmp = -(t * a);
	} else if (y <= -2.65e-188) {
		tmp = t_1;
	} else if (y <= 1.56e+38) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = y * -z
	tmp = 0
	if y <= -2.35e+179:
		tmp = b * y
	elif y <= -1.05e+94:
		tmp = t_2
	elif y <= -3.7e+33:
		tmp = t_1
	elif y <= -2.2:
		tmp = t_2
	elif y <= -3e-46:
		tmp = t_1
	elif y <= -8.5e-95:
		tmp = x + a
	elif y <= -9e-104:
		tmp = -(t * a)
	elif y <= -2.65e-188:
		tmp = t_1
	elif y <= 1.56e+38:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -2.35e+179)
		tmp = Float64(b * y);
	elseif (y <= -1.05e+94)
		tmp = t_2;
	elseif (y <= -3.7e+33)
		tmp = t_1;
	elseif (y <= -2.2)
		tmp = t_2;
	elseif (y <= -3e-46)
		tmp = t_1;
	elseif (y <= -8.5e-95)
		tmp = Float64(x + a);
	elseif (y <= -9e-104)
		tmp = Float64(-Float64(t * a));
	elseif (y <= -2.65e-188)
		tmp = t_1;
	elseif (y <= 1.56e+38)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = y * -z;
	tmp = 0.0;
	if (y <= -2.35e+179)
		tmp = b * y;
	elseif (y <= -1.05e+94)
		tmp = t_2;
	elseif (y <= -3.7e+33)
		tmp = t_1;
	elseif (y <= -2.2)
		tmp = t_2;
	elseif (y <= -3e-46)
		tmp = t_1;
	elseif (y <= -8.5e-95)
		tmp = x + a;
	elseif (y <= -9e-104)
		tmp = -(t * a);
	elseif (y <= -2.65e-188)
		tmp = t_1;
	elseif (y <= 1.56e+38)
		tmp = a * (1.0 - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -2.35e+179], N[(b * y), $MachinePrecision], If[LessEqual[y, -1.05e+94], t$95$2, If[LessEqual[y, -3.7e+33], t$95$1, If[LessEqual[y, -2.2], t$95$2, If[LessEqual[y, -3e-46], t$95$1, If[LessEqual[y, -8.5e-95], N[(x + a), $MachinePrecision], If[LessEqual[y, -9e-104], (-N[(t * a), $MachinePrecision]), If[LessEqual[y, -2.65e-188], t$95$1, If[LessEqual[y, 1.56e+38], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.35000000000000003e179

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf 54.8%

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

   4. Taylor expanded in y around inf 54.7%

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

   if -2.35000000000000003e179 < y < -1.04999999999999995e94 or -3.6999999999999999e33 < y < -2.2000000000000002 or 1.5599999999999999e38 < y

   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 y around inf 75.9%

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

   4. Taylor expanded in b around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. *-commutative 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

   6. Simplified 52.9%

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

   if -1.04999999999999995e94 < y < -3.6999999999999999e33 or -2.2000000000000002 < y < -2.99999999999999987e-46 or -8.9999999999999995e-104 < y < -2.65000000000000007e-188

   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 b around inf 65.1%

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

   4. Taylor expanded in y around 0 54.8%

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

   if -2.99999999999999987e-46 < y < -8.4999999999999995e-95

   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 b around 0 100.0%

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

   4. Taylor expanded in a around inf 95.1%

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

   5. Taylor expanded in t around 0 67.6%

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

      1. sub-neg 67.6%

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

      2. neg-mul-1 67.6%

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

      3. remove-double-neg 67.6%

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

   7. Simplified 67.6%

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

   if -8.4999999999999995e-95 < y < -8.9999999999999995e-104

   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 b around 0 76.1%

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

   4. Taylor expanded in t around inf 52.1%

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

   5. Taylor expanded in x around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. distribute-lft-neg-out 52.1%

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

      3. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if -2.65000000000000007e-188 < y < 1.5599999999999999e38

   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 44.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+179}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.2:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-95}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-104}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ y t) 2.0)) (+ (- x (* z (+ y -1.0))) (* a (- 1.0 t))))))
   (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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)))
	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(b * Float64(Float64(y + t) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y + -1.0))) + Float64(a * Float64(1.0 - t))))
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $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 69.3%

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

4. Final simplification 98.4%

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

Alternative 4: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := \left(x + b \cdot y\right) + z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-123}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (+ (+ x (* b y)) (* z (- 1.0 y)))))
   (if (<= t -1.3e+218)
     t_1
     (if (<= t -5.8e+127)
       (+ x (* b (- (+ y t) 2.0)))
       (if (<= t -2.35e+33)
         t_1
         (if (<= t -1.1e-121)
           t_2
           (if (<= t 1.9e-123)
             (+ x (- a (* z (+ y -1.0))))
             (if (<= t 7e+51) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = (x + (b * y)) + (z * (1.0 - y));
	double tmp;
	if (t <= -1.3e+218) {
		tmp = t_1;
	} else if (t <= -5.8e+127) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (t <= -2.35e+33) {
		tmp = t_1;
	} else if (t <= -1.1e-121) {
		tmp = t_2;
	} else if (t <= 1.9e-123) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (t <= 7e+51) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = (x + (b * y)) + (z * (1.0d0 - y))
    if (t <= (-1.3d+218)) then
        tmp = t_1
    else if (t <= (-5.8d+127)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (t <= (-2.35d+33)) then
        tmp = t_1
    else if (t <= (-1.1d-121)) then
        tmp = t_2
    else if (t <= 1.9d-123) then
        tmp = x + (a - (z * (y + (-1.0d0))))
    else if (t <= 7d+51) then
        tmp = t_2
    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 t_2 = (x + (b * y)) + (z * (1.0 - y));
	double tmp;
	if (t <= -1.3e+218) {
		tmp = t_1;
	} else if (t <= -5.8e+127) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (t <= -2.35e+33) {
		tmp = t_1;
	} else if (t <= -1.1e-121) {
		tmp = t_2;
	} else if (t <= 1.9e-123) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (t <= 7e+51) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = (x + (b * y)) + (z * (1.0 - y))
	tmp = 0
	if t <= -1.3e+218:
		tmp = t_1
	elif t <= -5.8e+127:
		tmp = x + (b * ((y + t) - 2.0))
	elif t <= -2.35e+33:
		tmp = t_1
	elif t <= -1.1e-121:
		tmp = t_2
	elif t <= 1.9e-123:
		tmp = x + (a - (z * (y + -1.0)))
	elif t <= 7e+51:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(Float64(x + Float64(b * y)) + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (t <= -1.3e+218)
		tmp = t_1;
	elseif (t <= -5.8e+127)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (t <= -2.35e+33)
		tmp = t_1;
	elseif (t <= -1.1e-121)
		tmp = t_2;
	elseif (t <= 1.9e-123)
		tmp = Float64(x + Float64(a - Float64(z * Float64(y + -1.0))));
	elseif (t <= 7e+51)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = (x + (b * y)) + (z * (1.0 - y));
	tmp = 0.0;
	if (t <= -1.3e+218)
		tmp = t_1;
	elseif (t <= -5.8e+127)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (t <= -2.35e+33)
		tmp = t_1;
	elseif (t <= -1.1e-121)
		tmp = t_2;
	elseif (t <= 1.9e-123)
		tmp = x + (a - (z * (y + -1.0)));
	elseif (t <= 7e+51)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x + N[(b * y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+218], t$95$1, If[LessEqual[t, -5.8e+127], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.35e+33], t$95$1, If[LessEqual[t, -1.1e-121], t$95$2, If[LessEqual[t, 1.9e-123], N[(x + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+51], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.30000000000000001e218 or -5.8000000000000004e127 < t < -2.3499999999999999e33 or 7e51 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 77.6%

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

   if -1.30000000000000001e218 < t < -5.8000000000000004e127

   1. Initial program 86.6%

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

   3. Taylor expanded in y around -inf 66.7%

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

      1. associate-*r* 66.7%

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

      2. distribute-lft-out-- 66.7%

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

      3. associate-*r* 66.7%

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

      4. neg-mul-1 66.7%

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

      5. distribute-lft-neg-in 66.7%

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

      6. *-commutative 66.7%

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

      7. distribute-lft-neg-in 66.7%

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

      8. metadata-eval 66.7%

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

      9. *-lft-identity 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 90.0%

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

   if -2.3499999999999999e33 < t < -1.10000000000000011e-121 or 1.89999999999999998e-123 < t < 7e51

   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 a around 0 85.2%

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

   4. Taylor expanded in y around inf 76.0%

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

   if -1.10000000000000011e-121 < t < 1.89999999999999998e-123

   1. Initial program 94.7%

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

   3. Taylor expanded in b around 0 73.8%

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

   4. Taylor expanded in t around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. sub-neg 73.8%

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

      3. metadata-eval 73.8%

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

      4. mul-1-neg 73.8%

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

      5. unsub-neg 73.8%

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

      6. +-commutative 73.8%

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

   6. Simplified 73.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;\left(x + b \cdot y\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-123}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+51}:\\ \;\;\;\;\left(x + b \cdot y\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -0.17:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.5e+93)
     t_1
     (if (<= y -6.1e+34)
       (* b (- (+ y t) 2.0))
       (if (<= y -0.17)
         (* z (- 1.0 y))
         (if (<= y -8.8e-33)
           (* b (- t 2.0))
           (if (<= y -2.5e-95)
             (+ x (+ z a))
             (if (<= y -2.2e-236)
               (* t (- b a))
               (if (<= y 2.5e+33) (- x (* t a)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.5e+93) {
		tmp = t_1;
	} else if (y <= -6.1e+34) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= -0.17) {
		tmp = z * (1.0 - y);
	} else if (y <= -8.8e-33) {
		tmp = b * (t - 2.0);
	} else if (y <= -2.5e-95) {
		tmp = x + (z + a);
	} else if (y <= -2.2e-236) {
		tmp = t * (b - a);
	} else if (y <= 2.5e+33) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-6.5d+93)) then
        tmp = t_1
    else if (y <= (-6.1d+34)) then
        tmp = b * ((y + t) - 2.0d0)
    else if (y <= (-0.17d0)) then
        tmp = z * (1.0d0 - y)
    else if (y <= (-8.8d-33)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-2.5d-95)) then
        tmp = x + (z + a)
    else if (y <= (-2.2d-236)) then
        tmp = t * (b - a)
    else if (y <= 2.5d+33) then
        tmp = x - (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.5e+93) {
		tmp = t_1;
	} else if (y <= -6.1e+34) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= -0.17) {
		tmp = z * (1.0 - y);
	} else if (y <= -8.8e-33) {
		tmp = b * (t - 2.0);
	} else if (y <= -2.5e-95) {
		tmp = x + (z + a);
	} else if (y <= -2.2e-236) {
		tmp = t * (b - a);
	} else if (y <= 2.5e+33) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6.5e+93:
		tmp = t_1
	elif y <= -6.1e+34:
		tmp = b * ((y + t) - 2.0)
	elif y <= -0.17:
		tmp = z * (1.0 - y)
	elif y <= -8.8e-33:
		tmp = b * (t - 2.0)
	elif y <= -2.5e-95:
		tmp = x + (z + a)
	elif y <= -2.2e-236:
		tmp = t * (b - a)
	elif y <= 2.5e+33:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.5e+93)
		tmp = t_1;
	elseif (y <= -6.1e+34)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (y <= -0.17)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= -8.8e-33)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -2.5e-95)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= -2.2e-236)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 2.5e+33)
		tmp = Float64(x - Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.5e+93)
		tmp = t_1;
	elseif (y <= -6.1e+34)
		tmp = b * ((y + t) - 2.0);
	elseif (y <= -0.17)
		tmp = z * (1.0 - y);
	elseif (y <= -8.8e-33)
		tmp = b * (t - 2.0);
	elseif (y <= -2.5e-95)
		tmp = x + (z + a);
	elseif (y <= -2.2e-236)
		tmp = t * (b - a);
	elseif (y <= 2.5e+33)
		tmp = x - (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+93], t$95$1, If[LessEqual[y, -6.1e+34], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.17], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e-33], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-95], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-236], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+33], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -6.4999999999999998e93 or 2.49999999999999986e33 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -6.4999999999999998e93 < y < -6.09999999999999996e34

   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 b around inf 69.5%

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

   if -6.09999999999999996e34 < y < -0.170000000000000012

   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 100.0%

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

   if -0.170000000000000012 < y < -8.80000000000000022e-33

   1. Initial program 75.0%

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

   3. Taylor expanded in b around inf 76.7%

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

   4. Taylor expanded in y around 0 76.7%

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

   if -8.80000000000000022e-33 < y < -2.4999999999999999e-95

   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 b around 0 91.3%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul-1-neg 73.7%

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

      5. unsub-neg 73.7%

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

      6. +-commutative 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around 0 73.7%

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

      1. mul-1-neg 73.7%

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

   9. Simplified 73.7%

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

   if -2.4999999999999999e-95 < y < -2.19999999999999992e-236

   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 t around inf 73.4%

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

   if -2.19999999999999992e-236 < y < 2.49999999999999986e33

   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 b around 0 78.0%

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

   4. Taylor expanded in t around inf 51.8%

      \[\leadsto x - \color{blue}{a \cdot t} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -0.17:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := t\_2 + t\_1\\ t_4 := t\_2 + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+98}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -0.84:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-76}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-9}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;x - z \cdot \left(-1 - \left(\frac{t\_1}{z} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ t_2 t_1))
        (t_4 (+ t_2 (* z (- 1.0 y)))))
   (if (<= b -9.8e+98)
     t_3
     (if (<= b -0.84)
       t_4
       (if (<= b 4.4e-76)
         (+ x (- t_1 (* z (+ y -1.0))))
         (if (<= b 2.05e-9)
           t_4
           (if (<= b 4.8e+74) (- x (* z (- -1.0 (- (/ t_1 z) y)))) t_3)))))))

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 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = t_2 + (z * (1.0 - y));
	double tmp;
	if (b <= -9.8e+98) {
		tmp = t_3;
	} else if (b <= -0.84) {
		tmp = t_4;
	} else if (b <= 4.4e-76) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else if (b <= 2.05e-9) {
		tmp = t_4;
	} else if (b <= 4.8e+74) {
		tmp = x - (z * (-1.0 - ((t_1 / z) - y)));
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = t_2 + t_1
    t_4 = t_2 + (z * (1.0d0 - y))
    if (b <= (-9.8d+98)) then
        tmp = t_3
    else if (b <= (-0.84d0)) then
        tmp = t_4
    else if (b <= 4.4d-76) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else if (b <= 2.05d-9) then
        tmp = t_4
    else if (b <= 4.8d+74) then
        tmp = x - (z * ((-1.0d0) - ((t_1 / z) - y)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = t_2 + (z * (1.0 - y));
	double tmp;
	if (b <= -9.8e+98) {
		tmp = t_3;
	} else if (b <= -0.84) {
		tmp = t_4;
	} else if (b <= 4.4e-76) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else if (b <= 2.05e-9) {
		tmp = t_4;
	} else if (b <= 4.8e+74) {
		tmp = x - (z * (-1.0 - ((t_1 / z) - y)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = t_2 + t_1
	t_4 = t_2 + (z * (1.0 - y))
	tmp = 0
	if b <= -9.8e+98:
		tmp = t_3
	elif b <= -0.84:
		tmp = t_4
	elif b <= 4.4e-76:
		tmp = x + (t_1 - (z * (y + -1.0)))
	elif b <= 2.05e-9:
		tmp = t_4
	elif b <= 4.8e+74:
		tmp = x - (z * (-1.0 - ((t_1 / z) - y)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(t_2 + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -9.8e+98)
		tmp = t_3;
	elseif (b <= -0.84)
		tmp = t_4;
	elseif (b <= 4.4e-76)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	elseif (b <= 2.05e-9)
		tmp = t_4;
	elseif (b <= 4.8e+74)
		tmp = Float64(x - Float64(z * Float64(-1.0 - Float64(Float64(t_1 / z) - y))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = t_2 + t_1;
	t_4 = t_2 + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -9.8e+98)
		tmp = t_3;
	elseif (b <= -0.84)
		tmp = t_4;
	elseif (b <= 4.4e-76)
		tmp = x + (t_1 - (z * (y + -1.0)));
	elseif (b <= 2.05e-9)
		tmp = t_4;
	elseif (b <= 4.8e+74)
		tmp = x - (z * (-1.0 - ((t_1 / z) - y)));
	else
		tmp = t_3;
	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[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+98], t$95$3, If[LessEqual[b, -0.84], t$95$4, If[LessEqual[b, 4.4e-76], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-9], t$95$4, If[LessEqual[b, 4.8e+74], N[(x - N[(z * N[(-1.0 - N[(N[(t$95$1 / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.79999999999999958e98 or 4.80000000000000017e74 < b

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 93.0%

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

   if -9.79999999999999958e98 < b < -0.839999999999999969 or 4.39999999999999999e-76 < b < 2.0500000000000002e-9

   1. Initial program 97.1%

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

   3. Taylor expanded in a around 0 87.2%

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

   if -0.839999999999999969 < b < 4.39999999999999999e-76

   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 b around 0 95.9%

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

   if 2.0500000000000002e-9 < b < 4.80000000000000017e74

   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 b around 0 83.3%

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

   4. Taylor expanded in z around inf 88.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+98}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -0.84:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-76}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-9}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;x - z \cdot \left(-1 - \left(\frac{a \cdot \left(1 - t\right)}{z} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -t \cdot a\\ \mathbf{if}\;t \leq -4 \cdot 10^{+97}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+232} \lor \neg \left(t \leq 7.4 \cdot 10^{+259}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* t a))))
   (if (<= t -4e+97)
     (* b t)
     (if (<= t -4.6e+31)
       t_1
       (if (<= t 4.1e-198)
         (* y (- z))
         (if (<= t 7.5e+42)
           (+ x a)
           (if (or (<= t 3.4e+232) (not (<= t 7.4e+259))) t_1 (* b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(t * a);
	double tmp;
	if (t <= -4e+97) {
		tmp = b * t;
	} else if (t <= -4.6e+31) {
		tmp = t_1;
	} else if (t <= 4.1e-198) {
		tmp = y * -z;
	} else if (t <= 7.5e+42) {
		tmp = x + a;
	} else if ((t <= 3.4e+232) || !(t <= 7.4e+259)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -(t * a)
    if (t <= (-4d+97)) then
        tmp = b * t
    else if (t <= (-4.6d+31)) then
        tmp = t_1
    else if (t <= 4.1d-198) then
        tmp = y * -z
    else if (t <= 7.5d+42) then
        tmp = x + a
    else if ((t <= 3.4d+232) .or. (.not. (t <= 7.4d+259))) then
        tmp = t_1
    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 t_1 = -(t * a);
	double tmp;
	if (t <= -4e+97) {
		tmp = b * t;
	} else if (t <= -4.6e+31) {
		tmp = t_1;
	} else if (t <= 4.1e-198) {
		tmp = y * -z;
	} else if (t <= 7.5e+42) {
		tmp = x + a;
	} else if ((t <= 3.4e+232) || !(t <= 7.4e+259)) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(t * a)
	tmp = 0
	if t <= -4e+97:
		tmp = b * t
	elif t <= -4.6e+31:
		tmp = t_1
	elif t <= 4.1e-198:
		tmp = y * -z
	elif t <= 7.5e+42:
		tmp = x + a
	elif (t <= 3.4e+232) or not (t <= 7.4e+259):
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(t * a))
	tmp = 0.0
	if (t <= -4e+97)
		tmp = Float64(b * t);
	elseif (t <= -4.6e+31)
		tmp = t_1;
	elseif (t <= 4.1e-198)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 7.5e+42)
		tmp = Float64(x + a);
	elseif ((t <= 3.4e+232) || !(t <= 7.4e+259))
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(t * a);
	tmp = 0.0;
	if (t <= -4e+97)
		tmp = b * t;
	elseif (t <= -4.6e+31)
		tmp = t_1;
	elseif (t <= 4.1e-198)
		tmp = y * -z;
	elseif (t <= 7.5e+42)
		tmp = x + a;
	elseif ((t <= 3.4e+232) || ~((t <= 7.4e+259)))
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(t * a), $MachinePrecision])}, If[LessEqual[t, -4e+97], N[(b * t), $MachinePrecision], If[LessEqual[t, -4.6e+31], t$95$1, If[LessEqual[t, 4.1e-198], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 7.5e+42], N[(x + a), $MachinePrecision], If[Or[LessEqual[t, 3.4e+232], N[Not[LessEqual[t, 7.4e+259]], $MachinePrecision]], t$95$1, N[(b * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.0000000000000003e97 or 3.3999999999999998e232 < t < 7.40000000000000029e259

   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 t around inf 76.0%

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

   4. Taylor expanded in b around inf 56.5%

      \[\leadsto \color{blue}{b \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   if -4.0000000000000003e97 < t < -4.5999999999999999e31 or 7.50000000000000041e42 < t < 3.3999999999999998e232 or 7.40000000000000029e259 < t

   1. Initial program 97.0%

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

   3. Taylor expanded in b around 0 78.3%

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

   4. Taylor expanded in t around inf 63.8%

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

   5. Taylor expanded in x around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-lft-neg-out 58.1%

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

      3. *-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -4.5999999999999999e31 < t < 4.10000000000000012e-198

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 56.5%

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

   4. Taylor expanded in b around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. *-commutative 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

   6. Simplified 34.8%

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

   if 4.10000000000000012e-198 < t < 7.50000000000000041e42

   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 b around 0 64.2%

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

   4. Taylor expanded in a around inf 39.1%

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

   5. Taylor expanded in t around 0 35.1%

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

      1. sub-neg 35.1%

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

      2. neg-mul-1 35.1%

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

      3. remove-double-neg 35.1%

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

   7. Simplified 35.1%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+97}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+31}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+232} \lor \neg \left(t \leq 7.4 \cdot 10^{+259}\right):\\ \;\;\;\;-t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{+31} \lor \neg \left(t \leq 5.4 \cdot 10^{-166} \lor \neg \left(t \leq 8.5 \cdot 10^{-106}\right) \land t \leq 6 \cdot 10^{+51}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot y\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.45e+31)
         (not (or (<= t 5.4e-166) (and (not (<= t 8.5e-106)) (<= t 6e+51)))))
   (+ (* b (- (+ y t) 2.0)) (* a (- 1.0 t)))
   (+ (+ x (* b y)) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.45e+31) || !((t <= 5.4e-166) || (!(t <= 8.5e-106) && (t <= 6e+51)))) {
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	} else {
		tmp = (x + (b * y)) + (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 ((t <= (-3.45d+31)) .or. (.not. (t <= 5.4d-166) .or. (.not. (t <= 8.5d-106)) .and. (t <= 6d+51))) then
        tmp = (b * ((y + t) - 2.0d0)) + (a * (1.0d0 - t))
    else
        tmp = (x + (b * y)) + (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 ((t <= -3.45e+31) || !((t <= 5.4e-166) || (!(t <= 8.5e-106) && (t <= 6e+51)))) {
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	} else {
		tmp = (x + (b * y)) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.45e+31) or not ((t <= 5.4e-166) or (not (t <= 8.5e-106) and (t <= 6e+51))):
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t))
	else:
		tmp = (x + (b * y)) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.45e+31) || !((t <= 5.4e-166) || (!(t <= 8.5e-106) && (t <= 6e+51))))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(x + Float64(b * y)) + 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 ((t <= -3.45e+31) || ~(((t <= 5.4e-166) || (~((t <= 8.5e-106)) && (t <= 6e+51)))))
		tmp = (b * ((y + t) - 2.0)) + (a * (1.0 - t));
	else
		tmp = (x + (b * y)) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.45e+31], N[Not[Or[LessEqual[t, 5.4e-166], And[N[Not[LessEqual[t, 8.5e-106]], $MachinePrecision], LessEqual[t, 6e+51]]]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4499999999999999e31 or 5.40000000000000013e-166 < t < 8.4999999999999998e-106 or 6e51 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in y around -inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. distribute-lft-out-- 75.4%

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

      3. associate-*r* 75.4%

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

      4. neg-mul-1 75.4%

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

      5. distribute-lft-neg-in 75.4%

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

      6. *-commutative 75.4%

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

      7. distribute-lft-neg-in 75.4%

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

      8. metadata-eval 75.4%

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

      9. *-lft-identity 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around -inf 79.1%

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

   if -3.4499999999999999e31 < t < 5.40000000000000013e-166 or 8.4999999999999998e-106 < t < 6e51

   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 a around 0 82.5%

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

   4. Taylor expanded in y around inf 74.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{+31} \lor \neg \left(t \leq 5.4 \cdot 10^{-166} \lor \neg \left(t \leq 8.5 \cdot 10^{-106}\right) \land t \leq 6 \cdot 10^{+51}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot y\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (* y (- b z))))
   (if (<= y -1.2e+145)
     t_2
     (if (<= y -1.65e+33)
       t_1
       (if (<= y -2.2)
         (* z (- 1.0 y))
         (if (<= y -5.8e-185)
           t_1
           (if (<= y 1.3e+36) (+ x (* a (- 1.0 t))) t_2)))))))

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 t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+145) {
		tmp = t_2;
	} else if (y <= -1.65e+33) {
		tmp = t_1;
	} else if (y <= -2.2) {
		tmp = z * (1.0 - y);
	} else if (y <= -5.8e-185) {
		tmp = t_1;
	} else if (y <= 1.3e+36) {
		tmp = x + (a * (1.0 - t));
	} 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 + (b * ((y + t) - 2.0d0))
    t_2 = y * (b - z)
    if (y <= (-1.2d+145)) then
        tmp = t_2
    else if (y <= (-1.65d+33)) then
        tmp = t_1
    else if (y <= (-2.2d0)) then
        tmp = z * (1.0d0 - y)
    else if (y <= (-5.8d-185)) then
        tmp = t_1
    else if (y <= 1.3d+36) then
        tmp = x + (a * (1.0d0 - t))
    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 + (b * ((y + t) - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.2e+145) {
		tmp = t_2;
	} else if (y <= -1.65e+33) {
		tmp = t_1;
	} else if (y <= -2.2) {
		tmp = z * (1.0 - y);
	} else if (y <= -5.8e-185) {
		tmp = t_1;
	} else if (y <= 1.3e+36) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.2e+145:
		tmp = t_2
	elif y <= -1.65e+33:
		tmp = t_1
	elif y <= -2.2:
		tmp = z * (1.0 - y)
	elif y <= -5.8e-185:
		tmp = t_1
	elif y <= 1.3e+36:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.2e+145)
		tmp = t_2;
	elseif (y <= -1.65e+33)
		tmp = t_1;
	elseif (y <= -2.2)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= -5.8e-185)
		tmp = t_1;
	elseif (y <= 1.3e+36)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.2e+145)
		tmp = t_2;
	elseif (y <= -1.65e+33)
		tmp = t_1;
	elseif (y <= -2.2)
		tmp = z * (1.0 - y);
	elseif (y <= -5.8e-185)
		tmp = t_1;
	elseif (y <= 1.3e+36)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+145], t$95$2, If[LessEqual[y, -1.65e+33], t$95$1, If[LessEqual[y, -2.2], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-185], t$95$1, If[LessEqual[y, 1.3e+36], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.19999999999999996e145 or 1.3000000000000001e36 < y

   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 y around inf 79.8%

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

   if -1.19999999999999996e145 < y < -1.64999999999999988e33 or -2.2000000000000002 < y < -5.79999999999999989e-185

   1. Initial program 93.2%

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

   3. Taylor expanded in y around -inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. distribute-lft-out-- 83.4%

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

      3. associate-*r* 83.4%

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

      4. neg-mul-1 83.4%

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

      5. distribute-lft-neg-in 83.4%

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

      6. *-commutative 83.4%

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

      7. distribute-lft-neg-in 83.4%

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

      8. metadata-eval 83.4%

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

      9. *-lft-identity 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in x around inf 68.6%

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

   if -1.64999999999999988e33 < y < -2.2000000000000002

   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 100.0%

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

   if -5.79999999999999989e-185 < y < 1.3000000000000001e36

   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 b around 0 77.4%

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

   4. Taylor expanded in a around inf 64.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -2.2:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-185}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.000115:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-11}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+75}:\\ \;\;\;\;x + z \cdot \left(1 + \left(\frac{a}{z} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -0.000115)
     t_1
     (if (<= b 1.2e-11)
       (+ x (- a (* z (+ y -1.0))))
       (if (<= b 1.14e+18)
         (* t (- b a))
         (if (<= b 1.12e+75) (+ x (* z (+ 1.0 (- (/ a z) y)))) t_1))))))

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 (b <= -0.000115) {
		tmp = t_1;
	} else if (b <= 1.2e-11) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (b <= 1.14e+18) {
		tmp = t * (b - a);
	} else if (b <= 1.12e+75) {
		tmp = x + (z * (1.0 + ((a / z) - 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 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-0.000115d0)) then
        tmp = t_1
    else if (b <= 1.2d-11) then
        tmp = x + (a - (z * (y + (-1.0d0))))
    else if (b <= 1.14d+18) then
        tmp = t * (b - a)
    else if (b <= 1.12d+75) then
        tmp = x + (z * (1.0d0 + ((a / z) - 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 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -0.000115) {
		tmp = t_1;
	} else if (b <= 1.2e-11) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (b <= 1.14e+18) {
		tmp = t * (b - a);
	} else if (b <= 1.12e+75) {
		tmp = x + (z * (1.0 + ((a / z) - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -0.000115:
		tmp = t_1
	elif b <= 1.2e-11:
		tmp = x + (a - (z * (y + -1.0)))
	elif b <= 1.14e+18:
		tmp = t * (b - a)
	elif b <= 1.12e+75:
		tmp = x + (z * (1.0 + ((a / z) - y)))
	else:
		tmp = t_1
	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 (b <= -0.000115)
		tmp = t_1;
	elseif (b <= 1.2e-11)
		tmp = Float64(x + Float64(a - Float64(z * Float64(y + -1.0))));
	elseif (b <= 1.14e+18)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 1.12e+75)
		tmp = Float64(x + Float64(z * Float64(1.0 + Float64(Float64(a / z) - y))));
	else
		tmp = t_1;
	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 (b <= -0.000115)
		tmp = t_1;
	elseif (b <= 1.2e-11)
		tmp = x + (a - (z * (y + -1.0)));
	elseif (b <= 1.14e+18)
		tmp = t * (b - a);
	elseif (b <= 1.12e+75)
		tmp = x + (z * (1.0 + ((a / z) - y)));
	else
		tmp = t_1;
	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[b, -0.000115], t$95$1, If[LessEqual[b, 1.2e-11], N[(x + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.14e+18], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+75], N[(x + N[(z * N[(1.0 + N[(N[(a / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e-4 or 1.12000000000000001e75 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in y around -inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. distribute-lft-out-- 70.6%

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

      3. associate-*r* 70.6%

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

      4. neg-mul-1 70.6%

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

      5. distribute-lft-neg-in 70.6%

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

      6. *-commutative 70.6%

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

      7. distribute-lft-neg-in 70.6%

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

      8. metadata-eval 70.6%

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

      9. *-lft-identity 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in x around inf 78.6%

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

   if -1.15e-4 < b < 1.2000000000000001e-11

   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 b around 0 91.5%

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

   4. Taylor expanded in t around 0 67.0%

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

      1. +-commutative 67.0%

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

      2. sub-neg 67.0%

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

      3. metadata-eval 67.0%

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

      4. mul-1-neg 67.0%

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

      5. unsub-neg 67.0%

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

      6. +-commutative 67.0%

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

   6. Simplified 67.0%

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

   if 1.2000000000000001e-11 < b < 1.14e18

   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 100.0%

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

   if 1.14e18 < b < 1.12000000000000001e75

   1. Initial program 92.3%

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

   3. Taylor expanded in b around 0 78.2%

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

   4. Taylor expanded in t around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. sub-neg 70.5%

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

      3. metadata-eval 70.5%

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

      4. mul-1-neg 70.5%

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

      5. unsub-neg 70.5%

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

      6. +-commutative 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in z around inf 77.6%

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

      1. sub-neg 77.6%

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

      2. mul-1-neg 77.6%

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

      3. unsub-neg 77.6%

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

      4. metadata-eval 77.6%

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

   9. Simplified 77.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.000115:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-11}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+75}:\\ \;\;\;\;x + z \cdot \left(1 + \left(\frac{a}{z} - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+35}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq -2.2 \lor \neg \left(y \leq 1.02 \cdot 10^{+40}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.6e+179)
     (* b y)
     (if (<= y -6.2e+93)
       t_1
       (if (<= y -2.35e+35)
         (* b t)
         (if (or (<= y -2.2) (not (<= y 1.02e+40))) t_1 (* a (- 1.0 t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.6e+179) {
		tmp = b * y;
	} else if (y <= -6.2e+93) {
		tmp = t_1;
	} else if (y <= -2.35e+35) {
		tmp = b * t;
	} else if ((y <= -2.2) || !(y <= 1.02e+40)) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-1.6d+179)) then
        tmp = b * y
    else if (y <= (-6.2d+93)) then
        tmp = t_1
    else if (y <= (-2.35d+35)) then
        tmp = b * t
    else if ((y <= (-2.2d0)) .or. (.not. (y <= 1.02d+40))) then
        tmp = t_1
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.6e+179) {
		tmp = b * y;
	} else if (y <= -6.2e+93) {
		tmp = t_1;
	} else if (y <= -2.35e+35) {
		tmp = b * t;
	} else if ((y <= -2.2) || !(y <= 1.02e+40)) {
		tmp = t_1;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.6e+179:
		tmp = b * y
	elif y <= -6.2e+93:
		tmp = t_1
	elif y <= -2.35e+35:
		tmp = b * t
	elif (y <= -2.2) or not (y <= 1.02e+40):
		tmp = t_1
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.6e+179)
		tmp = Float64(b * y);
	elseif (y <= -6.2e+93)
		tmp = t_1;
	elseif (y <= -2.35e+35)
		tmp = Float64(b * t);
	elseif ((y <= -2.2) || !(y <= 1.02e+40))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -1.6e+179)
		tmp = b * y;
	elseif (y <= -6.2e+93)
		tmp = t_1;
	elseif (y <= -2.35e+35)
		tmp = b * t;
	elseif ((y <= -2.2) || ~((y <= 1.02e+40)))
		tmp = t_1;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.6e+179], N[(b * y), $MachinePrecision], If[LessEqual[y, -6.2e+93], t$95$1, If[LessEqual[y, -2.35e+35], N[(b * t), $MachinePrecision], If[Or[LessEqual[y, -2.2], N[Not[LessEqual[y, 1.02e+40]], $MachinePrecision]], t$95$1, N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e179

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf 54.8%

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

   4. Taylor expanded in y around inf 54.7%

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

   if -1.6000000000000001e179 < y < -6.20000000000000038e93 or -2.35000000000000017e35 < y < -2.2000000000000002 or 1.02e40 < y

   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 y around inf 75.9%

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

   4. Taylor expanded in b around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. *-commutative 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

   6. Simplified 52.9%

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

   if -6.20000000000000038e93 < y < -2.35000000000000017e35

   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 63.8%

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

   4. Taylor expanded in b around inf 45.1%

      \[\leadsto \color{blue}{b \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 45.1%

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

   6. Simplified 45.1%

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

   if -2.2000000000000002 < y < 1.02e40

   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 a around inf 41.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+35}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq -2.2 \lor \neg \left(y \leq 1.02 \cdot 10^{+40}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.95:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -6.5e+93)
     t_2
     (if (<= y -3.8e+38)
       t_1
       (if (<= y -1.95)
         (* z (- 1.0 y))
         (if (<= y -1.95e-235) t_1 (if (<= y 2.3e+30) (- x (* t a)) 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 <= -6.5e+93) {
		tmp = t_2;
	} else if (y <= -3.8e+38) {
		tmp = t_1;
	} else if (y <= -1.95) {
		tmp = z * (1.0 - y);
	} else if (y <= -1.95e-235) {
		tmp = t_1;
	} else if (y <= 2.3e+30) {
		tmp = x - (t * a);
	} 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 <= (-6.5d+93)) then
        tmp = t_2
    else if (y <= (-3.8d+38)) then
        tmp = t_1
    else if (y <= (-1.95d0)) then
        tmp = z * (1.0d0 - y)
    else if (y <= (-1.95d-235)) then
        tmp = t_1
    else if (y <= 2.3d+30) then
        tmp = x - (t * a)
    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 <= -6.5e+93) {
		tmp = t_2;
	} else if (y <= -3.8e+38) {
		tmp = t_1;
	} else if (y <= -1.95) {
		tmp = z * (1.0 - y);
	} else if (y <= -1.95e-235) {
		tmp = t_1;
	} else if (y <= 2.3e+30) {
		tmp = x - (t * a);
	} 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 <= -6.5e+93:
		tmp = t_2
	elif y <= -3.8e+38:
		tmp = t_1
	elif y <= -1.95:
		tmp = z * (1.0 - y)
	elif y <= -1.95e-235:
		tmp = t_1
	elif y <= 2.3e+30:
		tmp = x - (t * a)
	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 <= -6.5e+93)
		tmp = t_2;
	elseif (y <= -3.8e+38)
		tmp = t_1;
	elseif (y <= -1.95)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= -1.95e-235)
		tmp = t_1;
	elseif (y <= 2.3e+30)
		tmp = Float64(x - Float64(t * a));
	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 <= -6.5e+93)
		tmp = t_2;
	elseif (y <= -3.8e+38)
		tmp = t_1;
	elseif (y <= -1.95)
		tmp = z * (1.0 - y);
	elseif (y <= -1.95e-235)
		tmp = t_1;
	elseif (y <= 2.3e+30)
		tmp = x - (t * a);
	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, -6.5e+93], t$95$2, If[LessEqual[y, -3.8e+38], t$95$1, If[LessEqual[y, -1.95], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-235], t$95$1, If[LessEqual[y, 2.3e+30], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4999999999999998e93 or 2.3e30 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -6.4999999999999998e93 < y < -3.7999999999999998e38 or -1.94999999999999996 < y < -1.94999999999999985e-235

   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 t around inf 62.6%

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

   if -3.7999999999999998e38 < y < -1.94999999999999996

   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 84.2%

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

   if -1.94999999999999985e-235 < y < 2.3e30

   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 b around 0 78.0%

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

   4. Taylor expanded in t around inf 51.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.95:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+30}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -t \cdot a\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+97}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.14 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+233} \lor \neg \left(t \leq 2.3 \cdot 10^{+257}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* t a))))
   (if (<= t -4.4e+97)
     (* b t)
     (if (<= t -1.14e+27)
       t_1
       (if (<= t 1.12e+43)
         (+ x a)
         (if (or (<= t 4.2e+233) (not (<= t 2.3e+257))) t_1 (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(t * a);
	double tmp;
	if (t <= -4.4e+97) {
		tmp = b * t;
	} else if (t <= -1.14e+27) {
		tmp = t_1;
	} else if (t <= 1.12e+43) {
		tmp = x + a;
	} else if ((t <= 4.2e+233) || !(t <= 2.3e+257)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -(t * a)
    if (t <= (-4.4d+97)) then
        tmp = b * t
    else if (t <= (-1.14d+27)) then
        tmp = t_1
    else if (t <= 1.12d+43) then
        tmp = x + a
    else if ((t <= 4.2d+233) .or. (.not. (t <= 2.3d+257))) then
        tmp = t_1
    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 t_1 = -(t * a);
	double tmp;
	if (t <= -4.4e+97) {
		tmp = b * t;
	} else if (t <= -1.14e+27) {
		tmp = t_1;
	} else if (t <= 1.12e+43) {
		tmp = x + a;
	} else if ((t <= 4.2e+233) || !(t <= 2.3e+257)) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(t * a)
	tmp = 0
	if t <= -4.4e+97:
		tmp = b * t
	elif t <= -1.14e+27:
		tmp = t_1
	elif t <= 1.12e+43:
		tmp = x + a
	elif (t <= 4.2e+233) or not (t <= 2.3e+257):
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(t * a))
	tmp = 0.0
	if (t <= -4.4e+97)
		tmp = Float64(b * t);
	elseif (t <= -1.14e+27)
		tmp = t_1;
	elseif (t <= 1.12e+43)
		tmp = Float64(x + a);
	elseif ((t <= 4.2e+233) || !(t <= 2.3e+257))
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(t * a);
	tmp = 0.0;
	if (t <= -4.4e+97)
		tmp = b * t;
	elseif (t <= -1.14e+27)
		tmp = t_1;
	elseif (t <= 1.12e+43)
		tmp = x + a;
	elseif ((t <= 4.2e+233) || ~((t <= 2.3e+257)))
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(t * a), $MachinePrecision])}, If[LessEqual[t, -4.4e+97], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.14e+27], t$95$1, If[LessEqual[t, 1.12e+43], N[(x + a), $MachinePrecision], If[Or[LessEqual[t, 4.2e+233], N[Not[LessEqual[t, 2.3e+257]], $MachinePrecision]], t$95$1, N[(b * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4000000000000002e97 or 4.19999999999999993e233 < t < 2.3e257

   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 t around inf 76.0%

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

   4. Taylor expanded in b around inf 56.5%

      \[\leadsto \color{blue}{b \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   if -4.4000000000000002e97 < t < -1.1400000000000001e27 or 1.12e43 < t < 4.19999999999999993e233 or 2.3e257 < t

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 78.6%

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

   4. Taylor expanded in t around inf 62.9%

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

   5. Taylor expanded in x around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-lft-neg-out 57.4%

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

      3. *-commutative 57.4%

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

   7. Simplified 57.4%

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

   if -1.1400000000000001e27 < t < 1.12e43

   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 b around 0 68.5%

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

   4. Taylor expanded in a around inf 33.3%

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

   5. Taylor expanded in t around 0 30.8%

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

      1. sub-neg 30.8%

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

      2. neg-mul-1 30.8%

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

      3. remove-double-neg 30.8%

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

   7. Simplified 30.8%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+97}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.14 \cdot 10^{+27}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+233} \lor \neg \left(t \leq 2.3 \cdot 10^{+257}\right):\\ \;\;\;\;-t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - z \cdot \left(y + -1\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.33:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* z (+ y -1.0))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -0.33)
     t_2
     (if (<= b 6.5e-12)
       t_1
       (if (<= b 8.2e+17) (* t (- b a)) (if (<= b 6.2e+76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (z * (y + -1.0)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -0.33) {
		tmp = t_2;
	} else if (b <= 6.5e-12) {
		tmp = t_1;
	} else if (b <= 8.2e+17) {
		tmp = t * (b - a);
	} else if (b <= 6.2e+76) {
		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 + (a - (z * (y + (-1.0d0))))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-0.33d0)) then
        tmp = t_2
    else if (b <= 6.5d-12) then
        tmp = t_1
    else if (b <= 8.2d+17) then
        tmp = t * (b - a)
    else if (b <= 6.2d+76) 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 + (a - (z * (y + -1.0)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -0.33) {
		tmp = t_2;
	} else if (b <= 6.5e-12) {
		tmp = t_1;
	} else if (b <= 8.2e+17) {
		tmp = t * (b - a);
	} else if (b <= 6.2e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (z * (y + -1.0)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -0.33:
		tmp = t_2
	elif b <= 6.5e-12:
		tmp = t_1
	elif b <= 8.2e+17:
		tmp = t * (b - a)
	elif b <= 6.2e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(z * Float64(y + -1.0))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -0.33)
		tmp = t_2;
	elseif (b <= 6.5e-12)
		tmp = t_1;
	elseif (b <= 8.2e+17)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 6.2e+76)
		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 + (a - (z * (y + -1.0)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -0.33)
		tmp = t_2;
	elseif (b <= 6.5e-12)
		tmp = t_1;
	elseif (b <= 8.2e+17)
		tmp = t * (b - a);
	elseif (b <= 6.2e+76)
		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[(a - N[(z * N[(y + -1.0), $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, -0.33], t$95$2, If[LessEqual[b, 6.5e-12], t$95$1, If[LessEqual[b, 8.2e+17], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.330000000000000016 or 6.20000000000000023e76 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in y around -inf 70.4%

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

      1. associate-*r* 70.4%

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

      2. distribute-lft-out-- 70.4%

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

      3. associate-*r* 70.4%

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

      4. neg-mul-1 70.4%

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

      5. distribute-lft-neg-in 70.4%

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

      6. *-commutative 70.4%

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

      7. distribute-lft-neg-in 70.4%

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

      8. metadata-eval 70.4%

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

      9. *-lft-identity 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in x around inf 79.3%

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

   if -0.330000000000000016 < b < 6.5000000000000002e-12 or 8.2e17 < b < 6.20000000000000023e76

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 90.3%

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

   4. Taylor expanded in t around 0 67.4%

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

      1. +-commutative 67.4%

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

      2. sub-neg 67.4%

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

      3. metadata-eval 67.4%

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

      4. mul-1-neg 67.4%

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

      5. unsub-neg 67.4%

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

      6. +-commutative 67.4%

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

   6. Simplified 67.4%

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

   if 6.5000000000000002e-12 < b < 8.2e17

   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 100.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.33:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -2.1:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.2e+93)
     t_1
     (if (<= y -1.65e+33)
       (* b (- (+ y t) 2.0))
       (if (<= y -2.1)
         (* z (- 1.0 y))
         (if (<= y 1.1e+34) (+ 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 = y * (b - z);
	double tmp;
	if (y <= -6.2e+93) {
		tmp = t_1;
	} else if (y <= -1.65e+33) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= -2.1) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.1e+34) {
		tmp = x + (a * (1.0 - t));
	} 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 <= (-6.2d+93)) then
        tmp = t_1
    else if (y <= (-1.65d+33)) then
        tmp = b * ((y + t) - 2.0d0)
    else if (y <= (-2.1d0)) then
        tmp = z * (1.0d0 - y)
    else if (y <= 1.1d+34) then
        tmp = x + (a * (1.0d0 - t))
    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 <= -6.2e+93) {
		tmp = t_1;
	} else if (y <= -1.65e+33) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= -2.1) {
		tmp = z * (1.0 - y);
	} else if (y <= 1.1e+34) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6.2e+93:
		tmp = t_1
	elif y <= -1.65e+33:
		tmp = b * ((y + t) - 2.0)
	elif y <= -2.1:
		tmp = z * (1.0 - y)
	elif y <= 1.1e+34:
		tmp = x + (a * (1.0 - t))
	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 <= -6.2e+93)
		tmp = t_1;
	elseif (y <= -1.65e+33)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (y <= -2.1)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 1.1e+34)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	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 <= -6.2e+93)
		tmp = t_1;
	elseif (y <= -1.65e+33)
		tmp = b * ((y + t) - 2.0);
	elseif (y <= -2.1)
		tmp = z * (1.0 - y);
	elseif (y <= 1.1e+34)
		tmp = x + (a * (1.0 - t));
	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, -6.2e+93], t$95$1, If[LessEqual[y, -1.65e+33], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+34], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000038e93 or 1.1000000000000001e34 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 77.5%

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

   if -6.20000000000000038e93 < y < -1.64999999999999988e33

   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 b around inf 69.5%

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

   if -1.64999999999999988e33 < y < -2.10000000000000009

   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 100.0%

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

   if -2.10000000000000009 < y < 1.1000000000000001e34

   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 b around 0 73.7%

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

   4. Taylor expanded in a around inf 62.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -2.1:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -0.0045 \lor \neg \left(b \leq 4.5 \cdot 10^{-50}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -0.0045) (not (<= b 4.5e-50)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (- t_1 (* z (+ y -1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -0.0045) || !(b <= 4.5e-50)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-0.0045d0)) .or. (.not. (b <= 4.5d-50))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -0.0045) || !(b <= 4.5e-50)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -0.0045) or not (b <= 4.5e-50):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -0.0045) || !(b <= 4.5e-50))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -0.0045) || ~((b <= 4.5e-50)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 - (z * (y + -1.0)));
	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]}, If[Or[LessEqual[b, -0.0045], N[Not[LessEqual[b, 4.5e-50]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -0.00449999999999999966 or 4.49999999999999962e-50 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 85.6%

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

   if -0.00449999999999999966 < b < 4.49999999999999962e-50

   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 b around 0 94.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0045 \lor \neg \left(b \leq 4.5 \cdot 10^{-50}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;x + t\_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

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 -6.2e+74)
     (+ x t_2)
     (if (<= b 5.2e+91) (+ x (- t_1 (* z (+ y -1.0)))) (+ 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 <= -6.2e+74) {
		tmp = x + t_2;
	} else if (b <= 5.2e+91) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = 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 <= (-6.2d+74)) then
        tmp = x + t_2
    else if (b <= 5.2d+91) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else
        tmp = 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 <= -6.2e+74) {
		tmp = x + t_2;
	} else if (b <= 5.2e+91) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = 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 <= -6.2e+74:
		tmp = x + t_2
	elif b <= 5.2e+91:
		tmp = x + (t_1 - (z * (y + -1.0)))
	else:
		tmp = 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 <= -6.2e+74)
		tmp = Float64(x + t_2);
	elseif (b <= 5.2e+91)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(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 <= -6.2e+74)
		tmp = x + t_2;
	elseif (b <= 5.2e+91)
		tmp = x + (t_1 - (z * (y + -1.0)));
	else
		tmp = 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, -6.2e+74], N[(x + t$95$2), $MachinePrecision], If[LessEqual[b, 5.2e+91], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.20000000000000043e74

   1. Initial program 83.3%

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

   3. Taylor expanded in y around -inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. associate-*r* 67.3%

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

      4. neg-mul-1 67.3%

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

      5. distribute-lft-neg-in 67.3%

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

      6. *-commutative 67.3%

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

      7. distribute-lft-neg-in 67.3%

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

      8. metadata-eval 67.3%

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

      9. *-lft-identity 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in x around inf 87.3%

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

   if -6.20000000000000043e74 < b < 5.2000000000000001e91

   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 87.1%

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

   if 5.2000000000000001e91 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in y around -inf 71.2%

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

      1. associate-*r* 71.2%

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

      2. distribute-lft-out-- 71.2%

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

      3. associate-*r* 71.2%

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

      4. neg-mul-1 71.2%

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

      5. distribute-lft-neg-in 71.2%

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

      6. *-commutative 71.2%

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

      7. distribute-lft-neg-in 71.2%

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

      8. metadata-eval 71.2%

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

      9. *-lft-identity 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in a around -inf 92.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+41}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -5.6e+30)
     t_1
     (if (<= t 5.2e-197) (* y (- z)) (if (<= t 6e+41) (+ x a) 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 <= -5.6e+30) {
		tmp = t_1;
	} else if (t <= 5.2e-197) {
		tmp = y * -z;
	} else if (t <= 6e+41) {
		tmp = x + 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 = t * (b - a)
    if (t <= (-5.6d+30)) then
        tmp = t_1
    else if (t <= 5.2d-197) then
        tmp = y * -z
    else if (t <= 6d+41) then
        tmp = x + 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 = t * (b - a);
	double tmp;
	if (t <= -5.6e+30) {
		tmp = t_1;
	} else if (t <= 5.2e-197) {
		tmp = y * -z;
	} else if (t <= 6e+41) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -5.6e+30:
		tmp = t_1
	elif t <= 5.2e-197:
		tmp = y * -z
	elif t <= 6e+41:
		tmp = x + a
	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 <= -5.6e+30)
		tmp = t_1;
	elseif (t <= 5.2e-197)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 6e+41)
		tmp = Float64(x + a);
	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 <= -5.6e+30)
		tmp = t_1;
	elseif (t <= 5.2e-197)
		tmp = y * -z;
	elseif (t <= 6e+41)
		tmp = x + a;
	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, -5.6e+30], t$95$1, If[LessEqual[t, 5.2e-197], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 6e+41], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.59999999999999966e30 or 5.9999999999999997e41 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf 74.9%

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

   if -5.59999999999999966e30 < t < 5.2000000000000003e-197

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 56.5%

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

   4. Taylor expanded in b around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. *-commutative 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

   6. Simplified 34.8%

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

   if 5.2000000000000003e-197 < t < 5.9999999999999997e41

   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 b around 0 64.2%

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

   4. Taylor expanded in a around inf 39.1%

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

   5. Taylor expanded in t around 0 35.1%

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

      1. sub-neg 35.1%

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

      2. neg-mul-1 35.1%

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

      3. remove-double-neg 35.1%

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

   7. Simplified 35.1%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+41}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+117}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-235}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+117)
   (* b y)
   (if (<= y -2.5e-235) (* b t) (if (<= y 2.6e+34) (+ x a) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+117) {
		tmp = b * y;
	} else if (y <= -2.5e-235) {
		tmp = b * t;
	} else if (y <= 2.6e+34) {
		tmp = x + a;
	} else {
		tmp = b * 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 (y <= (-2.9d+117)) then
        tmp = b * y
    else if (y <= (-2.5d-235)) then
        tmp = b * t
    else if (y <= 2.6d+34) then
        tmp = x + a
    else
        tmp = b * 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 (y <= -2.9e+117) {
		tmp = b * y;
	} else if (y <= -2.5e-235) {
		tmp = b * t;
	} else if (y <= 2.6e+34) {
		tmp = x + a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.9e+117:
		tmp = b * y
	elif y <= -2.5e-235:
		tmp = b * t
	elif y <= 2.6e+34:
		tmp = x + a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+117)
		tmp = Float64(b * y);
	elseif (y <= -2.5e-235)
		tmp = Float64(b * t);
	elseif (y <= 2.6e+34)
		tmp = Float64(x + a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.9e+117)
		tmp = b * y;
	elseif (y <= -2.5e-235)
		tmp = b * t;
	elseif (y <= 2.6e+34)
		tmp = x + a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+117], N[(b * y), $MachinePrecision], If[LessEqual[y, -2.5e-235], N[(b * t), $MachinePrecision], If[LessEqual[y, 2.6e+34], N[(x + a), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.90000000000000027e117 or 2.59999999999999997e34 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf 42.9%

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

   4. Taylor expanded in y around inf 37.3%

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

   if -2.90000000000000027e117 < y < -2.4999999999999999e-235

   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 t around inf 54.5%

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

   4. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{b \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 35.6%

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

   6. Simplified 35.6%

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

   if -2.4999999999999999e-235 < y < 2.59999999999999997e34

   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 b around 0 78.0%

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

   4. Taylor expanded in a around inf 64.6%

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

   5. Taylor expanded in t around 0 34.0%

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

      1. sub-neg 34.0%

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

      2. neg-mul-1 34.0%

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

      3. remove-double-neg 34.0%

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

   7. Simplified 34.0%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+117}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-235}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+32} \lor \neg \left(t \leq 1.25 \cdot 10^{+40}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.8e+32) (not (<= t 1.25e+40))) (* t (- b a)) (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+32) || !(t <= 1.25e+40)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.8d+32)) .or. (.not. (t <= 1.25d+40))) then
        tmp = t * (b - a)
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+32) || !(t <= 1.25e+40)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.8e+32) or not (t <= 1.25e+40):
		tmp = t * (b - a)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.8e+32) || !(t <= 1.25e+40))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.8e+32) || ~((t <= 1.25e+40)))
		tmp = t * (b - a);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.8e+32], N[Not[LessEqual[t, 1.25e+40]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7999999999999998e32 or 1.25000000000000001e40 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 74.3%

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

   if -1.7999999999999998e32 < t < 1.25000000000000001e40

   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 y around inf 50.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+32} \lor \neg \left(t \leq 1.25 \cdot 10^{+40}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-24} \lor \neg \left(y \leq 6.8 \cdot 10^{+30}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.7e-24) (not (<= y 6.8e+30))) (* b y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.7e-24) || !(y <= 6.8e+30)) {
		tmp = b * y;
	} 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 ((y <= (-3.7d-24)) .or. (.not. (y <= 6.8d+30))) then
        tmp = b * y
    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 ((y <= -3.7e-24) || !(y <= 6.8e+30)) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.7e-24) or not (y <= 6.8e+30):
		tmp = b * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.7e-24) || !(y <= 6.8e+30))
		tmp = Float64(b * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.7e-24) || ~((y <= 6.8e+30)))
		tmp = b * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.7e-24], N[Not[LessEqual[y, 6.8e+30]], $MachinePrecision]], N[(b * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999981e-24 or 6.8000000000000005e30 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in b around inf 45.2%

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

   4. Taylor expanded in y around inf 32.9%

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

   if -3.69999999999999981e-24 < y < 6.8000000000000005e30

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 22.2%

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

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-24} \lor \neg \left(y \leq 6.8 \cdot 10^{+30}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+87} \lor \neg \left(t \leq 2 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e+87) (not (<= t 2e+24))) (* b t) (* b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e+87) || !(t <= 2e+24)) {
		tmp = b * t;
	} else {
		tmp = b * 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 <= (-1.4d+87)) .or. (.not. (t <= 2d+24))) then
        tmp = b * t
    else
        tmp = b * 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 <= -1.4e+87) || !(t <= 2e+24)) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e+87) or not (t <= 2e+24):
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e+87) || !(t <= 2e+24))
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.4e+87) || ~((t <= 2e+24)))
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e+87], N[Not[LessEqual[t, 2e+24]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000008e87 or 2e24 < t

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 72.9%

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

   4. Taylor expanded in b around inf 38.9%

      \[\leadsto \color{blue}{b \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 38.9%

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

   6. Simplified 38.9%

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

   if -1.40000000000000008e87 < t < 2e24

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 33.4%

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

   4. Taylor expanded in y around inf 25.2%

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

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+87} \lor \neg \left(t \leq 2 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 16.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 x around inf 14.5%

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

4. Final simplification 14.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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)))