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

Percentage Accurate: 95.2% → 97.8%

Time: 17.0s

Alternatives: 22

Speedup: 1.0×

• 36.7% 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: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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. Step-by-step derivation

   1. +-commutative 98.8%

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

   2. fma-define 98.8%

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

   3. associate--l+ 98.8%

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

   4. sub-neg 98.8%

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

   5. metadata-eval 98.8%

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

   6. sub-neg 98.8%

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

   7. associate-+l- 98.8%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x - y \cdot z\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-225}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (- x (* y z))))
   (if (<= b -6.5e+14)
     t_1
     (if (<= b -2.6e-116)
       (* a (- 1.0 t))
       (if (<= b -2.2e-203)
         t_2
         (if (<= b 7e-308)
           (* z (- 1.0 y))
           (if (<= b 2.4e-225) t_2 (if (<= b 3.2e-70) (- x (* t a)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = x - (y * z);
	double tmp;
	if (b <= -6.5e+14) {
		tmp = t_1;
	} else if (b <= -2.6e-116) {
		tmp = a * (1.0 - t);
	} else if (b <= -2.2e-203) {
		tmp = t_2;
	} else if (b <= 7e-308) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.4e-225) {
		tmp = t_2;
	} else if (b <= 3.2e-70) {
		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) :: t_2
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    t_2 = x - (y * z)
    if (b <= (-6.5d+14)) then
        tmp = t_1
    else if (b <= (-2.6d-116)) then
        tmp = a * (1.0d0 - t)
    else if (b <= (-2.2d-203)) then
        tmp = t_2
    else if (b <= 7d-308) then
        tmp = z * (1.0d0 - y)
    else if (b <= 2.4d-225) then
        tmp = t_2
    else if (b <= 3.2d-70) 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 = b * ((y + t) - 2.0);
	double t_2 = x - (y * z);
	double tmp;
	if (b <= -6.5e+14) {
		tmp = t_1;
	} else if (b <= -2.6e-116) {
		tmp = a * (1.0 - t);
	} else if (b <= -2.2e-203) {
		tmp = t_2;
	} else if (b <= 7e-308) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.4e-225) {
		tmp = t_2;
	} else if (b <= 3.2e-70) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = x - (y * z)
	tmp = 0
	if b <= -6.5e+14:
		tmp = t_1
	elif b <= -2.6e-116:
		tmp = a * (1.0 - t)
	elif b <= -2.2e-203:
		tmp = t_2
	elif b <= 7e-308:
		tmp = z * (1.0 - y)
	elif b <= 2.4e-225:
		tmp = t_2
	elif b <= 3.2e-70:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (b <= -6.5e+14)
		tmp = t_1;
	elseif (b <= -2.6e-116)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= -2.2e-203)
		tmp = t_2;
	elseif (b <= 7e-308)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 2.4e-225)
		tmp = t_2;
	elseif (b <= 3.2e-70)
		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 = b * ((y + t) - 2.0);
	t_2 = x - (y * z);
	tmp = 0.0;
	if (b <= -6.5e+14)
		tmp = t_1;
	elseif (b <= -2.6e-116)
		tmp = a * (1.0 - t);
	elseif (b <= -2.2e-203)
		tmp = t_2;
	elseif (b <= 7e-308)
		tmp = z * (1.0 - y);
	elseif (b <= 2.4e-225)
		tmp = t_2;
	elseif (b <= 3.2e-70)
		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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+14], t$95$1, If[LessEqual[b, -2.6e-116], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-203], t$95$2, If[LessEqual[b, 7e-308], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-225], t$95$2, If[LessEqual[b, 3.2e-70], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.5e14 or 3.1999999999999997e-70 < b

   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 inf 67.1%

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

   if -6.5e14 < b < -2.6e-116

   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 57.5%

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

   if -2.6e-116 < b < -2.2e-203 or 7e-308 < b < 2.39999999999999996e-225

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 93.5%

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

   4. Taylor expanded in y around inf 66.6%

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

   if -2.2e-203 < b < 7e-308

   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 56.2%

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

   if 2.39999999999999996e-225 < b < 3.1999999999999997e-70

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 90.8%

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

   4. Taylor expanded in t around inf 60.9%

      \[\leadsto x - \color{blue}{a \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-203}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-225}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-201}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-232}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-307}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -8.2e-17)
     t_1
     (if (<= a -3e-201)
       (+ x z)
       (if (<= a -1.95e-232)
         (* y b)
         (if (<= a -3e-307)
           (+ x z)
           (if (<= a 1.6e-110) (* y b) (if (<= a 2.4e+101) (+ x z) 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 tmp;
	if (a <= -8.2e-17) {
		tmp = t_1;
	} else if (a <= -3e-201) {
		tmp = x + z;
	} else if (a <= -1.95e-232) {
		tmp = y * b;
	} else if (a <= -3e-307) {
		tmp = x + z;
	} else if (a <= 1.6e-110) {
		tmp = y * b;
	} else if (a <= 2.4e+101) {
		tmp = x + z;
	} 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 = a * (1.0d0 - t)
    if (a <= (-8.2d-17)) then
        tmp = t_1
    else if (a <= (-3d-201)) then
        tmp = x + z
    else if (a <= (-1.95d-232)) then
        tmp = y * b
    else if (a <= (-3d-307)) then
        tmp = x + z
    else if (a <= 1.6d-110) then
        tmp = y * b
    else if (a <= 2.4d+101) then
        tmp = x + z
    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 = a * (1.0 - t);
	double tmp;
	if (a <= -8.2e-17) {
		tmp = t_1;
	} else if (a <= -3e-201) {
		tmp = x + z;
	} else if (a <= -1.95e-232) {
		tmp = y * b;
	} else if (a <= -3e-307) {
		tmp = x + z;
	} else if (a <= 1.6e-110) {
		tmp = y * b;
	} else if (a <= 2.4e+101) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -8.2e-17:
		tmp = t_1
	elif a <= -3e-201:
		tmp = x + z
	elif a <= -1.95e-232:
		tmp = y * b
	elif a <= -3e-307:
		tmp = x + z
	elif a <= 1.6e-110:
		tmp = y * b
	elif a <= 2.4e+101:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -8.2e-17)
		tmp = t_1;
	elseif (a <= -3e-201)
		tmp = Float64(x + z);
	elseif (a <= -1.95e-232)
		tmp = Float64(y * b);
	elseif (a <= -3e-307)
		tmp = Float64(x + z);
	elseif (a <= 1.6e-110)
		tmp = Float64(y * b);
	elseif (a <= 2.4e+101)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	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 (a <= -8.2e-17)
		tmp = t_1;
	elseif (a <= -3e-201)
		tmp = x + z;
	elseif (a <= -1.95e-232)
		tmp = y * b;
	elseif (a <= -3e-307)
		tmp = x + z;
	elseif (a <= 1.6e-110)
		tmp = y * b;
	elseif (a <= 2.4e+101)
		tmp = x + z;
	else
		tmp = 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]}, If[LessEqual[a, -8.2e-17], t$95$1, If[LessEqual[a, -3e-201], N[(x + z), $MachinePrecision], If[LessEqual[a, -1.95e-232], N[(y * b), $MachinePrecision], If[LessEqual[a, -3e-307], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.6e-110], N[(y * b), $MachinePrecision], If[LessEqual[a, 2.4e+101], N[(x + z), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.2000000000000001e-17 or 2.39999999999999988e101 < a

   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 60.7%

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

   if -8.2000000000000001e-17 < a < -3.00000000000000002e-201 or -1.9499999999999999e-232 < a < -2.9999999999999999e-307 or 1.60000000000000014e-110 < a < 2.39999999999999988e101

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0 62.6%

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

   4. Taylor expanded in a around 0 51.7%

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

   5. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

   7. Simplified 36.3%

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

   if -3.00000000000000002e-201 < a < -1.9499999999999999e-232 or -2.9999999999999999e-307 < a < 1.60000000000000014e-110

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 96.1%

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

   4. Taylor expanded in z around 0 68.4%

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

   5. Taylor expanded in y around inf 40.1%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-201}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-232}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-307}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+101}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y - \frac{a}{z}\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (- x (* a (+ t -1.0)))))
   (if (<= b -8e+19)
     t_1
     (if (<= b 2.2e-219)
       (+ x (+ a (* z (- 1.0 y))))
       (if (<= b 8.2e-176)
         t_2
         (if (<= b 1.7e-20)
           (- x (* z (+ -1.0 (- y (/ a z)))))
           (if (<= b 4.3e+94) t_2 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 t_2 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -8e+19) {
		tmp = t_1;
	} else if (b <= 2.2e-219) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 8.2e-176) {
		tmp = t_2;
	} else if (b <= 1.7e-20) {
		tmp = x - (z * (-1.0 + (y - (a / z))));
	} else if (b <= 4.3e+94) {
		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 = x + (b * ((y + t) - 2.0d0))
    t_2 = x - (a * (t + (-1.0d0)))
    if (b <= (-8d+19)) then
        tmp = t_1
    else if (b <= 2.2d-219) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else if (b <= 8.2d-176) then
        tmp = t_2
    else if (b <= 1.7d-20) then
        tmp = x - (z * ((-1.0d0) + (y - (a / z))))
    else if (b <= 4.3d+94) 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 = x + (b * ((y + t) - 2.0));
	double t_2 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -8e+19) {
		tmp = t_1;
	} else if (b <= 2.2e-219) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 8.2e-176) {
		tmp = t_2;
	} else if (b <= 1.7e-20) {
		tmp = x - (z * (-1.0 + (y - (a / z))));
	} else if (b <= 4.3e+94) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = x - (a * (t + -1.0))
	tmp = 0
	if b <= -8e+19:
		tmp = t_1
	elif b <= 2.2e-219:
		tmp = x + (a + (z * (1.0 - y)))
	elif b <= 8.2e-176:
		tmp = t_2
	elif b <= 1.7e-20:
		tmp = x - (z * (-1.0 + (y - (a / z))))
	elif b <= 4.3e+94:
		tmp = t_2
	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)))
	t_2 = Float64(x - Float64(a * Float64(t + -1.0)))
	tmp = 0.0
	if (b <= -8e+19)
		tmp = t_1;
	elseif (b <= 2.2e-219)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	elseif (b <= 8.2e-176)
		tmp = t_2;
	elseif (b <= 1.7e-20)
		tmp = Float64(x - Float64(z * Float64(-1.0 + Float64(y - Float64(a / z)))));
	elseif (b <= 4.3e+94)
		tmp = t_2;
	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));
	t_2 = x - (a * (t + -1.0));
	tmp = 0.0;
	if (b <= -8e+19)
		tmp = t_1;
	elseif (b <= 2.2e-219)
		tmp = x + (a + (z * (1.0 - y)));
	elseif (b <= 8.2e-176)
		tmp = t_2;
	elseif (b <= 1.7e-20)
		tmp = x - (z * (-1.0 + (y - (a / z))));
	elseif (b <= 4.3e+94)
		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[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+19], t$95$1, If[LessEqual[b, 2.2e-219], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-176], t$95$2, If[LessEqual[b, 1.7e-20], N[(x - N[(z * N[(-1.0 + N[(y - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+94], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8e19 or 4.3e94 < b

   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 a around 0 85.1%

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

   4. Taylor expanded in z around 0 79.8%

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

   if -8e19 < b < 2.1999999999999999e-219

   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 93.0%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. sub-neg 74.4%

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

      3. metadata-eval 74.4%

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

      4. neg-mul-1 74.4%

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

      5. unsub-neg 74.4%

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

      6. +-commutative 74.4%

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

   6. Simplified 74.4%

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

   if 2.1999999999999999e-219 < b < 8.2000000000000005e-176 or 1.6999999999999999e-20 < b < 4.3e94

   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 81.0%

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

   4. Taylor expanded in a around inf 77.0%

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

   if 8.2000000000000005e-176 < b < 1.6999999999999999e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 76.2%

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

   4. Taylor expanded in z around inf 72.8%

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

   5. Taylor expanded in t around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   7. Simplified 59.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+19}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-176}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-20}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y - \frac{a}{z}\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+94}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \left(-1 + \left(y + t \cdot \frac{a}{z}\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-176}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (+ -1.0 (+ y (* t (/ a z)))))))
        (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -9.5e+30)
     t_2
     (if (<= b 2.2e-219)
       t_1
       (if (<= b 2.6e-176)
         (- x (* a (+ t -1.0)))
         (if (<= b 1.35e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (-1.0 + (y + (t * (a / z)))));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9.5e+30) {
		tmp = t_2;
	} else if (b <= 2.2e-219) {
		tmp = t_1;
	} else if (b <= 2.6e-176) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1.35e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (z * ((-1.0d0) + (y + (t * (a / z)))))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-9.5d+30)) then
        tmp = t_2
    else if (b <= 2.2d-219) then
        tmp = t_1
    else if (b <= 2.6d-176) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (b <= 1.35d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (-1.0 + (y + (t * (a / z)))));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9.5e+30) {
		tmp = t_2;
	} else if (b <= 2.2e-219) {
		tmp = t_1;
	} else if (b <= 2.6e-176) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1.35e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (-1.0 + (y + (t * (a / z)))))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -9.5e+30:
		tmp = t_2
	elif b <= 2.2e-219:
		tmp = t_1
	elif b <= 2.6e-176:
		tmp = x - (a * (t + -1.0))
	elif b <= 1.35e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(-1.0 + Float64(y + Float64(t * Float64(a / z))))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -9.5e+30)
		tmp = t_2;
	elseif (b <= 2.2e-219)
		tmp = t_1;
	elseif (b <= 2.6e-176)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (b <= 1.35e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (-1.0 + (y + (t * (a / z)))));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -9.5e+30)
		tmp = t_2;
	elseif (b <= 2.2e-219)
		tmp = t_1;
	elseif (b <= 2.6e-176)
		tmp = x - (a * (t + -1.0));
	elseif (b <= 1.35e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(-1.0 + N[(y + N[(t * N[(a / z), $MachinePrecision]), $MachinePrecision]), $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, -9.5e+30], t$95$2, If[LessEqual[b, 2.2e-219], t$95$1, If[LessEqual[b, 2.6e-176], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000003e30 or 1.35e14 < b

   1. Initial program 97.3%

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

   3. Taylor expanded in a around 0 82.1%

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

   4. Taylor expanded in z around 0 77.9%

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

   if -9.5000000000000003e30 < b < 2.1999999999999999e-219 or 2.59999999999999992e-176 < b < 1.35e14

   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 88.4%

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

   4. Taylor expanded in z around inf 76.6%

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

   5. Taylor expanded in t around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*r/ 72.8%

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

   7. Simplified 72.8%

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

   if 2.1999999999999999e-219 < b < 2.59999999999999992e-176

   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 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y + t \cdot \frac{a}{z}\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-176}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+14}:\\ \;\;\;\;x - z \cdot \left(-1 + \left(y + t \cdot \frac{a}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-191}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.1e+66)
     t_1
     (if (<= t -8e-191)
       (+ x z)
       (if (<= t 4.6e-297)
         (* a (- 1.0 t))
         (if (<= t 2.4e-143) (* y b) (if (<= t 3e-21) (* y (- z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.1e+66) {
		tmp = t_1;
	} else if (t <= -8e-191) {
		tmp = x + z;
	} else if (t <= 4.6e-297) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-143) {
		tmp = y * b;
	} else if (t <= 3e-21) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-4.1d+66)) then
        tmp = t_1
    else if (t <= (-8d-191)) then
        tmp = x + z
    else if (t <= 4.6d-297) then
        tmp = a * (1.0d0 - t)
    else if (t <= 2.4d-143) then
        tmp = y * b
    else if (t <= 3d-21) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.1e+66) {
		tmp = t_1;
	} else if (t <= -8e-191) {
		tmp = x + z;
	} else if (t <= 4.6e-297) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-143) {
		tmp = y * b;
	} else if (t <= 3e-21) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.1e+66:
		tmp = t_1
	elif t <= -8e-191:
		tmp = x + z
	elif t <= 4.6e-297:
		tmp = a * (1.0 - t)
	elif t <= 2.4e-143:
		tmp = y * b
	elif t <= 3e-21:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.1e+66)
		tmp = t_1;
	elseif (t <= -8e-191)
		tmp = Float64(x + z);
	elseif (t <= 4.6e-297)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 2.4e-143)
		tmp = Float64(y * b);
	elseif (t <= 3e-21)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.1e+66)
		tmp = t_1;
	elseif (t <= -8e-191)
		tmp = x + z;
	elseif (t <= 4.6e-297)
		tmp = a * (1.0 - t);
	elseif (t <= 2.4e-143)
		tmp = y * b;
	elseif (t <= 3e-21)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+66], t$95$1, If[LessEqual[t, -8e-191], N[(x + z), $MachinePrecision], If[LessEqual[t, 4.6e-297], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-143], N[(y * b), $MachinePrecision], If[LessEqual[t, 3e-21], N[(y * (-z)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.09999999999999994e66 or 2.99999999999999991e-21 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 66.1%

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

   if -4.09999999999999994e66 < t < -8.0000000000000002e-191

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 61.4%

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

   4. Taylor expanded in a around 0 49.6%

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

   5. Taylor expanded in y around 0 32.8%

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

      1. mul-1-neg 32.8%

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

   7. Simplified 32.8%

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

   if -8.0000000000000002e-191 < t < 4.5999999999999998e-297

   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 41.5%

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

   if 4.5999999999999998e-297 < t < 2.3999999999999999e-143

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 97.2%

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

   4. Taylor expanded in z around 0 79.4%

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

   5. Taylor expanded in y around inf 35.1%

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

   if 2.3999999999999999e-143 < t < 2.99999999999999991e-21

   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 y around inf 37.6%

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

   4. Taylor expanded in b around 0 36.8%

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

      1. associate-*r* 36.8%

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

      2. mul-1-neg 36.8%

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

   6. Simplified 36.8%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-191}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-143}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-228}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -6e+85)
     t_2
     (if (<= y -1.75e-254)
       (- x (* t a))
       (if (<= y 4e-263)
         t_1
         (if (<= y 9.8e-228) (+ x z) (if (<= y 1.65e+44) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -6e+85) {
		tmp = t_2;
	} else if (y <= -1.75e-254) {
		tmp = x - (t * a);
	} else if (y <= 4e-263) {
		tmp = t_1;
	} else if (y <= 9.8e-228) {
		tmp = x + z;
	} else if (y <= 1.65e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-6d+85)) then
        tmp = t_2
    else if (y <= (-1.75d-254)) then
        tmp = x - (t * a)
    else if (y <= 4d-263) then
        tmp = t_1
    else if (y <= 9.8d-228) then
        tmp = x + z
    else if (y <= 1.65d+44) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -6e+85) {
		tmp = t_2;
	} else if (y <= -1.75e-254) {
		tmp = x - (t * a);
	} else if (y <= 4e-263) {
		tmp = t_1;
	} else if (y <= 9.8e-228) {
		tmp = x + z;
	} else if (y <= 1.65e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -6e+85:
		tmp = t_2
	elif y <= -1.75e-254:
		tmp = x - (t * a)
	elif y <= 4e-263:
		tmp = t_1
	elif y <= 9.8e-228:
		tmp = x + z
	elif y <= 1.65e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6e+85)
		tmp = t_2;
	elseif (y <= -1.75e-254)
		tmp = Float64(x - Float64(t * a));
	elseif (y <= 4e-263)
		tmp = t_1;
	elseif (y <= 9.8e-228)
		tmp = Float64(x + z);
	elseif (y <= 1.65e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -6e+85)
		tmp = t_2;
	elseif (y <= -1.75e-254)
		tmp = x - (t * a);
	elseif (y <= 4e-263)
		tmp = t_1;
	elseif (y <= 9.8e-228)
		tmp = x + z;
	elseif (y <= 1.65e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+85], t$95$2, If[LessEqual[y, -1.75e-254], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-263], t$95$1, If[LessEqual[y, 9.8e-228], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.65e+44], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.0000000000000001e85 or 1.65000000000000007e44 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 74.0%

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

   if -6.0000000000000001e85 < y < -1.75000000000000004e-254

   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 71.6%

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

   4. Taylor expanded in t around inf 51.1%

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

   if -1.75000000000000004e-254 < y < 4e-263 or 9.79999999999999976e-228 < y < 1.65000000000000007e44

   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 47.6%

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

   if 4e-263 < y < 9.79999999999999976e-228

   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 0 61.0%

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

   5. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-263}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-228}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(t + -1\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-245}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (+ t -1.0)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -4.4e+14)
     t_2
     (if (<= b -1.3e-115)
       t_1
       (if (<= b 7.1e-245)
         (+ x (* z (- 1.0 y)))
         (if (<= b 1.1e-61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (a * (t + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -4.4e+14) {
		tmp = t_2;
	} else if (b <= -1.3e-115) {
		tmp = t_1;
	} else if (b <= 7.1e-245) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.1e-61) {
		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 * (t + (-1.0d0)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-4.4d+14)) then
        tmp = t_2
    else if (b <= (-1.3d-115)) then
        tmp = t_1
    else if (b <= 7.1d-245) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.1d-61) 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 * (t + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -4.4e+14) {
		tmp = t_2;
	} else if (b <= -1.3e-115) {
		tmp = t_1;
	} else if (b <= 7.1e-245) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.1e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (t + -1.0))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -4.4e+14:
		tmp = t_2
	elif b <= -1.3e-115:
		tmp = t_1
	elif b <= 7.1e-245:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.1e-61:
		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(t + -1.0)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -4.4e+14)
		tmp = t_2;
	elseif (b <= -1.3e-115)
		tmp = t_1;
	elseif (b <= 7.1e-245)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.1e-61)
		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 * (t + -1.0));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -4.4e+14)
		tmp = t_2;
	elseif (b <= -1.3e-115)
		tmp = t_1;
	elseif (b <= 7.1e-245)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.1e-61)
		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[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+14], t$95$2, If[LessEqual[b, -1.3e-115], t$95$1, If[LessEqual[b, 7.1e-245], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4e14 or 1.10000000000000004e-61 < b

   1. Initial program 97.6%

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

   3. Taylor expanded in a around 0 81.2%

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

   4. Taylor expanded in z around 0 73.7%

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

   if -4.4e14 < b < -1.30000000000000002e-115 or 7.10000000000000016e-245 < b < 1.10000000000000004e-61

   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 a around inf 71.7%

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

   if -1.30000000000000002e-115 < b < 7.10000000000000016e-245

   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 93.2%

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

   4. Taylor expanded in a around 0 69.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-115}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-245}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-61}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(t + -1\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (+ t -1.0)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -9.4e+54)
     t_2
     (if (<= b -2.8e-249)
       t_1
       (if (<= b 2.85e-300) (* z (- 1.0 y)) (if (<= b 4.5e+101) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (a * (t + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.4e+54) {
		tmp = t_2;
	} else if (b <= -2.8e-249) {
		tmp = t_1;
	} else if (b <= 2.85e-300) {
		tmp = z * (1.0 - y);
	} else if (b <= 4.5e+101) {
		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 * (t + (-1.0d0)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-9.4d+54)) then
        tmp = t_2
    else if (b <= (-2.8d-249)) then
        tmp = t_1
    else if (b <= 2.85d-300) then
        tmp = z * (1.0d0 - y)
    else if (b <= 4.5d+101) 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 * (t + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.4e+54) {
		tmp = t_2;
	} else if (b <= -2.8e-249) {
		tmp = t_1;
	} else if (b <= 2.85e-300) {
		tmp = z * (1.0 - y);
	} else if (b <= 4.5e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (t + -1.0))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9.4e+54:
		tmp = t_2
	elif b <= -2.8e-249:
		tmp = t_1
	elif b <= 2.85e-300:
		tmp = z * (1.0 - y)
	elif b <= 4.5e+101:
		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(t + -1.0)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9.4e+54)
		tmp = t_2;
	elseif (b <= -2.8e-249)
		tmp = t_1;
	elseif (b <= 2.85e-300)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 4.5e+101)
		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 * (t + -1.0));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9.4e+54)
		tmp = t_2;
	elseif (b <= -2.8e-249)
		tmp = t_1;
	elseif (b <= 2.85e-300)
		tmp = z * (1.0 - y);
	elseif (b <= 4.5e+101)
		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[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.4e+54], t$95$2, If[LessEqual[b, -2.8e-249], t$95$1, If[LessEqual[b, 2.85e-300], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.39999999999999985e54 or 4.5000000000000002e101 < b

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 78.7%

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

   if -9.39999999999999985e54 < b < -2.7999999999999999e-249 or 2.8499999999999999e-300 < b < 4.5000000000000002e101

   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 84.9%

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

   4. Taylor expanded in a around inf 60.2%

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

   if -2.7999999999999999e-249 < b < 2.8499999999999999e-300

   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 73.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-249}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{-300}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \left(t + -1\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.04 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-248}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (+ t -1.0)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.04e+55)
     t_2
     (if (<= b -1.35e-118)
       t_1
       (if (<= b 1.85e-248)
         (+ x (* z (- 1.0 y)))
         (if (<= b 2e+100) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (a * (t + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.04e+55) {
		tmp = t_2;
	} else if (b <= -1.35e-118) {
		tmp = t_1;
	} else if (b <= 1.85e-248) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2e+100) {
		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 * (t + (-1.0d0)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.04d+55)) then
        tmp = t_2
    else if (b <= (-1.35d-118)) then
        tmp = t_1
    else if (b <= 1.85d-248) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 2d+100) 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 * (t + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.04e+55) {
		tmp = t_2;
	} else if (b <= -1.35e-118) {
		tmp = t_1;
	} else if (b <= 1.85e-248) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (t + -1.0))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.04e+55:
		tmp = t_2
	elif b <= -1.35e-118:
		tmp = t_1
	elif b <= 1.85e-248:
		tmp = x + (z * (1.0 - y))
	elif b <= 2e+100:
		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(t + -1.0)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.04e+55)
		tmp = t_2;
	elseif (b <= -1.35e-118)
		tmp = t_1;
	elseif (b <= 1.85e-248)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2e+100)
		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 * (t + -1.0));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.04e+55)
		tmp = t_2;
	elseif (b <= -1.35e-118)
		tmp = t_1;
	elseif (b <= 1.85e-248)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 2e+100)
		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[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.04e+55], t$95$2, If[LessEqual[b, -1.35e-118], t$95$1, If[LessEqual[b, 1.85e-248], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.04000000000000003e55 or 2.00000000000000003e100 < b

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 78.7%

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

   if -1.04000000000000003e55 < b < -1.34999999999999997e-118 or 1.85000000000000013e-248 < b < 2.00000000000000003e100

   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 81.1%

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

   4. Taylor expanded in a around inf 63.4%

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

   if -1.34999999999999997e-118 < b < 1.85000000000000013e-248

   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 93.2%

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

   4. Taylor expanded in a around 0 69.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.04 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-118}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-248}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+100}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+67} \lor \neg \left(t \leq 0.0037\right):\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= t -4.5e+67) (not (<= t 0.0037)))
     (+ x (+ t_1 (* a (- 1.0 t))))
     (+ a (+ x (+ (* b (- y 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((t <= -4.5e+67) || !(t <= 0.0037)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((t <= (-4.5d+67)) .or. (.not. (t <= 0.0037d0))) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    else
        tmp = a + (x + ((b * (y - 2.0d0)) + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((t <= -4.5e+67) || !(t <= 0.0037)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (t <= -4.5e+67) or not (t <= 0.0037):
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = a + (x + ((b * (y - 2.0)) + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((t <= -4.5e+67) || !(t <= 0.0037))
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(a + Float64(x + Float64(Float64(b * Float64(y - 2.0)) + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((t <= -4.5e+67) || ~((t <= 0.0037)))
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = a + (x + ((b * (y - 2.0)) + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -4.5e+67], N[Not[LessEqual[t, 0.0037]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999998e67 or 0.0037000000000000002 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 71.8%

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

   if -4.4999999999999998e67 < t < 0.0037000000000000002

   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 t around -inf 55.7%

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

      1. associate-*r* 55.7%

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

      2. neg-mul-1 55.7%

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

      3. distribute-lft-out-- 55.7%

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

      4. associate-*r* 55.7%

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

      5. distribute-lft-neg-in 55.7%

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

      6. *-commutative 55.7%

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

      7. neg-mul-1 55.7%

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

      8. remove-double-neg 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 97.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+67} \lor \neg \left(t \leq 0.0037\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + z \cdot \left(1 - y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-35} \lor \neg \left(a \leq 1.02 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= a -2.2e-35) (not (<= a 1.02e+86)))
     (+ x (+ t_1 (* a (- 1.0 t))))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -2.2e-35) || !(a <= 1.02e+86)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((a <= (-2.2d-35)) .or. (.not. (a <= 1.02d+86))) then
        tmp = x + (t_1 + (a * (1.0d0 - t)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -2.2e-35) || !(a <= 1.02e+86)) {
		tmp = x + (t_1 + (a * (1.0 - t)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (a <= -2.2e-35) or not (a <= 1.02e+86):
		tmp = x + (t_1 + (a * (1.0 - t)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((a <= -2.2e-35) || !(a <= 1.02e+86))
		tmp = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((a <= -2.2e-35) || ~((a <= 1.02e+86)))
		tmp = x + (t_1 + (a * (1.0 - t)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -2.2e-35], N[Not[LessEqual[a, 1.02e+86]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.19999999999999994e-35 or 1.01999999999999996e86 < a

   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 83.0%

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

   if -2.19999999999999994e-35 < a < 1.01999999999999996e86

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 92.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-35} \lor \neg \left(a \leq 1.02 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+19} \lor \neg \left(b \leq 4.5 \cdot 10^{-62}\right):\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+19) (not (<= b 4.5e-62)))
   (+ a (+ x (+ (* b (- y 2.0)) (* t (- b a)))))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+19) || !(b <= 4.5e-62)) {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.5d+19)) .or. (.not. (b <= 4.5d-62))) then
        tmp = a + (x + ((b * (y - 2.0d0)) + (t * (b - a))))
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e+19) || !(b <= 4.5e-62)) {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e+19) or not (b <= 4.5e-62):
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))))
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.5e+19) || !(b <= 4.5e-62))
		tmp = Float64(a + Float64(x + Float64(Float64(b * Float64(y - 2.0)) + Float64(t * Float64(b - a)))));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.5e+19) || ~((b <= 4.5e-62)))
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.5e+19], N[Not[LessEqual[b, 4.5e-62]], $MachinePrecision]], N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5e19 or 4.50000000000000018e-62 < b

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0 95.2%

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

   4. Taylor expanded in z around 0 89.1%

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

   if -6.5e19 < b < 4.50000000000000018e-62

   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 92.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+19} \lor \neg \left(b \leq 4.5 \cdot 10^{-62}\right):\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-223}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-63}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.02e+19)
     t_1
     (if (<= b 6.6e-223)
       (+ x (+ a (* z (- 1.0 y))))
       (if (<= b 9.2e-63) (- x (* a (+ t -1.0))) 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 <= -1.02e+19) {
		tmp = t_1;
	} else if (b <= 6.6e-223) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 9.2e-63) {
		tmp = x - (a * (t + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.02d+19)) then
        tmp = t_1
    else if (b <= 6.6d-223) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else if (b <= 9.2d-63) then
        tmp = x - (a * (t + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.02e+19) {
		tmp = t_1;
	} else if (b <= 6.6e-223) {
		tmp = x + (a + (z * (1.0 - y)));
	} else if (b <= 9.2e-63) {
		tmp = x - (a * (t + -1.0));
	} 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 <= -1.02e+19:
		tmp = t_1
	elif b <= 6.6e-223:
		tmp = x + (a + (z * (1.0 - y)))
	elif b <= 9.2e-63:
		tmp = x - (a * (t + -1.0))
	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 <= -1.02e+19)
		tmp = t_1;
	elseif (b <= 6.6e-223)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	elseif (b <= 9.2e-63)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	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 <= -1.02e+19)
		tmp = t_1;
	elseif (b <= 6.6e-223)
		tmp = x + (a + (z * (1.0 - y)));
	elseif (b <= 9.2e-63)
		tmp = x - (a * (t + -1.0));
	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, -1.02e+19], t$95$1, If[LessEqual[b, 6.6e-223], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-63], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.02e19 or 9.2e-63 < b

   1. Initial program 97.6%

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

   3. Taylor expanded in a around 0 81.0%

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

   4. Taylor expanded in z around 0 74.3%

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

   if -1.02e19 < b < 6.59999999999999988e-223

   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 93.0%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. sub-neg 74.4%

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

      3. metadata-eval 74.4%

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

      4. neg-mul-1 74.4%

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

      5. unsub-neg 74.4%

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

      6. +-commutative 74.4%

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

   6. Simplified 74.4%

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

   if 6.59999999999999988e-223 < b < 9.2e-63

   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 90.5%

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

   4. Taylor expanded in a around inf 67.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+19}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-223}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-63}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+147} \lor \neg \left(b \leq 2.4 \cdot 10^{+95}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.1e+147) (not (<= b 2.4e+95)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.1e+147) || !(b <= 2.4e+95)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.1d+147)) .or. (.not. (b <= 2.4d+95))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.1e+147) || !(b <= 2.4e+95)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.1e+147) or not (b <= 2.4e+95):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.1e+147) || !(b <= 2.4e+95))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.1e+147) || ~((b <= 2.4e+95)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.1e+147], N[Not[LessEqual[b, 2.4e+95]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.10000000000000033e147 or 2.4e95 < b

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 88.7%

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

   4. Taylor expanded in z around 0 87.6%

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

   if -6.10000000000000033e147 < b < 2.4e95

   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 84.1%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+147} \lor \neg \left(b \leq 2.4 \cdot 10^{+95}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z * (1.0d0 - y))) + (a * (1.0d0 - t))) + (b * ((y + t) - 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 98.8%

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

Alternative 17: 26.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+57)
   (* y b)
   (if (<= y -1.05e-252) x (if (<= y 6.8e+43) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+57) {
		tmp = y * b;
	} else if (y <= -1.05e-252) {
		tmp = x;
	} else if (y <= 6.8e+43) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.9d+57)) then
        tmp = y * b
    else if (y <= (-1.05d-252)) then
        tmp = x
    else if (y <= 6.8d+43) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+57) {
		tmp = y * b;
	} else if (y <= -1.05e-252) {
		tmp = x;
	} else if (y <= 6.8e+43) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.9e+57:
		tmp = y * b
	elif y <= -1.05e-252:
		tmp = x
	elif y <= 6.8e+43:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+57)
		tmp = Float64(y * b);
	elseif (y <= -1.05e-252)
		tmp = x;
	elseif (y <= 6.8e+43)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.9e+57)
		tmp = y * b;
	elseif (y <= -1.05e-252)
		tmp = x;
	elseif (y <= 6.8e+43)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+57], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.05e-252], x, If[LessEqual[y, 6.8e+43], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000002e57 or 6.80000000000000024e43 < y

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 94.6%

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

   4. Taylor expanded in z around 0 62.8%

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

   5. Taylor expanded in y around inf 38.7%

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

   if -2.9000000000000002e57 < y < -1.05e-252

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 29.8%

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

   if -1.05e-252 < y < 6.80000000000000024e43

   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 0 65.5%

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

   4. Taylor expanded in t around inf 23.8%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e+61)
   (* y (- z))
   (if (<= y -4.3e-249) x (if (<= y 1.5e+45) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e+61) {
		tmp = y * -z;
	} else if (y <= -4.3e-249) {
		tmp = x;
	} else if (y <= 1.5e+45) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.4d+61)) then
        tmp = y * -z
    else if (y <= (-4.3d-249)) then
        tmp = x
    else if (y <= 1.5d+45) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e+61) {
		tmp = y * -z;
	} else if (y <= -4.3e-249) {
		tmp = x;
	} else if (y <= 1.5e+45) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e+61:
		tmp = y * -z
	elif y <= -4.3e-249:
		tmp = x
	elif y <= 1.5e+45:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e+61)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -4.3e-249)
		tmp = x;
	elseif (y <= 1.5e+45)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e+61)
		tmp = y * -z;
	elseif (y <= -4.3e-249)
		tmp = x;
	elseif (y <= 1.5e+45)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e+61], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -4.3e-249], x, If[LessEqual[y, 1.5e+45], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3999999999999999e61

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 74.5%

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

   4. Taylor expanded in b around 0 49.3%

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

      1. associate-*r* 49.3%

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

      2. mul-1-neg 49.3%

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

   6. Simplified 49.3%

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

   if -2.3999999999999999e61 < y < -4.3000000000000002e-249

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 29.4%

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

   if -4.3000000000000002e-249 < y < 1.50000000000000005e45

   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 0 65.5%

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

   4. Taylor expanded in t around inf 23.8%

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

   if 1.50000000000000005e45 < y

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 96.0%

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

   4. Taylor expanded in z around 0 68.7%

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

   5. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{b \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+68} \lor \neg \left(t \leq 4100000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e+68) (not (<= t 4100000.0))) (* 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 <= -2.6e+68) || !(t <= 4100000.0)) {
		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 <= (-2.6d+68)) .or. (.not. (t <= 4100000.0d0))) 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 <= -2.6e+68) || !(t <= 4100000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e+68) or not (t <= 4100000.0):
		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 <= -2.6e+68) || !(t <= 4100000.0))
		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 <= -2.6e+68) || ~((t <= 4100000.0)))
		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, -2.6e+68], N[Not[LessEqual[t, 4100000.0]], $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 < -2.5999999999999998e68 or 4.1e6 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 68.7%

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

   if -2.5999999999999998e68 < t < 4.1e6

   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 y around inf 41.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+68} \lor \neg \left(t \leq 4100000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+66} \lor \neg \left(t \leq 5.6 \cdot 10^{+52}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.6e+66) (not (<= t 5.6e+52))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+66) || !(t <= 5.6e+52)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.6d+66)) .or. (.not. (t <= 5.6d+52))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+66) || !(t <= 5.6e+52)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.6e+66) or not (t <= 5.6e+52):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.6e+66) || !(t <= 5.6e+52))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.6e+66) || ~((t <= 5.6e+52)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.6e+66], N[Not[LessEqual[t, 5.6e+52]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e66 or 5.6e52 < t

   1. Initial program 98.2%

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

   3. Taylor expanded in a around 0 65.2%

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

   4. Taylor expanded in t around inf 34.7%

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

   if -4.6e66 < t < 5.6e52

   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 x around inf 19.3%

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

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+66} \lor \neg \left(t \leq 5.6 \cdot 10^{+52}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-5}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e+83) (* y (- z)) (if (<= y 1.06e-5) (+ x z) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+83) {
		tmp = y * -z;
	} else if (y <= 1.06e-5) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.5d+83)) then
        tmp = y * -z
    else if (y <= 1.06d-5) then
        tmp = x + z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+83) {
		tmp = y * -z;
	} else if (y <= 1.06e-5) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e+83:
		tmp = y * -z
	elif y <= 1.06e-5:
		tmp = x + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e+83)
		tmp = Float64(y * Float64(-z));
	elseif (y <= 1.06e-5)
		tmp = Float64(x + z);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.5e+83)
		tmp = y * -z;
	elseif (y <= 1.06e-5)
		tmp = x + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e+83], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, 1.06e-5], N[(x + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999995e83

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf 76.9%

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

   4. Taylor expanded in b around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. mul-1-neg 50.9%

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

   6. Simplified 50.9%

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

   if -8.4999999999999995e83 < y < 1.06e-5

   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 68.0%

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

   4. Taylor expanded in a around 0 35.9%

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

   5. Taylor expanded in y around 0 33.8%

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

      1. mul-1-neg 33.8%

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

   7. Simplified 33.8%

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

   if 1.06e-5 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 96.4%

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

   4. Taylor expanded in z around 0 70.3%

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

   5. Taylor expanded in y around inf 39.7%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-5}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 15.4% 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 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 x around inf 14.7%

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

4. Final simplification 14.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(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)))