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

Percentage Accurate: 95.4% → 97.4%

Time: 18.2s

Alternatives: 26

Speedup: 0.5×

• 35.7% 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: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% 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 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 99.2%

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

   3. associate--l+ 99.2%

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

   4. sub-neg 99.2%

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

   5. metadata-eval 99.2%

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

   6. sub-neg 99.2%

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

   7. associate-+l- 99.2%

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

   8. fma-neg 99.2%

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

   9. sub-neg 99.2%

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

   10. metadata-eval 99.2%

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

   11. remove-double-neg 99.2%

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

   12. sub-neg 99.2%

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

   13. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 44.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-262}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-267}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+30}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= y -1.35e+183)
     (- x (* y z))
     (if (<= y -6.4e+34)
       t_1
       (if (<= y -2.2e-107)
         t_2
         (if (<= y -6.2e-168)
           (+ x a)
           (if (<= y -1.65e-262)
             t_2
             (if (<= y -5.4e-267)
               (+ x a)
               (if (<= y 2.25e-304)
                 (* b (- y 2.0))
                 (if (<= y 1.2e-289)
                   z
                   (if (<= y 7.8e+30) (+ x a) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (y <= -1.35e+183) {
		tmp = x - (y * z);
	} else if (y <= -6.4e+34) {
		tmp = t_1;
	} else if (y <= -2.2e-107) {
		tmp = t_2;
	} else if (y <= -6.2e-168) {
		tmp = x + a;
	} else if (y <= -1.65e-262) {
		tmp = t_2;
	} else if (y <= -5.4e-267) {
		tmp = x + a;
	} else if (y <= 2.25e-304) {
		tmp = b * (y - 2.0);
	} else if (y <= 1.2e-289) {
		tmp = z;
	} else if (y <= 7.8e+30) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (y <= (-1.35d+183)) then
        tmp = x - (y * z)
    else if (y <= (-6.4d+34)) then
        tmp = t_1
    else if (y <= (-2.2d-107)) then
        tmp = t_2
    else if (y <= (-6.2d-168)) then
        tmp = x + a
    else if (y <= (-1.65d-262)) then
        tmp = t_2
    else if (y <= (-5.4d-267)) then
        tmp = x + a
    else if (y <= 2.25d-304) then
        tmp = b * (y - 2.0d0)
    else if (y <= 1.2d-289) then
        tmp = z
    else if (y <= 7.8d+30) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (y <= -1.35e+183) {
		tmp = x - (y * z);
	} else if (y <= -6.4e+34) {
		tmp = t_1;
	} else if (y <= -2.2e-107) {
		tmp = t_2;
	} else if (y <= -6.2e-168) {
		tmp = x + a;
	} else if (y <= -1.65e-262) {
		tmp = t_2;
	} else if (y <= -5.4e-267) {
		tmp = x + a;
	} else if (y <= 2.25e-304) {
		tmp = b * (y - 2.0);
	} else if (y <= 1.2e-289) {
		tmp = z;
	} else if (y <= 7.8e+30) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if y <= -1.35e+183:
		tmp = x - (y * z)
	elif y <= -6.4e+34:
		tmp = t_1
	elif y <= -2.2e-107:
		tmp = t_2
	elif y <= -6.2e-168:
		tmp = x + a
	elif y <= -1.65e-262:
		tmp = t_2
	elif y <= -5.4e-267:
		tmp = x + a
	elif y <= 2.25e-304:
		tmp = b * (y - 2.0)
	elif y <= 1.2e-289:
		tmp = z
	elif y <= 7.8e+30:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (y <= -1.35e+183)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= -6.4e+34)
		tmp = t_1;
	elseif (y <= -2.2e-107)
		tmp = t_2;
	elseif (y <= -6.2e-168)
		tmp = Float64(x + a);
	elseif (y <= -1.65e-262)
		tmp = t_2;
	elseif (y <= -5.4e-267)
		tmp = Float64(x + a);
	elseif (y <= 2.25e-304)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (y <= 1.2e-289)
		tmp = z;
	elseif (y <= 7.8e+30)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (y <= -1.35e+183)
		tmp = x - (y * z);
	elseif (y <= -6.4e+34)
		tmp = t_1;
	elseif (y <= -2.2e-107)
		tmp = t_2;
	elseif (y <= -6.2e-168)
		tmp = x + a;
	elseif (y <= -1.65e-262)
		tmp = t_2;
	elseif (y <= -5.4e-267)
		tmp = x + a;
	elseif (y <= 2.25e-304)
		tmp = b * (y - 2.0);
	elseif (y <= 1.2e-289)
		tmp = z;
	elseif (y <= 7.8e+30)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+183], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.4e+34], t$95$1, If[LessEqual[y, -2.2e-107], t$95$2, If[LessEqual[y, -6.2e-168], N[(x + a), $MachinePrecision], If[LessEqual[y, -1.65e-262], t$95$2, If[LessEqual[y, -5.4e-267], N[(x + a), $MachinePrecision], If[LessEqual[y, 2.25e-304], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-289], z, If[LessEqual[y, 7.8e+30], N[(x + a), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.34999999999999991e183

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 82.5%

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

   4. Taylor expanded in y around inf 82.5%

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

   5. Taylor expanded in a around 0 75.3%

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

   if -1.34999999999999991e183 < y < -6.3999999999999997e34 or 7.80000000000000021e30 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 74.7%

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

   if -6.3999999999999997e34 < y < -2.20000000000000012e-107 or -6.2e-168 < y < -1.6500000000000001e-262

   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 60.9%

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

   if -2.20000000000000012e-107 < y < -6.2e-168 or -1.6500000000000001e-262 < y < -5.39999999999999975e-267 or 1.19999999999999997e-289 < y < 7.80000000000000021e30

   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 0 100.0%

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

   4. Taylor expanded in t around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. metadata-eval 74.1%

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

      3. +-commutative 74.1%

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

      4. sub-neg 74.1%

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

      5. metadata-eval 74.1%

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

      6. mul-1-neg 74.1%

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

      7. sub-neg 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in z around 0 57.3%

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

   8. Taylor expanded in b around 0 53.3%

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

   if -5.39999999999999975e-267 < y < 2.2499999999999999e-304

   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 0 100.0%

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

   4. Taylor expanded in t around 0 72.8%

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

      1. sub-neg 72.8%

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

      2. metadata-eval 72.8%

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

      3. +-commutative 72.8%

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

      4. sub-neg 72.8%

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

      5. metadata-eval 72.8%

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

      6. mul-1-neg 72.8%

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

      7. sub-neg 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in b around inf 57.7%

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

   if 2.2499999999999999e-304 < y < 1.19999999999999997e-289

   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 55.2%

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

   4. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-168}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-267}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+30}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ (+ (+ x (* z (- 1.0 y))) t_1) (* b (- (+ y t) 2.0)))))
   (if (<= t_2 INFINITY) t_2 (+ x (- t_1 (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((x + (z * (1.0 - y))) + t_1) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = x + (t_1 - (y * z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((x + (z * (1.0 - y))) + t_1) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = x + (t_1 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = ((x + (z * (1.0 - y))) + t_1) + (b * ((y + t) - 2.0))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = x + (t_1 - (y * z))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = ((x + (z * (1.0 - y))) + t_1) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = x + (t_1 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in b around 0 75.0%

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

   4. Taylor expanded in y around inf 75.0%

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

4. Final simplification 99.2%

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

Alternative 4: 47.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.95 \cdot 10^{+30}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -3.9e+31)
     t_2
     (if (<= y -2.35e-107)
       t_1
       (if (<= y -1.6e-170)
         (+ x a)
         (if (<= y -2.9e-260)
           t_1
           (if (<= y -3.1e-267)
             (+ x a)
             (if (<= y 4.25e-305)
               (* b (- y 2.0))
               (if (<= y 1.2e-289) z (if (<= y 4.95e+30) (+ x a) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.9e+31) {
		tmp = t_2;
	} else if (y <= -2.35e-107) {
		tmp = t_1;
	} else if (y <= -1.6e-170) {
		tmp = x + a;
	} else if (y <= -2.9e-260) {
		tmp = t_1;
	} else if (y <= -3.1e-267) {
		tmp = x + a;
	} else if (y <= 4.25e-305) {
		tmp = b * (y - 2.0);
	} else if (y <= 1.2e-289) {
		tmp = z;
	} else if (y <= 4.95e+30) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-3.9d+31)) then
        tmp = t_2
    else if (y <= (-2.35d-107)) then
        tmp = t_1
    else if (y <= (-1.6d-170)) then
        tmp = x + a
    else if (y <= (-2.9d-260)) then
        tmp = t_1
    else if (y <= (-3.1d-267)) then
        tmp = x + a
    else if (y <= 4.25d-305) then
        tmp = b * (y - 2.0d0)
    else if (y <= 1.2d-289) then
        tmp = z
    else if (y <= 4.95d+30) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.9e+31) {
		tmp = t_2;
	} else if (y <= -2.35e-107) {
		tmp = t_1;
	} else if (y <= -1.6e-170) {
		tmp = x + a;
	} else if (y <= -2.9e-260) {
		tmp = t_1;
	} else if (y <= -3.1e-267) {
		tmp = x + a;
	} else if (y <= 4.25e-305) {
		tmp = b * (y - 2.0);
	} else if (y <= 1.2e-289) {
		tmp = z;
	} else if (y <= 4.95e+30) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -3.9e+31:
		tmp = t_2
	elif y <= -2.35e-107:
		tmp = t_1
	elif y <= -1.6e-170:
		tmp = x + a
	elif y <= -2.9e-260:
		tmp = t_1
	elif y <= -3.1e-267:
		tmp = x + a
	elif y <= 4.25e-305:
		tmp = b * (y - 2.0)
	elif y <= 1.2e-289:
		tmp = z
	elif y <= 4.95e+30:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3.9e+31)
		tmp = t_2;
	elseif (y <= -2.35e-107)
		tmp = t_1;
	elseif (y <= -1.6e-170)
		tmp = Float64(x + a);
	elseif (y <= -2.9e-260)
		tmp = t_1;
	elseif (y <= -3.1e-267)
		tmp = Float64(x + a);
	elseif (y <= 4.25e-305)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (y <= 1.2e-289)
		tmp = z;
	elseif (y <= 4.95e+30)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.9e+31)
		tmp = t_2;
	elseif (y <= -2.35e-107)
		tmp = t_1;
	elseif (y <= -1.6e-170)
		tmp = x + a;
	elseif (y <= -2.9e-260)
		tmp = t_1;
	elseif (y <= -3.1e-267)
		tmp = x + a;
	elseif (y <= 4.25e-305)
		tmp = b * (y - 2.0);
	elseif (y <= 1.2e-289)
		tmp = z;
	elseif (y <= 4.95e+30)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+31], t$95$2, If[LessEqual[y, -2.35e-107], t$95$1, If[LessEqual[y, -1.6e-170], N[(x + a), $MachinePrecision], If[LessEqual[y, -2.9e-260], t$95$1, If[LessEqual[y, -3.1e-267], N[(x + a), $MachinePrecision], If[LessEqual[y, 4.25e-305], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-289], z, If[LessEqual[y, 4.95e+30], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.89999999999999999e31 or 4.9500000000000001e30 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 71.7%

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

   if -3.89999999999999999e31 < y < -2.34999999999999999e-107 or -1.6e-170 < y < -2.8999999999999999e-260

   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 60.9%

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

   if -2.34999999999999999e-107 < y < -1.6e-170 or -2.8999999999999999e-260 < y < -3.1000000000000001e-267 or 1.19999999999999997e-289 < y < 4.9500000000000001e30

   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 0 100.0%

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

   4. Taylor expanded in t around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. metadata-eval 74.1%

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

      3. +-commutative 74.1%

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

      4. sub-neg 74.1%

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

      5. metadata-eval 74.1%

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

      6. mul-1-neg 74.1%

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

      7. sub-neg 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in z around 0 57.3%

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

   8. Taylor expanded in b around 0 53.3%

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

   if -3.1000000000000001e-267 < y < 4.2499999999999998e-305

   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 0 100.0%

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

   4. Taylor expanded in t around 0 72.8%

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

      1. sub-neg 72.8%

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

      2. metadata-eval 72.8%

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

      3. +-commutative 72.8%

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

      4. sub-neg 72.8%

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

      5. metadata-eval 72.8%

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

      6. mul-1-neg 72.8%

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

      7. sub-neg 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in b around inf 57.7%

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

   if 4.2499999999999998e-305 < y < 1.19999999999999997e-289

   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 55.2%

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

   4. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.25 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.95 \cdot 10^{+30}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := \left(x + a\right) + -2 \cdot b\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))) (t_3 (+ (+ x a) (* -2.0 b))))
   (if (<= y -1.6e+183)
     (- x (* y z))
     (if (<= y -5e+31)
       t_1
       (if (<= y -1.7e-94)
         t_2
         (if (<= y -3.2e-168)
           t_3
           (if (<= y -1.75e-231)
             t_2
             (if (<= y -2.15e-240)
               (* b (- (+ y t) 2.0))
               (if (<= y 1.08e+27) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = (x + a) + (-2.0 * b);
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if (y <= -5e+31) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_2;
	} else if (y <= -3.2e-168) {
		tmp = t_3;
	} else if (y <= -1.75e-231) {
		tmp = t_2;
	} else if (y <= -2.15e-240) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= 1.08e+27) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    t_3 = (x + a) + ((-2.0d0) * b)
    if (y <= (-1.6d+183)) then
        tmp = x - (y * z)
    else if (y <= (-5d+31)) then
        tmp = t_1
    else if (y <= (-1.7d-94)) then
        tmp = t_2
    else if (y <= (-3.2d-168)) then
        tmp = t_3
    else if (y <= (-1.75d-231)) then
        tmp = t_2
    else if (y <= (-2.15d-240)) then
        tmp = b * ((y + t) - 2.0d0)
    else if (y <= 1.08d+27) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double t_3 = (x + a) + (-2.0 * b);
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if (y <= -5e+31) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_2;
	} else if (y <= -3.2e-168) {
		tmp = t_3;
	} else if (y <= -1.75e-231) {
		tmp = t_2;
	} else if (y <= -2.15e-240) {
		tmp = b * ((y + t) - 2.0);
	} else if (y <= 1.08e+27) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	t_3 = (x + a) + (-2.0 * b)
	tmp = 0
	if y <= -1.6e+183:
		tmp = x - (y * z)
	elif y <= -5e+31:
		tmp = t_1
	elif y <= -1.7e-94:
		tmp = t_2
	elif y <= -3.2e-168:
		tmp = t_3
	elif y <= -1.75e-231:
		tmp = t_2
	elif y <= -2.15e-240:
		tmp = b * ((y + t) - 2.0)
	elif y <= 1.08e+27:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(Float64(x + a) + Float64(-2.0 * b))
	tmp = 0.0
	if (y <= -1.6e+183)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= -5e+31)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_2;
	elseif (y <= -3.2e-168)
		tmp = t_3;
	elseif (y <= -1.75e-231)
		tmp = t_2;
	elseif (y <= -2.15e-240)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (y <= 1.08e+27)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	t_3 = (x + a) + (-2.0 * b);
	tmp = 0.0;
	if (y <= -1.6e+183)
		tmp = x - (y * z);
	elseif (y <= -5e+31)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_2;
	elseif (y <= -3.2e-168)
		tmp = t_3;
	elseif (y <= -1.75e-231)
		tmp = t_2;
	elseif (y <= -2.15e-240)
		tmp = b * ((y + t) - 2.0);
	elseif (y <= 1.08e+27)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + a), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+183], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e+31], t$95$1, If[LessEqual[y, -1.7e-94], t$95$2, If[LessEqual[y, -3.2e-168], t$95$3, If[LessEqual[y, -1.75e-231], t$95$2, If[LessEqual[y, -2.15e-240], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+27], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.6000000000000001e183

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 82.5%

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

   4. Taylor expanded in y around inf 82.5%

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

   5. Taylor expanded in a around 0 75.3%

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

   if -1.6000000000000001e183 < y < -5.00000000000000027e31 or 1.08e27 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 74.7%

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

   if -5.00000000000000027e31 < y < -1.6999999999999999e-94 or -3.20000000000000006e-168 < y < -1.7500000000000001e-231

   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 65.8%

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

   if -1.6999999999999999e-94 < y < -3.20000000000000006e-168 or -2.15000000000000007e-240 < y < 1.08e27

   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 0 100.0%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. sub-neg 72.4%

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

      2. metadata-eval 72.4%

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

      3. +-commutative 72.4%

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

      4. sub-neg 72.4%

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

      5. metadata-eval 72.4%

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

      6. mul-1-neg 72.4%

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

      7. sub-neg 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in z around 0 56.2%

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

   8. Taylor expanded in y around 0 56.3%

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

      1. associate-+r+ 56.3%

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

      2. *-commutative 56.3%

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

   10. Simplified 56.3%

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

   if -1.7500000000000001e-231 < y < -2.15000000000000007e-240

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 99.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-168}:\\ \;\;\;\;\left(x + a\right) + -2 \cdot b\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;\left(x + a\right) + -2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-298}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 720000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -6.5e+18)
     t_2
     (if (<= t -2.2e-204)
       (+ x a)
       (if (<= t -2.5e-245)
         t_1
         (if (<= t 2e-298)
           (+ x a)
           (if (<= t 4.8e-265)
             t_1
             (if (<= t 3.1e-96)
               (* y (- z))
               (if (<= t 720000000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.5e+18) {
		tmp = t_2;
	} else if (t <= -2.2e-204) {
		tmp = x + a;
	} else if (t <= -2.5e-245) {
		tmp = t_1;
	} else if (t <= 2e-298) {
		tmp = x + a;
	} else if (t <= 4.8e-265) {
		tmp = t_1;
	} else if (t <= 3.1e-96) {
		tmp = y * -z;
	} else if (t <= 720000000.0) {
		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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-6.5d+18)) then
        tmp = t_2
    else if (t <= (-2.2d-204)) then
        tmp = x + a
    else if (t <= (-2.5d-245)) then
        tmp = t_1
    else if (t <= 2d-298) then
        tmp = x + a
    else if (t <= 4.8d-265) then
        tmp = t_1
    else if (t <= 3.1d-96) then
        tmp = y * -z
    else if (t <= 720000000.0d0) 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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.5e+18) {
		tmp = t_2;
	} else if (t <= -2.2e-204) {
		tmp = x + a;
	} else if (t <= -2.5e-245) {
		tmp = t_1;
	} else if (t <= 2e-298) {
		tmp = x + a;
	} else if (t <= 4.8e-265) {
		tmp = t_1;
	} else if (t <= 3.1e-96) {
		tmp = y * -z;
	} else if (t <= 720000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6.5e+18:
		tmp = t_2
	elif t <= -2.2e-204:
		tmp = x + a
	elif t <= -2.5e-245:
		tmp = t_1
	elif t <= 2e-298:
		tmp = x + a
	elif t <= 4.8e-265:
		tmp = t_1
	elif t <= 3.1e-96:
		tmp = y * -z
	elif t <= 720000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.5e+18)
		tmp = t_2;
	elseif (t <= -2.2e-204)
		tmp = Float64(x + a);
	elseif (t <= -2.5e-245)
		tmp = t_1;
	elseif (t <= 2e-298)
		tmp = Float64(x + a);
	elseif (t <= 4.8e-265)
		tmp = t_1;
	elseif (t <= 3.1e-96)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 720000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.5e+18)
		tmp = t_2;
	elseif (t <= -2.2e-204)
		tmp = x + a;
	elseif (t <= -2.5e-245)
		tmp = t_1;
	elseif (t <= 2e-298)
		tmp = x + a;
	elseif (t <= 4.8e-265)
		tmp = t_1;
	elseif (t <= 3.1e-96)
		tmp = y * -z;
	elseif (t <= 720000000.0)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+18], t$95$2, If[LessEqual[t, -2.2e-204], N[(x + a), $MachinePrecision], If[LessEqual[t, -2.5e-245], t$95$1, If[LessEqual[t, 2e-298], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.8e-265], t$95$1, If[LessEqual[t, 3.1e-96], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 720000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.5e18 or 7.2e8 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in t around inf 65.4%

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

   if -6.5e18 < t < -2.1999999999999998e-204 or -2.4999999999999998e-245 < t < 1.99999999999999982e-298

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 97.0%

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

   4. Taylor expanded in t around 0 96.6%

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

      1. sub-neg 96.6%

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

      2. metadata-eval 96.6%

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

      3. +-commutative 96.6%

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

      4. sub-neg 96.6%

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

      5. metadata-eval 96.6%

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

      6. mul-1-neg 96.6%

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

      7. sub-neg 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in z around 0 75.2%

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

   8. Taylor expanded in b around 0 53.1%

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

   if -2.1999999999999998e-204 < t < -2.4999999999999998e-245 or 1.99999999999999982e-298 < t < 4.7999999999999999e-265 or 3.0999999999999999e-96 < t < 7.2e8

   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 97.3%

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

   4. Taylor expanded in t around 0 94.6%

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

      1. sub-neg 94.6%

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

      2. metadata-eval 94.6%

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

      3. +-commutative 94.6%

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

      4. sub-neg 94.6%

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

      5. metadata-eval 94.6%

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

      6. mul-1-neg 94.6%

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

      7. sub-neg 94.6%

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

   6. Simplified 94.6%

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

   7. Taylor expanded in b around inf 58.4%

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

   if 4.7999999999999999e-265 < t < 3.0999999999999999e-96

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 49.4%

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

   4. Taylor expanded in y around inf 35.0%

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

      1. mul-1-neg 35.0%

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

      2. distribute-lft-neg-out 35.0%

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

      3. *-commutative 35.0%

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

   6. Simplified 35.0%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-245}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-298}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-265}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 720000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - y\right)\\ t_2 := a + t\_1\\ t_3 := t \cdot \left(b - a\right)\\ t_4 := x - y \cdot z\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-96}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 y))))
        (t_2 (+ a t_1))
        (t_3 (* t (- b a)))
        (t_4 (- x (* y z))))
   (if (<= t -1.1e+53)
     t_3
     (if (<= t 3.2e-144)
       t_2
       (if (<= t 3.1e-96)
         t_4
         (if (<= t 8e-36)
           t_2
           (if (<= t 2.4e+79) t_4 (if (<= t 1.12e+98) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - y));
	double t_2 = a + t_1;
	double t_3 = t * (b - a);
	double t_4 = x - (y * z);
	double tmp;
	if (t <= -1.1e+53) {
		tmp = t_3;
	} else if (t <= 3.2e-144) {
		tmp = t_2;
	} else if (t <= 3.1e-96) {
		tmp = t_4;
	} else if (t <= 8e-36) {
		tmp = t_2;
	} else if (t <= 2.4e+79) {
		tmp = t_4;
	} else if (t <= 1.12e+98) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - y))
    t_2 = a + t_1
    t_3 = t * (b - a)
    t_4 = x - (y * z)
    if (t <= (-1.1d+53)) then
        tmp = t_3
    else if (t <= 3.2d-144) then
        tmp = t_2
    else if (t <= 3.1d-96) then
        tmp = t_4
    else if (t <= 8d-36) then
        tmp = t_2
    else if (t <= 2.4d+79) then
        tmp = t_4
    else if (t <= 1.12d+98) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - y));
	double t_2 = a + t_1;
	double t_3 = t * (b - a);
	double t_4 = x - (y * z);
	double tmp;
	if (t <= -1.1e+53) {
		tmp = t_3;
	} else if (t <= 3.2e-144) {
		tmp = t_2;
	} else if (t <= 3.1e-96) {
		tmp = t_4;
	} else if (t <= 8e-36) {
		tmp = t_2;
	} else if (t <= 2.4e+79) {
		tmp = t_4;
	} else if (t <= 1.12e+98) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - y))
	t_2 = a + t_1
	t_3 = t * (b - a)
	t_4 = x - (y * z)
	tmp = 0
	if t <= -1.1e+53:
		tmp = t_3
	elif t <= 3.2e-144:
		tmp = t_2
	elif t <= 3.1e-96:
		tmp = t_4
	elif t <= 8e-36:
		tmp = t_2
	elif t <= 2.4e+79:
		tmp = t_4
	elif t <= 1.12e+98:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - y)))
	t_2 = Float64(a + t_1)
	t_3 = Float64(t * Float64(b - a))
	t_4 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (t <= -1.1e+53)
		tmp = t_3;
	elseif (t <= 3.2e-144)
		tmp = t_2;
	elseif (t <= 3.1e-96)
		tmp = t_4;
	elseif (t <= 8e-36)
		tmp = t_2;
	elseif (t <= 2.4e+79)
		tmp = t_4;
	elseif (t <= 1.12e+98)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - y));
	t_2 = a + t_1;
	t_3 = t * (b - a);
	t_4 = x - (y * z);
	tmp = 0.0;
	if (t <= -1.1e+53)
		tmp = t_3;
	elseif (t <= 3.2e-144)
		tmp = t_2;
	elseif (t <= 3.1e-96)
		tmp = t_4;
	elseif (t <= 8e-36)
		tmp = t_2;
	elseif (t <= 2.4e+79)
		tmp = t_4;
	elseif (t <= 1.12e+98)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+53], t$95$3, If[LessEqual[t, 3.2e-144], t$95$2, If[LessEqual[t, 3.1e-96], t$95$4, If[LessEqual[t, 8e-36], t$95$2, If[LessEqual[t, 2.4e+79], t$95$4, If[LessEqual[t, 1.12e+98], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.09999999999999999e53 or 1.12e98 < t

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf 70.1%

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

   if -1.09999999999999999e53 < t < 3.19999999999999973e-144 or 3.0999999999999999e-96 < t < 7.9999999999999995e-36

   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 t around 0 97.8%

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

   4. Taylor expanded in t around 0 96.3%

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

      1. sub-neg 96.3%

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

      2. metadata-eval 96.3%

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

      3. +-commutative 96.3%

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

      4. sub-neg 96.3%

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

      5. metadata-eval 96.3%

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

      6. mul-1-neg 96.3%

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

      7. sub-neg 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in z around 0 72.4%

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

   if 3.19999999999999973e-144 < t < 3.0999999999999999e-96 or 7.9999999999999995e-36 < t < 2.39999999999999986e79

   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 0 86.9%

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

   4. Taylor expanded in y around inf 74.2%

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

   5. Taylor expanded in a around 0 67.9%

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

   if 2.39999999999999986e79 < t < 1.12e98

   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 0 50.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. sub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

   8. Taylor expanded in a around 0 100.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-96}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-36}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+79}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;x - b \cdot \left(2 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+67}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -2.4e+57)
     t_1
     (if (<= b -2.35e-113)
       (+ x a)
       (if (<= b -1.15e-274)
         (* y (- z))
         (if (<= b 7.6e+43)
           (+ x a)
           (if (<= b 2e+67) (* t b) (if (<= b 9.6e+72) x t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -2.4e+57) {
		tmp = t_1;
	} else if (b <= -2.35e-113) {
		tmp = x + a;
	} else if (b <= -1.15e-274) {
		tmp = y * -z;
	} else if (b <= 7.6e+43) {
		tmp = x + a;
	} else if (b <= 2e+67) {
		tmp = t * b;
	} else if (b <= 9.6e+72) {
		tmp = x;
	} 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 = b * (y - 2.0d0)
    if (b <= (-2.4d+57)) then
        tmp = t_1
    else if (b <= (-2.35d-113)) then
        tmp = x + a
    else if (b <= (-1.15d-274)) then
        tmp = y * -z
    else if (b <= 7.6d+43) then
        tmp = x + a
    else if (b <= 2d+67) then
        tmp = t * b
    else if (b <= 9.6d+72) then
        tmp = x
    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 - 2.0);
	double tmp;
	if (b <= -2.4e+57) {
		tmp = t_1;
	} else if (b <= -2.35e-113) {
		tmp = x + a;
	} else if (b <= -1.15e-274) {
		tmp = y * -z;
	} else if (b <= 7.6e+43) {
		tmp = x + a;
	} else if (b <= 2e+67) {
		tmp = t * b;
	} else if (b <= 9.6e+72) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -2.4e+57:
		tmp = t_1
	elif b <= -2.35e-113:
		tmp = x + a
	elif b <= -1.15e-274:
		tmp = y * -z
	elif b <= 7.6e+43:
		tmp = x + a
	elif b <= 2e+67:
		tmp = t * b
	elif b <= 9.6e+72:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -2.4e+57)
		tmp = t_1;
	elseif (b <= -2.35e-113)
		tmp = Float64(x + a);
	elseif (b <= -1.15e-274)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 7.6e+43)
		tmp = Float64(x + a);
	elseif (b <= 2e+67)
		tmp = Float64(t * b);
	elseif (b <= 9.6e+72)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -2.4e+57)
		tmp = t_1;
	elseif (b <= -2.35e-113)
		tmp = x + a;
	elseif (b <= -1.15e-274)
		tmp = y * -z;
	elseif (b <= 7.6e+43)
		tmp = x + a;
	elseif (b <= 2e+67)
		tmp = t * b;
	elseif (b <= 9.6e+72)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+57], t$95$1, If[LessEqual[b, -2.35e-113], N[(x + a), $MachinePrecision], If[LessEqual[b, -1.15e-274], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 7.6e+43], N[(x + a), $MachinePrecision], If[LessEqual[b, 2e+67], N[(t * b), $MachinePrecision], If[LessEqual[b, 9.6e+72], x, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.40000000000000005e57 or 9.6000000000000004e72 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in t around 0 89.8%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. sub-neg 76.1%

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

      2. metadata-eval 76.1%

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

      3. +-commutative 76.1%

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

      4. sub-neg 76.1%

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

      5. metadata-eval 76.1%

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

      6. mul-1-neg 76.1%

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

      7. sub-neg 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in b around inf 54.3%

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

   if -2.40000000000000005e57 < b < -2.3500000000000001e-113 or -1.14999999999999998e-274 < b < 7.60000000000000016e43

   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 0 100.0%

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

   4. Taylor expanded in t around 0 76.0%

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

      1. sub-neg 76.0%

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

      2. metadata-eval 76.0%

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

      3. +-commutative 76.0%

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

      4. sub-neg 76.0%

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

      5. metadata-eval 76.0%

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

      6. mul-1-neg 76.0%

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

      7. sub-neg 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in z around 0 50.0%

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

   8. Taylor expanded in b around 0 42.9%

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

   if -2.3500000000000001e-113 < b < -1.14999999999999998e-274

   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 54.1%

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

   4. Taylor expanded in y around inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. distribute-lft-neg-out 39.2%

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

      3. *-commutative 39.2%

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

   6. Simplified 39.2%

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

   if 7.60000000000000016e43 < b < 1.99999999999999997e67

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in b around inf 100.0%

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

   if 1.99999999999999997e67 < b < 9.6000000000000004e72

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 52.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+67}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-204}:\\ \;\;\;\;z + \left(\left(x + a\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ x (+ z (* a (- 1.0 t))))))
   (if (<= y -1.6e+183)
     (- (+ x a) (* z (+ y -1.0)))
     (if (<= y -8.8e+43)
       t_1
       (if (<= y -1.7e-231)
         t_2
         (if (<= y 1.6e-204)
           (+ z (+ (+ x a) (* -2.0 b)))
           (if (<= y 5.9e+28) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x + (z + (a * (1.0 - t)));
	double tmp;
	if (y <= -1.6e+183) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (y <= -8.8e+43) {
		tmp = t_1;
	} else if (y <= -1.7e-231) {
		tmp = t_2;
	} else if (y <= 1.6e-204) {
		tmp = z + ((x + a) + (-2.0 * b));
	} else if (y <= 5.9e+28) {
		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 = y * (b - z)
    t_2 = x + (z + (a * (1.0d0 - t)))
    if (y <= (-1.6d+183)) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if (y <= (-8.8d+43)) then
        tmp = t_1
    else if (y <= (-1.7d-231)) then
        tmp = t_2
    else if (y <= 1.6d-204) then
        tmp = z + ((x + a) + ((-2.0d0) * b))
    else if (y <= 5.9d+28) 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 = y * (b - z);
	double t_2 = x + (z + (a * (1.0 - t)));
	double tmp;
	if (y <= -1.6e+183) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (y <= -8.8e+43) {
		tmp = t_1;
	} else if (y <= -1.7e-231) {
		tmp = t_2;
	} else if (y <= 1.6e-204) {
		tmp = z + ((x + a) + (-2.0 * b));
	} else if (y <= 5.9e+28) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x + (z + (a * (1.0 - t)))
	tmp = 0
	if y <= -1.6e+183:
		tmp = (x + a) - (z * (y + -1.0))
	elif y <= -8.8e+43:
		tmp = t_1
	elif y <= -1.7e-231:
		tmp = t_2
	elif y <= 1.6e-204:
		tmp = z + ((x + a) + (-2.0 * b))
	elif y <= 5.9e+28:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	tmp = 0.0
	if (y <= -1.6e+183)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif (y <= -8.8e+43)
		tmp = t_1;
	elseif (y <= -1.7e-231)
		tmp = t_2;
	elseif (y <= 1.6e-204)
		tmp = Float64(z + Float64(Float64(x + a) + Float64(-2.0 * b)));
	elseif (y <= 5.9e+28)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = x + (z + (a * (1.0 - t)));
	tmp = 0.0;
	if (y <= -1.6e+183)
		tmp = (x + a) - (z * (y + -1.0));
	elseif (y <= -8.8e+43)
		tmp = t_1;
	elseif (y <= -1.7e-231)
		tmp = t_2;
	elseif (y <= 1.6e-204)
		tmp = z + ((x + a) + (-2.0 * b));
	elseif (y <= 5.9e+28)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+183], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e+43], t$95$1, If[LessEqual[y, -1.7e-231], t$95$2, If[LessEqual[y, 1.6e-204], N[(z + N[(N[(x + a), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e+28], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e183

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 92.6%

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

   4. Taylor expanded in t around 0 85.7%

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

      1. sub-neg 85.7%

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

      2. metadata-eval 85.7%

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

      3. +-commutative 85.7%

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

      4. sub-neg 85.7%

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

      5. metadata-eval 85.7%

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

      6. mul-1-neg 85.7%

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

      7. sub-neg 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in b around 0 75.6%

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

   if -1.6000000000000001e183 < y < -8.80000000000000002e43 or 5.9000000000000002e28 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 75.2%

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

   if -8.80000000000000002e43 < y < -1.7e-231 or 1.6e-204 < y < 5.9000000000000002e28

   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 80.2%

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

   4. Taylor expanded in y around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. sub-neg 78.0%

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

      3. metadata-eval 78.0%

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

      4. neg-mul-1 78.0%

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

      5. unsub-neg 78.0%

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

   6. Simplified 78.0%

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

   if -1.7e-231 < y < 1.6e-204

   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 0 100.0%

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

   4. Taylor expanded in t around 0 75.3%

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

      1. sub-neg 75.3%

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

      2. metadata-eval 75.3%

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

      3. +-commutative 75.3%

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

      4. sub-neg 75.3%

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

      5. metadata-eval 75.3%

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

      6. mul-1-neg 75.3%

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

      7. sub-neg 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. associate-+r+ 75.3%

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

      2. neg-mul-1 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-204}:\\ \;\;\;\;z + \left(\left(x + a\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+28}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(t\_1 + a \cdot \left(1 - t\right)\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+203}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+97}:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + \left(a + t\_1\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+168}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (+ t_1 (* a (- 1.0 t)))))
        (t_3 (* t (- b a))))
   (if (<= t -9e+203)
     t_3
     (if (<= t -3.4e+40)
       t_2
       (if (<= t 9.2e+97)
         (+ (+ x (* b (+ y -2.0))) (+ a t_1))
         (if (<= t 4.2e+168) t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (t_1 + (a * (1.0 - t)));
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -9e+203) {
		tmp = t_3;
	} else if (t <= -3.4e+40) {
		tmp = t_2;
	} else if (t <= 9.2e+97) {
		tmp = (x + (b * (y + -2.0))) + (a + t_1);
	} else if (t <= 4.2e+168) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (t_1 + (a * (1.0d0 - t)))
    t_3 = t * (b - a)
    if (t <= (-9d+203)) then
        tmp = t_3
    else if (t <= (-3.4d+40)) then
        tmp = t_2
    else if (t <= 9.2d+97) then
        tmp = (x + (b * (y + (-2.0d0)))) + (a + t_1)
    else if (t <= 4.2d+168) then
        tmp = t_3
    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 = z * (1.0 - y);
	double t_2 = x + (t_1 + (a * (1.0 - t)));
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -9e+203) {
		tmp = t_3;
	} else if (t <= -3.4e+40) {
		tmp = t_2;
	} else if (t <= 9.2e+97) {
		tmp = (x + (b * (y + -2.0))) + (a + t_1);
	} else if (t <= 4.2e+168) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (t_1 + (a * (1.0 - t)))
	t_3 = t * (b - a)
	tmp = 0
	if t <= -9e+203:
		tmp = t_3
	elif t <= -3.4e+40:
		tmp = t_2
	elif t <= 9.2e+97:
		tmp = (x + (b * (y + -2.0))) + (a + t_1)
	elif t <= 4.2e+168:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(t_1 + Float64(a * Float64(1.0 - t))))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9e+203)
		tmp = t_3;
	elseif (t <= -3.4e+40)
		tmp = t_2;
	elseif (t <= 9.2e+97)
		tmp = Float64(Float64(x + Float64(b * Float64(y + -2.0))) + Float64(a + t_1));
	elseif (t <= 4.2e+168)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (t_1 + (a * (1.0 - t)));
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -9e+203)
		tmp = t_3;
	elseif (t <= -3.4e+40)
		tmp = t_2;
	elseif (t <= 9.2e+97)
		tmp = (x + (b * (y + -2.0))) + (a + t_1);
	elseif (t <= 4.2e+168)
		tmp = t_3;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+203], t$95$3, If[LessEqual[t, -3.4e+40], t$95$2, If[LessEqual[t, 9.2e+97], N[(N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+168], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.0000000000000006e203 or 9.20000000000000022e97 < t < 4.20000000000000006e168

   1. Initial program 91.4%

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

   3. Taylor expanded in t around inf 83.7%

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

   if -9.0000000000000006e203 < t < -3.39999999999999989e40 or 4.20000000000000006e168 < 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 b around 0 83.7%

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

   if -3.39999999999999989e40 < t < 9.20000000000000022e97

   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 96.9%

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

   4. Taylor expanded in t around 0 95.0%

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

      1. sub-neg 95.0%

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

      2. metadata-eval 95.0%

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

      3. +-commutative 95.0%

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

      4. sub-neg 95.0%

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

      5. metadata-eval 95.0%

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

      6. mul-1-neg 95.0%

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

      7. sub-neg 95.0%

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

   6. Simplified 95.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+97}:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -2.25e+165)
     t_2
     (if (<= b 3e-134)
       t_1
       (if (<= b 4.3e+18)
         (* a (- 1.0 t))
         (if (<= b 5e+36) t_1 (if (<= b 2.05e+68) (* t (- b a)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.25e+165) {
		tmp = t_2;
	} else if (b <= 3e-134) {
		tmp = t_1;
	} else if (b <= 4.3e+18) {
		tmp = a * (1.0 - t);
	} else if (b <= 5e+36) {
		tmp = t_1;
	} else if (b <= 2.05e+68) {
		tmp = t * (b - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.25d+165)) then
        tmp = t_2
    else if (b <= 3d-134) then
        tmp = t_1
    else if (b <= 4.3d+18) then
        tmp = a * (1.0d0 - t)
    else if (b <= 5d+36) then
        tmp = t_1
    else if (b <= 2.05d+68) then
        tmp = t * (b - a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.25e+165) {
		tmp = t_2;
	} else if (b <= 3e-134) {
		tmp = t_1;
	} else if (b <= 4.3e+18) {
		tmp = a * (1.0 - t);
	} else if (b <= 5e+36) {
		tmp = t_1;
	} else if (b <= 2.05e+68) {
		tmp = t * (b - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.25e+165:
		tmp = t_2
	elif b <= 3e-134:
		tmp = t_1
	elif b <= 4.3e+18:
		tmp = a * (1.0 - t)
	elif b <= 5e+36:
		tmp = t_1
	elif b <= 2.05e+68:
		tmp = t * (b - a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.25e+165)
		tmp = t_2;
	elseif (b <= 3e-134)
		tmp = t_1;
	elseif (b <= 4.3e+18)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 5e+36)
		tmp = t_1;
	elseif (b <= 2.05e+68)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.25e+165)
		tmp = t_2;
	elseif (b <= 3e-134)
		tmp = t_1;
	elseif (b <= 4.3e+18)
		tmp = a * (1.0 - t);
	elseif (b <= 5e+36)
		tmp = t_1;
	elseif (b <= 2.05e+68)
		tmp = t * (b - a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.25e+165], t$95$2, If[LessEqual[b, 3e-134], t$95$1, If[LessEqual[b, 4.3e+18], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+36], t$95$1, If[LessEqual[b, 2.05e+68], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.2499999999999998e165 or 2.05e68 < b

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf 76.9%

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

   if -2.2499999999999998e165 < b < 3e-134 or 4.3e18 < b < 4.99999999999999977e36

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 89.5%

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

   4. Taylor expanded in y around inf 80.7%

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

   5. Taylor expanded in a around 0 54.1%

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

   if 3e-134 < b < 4.3e18

   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 a around inf 49.3%

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

   if 4.99999999999999977e36 < b < 2.05e68

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 85.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-134}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-130}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;x - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.55e+165)
     t_1
     (if (<= b 4.5e-130)
       (- x (* y z))
       (if (<= b 6.4e+16)
         (* a (- 1.0 t))
         (if (<= b 1.05e+23)
           (- x (* b (- 2.0 y)))
           (if (<= b 2.05e+68) (* t (- b 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 tmp;
	if (b <= -1.55e+165) {
		tmp = t_1;
	} else if (b <= 4.5e-130) {
		tmp = x - (y * z);
	} else if (b <= 6.4e+16) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.05e+23) {
		tmp = x - (b * (2.0 - y));
	} else if (b <= 2.05e+68) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.55d+165)) then
        tmp = t_1
    else if (b <= 4.5d-130) then
        tmp = x - (y * z)
    else if (b <= 6.4d+16) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.05d+23) then
        tmp = x - (b * (2.0d0 - y))
    else if (b <= 2.05d+68) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.55e+165) {
		tmp = t_1;
	} else if (b <= 4.5e-130) {
		tmp = x - (y * z);
	} else if (b <= 6.4e+16) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.05e+23) {
		tmp = x - (b * (2.0 - y));
	} else if (b <= 2.05e+68) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.55e+165:
		tmp = t_1
	elif b <= 4.5e-130:
		tmp = x - (y * z)
	elif b <= 6.4e+16:
		tmp = a * (1.0 - t)
	elif b <= 1.05e+23:
		tmp = x - (b * (2.0 - y))
	elif b <= 2.05e+68:
		tmp = t * (b - 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))
	tmp = 0.0
	if (b <= -1.55e+165)
		tmp = t_1;
	elseif (b <= 4.5e-130)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 6.4e+16)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.05e+23)
		tmp = Float64(x - Float64(b * Float64(2.0 - y)));
	elseif (b <= 2.05e+68)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.55e+165)
		tmp = t_1;
	elseif (b <= 4.5e-130)
		tmp = x - (y * z);
	elseif (b <= 6.4e+16)
		tmp = a * (1.0 - t);
	elseif (b <= 1.05e+23)
		tmp = x - (b * (2.0 - y));
	elseif (b <= 2.05e+68)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+165], t$95$1, If[LessEqual[b, 4.5e-130], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+16], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+23], N[(x - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+68], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.5500000000000001e165 or 2.05e68 < b

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf 76.9%

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

   if -1.5500000000000001e165 < b < 4.5e-130

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 89.3%

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

   4. Taylor expanded in y around inf 80.4%

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

   5. Taylor expanded in a around 0 53.5%

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

   if 4.5e-130 < b < 6.4e16

   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 a around inf 51.2%

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

   if 6.4e16 < b < 1.0500000000000001e23

   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 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. mul-1-neg 100.0%

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

      7. sub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 68.4%

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

   8. Taylor expanded in a around 0 68.4%

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

   if 1.0500000000000001e23 < b < 2.05e68

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 85.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-130}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;x - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;\left(x + a\right) + -2 \cdot b\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ x (* a (- 1.0 t)))))
   (if (<= y -1.6e+183)
     (- x (* y z))
     (if (<= y -2e+42)
       t_1
       (if (<= y -1.7e-231)
         t_2
         (if (<= y 4.5e-204)
           (+ (+ x a) (* -2.0 b))
           (if (<= y 1.65e+34) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if (y <= -2e+42) {
		tmp = t_1;
	} else if (y <= -1.7e-231) {
		tmp = t_2;
	} else if (y <= 4.5e-204) {
		tmp = (x + a) + (-2.0 * b);
	} else if (y <= 1.65e+34) {
		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 = y * (b - z)
    t_2 = x + (a * (1.0d0 - t))
    if (y <= (-1.6d+183)) then
        tmp = x - (y * z)
    else if (y <= (-2d+42)) then
        tmp = t_1
    else if (y <= (-1.7d-231)) then
        tmp = t_2
    else if (y <= 4.5d-204) then
        tmp = (x + a) + ((-2.0d0) * b)
    else if (y <= 1.65d+34) 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 = y * (b - z);
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if (y <= -2e+42) {
		tmp = t_1;
	} else if (y <= -1.7e-231) {
		tmp = t_2;
	} else if (y <= 4.5e-204) {
		tmp = (x + a) + (-2.0 * b);
	} else if (y <= 1.65e+34) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x + (a * (1.0 - t))
	tmp = 0
	if y <= -1.6e+183:
		tmp = x - (y * z)
	elif y <= -2e+42:
		tmp = t_1
	elif y <= -1.7e-231:
		tmp = t_2
	elif y <= 4.5e-204:
		tmp = (x + a) + (-2.0 * b)
	elif y <= 1.65e+34:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (y <= -1.6e+183)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= -2e+42)
		tmp = t_1;
	elseif (y <= -1.7e-231)
		tmp = t_2;
	elseif (y <= 4.5e-204)
		tmp = Float64(Float64(x + a) + Float64(-2.0 * b));
	elseif (y <= 1.65e+34)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (y <= -1.6e+183)
		tmp = x - (y * z);
	elseif (y <= -2e+42)
		tmp = t_1;
	elseif (y <= -1.7e-231)
		tmp = t_2;
	elseif (y <= 4.5e-204)
		tmp = (x + a) + (-2.0 * b);
	elseif (y <= 1.65e+34)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+183], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e+42], t$95$1, If[LessEqual[y, -1.7e-231], t$95$2, If[LessEqual[y, 4.5e-204], N[(N[(x + a), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+34], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e183

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 82.5%

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

   4. Taylor expanded in y around inf 82.5%

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

   5. Taylor expanded in a around 0 75.3%

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

   if -1.6000000000000001e183 < y < -2.00000000000000009e42 or 1.64999999999999994e34 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 75.2%

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

   if -2.00000000000000009e42 < y < -1.7e-231 or 4.49999999999999974e-204 < y < 1.64999999999999994e34

   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 80.2%

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

   4. Taylor expanded in a around inf 65.3%

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

   if -1.7e-231 < y < 4.49999999999999974e-204

   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 0 100.0%

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

   4. Taylor expanded in t around 0 75.3%

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

      1. sub-neg 75.3%

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

      2. metadata-eval 75.3%

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

      3. +-commutative 75.3%

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

      4. sub-neg 75.3%

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

      5. metadata-eval 75.3%

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

      6. mul-1-neg 75.3%

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

      7. sub-neg 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in z around 0 59.6%

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

   8. Taylor expanded in y around 0 59.6%

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

      1. associate-+r+ 59.6%

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

      2. *-commutative 59.6%

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

   10. Simplified 59.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-231}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-204}:\\ \;\;\;\;\left(x + a\right) + -2 \cdot b\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+85}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+79}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -2.5e+216)
     t_1
     (if (<= y -2.15e+85)
       (* y b)
       (if (<= y -4.2e+43)
         t_1
         (if (<= y -9e-278)
           (* a (- 1.0 t))
           (if (<= y 8.2e+79) (+ x a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.5e+216) {
		tmp = t_1;
	} else if (y <= -2.15e+85) {
		tmp = y * b;
	} else if (y <= -4.2e+43) {
		tmp = t_1;
	} else if (y <= -9e-278) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.2e+79) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-2.5d+216)) then
        tmp = t_1
    else if (y <= (-2.15d+85)) then
        tmp = y * b
    else if (y <= (-4.2d+43)) then
        tmp = t_1
    else if (y <= (-9d-278)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 8.2d+79) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.5e+216) {
		tmp = t_1;
	} else if (y <= -2.15e+85) {
		tmp = y * b;
	} else if (y <= -4.2e+43) {
		tmp = t_1;
	} else if (y <= -9e-278) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.2e+79) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -2.5e+216:
		tmp = t_1
	elif y <= -2.15e+85:
		tmp = y * b
	elif y <= -4.2e+43:
		tmp = t_1
	elif y <= -9e-278:
		tmp = a * (1.0 - t)
	elif y <= 8.2e+79:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -2.5e+216)
		tmp = t_1;
	elseif (y <= -2.15e+85)
		tmp = Float64(y * b);
	elseif (y <= -4.2e+43)
		tmp = t_1;
	elseif (y <= -9e-278)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 8.2e+79)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -2.5e+216)
		tmp = t_1;
	elseif (y <= -2.15e+85)
		tmp = y * b;
	elseif (y <= -4.2e+43)
		tmp = t_1;
	elseif (y <= -9e-278)
		tmp = a * (1.0 - t);
	elseif (y <= 8.2e+79)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -2.5e+216], t$95$1, If[LessEqual[y, -2.15e+85], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.2e+43], t$95$1, If[LessEqual[y, -9e-278], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+79], N[(x + a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999999e216 or -2.15e85 < y < -4.20000000000000003e43 or 8.2e79 < y

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 53.5%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-lft-neg-out 53.5%

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

      3. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   if -2.4999999999999999e216 < y < -2.15e85

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 65.0%

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

   4. Taylor expanded in b around inf 47.8%

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

   if -4.20000000000000003e43 < y < -8.9999999999999996e-278

   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 46.1%

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

   if -8.9999999999999996e-278 < y < 8.2e79

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 97.4%

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

   4. Taylor expanded in t around 0 72.7%

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

      1. sub-neg 72.7%

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

      2. metadata-eval 72.7%

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

      3. +-commutative 72.7%

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

      4. sub-neg 72.7%

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

      5. metadata-eval 72.7%

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

      6. mul-1-neg 72.7%

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

      7. sub-neg 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in z around 0 53.6%

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

   8. Taylor expanded in b around 0 42.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+85}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+79}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;x + \left(t\_2 + t\_1\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + \left(a + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- 1.0 y))))
   (if (<= z -1.9e+72)
     (+ x (+ t_2 t_1))
     (if (<= z 3.9e+48)
       (+ (- x (* b (- 2.0 (+ y t)))) t_1)
       (+ (+ x (* b (+ y -2.0))) (+ a t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -1.9e+72) {
		tmp = x + (t_2 + t_1);
	} else if (z <= 3.9e+48) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else {
		tmp = (x + (b * (y + -2.0))) + (a + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    if (z <= (-1.9d+72)) then
        tmp = x + (t_2 + t_1)
    else if (z <= 3.9d+48) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + t_1
    else
        tmp = (x + (b * (y + (-2.0d0)))) + (a + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -1.9e+72) {
		tmp = x + (t_2 + t_1);
	} else if (z <= 3.9e+48) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else {
		tmp = (x + (b * (y + -2.0))) + (a + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	tmp = 0
	if z <= -1.9e+72:
		tmp = x + (t_2 + t_1)
	elif z <= 3.9e+48:
		tmp = (x - (b * (2.0 - (y + t)))) + t_1
	else:
		tmp = (x + (b * (y + -2.0))) + (a + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.9e+72)
		tmp = Float64(x + Float64(t_2 + t_1));
	elseif (z <= 3.9e+48)
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + t_1);
	else
		tmp = Float64(Float64(x + Float64(b * Float64(y + -2.0))) + Float64(a + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.9e+72)
		tmp = x + (t_2 + t_1);
	elseif (z <= 3.9e+48)
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	else
		tmp = (x + (b * (y + -2.0))) + (a + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+72], N[(x + N[(t$95$2 + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+48], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000003e72

   1. Initial program 91.9%

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

   3. Taylor expanded in b around 0 89.3%

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

   if -1.90000000000000003e72 < z < 3.9000000000000001e48

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 94.9%

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

   if 3.9000000000000001e48 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 95.6%

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

   4. Taylor expanded in t around 0 86.0%

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

      1. sub-neg 86.0%

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

      2. metadata-eval 86.0%

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

      3. +-commutative 86.0%

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

      4. sub-neg 86.0%

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

      5. metadata-eval 86.0%

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

      6. mul-1-neg 86.0%

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

      7. sub-neg 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+43} \lor \neg \left(y \leq 1.65 \cdot 10^{+74}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -4e+216)
     t_1
     (if (<= y -2.4e+85)
       (* y b)
       (if (or (<= y -3.05e+43) (not (<= y 1.65e+74))) t_1 (+ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -4e+216) {
		tmp = t_1;
	} else if (y <= -2.4e+85) {
		tmp = y * b;
	} else if ((y <= -3.05e+43) || !(y <= 1.65e+74)) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-4d+216)) then
        tmp = t_1
    else if (y <= (-2.4d+85)) then
        tmp = y * b
    else if ((y <= (-3.05d+43)) .or. (.not. (y <= 1.65d+74))) then
        tmp = t_1
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -4e+216) {
		tmp = t_1;
	} else if (y <= -2.4e+85) {
		tmp = y * b;
	} else if ((y <= -3.05e+43) || !(y <= 1.65e+74)) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -4e+216:
		tmp = t_1
	elif y <= -2.4e+85:
		tmp = y * b
	elif (y <= -3.05e+43) or not (y <= 1.65e+74):
		tmp = t_1
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -4e+216)
		tmp = t_1;
	elseif (y <= -2.4e+85)
		tmp = Float64(y * b);
	elseif ((y <= -3.05e+43) || !(y <= 1.65e+74))
		tmp = t_1;
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -4e+216)
		tmp = t_1;
	elseif (y <= -2.4e+85)
		tmp = y * b;
	elseif ((y <= -3.05e+43) || ~((y <= 1.65e+74)))
		tmp = t_1;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -4e+216], t$95$1, If[LessEqual[y, -2.4e+85], N[(y * b), $MachinePrecision], If[Or[LessEqual[y, -3.05e+43], N[Not[LessEqual[y, 1.65e+74]], $MachinePrecision]], t$95$1, N[(x + a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0000000000000001e216 or -2.39999999999999997e85 < y < -3.0499999999999999e43 or 1.6500000000000001e74 < y

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 53.5%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-lft-neg-out 53.5%

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

      3. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   if -4.0000000000000001e216 < y < -2.39999999999999997e85

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 65.0%

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

   4. Taylor expanded in b around inf 47.8%

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

   if -3.0499999999999999e43 < y < 1.6500000000000001e74

   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 t around 0 98.5%

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

   4. Taylor expanded in t around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. metadata-eval 66.3%

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

      3. +-commutative 66.3%

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

      4. sub-neg 66.3%

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

      5. metadata-eval 66.3%

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

      6. mul-1-neg 66.3%

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

      7. sub-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in z around 0 50.4%

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

   8. Taylor expanded in b around 0 37.6%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+43} \lor \neg \left(y \leq 1.65 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{+40} \lor \neg \left(y \leq 2.35 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+183)
   (- x (* y z))
   (if (or (<= y -8.1e+40) (not (<= y 2.35e+31)))
     (* y (- b z))
     (+ x (+ z (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if ((y <= -8.1e+40) || !(y <= 2.35e+31)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.6d+183)) then
        tmp = x - (y * z)
    else if ((y <= (-8.1d+40)) .or. (.not. (y <= 2.35d+31))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+183) {
		tmp = x - (y * z);
	} else if ((y <= -8.1e+40) || !(y <= 2.35e+31)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+183:
		tmp = x - (y * z)
	elif (y <= -8.1e+40) or not (y <= 2.35e+31):
		tmp = y * (b - z)
	else:
		tmp = x + (z + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+183)
		tmp = Float64(x - Float64(y * z));
	elseif ((y <= -8.1e+40) || !(y <= 2.35e+31))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e+183)
		tmp = x - (y * z);
	elseif ((y <= -8.1e+40) || ~((y <= 2.35e+31)))
		tmp = y * (b - z);
	else
		tmp = x + (z + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+183], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.1e+40], N[Not[LessEqual[y, 2.35e+31]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e183

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 82.5%

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

   4. Taylor expanded in y around inf 82.5%

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

   5. Taylor expanded in a around 0 75.3%

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

   if -1.6000000000000001e183 < y < -8.0999999999999998e40 or 2.3500000000000001e31 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 75.2%

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

   if -8.0999999999999998e40 < y < 2.3500000000000001e31

   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 74.8%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. neg-mul-1 73.2%

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

      5. unsub-neg 73.2%

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

   6. Simplified 73.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{+40} \lor \neg \left(y \leq 2.35 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+42} \lor \neg \left(y \leq 2.85 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+183)
   (- (+ x a) (* z (+ y -1.0)))
   (if (or (<= y -9.4e+42) (not (<= y 2.85e+29)))
     (* y (- b z))
     (+ x (+ z (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+183) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if ((y <= -9.4e+42) || !(y <= 2.85e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.6d+183)) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if ((y <= (-9.4d+42)) .or. (.not. (y <= 2.85d+29))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.6e+183) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if ((y <= -9.4e+42) || !(y <= 2.85e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.6e+183:
		tmp = (x + a) - (z * (y + -1.0))
	elif (y <= -9.4e+42) or not (y <= 2.85e+29):
		tmp = y * (b - z)
	else:
		tmp = x + (z + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.6e+183)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif ((y <= -9.4e+42) || !(y <= 2.85e+29))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.6e+183)
		tmp = (x + a) - (z * (y + -1.0));
	elseif ((y <= -9.4e+42) || ~((y <= 2.85e+29)))
		tmp = y * (b - z);
	else
		tmp = x + (z + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+183], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -9.4e+42], N[Not[LessEqual[y, 2.85e+29]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6000000000000001e183

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 92.6%

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

   4. Taylor expanded in t around 0 85.7%

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

      1. sub-neg 85.7%

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

      2. metadata-eval 85.7%

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

      3. +-commutative 85.7%

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

      4. sub-neg 85.7%

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

      5. metadata-eval 85.7%

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

      6. mul-1-neg 85.7%

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

      7. sub-neg 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in b around 0 75.6%

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

   if -1.6000000000000001e183 < y < -9.39999999999999971e42 or 2.85e29 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 75.2%

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

   if -9.39999999999999971e42 < y < 2.85e29

   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 74.8%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. neg-mul-1 73.2%

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

      5. unsub-neg 73.2%

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

   6. Simplified 73.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+183}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+42} \lor \neg \left(y \leq 2.85 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+107}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.55e+165)
   (+ a (- x (* b (- 2.0 y))))
   (if (<= b 1.12e+107)
     (+ 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) {
	double tmp;
	if (b <= -1.55e+165) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 1.12e+107) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.55d+165)) then
        tmp = a + (x - (b * (2.0d0 - y)))
    else if (b <= 1.12d+107) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = b * ((y + t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.55e+165) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 1.12e+107) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.55e+165:
		tmp = a + (x - (b * (2.0 - y)))
	elif b <= 1.12e+107:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = b * ((y + t) - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.55e+165)
		tmp = Float64(a + Float64(x - Float64(b * Float64(2.0 - y))));
	elseif (b <= 1.12e+107)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.55e+165)
		tmp = a + (x - (b * (2.0 - y)));
	elseif (b <= 1.12e+107)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = b * ((y + t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.55e+165], N[(a + N[(x - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+107], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.5500000000000001e165

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 93.7%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. sub-neg 84.8%

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

      2. metadata-eval 84.8%

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

      3. +-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. metadata-eval 84.8%

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

      6. mul-1-neg 84.8%

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

      7. sub-neg 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around 0 83.7%

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

   if -1.5500000000000001e165 < b < 1.11999999999999997e107

   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 b around 0 85.5%

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

   if 1.11999999999999997e107 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf 81.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+165}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+107}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+166}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+107}:\\ \;\;\;\;x + \left(\left(a + z \cdot \left(1 - y\right)\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+166)
   (+ a (- x (* b (- 2.0 y))))
   (if (<= b 2.15e+107)
     (+ x (- (+ a (* z (- 1.0 y))) (* t a)))
     (* b (- (+ y t) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+166) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 2.15e+107) {
		tmp = x + ((a + (z * (1.0 - y))) - (t * a));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d+166)) then
        tmp = a + (x - (b * (2.0d0 - y)))
    else if (b <= 2.15d+107) then
        tmp = x + ((a + (z * (1.0d0 - y))) - (t * a))
    else
        tmp = b * ((y + t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+166) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 2.15e+107) {
		tmp = x + ((a + (z * (1.0 - y))) - (t * a));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+166:
		tmp = a + (x - (b * (2.0 - y)))
	elif b <= 2.15e+107:
		tmp = x + ((a + (z * (1.0 - y))) - (t * a))
	else:
		tmp = b * ((y + t) - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+166)
		tmp = Float64(a + Float64(x - Float64(b * Float64(2.0 - y))));
	elseif (b <= 2.15e+107)
		tmp = Float64(x + Float64(Float64(a + Float64(z * Float64(1.0 - y))) - Float64(t * a)));
	else
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+166)
		tmp = a + (x - (b * (2.0 - y)));
	elseif (b <= 2.15e+107)
		tmp = x + ((a + (z * (1.0 - y))) - (t * a));
	else
		tmp = b * ((y + t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+166], N[(a + N[(x - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+107], N[(x + N[(N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9000000000000001e166

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 93.7%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. sub-neg 84.8%

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

      2. metadata-eval 84.8%

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

      3. +-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. metadata-eval 84.8%

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

      6. mul-1-neg 84.8%

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

      7. sub-neg 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around 0 83.7%

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

   if -2.9000000000000001e166 < b < 2.15e107

   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 97.3%

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

   4. Taylor expanded in b around 0 85.5%

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

      1. associate--l+ 85.5%

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

      2. associate-*r* 85.5%

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

      3. mul-1-neg 85.5%

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

      4. +-commutative 85.5%

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

      5. sub-neg 85.5%

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

      6. metadata-eval 85.5%

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

      7. mul-1-neg 85.5%

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

      8. sub-neg 85.5%

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

   6. Simplified 85.5%

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

   if 2.15e107 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf 81.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+166}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+107}:\\ \;\;\;\;x + \left(\left(a + z \cdot \left(1 - y\right)\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{+40}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.25e+165)
   (+ a (- x (* b (- 2.0 y))))
   (if (<= b 7.1e+40)
     (+ x (- (* a (- 1.0 t)) (* y z)))
     (* b (- (+ y t) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.25e+165) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 7.1e+40) {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.25d+165)) then
        tmp = a + (x - (b * (2.0d0 - y)))
    else if (b <= 7.1d+40) then
        tmp = x + ((a * (1.0d0 - t)) - (y * z))
    else
        tmp = b * ((y + t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.25e+165) {
		tmp = a + (x - (b * (2.0 - y)));
	} else if (b <= 7.1e+40) {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.25e+165:
		tmp = a + (x - (b * (2.0 - y)))
	elif b <= 7.1e+40:
		tmp = x + ((a * (1.0 - t)) - (y * z))
	else:
		tmp = b * ((y + t) - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.25e+165)
		tmp = Float64(a + Float64(x - Float64(b * Float64(2.0 - y))));
	elseif (b <= 7.1e+40)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(y * z)));
	else
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.25e+165)
		tmp = a + (x - (b * (2.0 - y)));
	elseif (b <= 7.1e+40)
		tmp = x + ((a * (1.0 - t)) - (y * z));
	else
		tmp = b * ((y + t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.25e+165], N[(a + N[(x - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.1e+40], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2499999999999998e165

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 93.7%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. sub-neg 84.8%

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

      2. metadata-eval 84.8%

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

      3. +-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. metadata-eval 84.8%

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

      6. mul-1-neg 84.8%

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

      7. sub-neg 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around 0 83.7%

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

   if -2.2499999999999998e165 < b < 7.10000000000000037e40

   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 87.7%

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

   4. Taylor expanded in y around inf 80.3%

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

   if 7.10000000000000037e40 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in b around inf 74.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{+40}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-246}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+79}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.2e+76) x (if (<= x 3.5e-246) (* t b) (if (<= x 8.2e+79) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+76) {
		tmp = x;
	} else if (x <= 3.5e-246) {
		tmp = t * b;
	} else if (x <= 8.2e+79) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.2d+76)) then
        tmp = x
    else if (x <= 3.5d-246) then
        tmp = t * b
    else if (x <= 8.2d+79) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+76) {
		tmp = x;
	} else if (x <= 3.5e-246) {
		tmp = t * b;
	} else if (x <= 8.2e+79) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.2e+76:
		tmp = x
	elif x <= 3.5e-246:
		tmp = t * b
	elif x <= 8.2e+79:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.2e+76)
		tmp = x;
	elseif (x <= 3.5e-246)
		tmp = Float64(t * b);
	elseif (x <= 8.2e+79)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.2e+76)
		tmp = x;
	elseif (x <= 3.5e-246)
		tmp = t * b;
	elseif (x <= 8.2e+79)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.2e+76], x, If[LessEqual[x, 3.5e-246], N[(t * b), $MachinePrecision], If[LessEqual[x, 8.2e+79], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.20000000000000005e76 or 8.2e79 < x

   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 x around inf 42.8%

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

   if -9.20000000000000005e76 < x < 3.5000000000000002e-246

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 34.3%

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

   4. Taylor expanded in b around inf 21.5%

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

   if 3.5000000000000002e-246 < x < 8.2e79

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 97.1%

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

   4. Taylor expanded in t around 0 68.9%

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

      1. sub-neg 68.9%

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

      2. metadata-eval 68.9%

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

      3. +-commutative 68.9%

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

      4. sub-neg 68.9%

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

      5. metadata-eval 68.9%

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

      6. mul-1-neg 68.9%

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

      7. sub-neg 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in a around inf 18.4%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-246}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+79}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 24.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+68} \lor \neg \left(b \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.2e+68) (not (<= b 1.8e-43))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+68) || !(b <= 1.8e-43)) {
		tmp = y * 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 ((b <= (-8.2d+68)) .or. (.not. (b <= 1.8d-43))) then
        tmp = y * 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 ((b <= -8.2e+68) || !(b <= 1.8e-43)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.2e+68) or not (b <= 1.8e-43):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.2e+68) || !(b <= 1.8e-43))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.2e+68) || ~((b <= 1.8e-43)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.2e+68], N[Not[LessEqual[b, 1.8e-43]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -8.1999999999999998e68 or 1.7999999999999999e-43 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 51.1%

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

   4. Taylor expanded in b around inf 41.7%

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

   if -8.1999999999999998e68 < b < 1.7999999999999999e-43

   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 25.5%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+68} \lor \neg \left(b \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 32.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e-14) (not (<= y 5e+36))) (* y b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 5e+36)) {
		tmp = y * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.4d-14)) .or. (.not. (y <= 5d+36))) then
        tmp = y * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 5e+36)) {
		tmp = y * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e-14) or not (y <= 5e+36):
		tmp = y * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e-14) || !(y <= 5e+36))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e-14) || ~((y <= 5e+36)))
		tmp = y * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e-14], N[Not[LessEqual[y, 5e+36]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-14 or 4.99999999999999977e36 < y

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 67.4%

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

   4. Taylor expanded in b around inf 35.5%

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

   if -1.4e-14 < y < 4.99999999999999977e36

   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 0 100.0%

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

   4. Taylor expanded in t around 0 67.7%

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

      1. sub-neg 67.7%

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

      2. metadata-eval 67.7%

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

      3. +-commutative 67.7%

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

      4. sub-neg 67.7%

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

      5. metadata-eval 67.7%

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

      6. mul-1-neg 67.7%

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

      7. sub-neg 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in z around 0 51.0%

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

   8. Taylor expanded in b around 0 41.3%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 5 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+19) x (if (<= x 2.45e+76) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+19) {
		tmp = x;
	} else if (x <= 2.45e+76) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6d+19)) then
        tmp = x
    else if (x <= 2.45d+76) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+19) {
		tmp = x;
	} else if (x <= 2.45e+76) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+19:
		tmp = x
	elif x <= 2.45e+76:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+19)
		tmp = x;
	elseif (x <= 2.45e+76)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6e+19)
		tmp = x;
	elseif (x <= 2.45e+76)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+19], x, If[LessEqual[x, 2.45e+76], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6e19 or 2.45000000000000013e76 < x

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 39.9%

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

   if -6e19 < x < 2.45000000000000013e76

   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 t around 0 95.3%

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

   4. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. metadata-eval 68.3%

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

      3. +-commutative 68.3%

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

      4. sub-neg 68.3%

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

      5. metadata-eval 68.3%

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

      6. mul-1-neg 68.3%

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

      7. sub-neg 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in a around inf 18.3%

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

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 11.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in t around 0 95.7%

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

4. Taylor expanded in t around 0 74.5%

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

   1. sub-neg 74.5%

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

   2. metadata-eval 74.5%

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

   3. +-commutative 74.5%

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

   4. sub-neg 74.5%

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

   5. metadata-eval 74.5%

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

   6. mul-1-neg 74.5%

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

   7. sub-neg 74.5%

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

6. Simplified 74.5%

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

7. Taylor expanded in a around inf 11.8%

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

8. Final simplification 11.8%

   \[\leadsto a \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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)))