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

Percentage Accurate: 95.2% → 98.4%

Time: 15.1s

Alternatives: 23

Speedup: 0.5×

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-rgt-neg-in 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in t around inf 90.9%

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

      1. associate-+r+ 90.9%

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

      2. mul-1-neg 90.9%

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

      3. sub-neg 90.9%

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

      4. sub-neg 90.9%

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

      5. metadata-eval 90.9%

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

   8. Simplified 90.9%

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

4. Final simplification 99.6%

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

Alternative 2: 37.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- t 2.0))))
   (if (<= b -2.5e+193)
     (* y b)
     (if (<= b -3.9e+39)
       t_2
       (if (<= b 1.35e-260)
         t_1
         (if (<= b 6.5e-210)
           x
           (if (<= b 2.1e-158)
             t_1
             (if (<= b 2.45e-67)
               (* z (- y))
               (if (<= b 6.5e+113) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.5e+193) {
		tmp = y * b;
	} else if (b <= -3.9e+39) {
		tmp = t_2;
	} else if (b <= 1.35e-260) {
		tmp = t_1;
	} else if (b <= 6.5e-210) {
		tmp = x;
	} else if (b <= 2.1e-158) {
		tmp = t_1;
	} else if (b <= 2.45e-67) {
		tmp = z * -y;
	} else if (b <= 6.5e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (t - 2.0d0)
    if (b <= (-2.5d+193)) then
        tmp = y * b
    else if (b <= (-3.9d+39)) then
        tmp = t_2
    else if (b <= 1.35d-260) then
        tmp = t_1
    else if (b <= 6.5d-210) then
        tmp = x
    else if (b <= 2.1d-158) then
        tmp = t_1
    else if (b <= 2.45d-67) then
        tmp = z * -y
    else if (b <= 6.5d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.5e+193) {
		tmp = y * b;
	} else if (b <= -3.9e+39) {
		tmp = t_2;
	} else if (b <= 1.35e-260) {
		tmp = t_1;
	} else if (b <= 6.5e-210) {
		tmp = x;
	} else if (b <= 2.1e-158) {
		tmp = t_1;
	} else if (b <= 2.45e-67) {
		tmp = z * -y;
	} else if (b <= 6.5e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (t - 2.0)
	tmp = 0
	if b <= -2.5e+193:
		tmp = y * b
	elif b <= -3.9e+39:
		tmp = t_2
	elif b <= 1.35e-260:
		tmp = t_1
	elif b <= 6.5e-210:
		tmp = x
	elif b <= 2.1e-158:
		tmp = t_1
	elif b <= 2.45e-67:
		tmp = z * -y
	elif b <= 6.5e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -2.5e+193)
		tmp = Float64(y * b);
	elseif (b <= -3.9e+39)
		tmp = t_2;
	elseif (b <= 1.35e-260)
		tmp = t_1;
	elseif (b <= 6.5e-210)
		tmp = x;
	elseif (b <= 2.1e-158)
		tmp = t_1;
	elseif (b <= 2.45e-67)
		tmp = Float64(z * Float64(-y));
	elseif (b <= 6.5e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -2.5e+193)
		tmp = y * b;
	elseif (b <= -3.9e+39)
		tmp = t_2;
	elseif (b <= 1.35e-260)
		tmp = t_1;
	elseif (b <= 6.5e-210)
		tmp = x;
	elseif (b <= 2.1e-158)
		tmp = t_1;
	elseif (b <= 2.45e-67)
		tmp = z * -y;
	elseif (b <= 6.5e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+193], N[(y * b), $MachinePrecision], If[LessEqual[b, -3.9e+39], t$95$2, If[LessEqual[b, 1.35e-260], t$95$1, If[LessEqual[b, 6.5e-210], x, If[LessEqual[b, 2.1e-158], t$95$1, If[LessEqual[b, 2.45e-67], N[(z * (-y)), $MachinePrecision], If[LessEqual[b, 6.5e+113], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.49999999999999986e193

   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 y around inf 68.3%

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

   4. Taylor expanded in b around inf 74.5%

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

   if -2.49999999999999986e193 < b < -3.9000000000000001e39 or 6.5000000000000001e113 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in b around inf 69.2%

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

   4. Taylor expanded in y around 0 45.9%

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

   if -3.9000000000000001e39 < b < 1.35000000000000003e-260 or 6.49999999999999961e-210 < b < 2.09999999999999991e-158 or 2.44999999999999997e-67 < b < 6.5000000000000001e113

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 42.2%

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

   if 1.35000000000000003e-260 < b < 6.49999999999999961e-210

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 41.0%

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

   if 2.09999999999999991e-158 < b < 2.44999999999999997e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 98.1%

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

   4. Taylor expanded in y around inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. mul-1-neg 51.7%

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

   6. Simplified 51.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+193}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-210}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+64} \lor \neg \left(b \leq 1.85 \cdot 10^{-42} \lor \neg \left(b \leq 2.5 \cdot 10^{-18}\right) \land b \leq 7.8 \cdot 10^{+95}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e+64)
         (not (or (<= b 1.85e-42) (and (not (<= b 2.5e-18)) (<= b 7.8e+95)))))
   (+ (+ x (* (- (+ y t) 2.0) b)) (* a (- 1.0 t)))
   (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+64) || !((b <= 1.85e-42) || (!(b <= 2.5e-18) && (b <= 7.8e+95)))) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * 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 ((b <= (-1d+64)) .or. (.not. (b <= 1.85d-42) .or. (.not. (b <= 2.5d-18)) .and. (b <= 7.8d+95))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + (a * (1.0d0 - t))
    else
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * 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 ((b <= -1e+64) || !((b <= 1.85e-42) || (!(b <= 2.5e-18) && (b <= 7.8e+95)))) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1e+64) or not ((b <= 1.85e-42) or (not (b <= 2.5e-18) and (b <= 7.8e+95))):
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t))
	else:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1e+64) || !((b <= 1.85e-42) || (!(b <= 2.5e-18) && (b <= 7.8e+95))))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1e+64) || ~(((b <= 1.85e-42) || (~((b <= 2.5e-18)) && (b <= 7.8e+95)))))
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	else
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1e+64], N[Not[Or[LessEqual[b, 1.85e-42], And[N[Not[LessEqual[b, 2.5e-18]], $MachinePrecision], LessEqual[b, 7.8e+95]]]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.00000000000000002e64 or 1.8500000000000001e-42 < b < 2.50000000000000018e-18 or 7.7999999999999994e95 < b

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0 93.7%

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

   if -1.00000000000000002e64 < b < 1.8500000000000001e-42 or 2.50000000000000018e-18 < b < 7.7999999999999994e95

   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 b around 0 93.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+64} \lor \neg \left(b \leq 1.85 \cdot 10^{-42} \lor \neg \left(b \leq 2.5 \cdot 10^{-18}\right) \land b \leq 7.8 \cdot 10^{+95}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+37}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 10^{-67}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= b -2.75e+193)
     t_1
     (if (<= b -2.7e+70)
       (* b (- t 2.0))
       (if (<= b -2.1e+37)
         (* y b)
         (if (<= b 1.05e-158)
           t_2
           (if (<= b 1e-67) (* z (- y)) (if (<= b 1.2e+64) t_2 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 t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -2.75e+193) {
		tmp = t_1;
	} else if (b <= -2.7e+70) {
		tmp = b * (t - 2.0);
	} else if (b <= -2.1e+37) {
		tmp = y * b;
	} else if (b <= 1.05e-158) {
		tmp = t_2;
	} else if (b <= 1e-67) {
		tmp = z * -y;
	} else if (b <= 1.2e+64) {
		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 = b * (y - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (b <= (-2.75d+193)) then
        tmp = t_1
    else if (b <= (-2.7d+70)) then
        tmp = b * (t - 2.0d0)
    else if (b <= (-2.1d+37)) then
        tmp = y * b
    else if (b <= 1.05d-158) then
        tmp = t_2
    else if (b <= 1d-67) then
        tmp = z * -y
    else if (b <= 1.2d+64) 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 = b * (y - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -2.75e+193) {
		tmp = t_1;
	} else if (b <= -2.7e+70) {
		tmp = b * (t - 2.0);
	} else if (b <= -2.1e+37) {
		tmp = y * b;
	} else if (b <= 1.05e-158) {
		tmp = t_2;
	} else if (b <= 1e-67) {
		tmp = z * -y;
	} else if (b <= 1.2e+64) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if b <= -2.75e+193:
		tmp = t_1
	elif b <= -2.7e+70:
		tmp = b * (t - 2.0)
	elif b <= -2.1e+37:
		tmp = y * b
	elif b <= 1.05e-158:
		tmp = t_2
	elif b <= 1e-67:
		tmp = z * -y
	elif b <= 1.2e+64:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.75e+193)
		tmp = t_1;
	elseif (b <= -2.7e+70)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (b <= -2.1e+37)
		tmp = Float64(y * b);
	elseif (b <= 1.05e-158)
		tmp = t_2;
	elseif (b <= 1e-67)
		tmp = Float64(z * Float64(-y));
	elseif (b <= 1.2e+64)
		tmp = t_2;
	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);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.75e+193)
		tmp = t_1;
	elseif (b <= -2.7e+70)
		tmp = b * (t - 2.0);
	elseif (b <= -2.1e+37)
		tmp = y * b;
	elseif (b <= 1.05e-158)
		tmp = t_2;
	elseif (b <= 1e-67)
		tmp = z * -y;
	elseif (b <= 1.2e+64)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+193], t$95$1, If[LessEqual[b, -2.7e+70], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e+37], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.05e-158], t$95$2, If[LessEqual[b, 1e-67], N[(z * (-y)), $MachinePrecision], If[LessEqual[b, 1.2e+64], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.7500000000000001e193 or 1.2e64 < 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 inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-rgt-neg-in 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around 0 66.7%

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

   if -2.7500000000000001e193 < b < -2.7e70

   1. Initial program 88.0%

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

   3. Taylor expanded in b around inf 61.1%

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

   4. Taylor expanded in y around 0 53.2%

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

   if -2.7e70 < b < -2.1000000000000001e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in b around inf 44.9%

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

   if -2.1000000000000001e37 < b < 1.04999999999999996e-158 or 9.99999999999999943e-68 < b < 1.2e64

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf 40.8%

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

   if 1.04999999999999996e-158 < b < 9.99999999999999943e-68

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 98.1%

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

   4. Taylor expanded in y around inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. mul-1-neg 51.7%

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

   6. Simplified 51.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+37}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{-67}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 27.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+125} \lor \neg \left(y \leq 2.35 \cdot 10^{+222}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -6.8e+209)
     t_1
     (if (<= y -5.8e+83)
       (* y b)
       (if (<= y 1.8e-117)
         (* t (- a))
         (if (<= y 4.3e+18)
           x
           (if (or (<= y 1.7e+125) (not (<= y 2.35e+222))) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -6.8e+209) {
		tmp = t_1;
	} else if (y <= -5.8e+83) {
		tmp = y * b;
	} else if (y <= 1.8e-117) {
		tmp = t * -a;
	} else if (y <= 4.3e+18) {
		tmp = x;
	} else if ((y <= 1.7e+125) || !(y <= 2.35e+222)) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-6.8d+209)) then
        tmp = t_1
    else if (y <= (-5.8d+83)) then
        tmp = y * b
    else if (y <= 1.8d-117) then
        tmp = t * -a
    else if (y <= 4.3d+18) then
        tmp = x
    else if ((y <= 1.7d+125) .or. (.not. (y <= 2.35d+222))) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -6.8e+209) {
		tmp = t_1;
	} else if (y <= -5.8e+83) {
		tmp = y * b;
	} else if (y <= 1.8e-117) {
		tmp = t * -a;
	} else if (y <= 4.3e+18) {
		tmp = x;
	} else if ((y <= 1.7e+125) || !(y <= 2.35e+222)) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -6.8e+209:
		tmp = t_1
	elif y <= -5.8e+83:
		tmp = y * b
	elif y <= 1.8e-117:
		tmp = t * -a
	elif y <= 4.3e+18:
		tmp = x
	elif (y <= 1.7e+125) or not (y <= 2.35e+222):
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -6.8e+209)
		tmp = t_1;
	elseif (y <= -5.8e+83)
		tmp = Float64(y * b);
	elseif (y <= 1.8e-117)
		tmp = Float64(t * Float64(-a));
	elseif (y <= 4.3e+18)
		tmp = x;
	elseif ((y <= 1.7e+125) || !(y <= 2.35e+222))
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -6.8e+209)
		tmp = t_1;
	elseif (y <= -5.8e+83)
		tmp = y * b;
	elseif (y <= 1.8e-117)
		tmp = t * -a;
	elseif (y <= 4.3e+18)
		tmp = x;
	elseif ((y <= 1.7e+125) || ~((y <= 2.35e+222)))
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -6.8e+209], t$95$1, If[LessEqual[y, -5.8e+83], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.8e-117], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, 4.3e+18], x, If[Or[LessEqual[y, 1.7e+125], N[Not[LessEqual[y, 2.35e+222]], $MachinePrecision]], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.7999999999999993e209 or 4.3e18 < y < 1.6999999999999999e125 or 2.3499999999999999e222 < 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 b around 0 78.0%

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

   4. Taylor expanded in y around inf 51.1%

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

      1. associate-*r* 51.1%

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

      2. mul-1-neg 51.1%

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

   6. Simplified 51.1%

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

   if -6.7999999999999993e209 < y < -5.79999999999999999e83 or 1.6999999999999999e125 < y < 2.3499999999999999e222

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf 89.2%

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

   4. Taylor expanded in b around inf 60.3%

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

   if -5.79999999999999999e83 < y < 1.8e-117

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in t around inf 25.1%

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

      1. associate-*r* 25.1%

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

      2. mul-1-neg 25.1%

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

   6. Simplified 25.1%

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

   if 1.8e-117 < y < 4.3e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 38.5%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+125} \lor \neg \left(y \leq 2.35 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-67}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* a (- 1.0 t))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (+ a (* z (- 1.0 y))))))
   (if (<= b -7.2e+61)
     t_2
     (if (<= b 1.15e-260)
       t_1
       (if (<= b 1.7e-67)
         t_3
         (if (<= b 2e+61) t_1 (if (<= b 1.12e+133) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (b <= -7.2e+61) {
		tmp = t_2;
	} else if (b <= 1.15e-260) {
		tmp = t_1;
	} else if (b <= 1.7e-67) {
		tmp = t_3;
	} else if (b <= 2e+61) {
		tmp = t_1;
	} else if (b <= 1.12e+133) {
		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 = (x + z) + (a * (1.0d0 - t))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (a + (z * (1.0d0 - y)))
    if (b <= (-7.2d+61)) then
        tmp = t_2
    else if (b <= 1.15d-260) then
        tmp = t_1
    else if (b <= 1.7d-67) then
        tmp = t_3
    else if (b <= 2d+61) then
        tmp = t_1
    else if (b <= 1.12d+133) 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 = (x + z) + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (b <= -7.2e+61) {
		tmp = t_2;
	} else if (b <= 1.15e-260) {
		tmp = t_1;
	} else if (b <= 1.7e-67) {
		tmp = t_3;
	} else if (b <= 2e+61) {
		tmp = t_1;
	} else if (b <= 1.12e+133) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (a * (1.0 - t))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (a + (z * (1.0 - y)))
	tmp = 0
	if b <= -7.2e+61:
		tmp = t_2
	elif b <= 1.15e-260:
		tmp = t_1
	elif b <= 1.7e-67:
		tmp = t_3
	elif b <= 2e+61:
		tmp = t_1
	elif b <= 1.12e+133:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (b <= -7.2e+61)
		tmp = t_2;
	elseif (b <= 1.15e-260)
		tmp = t_1;
	elseif (b <= 1.7e-67)
		tmp = t_3;
	elseif (b <= 2e+61)
		tmp = t_1;
	elseif (b <= 1.12e+133)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (a * (1.0 - t));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (a + (z * (1.0 - y)));
	tmp = 0.0;
	if (b <= -7.2e+61)
		tmp = t_2;
	elseif (b <= 1.15e-260)
		tmp = t_1;
	elseif (b <= 1.7e-67)
		tmp = t_3;
	elseif (b <= 2e+61)
		tmp = t_1;
	elseif (b <= 1.12e+133)
		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[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+61], t$95$2, If[LessEqual[b, 1.15e-260], t$95$1, If[LessEqual[b, 1.7e-67], t$95$3, If[LessEqual[b, 2e+61], t$95$1, If[LessEqual[b, 1.12e+133], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000021e61 or 1.12e133 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 81.8%

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

   if -7.20000000000000021e61 < b < 1.15e-260 or 1.70000000000000005e-67 < b < 1.9999999999999999e61

   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 y around inf 95.0%

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

   4. Taylor expanded in y around 0 73.8%

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

      1. associate--r+ 73.8%

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

      2. *-commutative 73.8%

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

      3. cancel-sign-sub-inv 73.8%

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

      4. cancel-sign-sub-inv 73.8%

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

      5. metadata-eval 73.8%

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

      6. *-lft-identity 73.8%

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

      7. +-commutative 73.8%

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

      8. sub-neg 73.8%

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

      9. metadata-eval 73.8%

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

      10. +-commutative 73.8%

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

      11. distribute-neg-in 73.8%

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

      12. metadata-eval 73.8%

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

      13. sub-neg 73.8%

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

      14. *-commutative 73.8%

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

   6. Simplified 73.8%

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

   if 1.15e-260 < b < 1.70000000000000005e-67 or 1.9999999999999999e61 < b < 1.12e133

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0 95.2%

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

   4. Taylor expanded in t around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. sub-neg 84.7%

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

      3. metadata-eval 84.7%

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

      4. neg-mul-1 84.7%

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

      5. unsub-neg 84.7%

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

   6. Simplified 84.7%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-67}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+61}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-67}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+133}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* a (- 1.0 t))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -5.4e+61)
     t_2
     (if (<= b 4e-158)
       t_1
       (if (<= b 1e-67)
         t_3
         (if (<= b 3.7e+61) t_1 (if (<= b 3.15e+133) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -5.4e+61) {
		tmp = t_2;
	} else if (b <= 4e-158) {
		tmp = t_1;
	} else if (b <= 1e-67) {
		tmp = t_3;
	} else if (b <= 3.7e+61) {
		tmp = t_1;
	} else if (b <= 3.15e+133) {
		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 = (x + z) + (a * (1.0d0 - t))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-5.4d+61)) then
        tmp = t_2
    else if (b <= 4d-158) then
        tmp = t_1
    else if (b <= 1d-67) then
        tmp = t_3
    else if (b <= 3.7d+61) then
        tmp = t_1
    else if (b <= 3.15d+133) 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 = (x + z) + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -5.4e+61) {
		tmp = t_2;
	} else if (b <= 4e-158) {
		tmp = t_1;
	} else if (b <= 1e-67) {
		tmp = t_3;
	} else if (b <= 3.7e+61) {
		tmp = t_1;
	} else if (b <= 3.15e+133) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (a * (1.0 - t))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -5.4e+61:
		tmp = t_2
	elif b <= 4e-158:
		tmp = t_1
	elif b <= 1e-67:
		tmp = t_3
	elif b <= 3.7e+61:
		tmp = t_1
	elif b <= 3.15e+133:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -5.4e+61)
		tmp = t_2;
	elseif (b <= 4e-158)
		tmp = t_1;
	elseif (b <= 1e-67)
		tmp = t_3;
	elseif (b <= 3.7e+61)
		tmp = t_1;
	elseif (b <= 3.15e+133)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (a * (1.0 - t));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -5.4e+61)
		tmp = t_2;
	elseif (b <= 4e-158)
		tmp = t_1;
	elseif (b <= 1e-67)
		tmp = t_3;
	elseif (b <= 3.7e+61)
		tmp = t_1;
	elseif (b <= 3.15e+133)
		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[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e+61], t$95$2, If[LessEqual[b, 4e-158], t$95$1, If[LessEqual[b, 1e-67], t$95$3, If[LessEqual[b, 3.7e+61], t$95$1, If[LessEqual[b, 3.15e+133], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.4000000000000004e61 or 3.15000000000000025e133 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 81.8%

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

   if -5.4000000000000004e61 < b < 4.00000000000000026e-158 or 9.99999999999999943e-68 < b < 3.70000000000000003e61

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 95.3%

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

   4. Taylor expanded in y around 0 73.8%

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

      1. associate--r+ 73.8%

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

      2. *-commutative 73.8%

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

      3. cancel-sign-sub-inv 73.8%

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

      4. cancel-sign-sub-inv 73.8%

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

      5. metadata-eval 73.8%

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

      6. *-lft-identity 73.8%

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

      7. +-commutative 73.8%

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

      8. sub-neg 73.8%

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

      9. metadata-eval 73.8%

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

      10. +-commutative 73.8%

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

      11. distribute-neg-in 73.8%

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

      12. metadata-eval 73.8%

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

      13. sub-neg 73.8%

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

      14. *-commutative 73.8%

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

   6. Simplified 73.8%

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

   if 4.00000000000000026e-158 < b < 9.99999999999999943e-68 or 3.70000000000000003e61 < b < 3.15000000000000025e133

   1. Initial program 96.5%

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

   3. Taylor expanded in b around 0 94.1%

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

   4. Taylor expanded in a around 0 87.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+61}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-158}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{-67}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+61}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.15 \cdot 10^{+133}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-71}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (* t (- b a))))
   (if (<= t -3e+216)
     t_2
     (if (<= t -1.75e+92)
       (- x (* t a))
       (if (<= t -7.2e-22)
         t_1
         (if (<= t 5.2e-71)
           (+ a (+ x (* b (+ y -2.0))))
           (if (<= t 2.8e+117) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+216) {
		tmp = t_2;
	} else if (t <= -1.75e+92) {
		tmp = x - (t * a);
	} else if (t <= -7.2e-22) {
		tmp = t_1;
	} else if (t <= 5.2e-71) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (t <= 2.8e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = t * (b - a)
    if (t <= (-3d+216)) then
        tmp = t_2
    else if (t <= (-1.75d+92)) then
        tmp = x - (t * a)
    else if (t <= (-7.2d-22)) then
        tmp = t_1
    else if (t <= 5.2d-71) then
        tmp = a + (x + (b * (y + (-2.0d0))))
    else if (t <= 2.8d+117) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3e+216) {
		tmp = t_2;
	} else if (t <= -1.75e+92) {
		tmp = x - (t * a);
	} else if (t <= -7.2e-22) {
		tmp = t_1;
	} else if (t <= 5.2e-71) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (t <= 2.8e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3e+216:
		tmp = t_2
	elif t <= -1.75e+92:
		tmp = x - (t * a)
	elif t <= -7.2e-22:
		tmp = t_1
	elif t <= 5.2e-71:
		tmp = a + (x + (b * (y + -2.0)))
	elif t <= 2.8e+117:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3e+216)
		tmp = t_2;
	elseif (t <= -1.75e+92)
		tmp = Float64(x - Float64(t * a));
	elseif (t <= -7.2e-22)
		tmp = t_1;
	elseif (t <= 5.2e-71)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))));
	elseif (t <= 2.8e+117)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3e+216)
		tmp = t_2;
	elseif (t <= -1.75e+92)
		tmp = x - (t * a);
	elseif (t <= -7.2e-22)
		tmp = t_1;
	elseif (t <= 5.2e-71)
		tmp = a + (x + (b * (y + -2.0)));
	elseif (t <= 2.8e+117)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+216], t$95$2, If[LessEqual[t, -1.75e+92], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-22], t$95$1, If[LessEqual[t, 5.2e-71], N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+117], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9999999999999998e216 or 2.79999999999999997e117 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf 82.1%

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

   if -2.9999999999999998e216 < t < -1.74999999999999993e92

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 92.7%

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

   4. Taylor expanded in z around inf 81.9%

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

   5. Taylor expanded in t around inf 75.1%

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

   if -1.74999999999999993e92 < t < -7.1999999999999996e-22 or 5.1999999999999997e-71 < t < 2.79999999999999997e117

   1. Initial program 95.3%

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

   3. Taylor expanded in b around 0 83.3%

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

   4. Taylor expanded in a around 0 68.5%

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

   if -7.1999999999999996e-22 < t < 5.1999999999999997e-71

   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 z around 0 73.6%

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

   4. Taylor expanded in t around 0 73.6%

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

      1. sub-neg 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

      4. neg-mul-1 73.6%

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

      5. remove-double-neg 73.6%

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

   6. Simplified 73.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+92}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-71}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-255}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -8.6e+60)
     t_2
     (if (<= b -6.8e-164)
       t_1
       (if (<= b -1.65e-255)
         t_3
         (if (<= b 1.35e-260) t_1 (if (<= b 1.12e+133) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -8.6e+60) {
		tmp = t_2;
	} else if (b <= -6.8e-164) {
		tmp = t_1;
	} else if (b <= -1.65e-255) {
		tmp = t_3;
	} else if (b <= 1.35e-260) {
		tmp = t_1;
	} else if (b <= 1.12e+133) {
		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 = x + (a * (1.0d0 - t))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-8.6d+60)) then
        tmp = t_2
    else if (b <= (-6.8d-164)) then
        tmp = t_1
    else if (b <= (-1.65d-255)) then
        tmp = t_3
    else if (b <= 1.35d-260) then
        tmp = t_1
    else if (b <= 1.12d+133) 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 = x + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -8.6e+60) {
		tmp = t_2;
	} else if (b <= -6.8e-164) {
		tmp = t_1;
	} else if (b <= -1.65e-255) {
		tmp = t_3;
	} else if (b <= 1.35e-260) {
		tmp = t_1;
	} else if (b <= 1.12e+133) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -8.6e+60:
		tmp = t_2
	elif b <= -6.8e-164:
		tmp = t_1
	elif b <= -1.65e-255:
		tmp = t_3
	elif b <= 1.35e-260:
		tmp = t_1
	elif b <= 1.12e+133:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -8.6e+60)
		tmp = t_2;
	elseif (b <= -6.8e-164)
		tmp = t_1;
	elseif (b <= -1.65e-255)
		tmp = t_3;
	elseif (b <= 1.35e-260)
		tmp = t_1;
	elseif (b <= 1.12e+133)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -8.6e+60)
		tmp = t_2;
	elseif (b <= -6.8e-164)
		tmp = t_1;
	elseif (b <= -1.65e-255)
		tmp = t_3;
	elseif (b <= 1.35e-260)
		tmp = t_1;
	elseif (b <= 1.12e+133)
		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[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e+60], t$95$2, If[LessEqual[b, -6.8e-164], t$95$1, If[LessEqual[b, -1.65e-255], t$95$3, If[LessEqual[b, 1.35e-260], t$95$1, If[LessEqual[b, 1.12e+133], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.59999999999999942e60 or 1.12e133 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 81.8%

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

   if -8.59999999999999942e60 < b < -6.8e-164 or -1.64999999999999994e-255 < b < 1.35000000000000003e-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 z around 0 76.1%

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

   4. Taylor expanded in b around 0 67.3%

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

   if -6.8e-164 < b < -1.64999999999999994e-255 or 1.35000000000000003e-260 < b < 1.12e133

   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 b around 0 91.5%

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

   4. Taylor expanded in a around 0 67.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-164}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-255}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := x - y \cdot z\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)) (t_2 (- x (* y z))))
   (if (<= b -1.1e+61)
     t_1
     (if (<= b 1.15e-260)
       (- x (* t a))
       (if (<= b 1.4e-27)
         t_2
         (if (<= b 1.95e+62)
           (* a (- 1.0 t))
           (if (<= b 1.05e+133) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double t_2 = x - (y * z);
	double tmp;
	if (b <= -1.1e+61) {
		tmp = t_1;
	} else if (b <= 1.15e-260) {
		tmp = x - (t * a);
	} else if (b <= 1.4e-27) {
		tmp = t_2;
	} else if (b <= 1.95e+62) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.05e+133) {
		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 + t) - 2.0d0) * b
    t_2 = x - (y * z)
    if (b <= (-1.1d+61)) then
        tmp = t_1
    else if (b <= 1.15d-260) then
        tmp = x - (t * a)
    else if (b <= 1.4d-27) then
        tmp = t_2
    else if (b <= 1.95d+62) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.05d+133) 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 + t) - 2.0) * b;
	double t_2 = x - (y * z);
	double tmp;
	if (b <= -1.1e+61) {
		tmp = t_1;
	} else if (b <= 1.15e-260) {
		tmp = x - (t * a);
	} else if (b <= 1.4e-27) {
		tmp = t_2;
	} else if (b <= 1.95e+62) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.05e+133) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	t_2 = x - (y * z)
	tmp = 0
	if b <= -1.1e+61:
		tmp = t_1
	elif b <= 1.15e-260:
		tmp = x - (t * a)
	elif b <= 1.4e-27:
		tmp = t_2
	elif b <= 1.95e+62:
		tmp = a * (1.0 - t)
	elif b <= 1.05e+133:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_2 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (b <= -1.1e+61)
		tmp = t_1;
	elseif (b <= 1.15e-260)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.4e-27)
		tmp = t_2;
	elseif (b <= 1.95e+62)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.05e+133)
		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 + t) - 2.0) * b;
	t_2 = x - (y * z);
	tmp = 0.0;
	if (b <= -1.1e+61)
		tmp = t_1;
	elseif (b <= 1.15e-260)
		tmp = x - (t * a);
	elseif (b <= 1.4e-27)
		tmp = t_2;
	elseif (b <= 1.95e+62)
		tmp = a * (1.0 - t);
	elseif (b <= 1.05e+133)
		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[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+61], t$95$1, If[LessEqual[b, 1.15e-260], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-27], t$95$2, If[LessEqual[b, 1.95e+62], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+133], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.1e61 or 1.05e133 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 81.8%

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

   if -1.1e61 < b < 1.15e-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 b around 0 93.9%

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

   4. Taylor expanded in z around inf 82.7%

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

   5. Taylor expanded in t around inf 47.4%

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

   if 1.15e-260 < b < 1.4e-27 or 1.95e62 < b < 1.05e133

   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 92.7%

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

   4. Taylor expanded in y around inf 60.5%

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

   if 1.4e-27 < b < 1.95e62

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 45.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+61}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-260}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-27}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* t a) (* z (- 1.0 y))))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.5e+70)
     t_2
     (if (<= b 2.6e-32)
       t_1
       (if (<= b 4.2e-19)
         (+ a (+ x (* b (+ y -2.0))))
         (if (<= b 5.3e+133) t_1 (- t_2 (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t * a) - (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.5e+70) {
		tmp = t_2;
	} else if (b <= 2.6e-32) {
		tmp = t_1;
	} else if (b <= 4.2e-19) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (b <= 5.3e+133) {
		tmp = t_1;
	} else {
		tmp = t_2 - (t * 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) :: t_2
    real(8) :: tmp
    t_1 = x - ((t * a) - (z * (1.0d0 - y)))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-1.5d+70)) then
        tmp = t_2
    else if (b <= 2.6d-32) then
        tmp = t_1
    else if (b <= 4.2d-19) then
        tmp = a + (x + (b * (y + (-2.0d0))))
    else if (b <= 5.3d+133) then
        tmp = t_1
    else
        tmp = t_2 - (t * 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 = x - ((t * a) - (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.5e+70) {
		tmp = t_2;
	} else if (b <= 2.6e-32) {
		tmp = t_1;
	} else if (b <= 4.2e-19) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (b <= 5.3e+133) {
		tmp = t_1;
	} else {
		tmp = t_2 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((t * a) - (z * (1.0 - y)))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.5e+70:
		tmp = t_2
	elif b <= 2.6e-32:
		tmp = t_1
	elif b <= 4.2e-19:
		tmp = a + (x + (b * (y + -2.0)))
	elif b <= 5.3e+133:
		tmp = t_1
	else:
		tmp = t_2 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(t * a) - Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.5e+70)
		tmp = t_2;
	elseif (b <= 2.6e-32)
		tmp = t_1;
	elseif (b <= 4.2e-19)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))));
	elseif (b <= 5.3e+133)
		tmp = t_1;
	else
		tmp = Float64(t_2 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((t * a) - (z * (1.0 - y)));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.5e+70)
		tmp = t_2;
	elseif (b <= 2.6e-32)
		tmp = t_1;
	elseif (b <= 4.2e-19)
		tmp = a + (x + (b * (y + -2.0)));
	elseif (b <= 5.3e+133)
		tmp = t_1;
	else
		tmp = t_2 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t * a), $MachinePrecision] - N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.5e+70], t$95$2, If[LessEqual[b, 2.6e-32], t$95$1, If[LessEqual[b, 4.2e-19], N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.3e+133], t$95$1, N[(t$95$2 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.49999999999999988e70

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 81.4%

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

   if -1.49999999999999988e70 < b < 2.5999999999999997e-32 or 4.1999999999999998e-19 < b < 5.29999999999999997e133

   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 b around 0 93.5%

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

   4. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   if 2.5999999999999997e-32 < b < 4.1999999999999998e-19

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. sub-neg 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. neg-mul-1 77.6%

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

      5. remove-double-neg 77.6%

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

   6. Simplified 77.6%

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

   if 5.29999999999999997e133 < b

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-rgt-neg-in 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+133}:\\ \;\;\;\;x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* t a) (* z (- 1.0 y))))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -5.6e+68)
     t_2
     (if (<= b 2.6e-32)
       t_1
       (if (<= b 4.2e-19)
         (+ a (+ x (* b (+ y -2.0))))
         (if (<= b 7.5e+134) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t * a) - (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.6e+68) {
		tmp = t_2;
	} else if (b <= 2.6e-32) {
		tmp = t_1;
	} else if (b <= 4.2e-19) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (b <= 7.5e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t * a) - (z * (1.0d0 - y)))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-5.6d+68)) then
        tmp = t_2
    else if (b <= 2.6d-32) then
        tmp = t_1
    else if (b <= 4.2d-19) then
        tmp = a + (x + (b * (y + (-2.0d0))))
    else if (b <= 7.5d+134) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t * a) - (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.6e+68) {
		tmp = t_2;
	} else if (b <= 2.6e-32) {
		tmp = t_1;
	} else if (b <= 4.2e-19) {
		tmp = a + (x + (b * (y + -2.0)));
	} else if (b <= 7.5e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((t * a) - (z * (1.0 - y)))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -5.6e+68:
		tmp = t_2
	elif b <= 2.6e-32:
		tmp = t_1
	elif b <= 4.2e-19:
		tmp = a + (x + (b * (y + -2.0)))
	elif b <= 7.5e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(t * a) - Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.6e+68)
		tmp = t_2;
	elseif (b <= 2.6e-32)
		tmp = t_1;
	elseif (b <= 4.2e-19)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))));
	elseif (b <= 7.5e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((t * a) - (z * (1.0 - y)));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -5.6e+68)
		tmp = t_2;
	elseif (b <= 2.6e-32)
		tmp = t_1;
	elseif (b <= 4.2e-19)
		tmp = a + (x + (b * (y + -2.0)));
	elseif (b <= 7.5e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t * a), $MachinePrecision] - N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.6e+68], t$95$2, If[LessEqual[b, 2.6e-32], t$95$1, If[LessEqual[b, 4.2e-19], N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.6e68 or 7.5000000000000001e134 < b

   1. Initial program 90.7%

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

   3. Taylor expanded in b around inf 81.6%

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

   if -5.6e68 < b < 2.5999999999999997e-32 or 4.1999999999999998e-19 < b < 7.5000000000000001e134

   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 b around 0 93.5%

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

   4. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   if 2.5999999999999997e-32 < b < 4.1999999999999998e-19

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. sub-neg 77.6%

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

      2. sub-neg 77.6%

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

      3. metadata-eval 77.6%

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

      4. neg-mul-1 77.6%

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

      5. remove-double-neg 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+134}:\\ \;\;\;\;x - \left(t \cdot a - z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+93}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-294}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -9.2e+209)
     t_2
     (if (<= y -4e+93)
       (* y b)
       (if (<= y -3.2e-204)
         t_1
         (if (<= y -8e-294) z (if (<= y 9.2e+14) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -9.2e+209) {
		tmp = t_2;
	} else if (y <= -4e+93) {
		tmp = y * b;
	} else if (y <= -3.2e-204) {
		tmp = t_1;
	} else if (y <= -8e-294) {
		tmp = z;
	} else if (y <= 9.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * -y
    if (y <= (-9.2d+209)) then
        tmp = t_2
    else if (y <= (-4d+93)) then
        tmp = y * b
    else if (y <= (-3.2d-204)) then
        tmp = t_1
    else if (y <= (-8d-294)) then
        tmp = z
    else if (y <= 9.2d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -9.2e+209) {
		tmp = t_2;
	} else if (y <= -4e+93) {
		tmp = y * b;
	} else if (y <= -3.2e-204) {
		tmp = t_1;
	} else if (y <= -8e-294) {
		tmp = z;
	} else if (y <= 9.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * -y
	tmp = 0
	if y <= -9.2e+209:
		tmp = t_2
	elif y <= -4e+93:
		tmp = y * b
	elif y <= -3.2e-204:
		tmp = t_1
	elif y <= -8e-294:
		tmp = z
	elif y <= 9.2e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -9.2e+209)
		tmp = t_2;
	elseif (y <= -4e+93)
		tmp = Float64(y * b);
	elseif (y <= -3.2e-204)
		tmp = t_1;
	elseif (y <= -8e-294)
		tmp = z;
	elseif (y <= 9.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * -y;
	tmp = 0.0;
	if (y <= -9.2e+209)
		tmp = t_2;
	elseif (y <= -4e+93)
		tmp = y * b;
	elseif (y <= -3.2e-204)
		tmp = t_1;
	elseif (y <= -8e-294)
		tmp = z;
	elseif (y <= 9.2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -9.2e+209], t$95$2, If[LessEqual[y, -4e+93], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.2e-204], t$95$1, If[LessEqual[y, -8e-294], z, If[LessEqual[y, 9.2e+14], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.20000000000000038e209 or 9.2e14 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in b around 0 70.2%

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

   4. Taylor expanded in y around inf 46.1%

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

      1. associate-*r* 46.1%

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

      2. mul-1-neg 46.1%

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

   6. Simplified 46.1%

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

   if -9.20000000000000038e209 < y < -4.00000000000000017e93

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.1%

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

   4. Taylor expanded in b around inf 64.9%

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

   if -4.00000000000000017e93 < y < -3.2e-204 or -8.00000000000000013e-294 < y < 9.2e14

   1. Initial program 97.6%

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

   3. Taylor expanded in a around inf 41.1%

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

   if -3.2e-204 < y < -8.00000000000000013e-294

   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 40.5%

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

   4. Taylor expanded in y around 0 40.5%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+93}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-294}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2e+61)
     t_2
     (if (<= b 4.8e-158)
       t_1
       (if (<= b 7.8e-100) (* z (- 1.0 y)) (if (<= b 2.25e+76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2e+61) {
		tmp = t_2;
	} else if (b <= 4.8e-158) {
		tmp = t_1;
	} else if (b <= 7.8e-100) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.25e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2d+61)) then
        tmp = t_2
    else if (b <= 4.8d-158) then
        tmp = t_1
    else if (b <= 7.8d-100) then
        tmp = z * (1.0d0 - y)
    else if (b <= 2.25d+76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2e+61) {
		tmp = t_2;
	} else if (b <= 4.8e-158) {
		tmp = t_1;
	} else if (b <= 7.8e-100) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.25e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2e+61:
		tmp = t_2
	elif b <= 4.8e-158:
		tmp = t_1
	elif b <= 7.8e-100:
		tmp = z * (1.0 - y)
	elif b <= 2.25e+76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2e+61)
		tmp = t_2;
	elseif (b <= 4.8e-158)
		tmp = t_1;
	elseif (b <= 7.8e-100)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 2.25e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2e+61)
		tmp = t_2;
	elseif (b <= 4.8e-158)
		tmp = t_1;
	elseif (b <= 7.8e-100)
		tmp = z * (1.0 - y);
	elseif (b <= 2.25e+76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2e+61], t$95$2, If[LessEqual[b, 4.8e-158], t$95$1, If[LessEqual[b, 7.8e-100], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e61 or 2.2499999999999999e76 < b

   1. Initial program 91.6%

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

   3. Taylor expanded in b around inf 78.1%

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

   if -1.9999999999999999e61 < b < 4.80000000000000015e-158 or 7.79999999999999955e-100 < b < 2.2499999999999999e76

   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 0 66.6%

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

   4. Taylor expanded in b around 0 58.9%

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

   if 4.80000000000000015e-158 < b < 7.79999999999999955e-100

   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 83.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-158}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+76}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+70} \lor \neg \left(b \leq 2.35 \cdot 10^{+98}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + t\_1\right) + y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -7e+70) (not (<= b 2.35e+98)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ (+ (+ x (* z (- 1.0 y))) t_1) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -7e+70) || !(b <= 2.35e+98)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-7d+70)) .or. (.not. (b <= 2.35d+98))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = ((x + (z * (1.0d0 - y))) + t_1) + (y * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -7e+70) || !(b <= 2.35e+98)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -7e+70) or not (b <= 2.35e+98):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -7e+70) || !(b <= 2.35e+98))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + t_1) + Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -7e+70) || ~((b <= 2.35e+98)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -7e+70], N[Not[LessEqual[b, 2.35e+98]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.00000000000000005e70 or 2.34999999999999985e98 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 93.0%

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

   if -7.00000000000000005e70 < b < 2.34999999999999985e98

   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 y around inf 95.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+70} \lor \neg \left(b \leq 2.35 \cdot 10^{+98}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+134}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -5.8e+69)
     t_1
     (if (<= b 4.6e+134)
       (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
       (- t_1 (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5.8e+69) {
		tmp = t_1;
	} else if (b <= 4.6e+134) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 - (t * 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 + t) - 2.0d0) * b
    if (b <= (-5.8d+69)) then
        tmp = t_1
    else if (b <= 4.6d+134) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else
        tmp = t_1 - (t * 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 + t) - 2.0) * b;
	double tmp;
	if (b <= -5.8e+69) {
		tmp = t_1;
	} else if (b <= 4.6e+134) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -5.8e+69:
		tmp = t_1
	elif b <= 4.6e+134:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5.8e+69)
		tmp = t_1;
	elseif (b <= 4.6e+134)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -5.8e+69)
		tmp = t_1;
	elseif (b <= 4.6e+134)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5.8e+69], t$95$1, If[LessEqual[b, 4.6e+134], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.7999999999999997e69

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 81.4%

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

   if -5.7999999999999997e69 < b < 4.5999999999999996e134

   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 91.5%

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

   if 4.5999999999999996e134 < b

   1. Initial program 96.9%

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

   3. Taylor expanded in t around inf 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-rgt-neg-in 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+69}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+134}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.05e+80)
   (* y b)
   (if (<= y 7.8e-118) (* t (- a)) (if (<= y 2e+50) x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e+80) {
		tmp = y * b;
	} else if (y <= 7.8e-118) {
		tmp = t * -a;
	} else if (y <= 2e+50) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.05d+80)) then
        tmp = y * b
    else if (y <= 7.8d-118) then
        tmp = t * -a
    else if (y <= 2d+50) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.05e+80) {
		tmp = y * b;
	} else if (y <= 7.8e-118) {
		tmp = t * -a;
	} else if (y <= 2e+50) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.05e+80:
		tmp = y * b
	elif y <= 7.8e-118:
		tmp = t * -a
	elif y <= 2e+50:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.05e+80)
		tmp = Float64(y * b);
	elseif (y <= 7.8e-118)
		tmp = Float64(t * Float64(-a));
	elseif (y <= 2e+50)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.05e+80)
		tmp = y * b;
	elseif (y <= 7.8e-118)
		tmp = t * -a;
	elseif (y <= 2e+50)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.05e+80], N[(y * b), $MachinePrecision], If[LessEqual[y, 7.8e-118], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, 2e+50], x, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000001e80 or 2.0000000000000002e50 < y

   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 y around inf 90.0%

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

   4. Taylor expanded in b around inf 42.5%

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

   if -2.05000000000000001e80 < y < 7.80000000000000002e-118

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf 76.3%

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

   4. Taylor expanded in t around inf 25.1%

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

      1. associate-*r* 25.1%

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

      2. mul-1-neg 25.1%

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

   6. Simplified 25.1%

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

   if 7.80000000000000002e-118 < y < 2.0000000000000002e50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 37.4%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 26.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.6e-18)
   (* y b)
   (if (<= y 4.2e-119) z (if (<= y 7.5e+50) x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e-18) {
		tmp = y * b;
	} else if (y <= 4.2e-119) {
		tmp = z;
	} else if (y <= 7.5e+50) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.6d-18)) then
        tmp = y * b
    else if (y <= 4.2d-119) then
        tmp = z
    else if (y <= 7.5d+50) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e-18) {
		tmp = y * b;
	} else if (y <= 4.2e-119) {
		tmp = z;
	} else if (y <= 7.5e+50) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.6e-18:
		tmp = y * b
	elif y <= 4.2e-119:
		tmp = z
	elif y <= 7.5e+50:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.6e-18)
		tmp = Float64(y * b);
	elseif (y <= 4.2e-119)
		tmp = z;
	elseif (y <= 7.5e+50)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.6e-18)
		tmp = y * b;
	elseif (y <= 4.2e-119)
		tmp = z;
	elseif (y <= 7.5e+50)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.6e-18], N[(y * b), $MachinePrecision], If[LessEqual[y, 4.2e-119], z, If[LessEqual[y, 7.5e+50], x, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6000000000000002e-18 or 7.4999999999999999e50 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 89.7%

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

   4. Taylor expanded in b around inf 39.8%

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

   if -4.6000000000000002e-18 < y < 4.2e-119

   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 25.9%

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

   4. Taylor expanded in y around 0 25.9%

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

   if 4.2e-119 < y < 7.4999999999999999e50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 36.4%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-119}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+27} \lor \neg \left(y \leq 1.75 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.32e+27) (not (<= y 1.75e+15))) (* y (- b z)) (- x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.32e+27) || !(y <= 1.75e+15)) {
		tmp = y * (b - z);
	} else {
		tmp = x - (t * 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 <= (-2.32d+27)) .or. (.not. (y <= 1.75d+15))) then
        tmp = y * (b - z)
    else
        tmp = x - (t * 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 <= -2.32e+27) || !(y <= 1.75e+15)) {
		tmp = y * (b - z);
	} else {
		tmp = x - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.32e+27) or not (y <= 1.75e+15):
		tmp = y * (b - z)
	else:
		tmp = x - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.32e+27) || !(y <= 1.75e+15))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.32e+27) || ~((y <= 1.75e+15)))
		tmp = y * (b - z);
	else
		tmp = x - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.32e+27], N[Not[LessEqual[y, 1.75e+15]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.32e27 or 1.75e15 < y

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf 69.6%

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

   if -2.32e27 < y < 1.75e15

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 77.4%

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

   4. Taylor expanded in z around inf 64.5%

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

   5. Taylor expanded in t around inf 45.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+27} \lor \neg \left(y \leq 1.75 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+96} \lor \neg \left(y \leq 3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+96) (not (<= y 3e+17))) (* y (- b z)) (* a (- 1.0 t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+96) || !(y <= 3e+17)) {
		tmp = y * (b - z);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d+96)) .or. (.not. (y <= 3d+17))) then
        tmp = y * (b - z)
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+96) || !(y <= 3e+17)) {
		tmp = y * (b - z);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e+96) or not (y <= 3e+17):
		tmp = y * (b - z)
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+96) || !(y <= 3e+17))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = 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 <= -1.15e+96) || ~((y <= 3e+17)))
		tmp = y * (b - z);
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+96], N[Not[LessEqual[y, 3e+17]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000008e96 or 3e17 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 72.8%

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

   if -1.15000000000000008e96 < y < 3e17

   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 a around inf 37.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+96} \lor \neg \left(y \leq 3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 19.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+100) z (if (<= z 3.8e+47) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+100) {
		tmp = z;
	} else if (z <= 3.8e+47) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.5d+100)) then
        tmp = z
    else if (z <= 3.8d+47) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+100) {
		tmp = z;
	} else if (z <= 3.8e+47) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+100:
		tmp = z
	elif z <= 3.8e+47:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+100)
		tmp = z;
	elseif (z <= 3.8e+47)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+100)
		tmp = z;
	elseif (z <= 3.8e+47)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+100], z, If[LessEqual[z, 3.8e+47], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000043e100 or 3.8000000000000003e47 < z

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 60.1%

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

   4. Taylor expanded in y around 0 25.3%

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

   if -8.50000000000000043e100 < z < 3.8000000000000003e47

   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 x around inf 24.7%

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

Alternative 22: 19.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+162}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.05e+162) a (if (<= a 2.1e+147) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+162) {
		tmp = a;
	} else if (a <= 2.1e+147) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.05d+162)) then
        tmp = a
    else if (a <= 2.1d+147) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+162) {
		tmp = a;
	} else if (a <= 2.1e+147) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.05e+162:
		tmp = a
	elif a <= 2.1e+147:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.05e+162)
		tmp = a;
	elseif (a <= 2.1e+147)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.05e+162)
		tmp = a;
	elseif (a <= 2.1e+147)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.05e+162], a, If[LessEqual[a, 2.1e+147], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05e162 or 2.10000000000000006e147 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 69.4%

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

   4. Taylor expanded in t around 0 30.6%

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

   if -1.05e162 < a < 2.10000000000000006e147

   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 x around inf 21.1%

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

Alternative 23: 11.1% 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 95.7%

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

3. Taylor expanded in a around inf 27.9%

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

4. Taylor expanded in t around 0 11.3%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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)))