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

Percentage Accurate: 95.2% → 97.2%

Time: 12.5s

Alternatives: 18

Speedup: 0.5×

• 35.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.9e+180)
   (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0)))))
   (- x (* b (- 2.0 (+ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.9e+180) {
		tmp = fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
	} else {
		tmp = x - (b * (2.0 - (y + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.9e+180)
		tmp = fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))));
	else
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.9e+180], N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.90000000000000007e180

   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. Step-by-step derivation

      1. +-commutative 98.1%

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

      2. fma-define 99.5%

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

      3. associate--l+ 99.5%

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

      4. sub-neg 99.5%

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

      5. metadata-eval 99.5%

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

      6. sub-neg 99.5%

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

      7. associate-+l- 99.5%

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

      8. fma-neg 99.5%

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

      9. sub-neg 99.5%

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

      10. metadata-eval 99.5%

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

      11. remove-double-neg 99.5%

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

      12. sub-neg 99.5%

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

      13. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   if 2.90000000000000007e180 < b

   1. Initial program 85.0%

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

   3. Taylor expanded in a around 0 92.9%

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

   4. Taylor expanded in z around 0 95.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + t_1)
	tmp = 0.0
	if (t_2 <= Inf)
		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 + t) - 2.0);
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 b around inf 70.0%

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

4. Final simplification 98.8%

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

Alternative 3: 33.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+129}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-218}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -2.5e+129)
     (* b y)
     (if (<= y -7.2e+48)
       t_2
       (if (<= y -5.2e+47)
         (* b y)
         (if (<= y -3e-143)
           t_1
           (if (<= y 1.8e-218)
             (* b t)
             (if (<= y 68000000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -2.5e+129) {
		tmp = b * y;
	} else if (y <= -7.2e+48) {
		tmp = t_2;
	} else if (y <= -5.2e+47) {
		tmp = b * y;
	} else if (y <= -3e-143) {
		tmp = t_1;
	} else if (y <= 1.8e-218) {
		tmp = b * t;
	} else if (y <= 68000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * -y
    if (y <= (-2.5d+129)) then
        tmp = b * y
    else if (y <= (-7.2d+48)) then
        tmp = t_2
    else if (y <= (-5.2d+47)) then
        tmp = b * y
    else if (y <= (-3d-143)) then
        tmp = t_1
    else if (y <= 1.8d-218) then
        tmp = b * t
    else if (y <= 68000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -2.5e+129) {
		tmp = b * y;
	} else if (y <= -7.2e+48) {
		tmp = t_2;
	} else if (y <= -5.2e+47) {
		tmp = b * y;
	} else if (y <= -3e-143) {
		tmp = t_1;
	} else if (y <= 1.8e-218) {
		tmp = b * t;
	} else if (y <= 68000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * -y
	tmp = 0
	if y <= -2.5e+129:
		tmp = b * y
	elif y <= -7.2e+48:
		tmp = t_2
	elif y <= -5.2e+47:
		tmp = b * y
	elif y <= -3e-143:
		tmp = t_1
	elif y <= 1.8e-218:
		tmp = b * t
	elif y <= 68000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -2.5e+129)
		tmp = Float64(b * y);
	elseif (y <= -7.2e+48)
		tmp = t_2;
	elseif (y <= -5.2e+47)
		tmp = Float64(b * y);
	elseif (y <= -3e-143)
		tmp = t_1;
	elseif (y <= 1.8e-218)
		tmp = Float64(b * t);
	elseif (y <= 68000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * -y;
	tmp = 0.0;
	if (y <= -2.5e+129)
		tmp = b * y;
	elseif (y <= -7.2e+48)
		tmp = t_2;
	elseif (y <= -5.2e+47)
		tmp = b * y;
	elseif (y <= -3e-143)
		tmp = t_1;
	elseif (y <= 1.8e-218)
		tmp = b * t;
	elseif (y <= 68000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -2.5e+129], N[(b * y), $MachinePrecision], If[LessEqual[y, -7.2e+48], t$95$2, If[LessEqual[y, -5.2e+47], N[(b * y), $MachinePrecision], If[LessEqual[y, -3e-143], t$95$1, If[LessEqual[y, 1.8e-218], N[(b * t), $MachinePrecision], If[LessEqual[y, 68000000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5000000000000001e129 or -7.19999999999999967e48 < y < -5.20000000000000007e47

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 68.4%

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

   4. Taylor expanded in y around inf 54.2%

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

   if -2.5000000000000001e129 < y < -7.19999999999999967e48 or 6.8e13 < y

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 45.9%

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

   4. Taylor expanded in y around inf 45.7%

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

      1. mul-1-neg 45.7%

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

      2. *-commutative 45.7%

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

      3. distribute-rgt-neg-in 45.7%

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

   6. Simplified 45.7%

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

   if -5.20000000000000007e47 < y < -2.99999999999999985e-143 or 1.80000000000000006e-218 < y < 6.8e13

   1. Initial program 98.9%

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

   3. Taylor expanded in a around inf 35.4%

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

   if -2.99999999999999985e-143 < y < 1.80000000000000006e-218

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf 49.1%

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

   4. Taylor expanded in b around inf 33.0%

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

      1. *-commutative 33.0%

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

   6. Simplified 33.0%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+129}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-218}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -950:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-25}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -5.1e+36)
     t_2
     (if (<= b -950.0)
       t_1
       (if (<= b -1.65e-40)
         t_2
         (if (<= b 3e-50) t_1 (if (<= b 1e-25) (* z (- 1.0 y)) 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 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -5.1e+36) {
		tmp = t_2;
	} else if (b <= -950.0) {
		tmp = t_1;
	} else if (b <= -1.65e-40) {
		tmp = t_2;
	} else if (b <= 3e-50) {
		tmp = t_1;
	} else if (b <= 1e-25) {
		tmp = z * (1.0 - y);
	} 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 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-5.1d+36)) then
        tmp = t_2
    else if (b <= (-950.0d0)) then
        tmp = t_1
    else if (b <= (-1.65d-40)) then
        tmp = t_2
    else if (b <= 3d-50) then
        tmp = t_1
    else if (b <= 1d-25) then
        tmp = z * (1.0d0 - y)
    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 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -5.1e+36) {
		tmp = t_2;
	} else if (b <= -950.0) {
		tmp = t_1;
	} else if (b <= -1.65e-40) {
		tmp = t_2;
	} else if (b <= 3e-50) {
		tmp = t_1;
	} else if (b <= 1e-25) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -5.1e+36:
		tmp = t_2
	elif b <= -950.0:
		tmp = t_1
	elif b <= -1.65e-40:
		tmp = t_2
	elif b <= 3e-50:
		tmp = t_1
	elif b <= 1e-25:
		tmp = z * (1.0 - y)
	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(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -5.1e+36)
		tmp = t_2;
	elseif (b <= -950.0)
		tmp = t_1;
	elseif (b <= -1.65e-40)
		tmp = t_2;
	elseif (b <= 3e-50)
		tmp = t_1;
	elseif (b <= 1e-25)
		tmp = Float64(z * Float64(1.0 - y));
	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 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -5.1e+36)
		tmp = t_2;
	elseif (b <= -950.0)
		tmp = t_1;
	elseif (b <= -1.65e-40)
		tmp = t_2;
	elseif (b <= 3e-50)
		tmp = t_1;
	elseif (b <= 1e-25)
		tmp = z * (1.0 - y);
	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[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.1e+36], t$95$2, If[LessEqual[b, -950.0], t$95$1, If[LessEqual[b, -1.65e-40], t$95$2, If[LessEqual[b, 3e-50], t$95$1, If[LessEqual[b, 1e-25], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.09999999999999973e36 or -950 < b < -1.64999999999999996e-40 or 1.00000000000000004e-25 < b

   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 a around 0 86.2%

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

   4. Taylor expanded in z around 0 75.5%

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

   if -5.09999999999999973e36 < b < -950 or -1.64999999999999996e-40 < b < 2.9999999999999999e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 65.3%

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

   4. Taylor expanded in b around 0 60.2%

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

   if 2.9999999999999999e-50 < b < 1.00000000000000004e-25

   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 79.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+36}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -950:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-40}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-50}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{-25}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))))
        (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -9.8e+39)
     t_2
     (if (<= b 6.6e+31)
       t_1
       (if (<= b 1.76e+87)
         (- (* b (- (+ y t) 2.0)) (* t a))
         (if (<= b 4e+101) 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)) + (a * (1.0 - t)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -9.8e+39) {
		tmp = t_2;
	} else if (b <= 6.6e+31) {
		tmp = t_1;
	} else if (b <= 1.76e+87) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (b <= 4e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-9.8d+39)) then
        tmp = t_2
    else if (b <= 6.6d+31) then
        tmp = t_1
    else if (b <= 1.76d+87) then
        tmp = (b * ((y + t) - 2.0d0)) - (t * a)
    else if (b <= 4d+101) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -9.8e+39) {
		tmp = t_2;
	} else if (b <= 6.6e+31) {
		tmp = t_1;
	} else if (b <= 1.76e+87) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (b <= 4e+101) {
		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)) + (a * (1.0 - t)))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -9.8e+39:
		tmp = t_2
	elif b <= 6.6e+31:
		tmp = t_1
	elif b <= 1.76e+87:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	elif b <= 4e+101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -9.8e+39)
		tmp = t_2;
	elseif (b <= 6.6e+31)
		tmp = t_1;
	elseif (b <= 1.76e+87)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	elseif (b <= 4e+101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -9.8e+39)
		tmp = t_2;
	elseif (b <= 6.6e+31)
		tmp = t_1;
	elseif (b <= 1.76e+87)
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	elseif (b <= 4e+101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+39], t$95$2, If[LessEqual[b, 6.6e+31], t$95$1, If[LessEqual[b, 1.76e+87], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.79999999999999974e39 or 3.9999999999999999e101 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in a around 0 88.3%

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

   4. Taylor expanded in z around 0 84.2%

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

   if -9.79999999999999974e39 < b < 6.59999999999999985e31 or 1.76000000000000003e87 < b < 3.9999999999999999e101

   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 89.2%

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

   if 6.59999999999999985e31 < b < 1.76000000000000003e87

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. distribute-rgt-neg-in 92.4%

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

   5. Simplified 92.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+31}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+101}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.3e+37)
     t_2
     (if (<= b -1.06e-250)
       t_1
       (if (<= b -1.5e-296)
         t_3
         (if (<= b 3e-50) t_1 (if (<= b 2.5e+32) 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 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.3e+37) {
		tmp = t_2;
	} else if (b <= -1.06e-250) {
		tmp = t_1;
	} else if (b <= -1.5e-296) {
		tmp = t_3;
	} else if (b <= 3e-50) {
		tmp = t_1;
	} else if (b <= 2.5e+32) {
		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 = b * ((y + t) - 2.0d0)
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.3d+37)) then
        tmp = t_2
    else if (b <= (-1.06d-250)) then
        tmp = t_1
    else if (b <= (-1.5d-296)) then
        tmp = t_3
    else if (b <= 3d-50) then
        tmp = t_1
    else if (b <= 2.5d+32) 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 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.3e+37) {
		tmp = t_2;
	} else if (b <= -1.06e-250) {
		tmp = t_1;
	} else if (b <= -1.5e-296) {
		tmp = t_3;
	} else if (b <= 3e-50) {
		tmp = t_1;
	} else if (b <= 2.5e+32) {
		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 = b * ((y + t) - 2.0)
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.3e+37:
		tmp = t_2
	elif b <= -1.06e-250:
		tmp = t_1
	elif b <= -1.5e-296:
		tmp = t_3
	elif b <= 3e-50:
		tmp = t_1
	elif b <= 2.5e+32:
		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(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.3e+37)
		tmp = t_2;
	elseif (b <= -1.06e-250)
		tmp = t_1;
	elseif (b <= -1.5e-296)
		tmp = t_3;
	elseif (b <= 3e-50)
		tmp = t_1;
	elseif (b <= 2.5e+32)
		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 = b * ((y + t) - 2.0);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.3e+37)
		tmp = t_2;
	elseif (b <= -1.06e-250)
		tmp = t_1;
	elseif (b <= -1.5e-296)
		tmp = t_3;
	elseif (b <= 3e-50)
		tmp = t_1;
	elseif (b <= 2.5e+32)
		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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+37], t$95$2, If[LessEqual[b, -1.06e-250], t$95$1, If[LessEqual[b, -1.5e-296], t$95$3, If[LessEqual[b, 3e-50], t$95$1, If[LessEqual[b, 2.5e+32], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e37 or 2.4999999999999999e32 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf 71.5%

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

   if -1.3e37 < b < -1.05999999999999993e-250 or -1.4999999999999999e-296 < b < 2.9999999999999999e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 70.0%

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

   4. Taylor expanded in b around 0 60.4%

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

   if -1.05999999999999993e-250 < b < -1.4999999999999999e-296 or 2.9999999999999999e-50 < b < 2.4999999999999999e32

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 60.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{-250}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-50}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-169}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.5e+34)
     t_1
     (if (<= t -1.22e-169)
       (* b y)
       (if (<= t 4.2e-155)
         x
         (if (<= t 8.8e-30)
           (* a (- 1.0 t))
           (if (<= t 5.3e+36) (* z (- y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.5e+34) {
		tmp = t_1;
	} else if (t <= -1.22e-169) {
		tmp = b * y;
	} else if (t <= 4.2e-155) {
		tmp = x;
	} else if (t <= 8.8e-30) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.3e+36) {
		tmp = z * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-7.5d+34)) then
        tmp = t_1
    else if (t <= (-1.22d-169)) then
        tmp = b * y
    else if (t <= 4.2d-155) then
        tmp = x
    else if (t <= 8.8d-30) then
        tmp = a * (1.0d0 - t)
    else if (t <= 5.3d+36) then
        tmp = z * -y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.5e+34) {
		tmp = t_1;
	} else if (t <= -1.22e-169) {
		tmp = b * y;
	} else if (t <= 4.2e-155) {
		tmp = x;
	} else if (t <= 8.8e-30) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.3e+36) {
		tmp = z * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7.5e+34:
		tmp = t_1
	elif t <= -1.22e-169:
		tmp = b * y
	elif t <= 4.2e-155:
		tmp = x
	elif t <= 8.8e-30:
		tmp = a * (1.0 - t)
	elif t <= 5.3e+36:
		tmp = z * -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.5e+34)
		tmp = t_1;
	elseif (t <= -1.22e-169)
		tmp = Float64(b * y);
	elseif (t <= 4.2e-155)
		tmp = x;
	elseif (t <= 8.8e-30)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 5.3e+36)
		tmp = Float64(z * Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+34)
		tmp = t_1;
	elseif (t <= -1.22e-169)
		tmp = b * y;
	elseif (t <= 4.2e-155)
		tmp = x;
	elseif (t <= 8.8e-30)
		tmp = a * (1.0 - t);
	elseif (t <= 5.3e+36)
		tmp = z * -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+34], t$95$1, If[LessEqual[t, -1.22e-169], N[(b * y), $MachinePrecision], If[LessEqual[t, 4.2e-155], x, If[LessEqual[t, 8.8e-30], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+36], N[(z * (-y)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.49999999999999976e34 or 5.3e36 < t

   1. Initial program 94.3%

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

   3. Taylor expanded in t around inf 68.1%

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

   if -7.49999999999999976e34 < t < -1.22e-169

   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 z around 0 74.8%

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

   4. Taylor expanded in y around inf 33.1%

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

   if -1.22e-169 < t < 4.2000000000000003e-155

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf 37.2%

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

   if 4.2000000000000003e-155 < t < 8.79999999999999933e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 31.1%

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

   if 8.79999999999999933e-30 < t < 5.3e36

   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 64.5%

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

   4. Taylor expanded in y around inf 46.4%

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

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. distribute-rgt-neg-in 46.4%

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

   6. Simplified 46.4%

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

Alternative 8: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{elif}\;b \leq 10^{+123}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (+ t_2 t_1)))
   (if (<= b -1.02e-39)
     t_3
     (if (<= b 4.2e+30)
       (+ x (+ (* z (- 1.0 y)) t_1))
       (if (<= b 1e+123) t_3 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 = x - (b * (2.0 - (y + t)));
	double t_3 = t_2 + t_1;
	double tmp;
	if (b <= -1.02e-39) {
		tmp = t_3;
	} else if (b <= 4.2e+30) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else if (b <= 1e+123) {
		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 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = t_2 + t_1
    if (b <= (-1.02d-39)) then
        tmp = t_3
    else if (b <= 4.2d+30) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else if (b <= 1d+123) 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 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = t_2 + t_1;
	double tmp;
	if (b <= -1.02e-39) {
		tmp = t_3;
	} else if (b <= 4.2e+30) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else if (b <= 1e+123) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = t_2 + t_1
	tmp = 0
	if b <= -1.02e-39:
		tmp = t_3
	elif b <= 4.2e+30:
		tmp = x + ((z * (1.0 - y)) + t_1)
	elif b <= 1e+123:
		tmp = t_3
	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(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (b <= -1.02e-39)
		tmp = t_3;
	elseif (b <= 4.2e+30)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	elseif (b <= 1e+123)
		tmp = t_3;
	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 = x - (b * (2.0 - (y + t)));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (b <= -1.02e-39)
		tmp = t_3;
	elseif (b <= 4.2e+30)
		tmp = x + ((z * (1.0 - y)) + t_1);
	elseif (b <= 1e+123)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[b, -1.02e-39], t$95$3, If[LessEqual[b, 4.2e+30], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+123], t$95$3, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.02000000000000007e-39 or 4.2e30 < b < 9.99999999999999978e122

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 84.3%

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

   if -1.02000000000000007e-39 < b < 4.2e30

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 91.7%

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

   if 9.99999999999999978e122 < b

   1. Initial program 86.0%

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

   3. Taylor expanded in a around 0 92.3%

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

   4. Taylor expanded in z around 0 92.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-39}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 10^{+123}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 25.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-178}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e+128)
   (* b t)
   (if (<= t -1.4e+35)
     (* t (- a))
     (if (<= t -3.1e-178)
       (* b y)
       (if (<= t 5.2e-145) x (if (<= t 5.8e+173) (* z (- y)) (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+128) {
		tmp = b * t;
	} else if (t <= -1.4e+35) {
		tmp = t * -a;
	} else if (t <= -3.1e-178) {
		tmp = b * y;
	} else if (t <= 5.2e-145) {
		tmp = x;
	} else if (t <= 5.8e+173) {
		tmp = z * -y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.6d+128)) then
        tmp = b * t
    else if (t <= (-1.4d+35)) then
        tmp = t * -a
    else if (t <= (-3.1d-178)) then
        tmp = b * y
    else if (t <= 5.2d-145) then
        tmp = x
    else if (t <= 5.8d+173) then
        tmp = z * -y
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+128) {
		tmp = b * t;
	} else if (t <= -1.4e+35) {
		tmp = t * -a;
	} else if (t <= -3.1e-178) {
		tmp = b * y;
	} else if (t <= 5.2e-145) {
		tmp = x;
	} else if (t <= 5.8e+173) {
		tmp = z * -y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.6e+128:
		tmp = b * t
	elif t <= -1.4e+35:
		tmp = t * -a
	elif t <= -3.1e-178:
		tmp = b * y
	elif t <= 5.2e-145:
		tmp = x
	elif t <= 5.8e+173:
		tmp = z * -y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e+128)
		tmp = Float64(b * t);
	elseif (t <= -1.4e+35)
		tmp = Float64(t * Float64(-a));
	elseif (t <= -3.1e-178)
		tmp = Float64(b * y);
	elseif (t <= 5.2e-145)
		tmp = x;
	elseif (t <= 5.8e+173)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.6e+128)
		tmp = b * t;
	elseif (t <= -1.4e+35)
		tmp = t * -a;
	elseif (t <= -3.1e-178)
		tmp = b * y;
	elseif (t <= 5.2e-145)
		tmp = x;
	elseif (t <= 5.8e+173)
		tmp = z * -y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e+128], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.4e+35], N[(t * (-a)), $MachinePrecision], If[LessEqual[t, -3.1e-178], N[(b * y), $MachinePrecision], If[LessEqual[t, 5.2e-145], x, If[LessEqual[t, 5.8e+173], N[(z * (-y)), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.6e128 or 5.80000000000000014e173 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 81.0%

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

   4. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   if -2.6e128 < t < -1.39999999999999999e35

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-rgt-neg-in 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around inf 48.6%

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

   7. Taylor expanded in a around inf 30.6%

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

      1. associate-*r* 30.6%

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

      2. mul-1-neg 30.6%

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

   9. Simplified 30.6%

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

   if -1.39999999999999999e35 < t < -3.1e-178

   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 z around 0 74.8%

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

   4. Taylor expanded in y around inf 33.1%

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

   if -3.1e-178 < t < 5.1999999999999999e-145

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 37.8%

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

   if 5.1999999999999999e-145 < t < 5.80000000000000014e173

   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 40.1%

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

   4. Taylor expanded in y around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

      3. distribute-rgt-neg-in 29.0%

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

   6. Simplified 29.0%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-178}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-116}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;y \leq 20000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.8e+47)
   (* y (- b z))
   (if (<= y 8.5e-116)
     (+ x (+ z (* b (+ t -2.0))))
     (if (<= y 20000.0)
       (+ x (* a (- 1.0 t)))
       (- (* b (- (+ y t) 2.0)) (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = y * (b - z);
	} else if (y <= 8.5e-116) {
		tmp = x + (z + (b * (t + -2.0)));
	} else if (y <= 20000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.8d+47)) then
        tmp = y * (b - z)
    else if (y <= 8.5d-116) then
        tmp = x + (z + (b * (t + (-2.0d0))))
    else if (y <= 20000.0d0) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = (b * ((y + t) - 2.0d0)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+47) {
		tmp = y * (b - z);
	} else if (y <= 8.5e-116) {
		tmp = x + (z + (b * (t + -2.0)));
	} else if (y <= 20000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.8e+47:
		tmp = y * (b - z)
	elif y <= 8.5e-116:
		tmp = x + (z + (b * (t + -2.0)))
	elif y <= 20000.0:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = (b * ((y + t) - 2.0)) - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+47)
		tmp = Float64(y * Float64(b - z));
	elseif (y <= 8.5e-116)
		tmp = Float64(x + Float64(z + Float64(b * Float64(t + -2.0))));
	elseif (y <= 20000.0)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.8e+47)
		tmp = y * (b - z);
	elseif (y <= 8.5e-116)
		tmp = x + (z + (b * (t + -2.0)));
	elseif (y <= 20000.0)
		tmp = x + (a * (1.0 - t));
	else
		tmp = (b * ((y + t) - 2.0)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+47], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-116], N[(x + N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 20000.0], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999961e47

   1. Initial program 88.4%

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

   3. Taylor expanded in y around inf 76.0%

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

   if -5.79999999999999961e47 < y < 8.4999999999999995e-116

   1. Initial program 97.5%

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

   3. Taylor expanded in a around 0 74.1%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. associate--l+ 72.8%

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

      2. sub-neg 72.8%

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

      3. metadata-eval 72.8%

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

      4. neg-mul-1 72.8%

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

   6. Simplified 72.8%

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

   if 8.4999999999999995e-116 < y < 2e4

   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 94.3%

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

   4. Taylor expanded in b around 0 81.8%

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

   if 2e4 < y

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. distribute-rgt-neg-in 74.7%

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

   5. Simplified 74.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-116}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;y \leq 20000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;x + \left(t\_3 + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.05e-40)
     (+ t_2 t_1)
     (if (<= b 5.6e-53) (+ x (+ t_3 t_1)) (+ t_2 t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.05e-40) {
		tmp = t_2 + t_1;
	} else if (b <= 5.6e-53) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.05d-40)) then
        tmp = t_2 + t_1
    else if (b <= 5.6d-53) then
        tmp = x + (t_3 + t_1)
    else
        tmp = t_2 + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.05e-40) {
		tmp = t_2 + t_1;
	} else if (b <= 5.6e-53) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.05e-40:
		tmp = t_2 + t_1
	elif b <= 5.6e-53:
		tmp = x + (t_3 + t_1)
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.05e-40)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 5.6e-53)
		tmp = Float64(x + Float64(t_3 + t_1));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x - (b * (2.0 - (y + t)));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.05e-40)
		tmp = t_2 + t_1;
	elseif (b <= 5.6e-53)
		tmp = x + (t_3 + t_1);
	else
		tmp = t_2 + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e-40], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 5.6e-53], N[(x + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05000000000000009e-40

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 85.2%

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

   if -1.05000000000000009e-40 < b < 5.59999999999999971e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 94.7%

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

   if 5.59999999999999971e-53 < b

   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 a around 0 86.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-53}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-116}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;y \leq 65000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -8.5e+43)
     t_1
     (if (<= y 8.1e-116)
       (+ x (+ z (* b (+ t -2.0))))
       (if (<= y 65000.0) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -8.5e+43) {
		tmp = t_1;
	} else if (y <= 8.1e-116) {
		tmp = x + (z + (b * (t + -2.0)));
	} else if (y <= 65000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-8.5d+43)) then
        tmp = t_1
    else if (y <= 8.1d-116) then
        tmp = x + (z + (b * (t + (-2.0d0))))
    else if (y <= 65000.0d0) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -8.5e+43) {
		tmp = t_1;
	} else if (y <= 8.1e-116) {
		tmp = x + (z + (b * (t + -2.0)));
	} else if (y <= 65000.0) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -8.5e+43:
		tmp = t_1
	elif y <= 8.1e-116:
		tmp = x + (z + (b * (t + -2.0)))
	elif y <= 65000.0:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -8.5e+43)
		tmp = t_1;
	elseif (y <= 8.1e-116)
		tmp = Float64(x + Float64(z + Float64(b * Float64(t + -2.0))));
	elseif (y <= 65000.0)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -8.5e+43)
		tmp = t_1;
	elseif (y <= 8.1e-116)
		tmp = x + (z + (b * (t + -2.0)));
	elseif (y <= 65000.0)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+43], t$95$1, If[LessEqual[y, 8.1e-116], N[(x + N[(z + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 65000.0], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5e43 or 65000 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 67.9%

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

   if -8.5e43 < y < 8.1e-116

   1. Initial program 97.5%

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

   3. Taylor expanded in a around 0 74.1%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. associate--l+ 72.8%

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

      2. sub-neg 72.8%

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

      3. metadata-eval 72.8%

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

      4. neg-mul-1 72.8%

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

   6. Simplified 72.8%

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

   if 8.1e-116 < y < 65000

   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 94.3%

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

   4. Taylor expanded in b around 0 81.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{-116}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;y \leq 65000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 24.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.3e+79)
   (* b t)
   (if (<= t 4.6e-145) x (if (<= t 6e+173) (* z (- y)) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.3e+79) {
		tmp = b * t;
	} else if (t <= 4.6e-145) {
		tmp = x;
	} else if (t <= 6e+173) {
		tmp = z * -y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.3d+79)) then
        tmp = b * t
    else if (t <= 4.6d-145) then
        tmp = x
    else if (t <= 6d+173) then
        tmp = z * -y
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.3e+79) {
		tmp = b * t;
	} else if (t <= 4.6e-145) {
		tmp = x;
	} else if (t <= 6e+173) {
		tmp = z * -y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.3e+79:
		tmp = b * t
	elif t <= 4.6e-145:
		tmp = x
	elif t <= 6e+173:
		tmp = z * -y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.3e+79)
		tmp = Float64(b * t);
	elseif (t <= 4.6e-145)
		tmp = x;
	elseif (t <= 6e+173)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.3e+79)
		tmp = b * t;
	elseif (t <= 4.6e-145)
		tmp = x;
	elseif (t <= 6e+173)
		tmp = z * -y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.3e+79], N[(b * t), $MachinePrecision], If[LessEqual[t, 4.6e-145], x, If[LessEqual[t, 6e+173], N[(z * (-y)), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.29999999999999978e79 or 5.9999999999999995e173 < t

   1. Initial program 91.1%

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

   3. Taylor expanded in t around inf 75.8%

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

   4. Taylor expanded in b around inf 51.7%

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

      1. *-commutative 51.7%

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

   6. Simplified 51.7%

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

   if -5.29999999999999978e79 < t < 4.60000000000000014e-145

   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 28.5%

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

   if 4.60000000000000014e-145 < t < 5.9999999999999995e173

   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 40.1%

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

   4. Taylor expanded in y around inf 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

      3. distribute-rgt-neg-in 29.0%

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

   6. Simplified 29.0%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+44} \lor \neg \left(y \leq 9600000000000\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e+44) (not (<= y 9600000000000.0)))
   (* y (- b z))
   (* t (- b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+44) || !(y <= 9600000000000.0)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.6d+44)) .or. (.not. (y <= 9600000000000.0d0))) then
        tmp = y * (b - z)
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+44) || !(y <= 9600000000000.0)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6e+44) or not (y <= 9600000000000.0):
		tmp = y * (b - z)
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6e+44) || !(y <= 9600000000000.0))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.6e+44) || ~((y <= 9600000000000.0)))
		tmp = y * (b - z);
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6e+44], N[Not[LessEqual[y, 9600000000000.0]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000002e44 or 9.6e12 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 70.0%

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

   if -5.6000000000000002e44 < y < 9.6e12

   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 t around inf 44.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+44} \lor \neg \left(y \leq 9600000000000\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 24.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+80} \lor \neg \left(t \leq 3.5 \cdot 10^{+40}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.3e+80) (not (<= t 3.5e+40))) (* b t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e+80) || !(t <= 3.5e+40)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.3d+80)) .or. (.not. (t <= 3.5d+40))) then
        tmp = b * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.3e+80) || !(t <= 3.5e+40)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.3e+80) or not (t <= 3.5e+40):
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.3e+80) || !(t <= 3.5e+40))
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.3e+80) || ~((t <= 3.5e+40)))
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.3e+80], N[Not[LessEqual[t, 3.5e+40]], $MachinePrecision]], N[(b * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999991e80 or 3.4999999999999999e40 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 72.0%

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

   4. Taylor expanded in b around inf 44.0%

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

      1. *-commutative 44.0%

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

   6. Simplified 44.0%

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

   if -3.29999999999999991e80 < t < 3.4999999999999999e40

   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 x around inf 25.0%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+80} \lor \neg \left(t \leq 3.5 \cdot 10^{+40}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+40} \lor \neg \left(b \leq 0.00045\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e+40) (not (<= b 0.00045))) (* b y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+40) || !(b <= 0.00045)) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3d+40)) .or. (.not. (b <= 0.00045d0))) then
        tmp = b * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+40) || !(b <= 0.00045)) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3e+40) or not (b <= 0.00045):
		tmp = b * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e+40) || !(b <= 0.00045))
		tmp = Float64(b * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3e+40) || ~((b <= 0.00045)))
		tmp = b * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e+40], N[Not[LessEqual[b, 0.00045]], $MachinePrecision]], N[(b * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -3.0000000000000002e40 or 4.4999999999999999e-4 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 81.1%

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

   4. Taylor expanded in y around inf 29.4%

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

   if -3.0000000000000002e40 < b < 4.4999999999999999e-4

   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 24.7%

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

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+40} \lor \neg \left(b \leq 0.00045\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 20.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-47}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1e+70) x (if (<= x 2.3e-47) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+70) {
		tmp = x;
	} else if (x <= 2.3e-47) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1d+70)) then
        tmp = x
    else if (x <= 2.3d-47) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+70) {
		tmp = x;
	} else if (x <= 2.3e-47) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1e+70:
		tmp = x
	elif x <= 2.3e-47:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1e+70)
		tmp = x;
	elseif (x <= 2.3e-47)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1e+70)
		tmp = x;
	elseif (x <= 2.3e-47)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1e+70], x, If[LessEqual[x, 2.3e-47], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000007e70 or 2.29999999999999982e-47 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 30.7%

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

   if -1.00000000000000007e70 < x < 2.29999999999999982e-47

   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 z around inf 33.0%

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

   4. Taylor expanded in y around 0 15.7%

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

Alternative 18: 15.8% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in x around inf 16.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024091 
(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)))