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

Percentage Accurate: 94.9% → 98.4%

Time: 16.1s

Alternatives: 20

Speedup: 0.5×

• 37.1% 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: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 33.3%

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

      1. mul-1-neg 33.3%

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

      2. distribute-rgt-neg-in 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in t around inf 66.7%

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

      1. associate-+r+ 66.7%

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

      2. mul-1-neg 66.7%

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

      3. sub-neg 66.7%

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

      4. associate-/l* 88.9%

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

      5. sub-neg 88.9%

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

      6. metadata-eval 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 99.6%

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

Alternative 2: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 98.0%

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

   3. associate--l+ 98.0%

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

   4. sub-neg 98.0%

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

   5. metadata-eval 98.0%

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

   6. sub-neg 98.0%

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

   7. associate-+l- 98.0%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+26}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -3.2e+49)
     t_2
     (if (<= b -6.6e+36)
       t_1
       (if (<= b -3.2e-19)
         t_2
         (if (<= b 2.65e-187)
           (- x (* y z))
           (if (<= b 5.9e-24) t_1 (if (<= b 3e+26) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.2e+49) {
		tmp = t_2;
	} else if (b <= -6.6e+36) {
		tmp = t_1;
	} else if (b <= -3.2e-19) {
		tmp = t_2;
	} else if (b <= 2.65e-187) {
		tmp = x - (y * z);
	} else if (b <= 5.9e-24) {
		tmp = t_1;
	} else if (b <= 3e+26) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-3.2d+49)) then
        tmp = t_2
    else if (b <= (-6.6d+36)) then
        tmp = t_1
    else if (b <= (-3.2d-19)) then
        tmp = t_2
    else if (b <= 2.65d-187) then
        tmp = x - (y * z)
    else if (b <= 5.9d-24) then
        tmp = t_1
    else if (b <= 3d+26) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.2e+49) {
		tmp = t_2;
	} else if (b <= -6.6e+36) {
		tmp = t_1;
	} else if (b <= -3.2e-19) {
		tmp = t_2;
	} else if (b <= 2.65e-187) {
		tmp = x - (y * z);
	} else if (b <= 5.9e-24) {
		tmp = t_1;
	} else if (b <= 3e+26) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -3.2e+49:
		tmp = t_2
	elif b <= -6.6e+36:
		tmp = t_1
	elif b <= -3.2e-19:
		tmp = t_2
	elif b <= 2.65e-187:
		tmp = x - (y * z)
	elif b <= 5.9e-24:
		tmp = t_1
	elif b <= 3e+26:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -3.2e+49)
		tmp = t_2;
	elseif (b <= -6.6e+36)
		tmp = t_1;
	elseif (b <= -3.2e-19)
		tmp = t_2;
	elseif (b <= 2.65e-187)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 5.9e-24)
		tmp = t_1;
	elseif (b <= 3e+26)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -3.2e+49)
		tmp = t_2;
	elseif (b <= -6.6e+36)
		tmp = t_1;
	elseif (b <= -3.2e-19)
		tmp = t_2;
	elseif (b <= 2.65e-187)
		tmp = x - (y * z);
	elseif (b <= 5.9e-24)
		tmp = t_1;
	elseif (b <= 3e+26)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+49], t$95$2, If[LessEqual[b, -6.6e+36], t$95$1, If[LessEqual[b, -3.2e-19], t$95$2, If[LessEqual[b, 2.65e-187], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e-24], t$95$1, If[LessEqual[b, 3e+26], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.20000000000000014e49 or -6.5999999999999997e36 < b < -3.19999999999999982e-19 or 2.99999999999999997e26 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 70.1%

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

   if -3.20000000000000014e49 < b < -6.5999999999999997e36 or 2.65000000000000001e-187 < b < 5.9000000000000002e-24

   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 58.4%

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

   if -3.19999999999999982e-19 < b < 2.65000000000000001e-187

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 66.3%

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

   4. Taylor expanded in b around 0 60.0%

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

   5. Taylor expanded in y around inf 51.7%

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

   if 5.9000000000000002e-24 < b < 2.99999999999999997e26

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 88.7%

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

   4. Taylor expanded in y around 0 81.8%

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

      1. associate--l+ 81.8%

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

      2. sub-neg 81.8%

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

      3. metadata-eval 81.8%

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

      4. neg-mul-1 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in b around 0 68.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+26}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{-190}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -2.25e+49)
     t_2
     (if (<= b -7.8e+36)
       t_1
       (if (<= b -2.5e-15)
         t_2
         (if (<= b 1.76e-190)
           t_3
           (if (<= b 1.1e-24) t_1 (if (<= b 2.6e+28) 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 = b * ((y + t) - 2.0);
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -2.25e+49) {
		tmp = t_2;
	} else if (b <= -7.8e+36) {
		tmp = t_1;
	} else if (b <= -2.5e-15) {
		tmp = t_2;
	} else if (b <= 1.76e-190) {
		tmp = t_3;
	} else if (b <= 1.1e-24) {
		tmp = t_1;
	} else if (b <= 2.6e+28) {
		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 = b * ((y + t) - 2.0d0)
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-2.25d+49)) then
        tmp = t_2
    else if (b <= (-7.8d+36)) then
        tmp = t_1
    else if (b <= (-2.5d-15)) then
        tmp = t_2
    else if (b <= 1.76d-190) then
        tmp = t_3
    else if (b <= 1.1d-24) then
        tmp = t_1
    else if (b <= 2.6d+28) 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 = b * ((y + t) - 2.0);
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -2.25e+49) {
		tmp = t_2;
	} else if (b <= -7.8e+36) {
		tmp = t_1;
	} else if (b <= -2.5e-15) {
		tmp = t_2;
	} else if (b <= 1.76e-190) {
		tmp = t_3;
	} else if (b <= 1.1e-24) {
		tmp = t_1;
	} else if (b <= 2.6e+28) {
		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 = b * ((y + t) - 2.0)
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -2.25e+49:
		tmp = t_2
	elif b <= -7.8e+36:
		tmp = t_1
	elif b <= -2.5e-15:
		tmp = t_2
	elif b <= 1.76e-190:
		tmp = t_3
	elif b <= 1.1e-24:
		tmp = t_1
	elif b <= 2.6e+28:
		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(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -2.25e+49)
		tmp = t_2;
	elseif (b <= -7.8e+36)
		tmp = t_1;
	elseif (b <= -2.5e-15)
		tmp = t_2;
	elseif (b <= 1.76e-190)
		tmp = t_3;
	elseif (b <= 1.1e-24)
		tmp = t_1;
	elseif (b <= 2.6e+28)
		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 = b * ((y + t) - 2.0);
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -2.25e+49)
		tmp = t_2;
	elseif (b <= -7.8e+36)
		tmp = t_1;
	elseif (b <= -2.5e-15)
		tmp = t_2;
	elseif (b <= 1.76e-190)
		tmp = t_3;
	elseif (b <= 1.1e-24)
		tmp = t_1;
	elseif (b <= 2.6e+28)
		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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.25e+49], t$95$2, If[LessEqual[b, -7.8e+36], t$95$1, If[LessEqual[b, -2.5e-15], t$95$2, If[LessEqual[b, 1.76e-190], t$95$3, If[LessEqual[b, 1.1e-24], t$95$1, If[LessEqual[b, 2.6e+28], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.24999999999999991e49 or -7.80000000000000042e36 < b < -2.5e-15 or 2.6000000000000002e28 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 70.1%

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

   if -2.24999999999999991e49 < b < -7.80000000000000042e36 or 1.75999999999999998e-190 < b < 1.10000000000000001e-24

   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 58.4%

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

   if -2.5e-15 < b < 1.75999999999999998e-190 or 1.10000000000000001e-24 < b < 2.6000000000000002e28

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 69.4%

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

   4. Taylor expanded in b around 0 62.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{-190}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-218}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+124}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.06e+48)
     t_1
     (if (<= t -5e-33)
       (+ x z)
       (if (<= t -8e-260)
         (* y (- b z))
         (if (<= t 9e-218)
           (+ x z)
           (if (<= t 1.3e-102)
             (* b (- y 2.0))
             (if (<= t 2.8e+124) (- x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.06e+48) {
		tmp = t_1;
	} else if (t <= -5e-33) {
		tmp = x + z;
	} else if (t <= -8e-260) {
		tmp = y * (b - z);
	} else if (t <= 9e-218) {
		tmp = x + z;
	} else if (t <= 1.3e-102) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.8e+124) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.06d+48)) then
        tmp = t_1
    else if (t <= (-5d-33)) then
        tmp = x + z
    else if (t <= (-8d-260)) then
        tmp = y * (b - z)
    else if (t <= 9d-218) then
        tmp = x + z
    else if (t <= 1.3d-102) then
        tmp = b * (y - 2.0d0)
    else if (t <= 2.8d+124) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.06e+48) {
		tmp = t_1;
	} else if (t <= -5e-33) {
		tmp = x + z;
	} else if (t <= -8e-260) {
		tmp = y * (b - z);
	} else if (t <= 9e-218) {
		tmp = x + z;
	} else if (t <= 1.3e-102) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.8e+124) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.06e+48:
		tmp = t_1
	elif t <= -5e-33:
		tmp = x + z
	elif t <= -8e-260:
		tmp = y * (b - z)
	elif t <= 9e-218:
		tmp = x + z
	elif t <= 1.3e-102:
		tmp = b * (y - 2.0)
	elif t <= 2.8e+124:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.06e+48)
		tmp = t_1;
	elseif (t <= -5e-33)
		tmp = Float64(x + z);
	elseif (t <= -8e-260)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 9e-218)
		tmp = Float64(x + z);
	elseif (t <= 1.3e-102)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 2.8e+124)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.06e+48)
		tmp = t_1;
	elseif (t <= -5e-33)
		tmp = x + z;
	elseif (t <= -8e-260)
		tmp = y * (b - z);
	elseif (t <= 9e-218)
		tmp = x + z;
	elseif (t <= 1.3e-102)
		tmp = b * (y - 2.0);
	elseif (t <= 2.8e+124)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+48], t$95$1, If[LessEqual[t, -5e-33], N[(x + z), $MachinePrecision], If[LessEqual[t, -8e-260], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-218], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.3e-102], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+124], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.06e48 or 2.8e124 < t

   1. Initial program 92.8%

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

   3. Taylor expanded in t around inf 75.0%

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

   if -1.06e48 < t < -5.00000000000000028e-33 or -7.99999999999999969e-260 < t < 8.99999999999999953e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 80.4%

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

   4. Taylor expanded in y around 0 59.1%

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

      1. associate--l+ 59.1%

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

      2. sub-neg 59.1%

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

      3. metadata-eval 59.1%

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

      4. neg-mul-1 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in b around 0 49.6%

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

   if -5.00000000000000028e-33 < t < -7.99999999999999969e-260

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf 49.8%

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

   if 8.99999999999999953e-218 < t < 1.29999999999999993e-102

   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 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-rgt-neg-in 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in t around 0 54.5%

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

   if 1.29999999999999993e-102 < t < 2.8e124

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in b around 0 54.1%

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

   5. Taylor expanded in y around inf 42.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-218}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+124}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-216}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -8.5e+47)
     t_2
     (if (<= t -5.8e-31)
       (+ x z)
       (if (<= t -4.4e-274)
         t_1
         (if (<= t 1.25e-216) (+ x z) (if (<= t 1.3e+38) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.5e+47) {
		tmp = t_2;
	} else if (t <= -5.8e-31) {
		tmp = x + z;
	} else if (t <= -4.4e-274) {
		tmp = t_1;
	} else if (t <= 1.25e-216) {
		tmp = x + z;
	} else if (t <= 1.3e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-8.5d+47)) then
        tmp = t_2
    else if (t <= (-5.8d-31)) then
        tmp = x + z
    else if (t <= (-4.4d-274)) then
        tmp = t_1
    else if (t <= 1.25d-216) then
        tmp = x + z
    else if (t <= 1.3d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.5e+47) {
		tmp = t_2;
	} else if (t <= -5.8e-31) {
		tmp = x + z;
	} else if (t <= -4.4e-274) {
		tmp = t_1;
	} else if (t <= 1.25e-216) {
		tmp = x + z;
	} else if (t <= 1.3e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8.5e+47:
		tmp = t_2
	elif t <= -5.8e-31:
		tmp = x + z
	elif t <= -4.4e-274:
		tmp = t_1
	elif t <= 1.25e-216:
		tmp = x + z
	elif t <= 1.3e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.5e+47)
		tmp = t_2;
	elseif (t <= -5.8e-31)
		tmp = Float64(x + z);
	elseif (t <= -4.4e-274)
		tmp = t_1;
	elseif (t <= 1.25e-216)
		tmp = Float64(x + z);
	elseif (t <= 1.3e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.5e+47)
		tmp = t_2;
	elseif (t <= -5.8e-31)
		tmp = x + z;
	elseif (t <= -4.4e-274)
		tmp = t_1;
	elseif (t <= 1.25e-216)
		tmp = x + z;
	elseif (t <= 1.3e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+47], t$95$2, If[LessEqual[t, -5.8e-31], N[(x + z), $MachinePrecision], If[LessEqual[t, -4.4e-274], t$95$1, If[LessEqual[t, 1.25e-216], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.3e+38], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5000000000000008e47 or 1.3e38 < t

   1. Initial program 93.9%

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

   3. Taylor expanded in t around inf 67.9%

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

   if -8.5000000000000008e47 < t < -5.8000000000000001e-31 or -4.3999999999999999e-274 < t < 1.25000000000000005e-216

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 80.8%

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

   4. Taylor expanded in y around 0 57.4%

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

      1. associate--l+ 57.4%

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

      2. sub-neg 57.4%

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

      3. metadata-eval 57.4%

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

      4. neg-mul-1 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in b around 0 52.1%

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

   if -5.8000000000000001e-31 < t < -4.3999999999999999e-274 or 1.25000000000000005e-216 < t < 1.3e38

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-rgt-neg-in 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in t around 0 39.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-216}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+23}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -7.5e+31)
     t_2
     (if (<= y -5e-186)
       t_1
       (if (<= y -1.9e-269)
         (+ x z)
         (if (<= y 3.9e-283) t_1 (if (<= y 1.85e+23) (+ x z) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.5e+31) {
		tmp = t_2;
	} else if (y <= -5e-186) {
		tmp = t_1;
	} else if (y <= -1.9e-269) {
		tmp = x + z;
	} else if (y <= 3.9e-283) {
		tmp = t_1;
	} else if (y <= 1.85e+23) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-7.5d+31)) then
        tmp = t_2
    else if (y <= (-5d-186)) then
        tmp = t_1
    else if (y <= (-1.9d-269)) then
        tmp = x + z
    else if (y <= 3.9d-283) then
        tmp = t_1
    else if (y <= 1.85d+23) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.5e+31) {
		tmp = t_2;
	} else if (y <= -5e-186) {
		tmp = t_1;
	} else if (y <= -1.9e-269) {
		tmp = x + z;
	} else if (y <= 3.9e-283) {
		tmp = t_1;
	} else if (y <= 1.85e+23) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -7.5e+31:
		tmp = t_2
	elif y <= -5e-186:
		tmp = t_1
	elif y <= -1.9e-269:
		tmp = x + z
	elif y <= 3.9e-283:
		tmp = t_1
	elif y <= 1.85e+23:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.5e+31)
		tmp = t_2;
	elseif (y <= -5e-186)
		tmp = t_1;
	elseif (y <= -1.9e-269)
		tmp = Float64(x + z);
	elseif (y <= 3.9e-283)
		tmp = t_1;
	elseif (y <= 1.85e+23)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.5e+31)
		tmp = t_2;
	elseif (y <= -5e-186)
		tmp = t_1;
	elseif (y <= -1.9e-269)
		tmp = x + z;
	elseif (y <= 3.9e-283)
		tmp = t_1;
	elseif (y <= 1.85e+23)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+31], t$95$2, If[LessEqual[y, -5e-186], t$95$1, If[LessEqual[y, -1.9e-269], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.9e-283], t$95$1, If[LessEqual[y, 1.85e+23], N[(x + z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e31 or 1.85000000000000006e23 < y

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 64.8%

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

   if -7.5e31 < y < -5e-186 or -1.9000000000000001e-269 < y < 3.9000000000000002e-283

   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 48.9%

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

   if -5e-186 < y < -1.9000000000000001e-269 or 3.9000000000000002e-283 < y < 1.85000000000000006e23

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. associate--l+ 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

      4. neg-mul-1 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in b around 0 50.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-283}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+23}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -4.4e-14)
     t_2
     (if (<= b 7.2e-187)
       t_1
       (if (<= b 4.5e-21) (* a (- 1.0 t)) (if (<= b 5e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -4.4e-14) {
		tmp = t_2;
	} else if (b <= 7.2e-187) {
		tmp = t_1;
	} else if (b <= 4.5e-21) {
		tmp = a * (1.0 - t);
	} else if (b <= 5e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-4.4d-14)) then
        tmp = t_2
    else if (b <= 7.2d-187) then
        tmp = t_1
    else if (b <= 4.5d-21) then
        tmp = a * (1.0d0 - t)
    else if (b <= 5d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -4.4e-14) {
		tmp = t_2;
	} else if (b <= 7.2e-187) {
		tmp = t_1;
	} else if (b <= 4.5e-21) {
		tmp = a * (1.0 - t);
	} else if (b <= 5e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -4.4e-14:
		tmp = t_2
	elif b <= 7.2e-187:
		tmp = t_1
	elif b <= 4.5e-21:
		tmp = a * (1.0 - t)
	elif b <= 5e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -4.4e-14)
		tmp = t_2;
	elseif (b <= 7.2e-187)
		tmp = t_1;
	elseif (b <= 4.5e-21)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 5e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -4.4e-14)
		tmp = t_2;
	elseif (b <= 7.2e-187)
		tmp = t_1;
	elseif (b <= 4.5e-21)
		tmp = a * (1.0 - t);
	elseif (b <= 5e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e-14], t$95$2, If[LessEqual[b, 7.2e-187], t$95$1, If[LessEqual[b, 4.5e-21], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4000000000000002e-14 or 5e14 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in a around 0 81.0%

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

   4. Taylor expanded in z around 0 78.2%

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

   if -4.4000000000000002e-14 < b < 7.19999999999999989e-187 or 4.49999999999999968e-21 < b < 5e14

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 69.1%

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

   4. Taylor expanded in b around 0 61.8%

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

   if 7.19999999999999989e-187 < b < 4.49999999999999968e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 53.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-14}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-187}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+25}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.3e+74)
     t_1
     (if (<= y -2.8e-51)
       (+ x (* b (- (+ y t) 2.0)))
       (if (<= y -5.4e-74)
         (* a (- 1.0 t))
         (if (<= y 1.78e+25) (+ x (+ z (* (+ t -2.0) b))) 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 <= -1.3e+74) {
		tmp = t_1;
	} else if (y <= -2.8e-51) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -5.4e-74) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.78e+25) {
		tmp = x + (z + ((t + -2.0) * b));
	} 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 <= (-1.3d+74)) then
        tmp = t_1
    else if (y <= (-2.8d-51)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (y <= (-5.4d-74)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.78d+25) then
        tmp = x + (z + ((t + (-2.0d0)) * b))
    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 <= -1.3e+74) {
		tmp = t_1;
	} else if (y <= -2.8e-51) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -5.4e-74) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.78e+25) {
		tmp = x + (z + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.3e+74:
		tmp = t_1
	elif y <= -2.8e-51:
		tmp = x + (b * ((y + t) - 2.0))
	elif y <= -5.4e-74:
		tmp = a * (1.0 - t)
	elif y <= 1.78e+25:
		tmp = x + (z + ((t + -2.0) * b))
	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 <= -1.3e+74)
		tmp = t_1;
	elseif (y <= -2.8e-51)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (y <= -5.4e-74)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.78e+25)
		tmp = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)));
	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 <= -1.3e+74)
		tmp = t_1;
	elseif (y <= -2.8e-51)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (y <= -5.4e-74)
		tmp = a * (1.0 - t);
	elseif (y <= 1.78e+25)
		tmp = x + (z + ((t + -2.0) * b));
	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, -1.3e+74], t$95$1, If[LessEqual[y, -2.8e-51], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.4e-74], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.78e+25], N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e74 or 1.78000000000000005e25 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 66.1%

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

   if -1.3e74 < y < -2.8e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 73.4%

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

   4. Taylor expanded in z around 0 69.2%

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

   if -2.8e-51 < y < -5.40000000000000036e-74

   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 75.4%

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

   if -5.40000000000000036e-74 < y < 1.78000000000000005e25

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0 73.2%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. associate--l+ 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

      4. neg-mul-1 71.9%

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

   6. Simplified 71.9%

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

      1. sub-neg 71.9%

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

      2. add-sqr-sqrt 28.3%

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

      3. sqrt-unprod 51.9%

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

      4. sqr-neg 51.9%

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

      5. sqrt-unprod 35.8%

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

      6. add-sqr-sqrt 56.7%

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

      7. add-sqr-sqrt 20.9%

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

      8. sqrt-unprod 52.8%

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

      9. sqr-neg 52.8%

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

      10. sqrt-unprod 43.5%

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

      11. add-sqr-sqrt 71.9%

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

   8. Applied egg-rr 71.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+25}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + -2 \cdot b\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4500000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* -2.0 b)))) (t_2 (* y (- b z))))
   (if (<= y -4500000000.0)
     t_2
     (if (<= y -2.8e-51)
       t_1
       (if (<= y -2e-156) (* a (- 1.0 t)) (if (<= y 9.5e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (-2.0 * b));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4500000000.0) {
		tmp = t_2;
	} else if (y <= -2.8e-51) {
		tmp = t_1;
	} else if (y <= -2e-156) {
		tmp = a * (1.0 - t);
	} else if (y <= 9.5e+24) {
		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 + ((-2.0d0) * b))
    t_2 = y * (b - z)
    if (y <= (-4500000000.0d0)) then
        tmp = t_2
    else if (y <= (-2.8d-51)) then
        tmp = t_1
    else if (y <= (-2d-156)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 9.5d+24) 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 + (-2.0 * b));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4500000000.0) {
		tmp = t_2;
	} else if (y <= -2.8e-51) {
		tmp = t_1;
	} else if (y <= -2e-156) {
		tmp = a * (1.0 - t);
	} else if (y <= 9.5e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (-2.0 * b))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -4500000000.0:
		tmp = t_2
	elif y <= -2.8e-51:
		tmp = t_1
	elif y <= -2e-156:
		tmp = a * (1.0 - t)
	elif y <= 9.5e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(-2.0 * b)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4500000000.0)
		tmp = t_2;
	elseif (y <= -2.8e-51)
		tmp = t_1;
	elseif (y <= -2e-156)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 9.5e+24)
		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 + (-2.0 * b));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -4500000000.0)
		tmp = t_2;
	elseif (y <= -2.8e-51)
		tmp = t_1;
	elseif (y <= -2e-156)
		tmp = a * (1.0 - t);
	elseif (y <= 9.5e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4500000000.0], t$95$2, If[LessEqual[y, -2.8e-51], t$95$1, If[LessEqual[y, -2e-156], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e9 or 9.5000000000000001e24 < y

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 63.8%

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

   if -4.5e9 < y < -2.8e-51 or -2.00000000000000008e-156 < y < 9.5000000000000001e24

   1. Initial program 99.1%

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

   3. Taylor expanded in a around 0 75.9%

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

   4. Taylor expanded in y around 0 74.5%

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

      1. associate--l+ 74.5%

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

      2. sub-neg 74.5%

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

      3. metadata-eval 74.5%

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

      4. neg-mul-1 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in t around 0 56.6%

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

      1. *-commutative 56.6%

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

   9. Simplified 56.6%

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

   if -2.8e-51 < y < -2.00000000000000008e-156

   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 58.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4500000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-51}:\\ \;\;\;\;x + \left(z + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;x + \left(z + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-153}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -2.5e-51)
     t_1
     (if (<= a -6.5e-153)
       (+ x z)
       (if (<= a -9.5e-170) (* y b) (if (<= a 3.6e+25) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.5e-51) {
		tmp = t_1;
	} else if (a <= -6.5e-153) {
		tmp = x + z;
	} else if (a <= -9.5e-170) {
		tmp = y * b;
	} else if (a <= 3.6e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-2.5d-51)) then
        tmp = t_1
    else if (a <= (-6.5d-153)) then
        tmp = x + z
    else if (a <= (-9.5d-170)) then
        tmp = y * b
    else if (a <= 3.6d+25) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.5e-51) {
		tmp = t_1;
	} else if (a <= -6.5e-153) {
		tmp = x + z;
	} else if (a <= -9.5e-170) {
		tmp = y * b;
	} else if (a <= 3.6e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -2.5e-51:
		tmp = t_1
	elif a <= -6.5e-153:
		tmp = x + z
	elif a <= -9.5e-170:
		tmp = y * b
	elif a <= 3.6e+25:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.5e-51)
		tmp = t_1;
	elseif (a <= -6.5e-153)
		tmp = Float64(x + z);
	elseif (a <= -9.5e-170)
		tmp = Float64(y * b);
	elseif (a <= 3.6e+25)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.5e-51)
		tmp = t_1;
	elseif (a <= -6.5e-153)
		tmp = x + z;
	elseif (a <= -9.5e-170)
		tmp = y * b;
	elseif (a <= 3.6e+25)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-51], t$95$1, If[LessEqual[a, -6.5e-153], N[(x + z), $MachinePrecision], If[LessEqual[a, -9.5e-170], N[(y * b), $MachinePrecision], If[LessEqual[a, 3.6e+25], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.50000000000000002e-51 or 3.60000000000000015e25 < a

   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 a around inf 50.2%

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

   if -2.50000000000000002e-51 < a < -6.50000000000000032e-153 or -9.5000000000000001e-170 < a < 3.60000000000000015e25

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0 91.6%

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

   4. Taylor expanded in y around 0 62.0%

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

      1. associate--l+ 62.0%

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

      2. sub-neg 62.0%

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

      3. metadata-eval 62.0%

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

      4. neg-mul-1 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in b around 0 39.0%

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

   if -6.50000000000000032e-153 < a < -9.5000000000000001e-170

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 69.5%

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

   4. Taylor expanded in b around inf 69.6%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-153}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-225}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.8e-51)
     t_1
     (if (<= a -2.35e-225)
       (+ x z)
       (if (<= a -2.4e-279)
         (* b (- y 2.0))
         (if (<= a 3.2e+25) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.8e-51) {
		tmp = t_1;
	} else if (a <= -2.35e-225) {
		tmp = x + z;
	} else if (a <= -2.4e-279) {
		tmp = b * (y - 2.0);
	} else if (a <= 3.2e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.8d-51)) then
        tmp = t_1
    else if (a <= (-2.35d-225)) then
        tmp = x + z
    else if (a <= (-2.4d-279)) then
        tmp = b * (y - 2.0d0)
    else if (a <= 3.2d+25) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.8e-51) {
		tmp = t_1;
	} else if (a <= -2.35e-225) {
		tmp = x + z;
	} else if (a <= -2.4e-279) {
		tmp = b * (y - 2.0);
	} else if (a <= 3.2e+25) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.8e-51:
		tmp = t_1
	elif a <= -2.35e-225:
		tmp = x + z
	elif a <= -2.4e-279:
		tmp = b * (y - 2.0)
	elif a <= 3.2e+25:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.8e-51)
		tmp = t_1;
	elseif (a <= -2.35e-225)
		tmp = Float64(x + z);
	elseif (a <= -2.4e-279)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (a <= 3.2e+25)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.8e-51)
		tmp = t_1;
	elseif (a <= -2.35e-225)
		tmp = x + z;
	elseif (a <= -2.4e-279)
		tmp = b * (y - 2.0);
	elseif (a <= 3.2e+25)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e-51], t$95$1, If[LessEqual[a, -2.35e-225], N[(x + z), $MachinePrecision], If[LessEqual[a, -2.4e-279], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+25], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e-51 or 3.1999999999999999e25 < a

   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 a around inf 50.2%

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

   if -1.8e-51 < a < -2.35000000000000007e-225 or -2.3999999999999999e-279 < a < 3.1999999999999999e25

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 89.9%

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

   4. Taylor expanded in y around 0 62.3%

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

      1. associate--l+ 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. neg-mul-1 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in b around 0 39.5%

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

   if -2.35000000000000007e-225 < a < -2.3999999999999999e-279

   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 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around 0 64.1%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-225}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-17} \lor \neg \left(b \leq 200000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e-17) (not (<= b 200000000000.0)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (+ (- x (* t a)) (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-17) || !(b <= 200000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.1d-17)) .or. (.not. (b <= 200000000000.0d0))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = (x - (t * a)) + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-17) || !(b <= 200000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.1e-17) or not (b <= 200000000000.0):
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.1e-17) || !(b <= 200000000000.0))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(x - Float64(t * a)) + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.1e-17) || ~((b <= 200000000000.0)))
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e-17], N[Not[LessEqual[b, 200000000000.0]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e-17 or 2e11 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 90.8%

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

   if -1.1e-17 < b < 2e11

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 99.2%

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

   4. Taylor expanded in b around 0 90.6%

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

      1. sub-neg 90.6%

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

      2. mul-1-neg 90.6%

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

      3. *-commutative 90.6%

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

      4. unsub-neg 90.6%

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

      5. sub-neg 90.6%

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

      6. metadata-eval 90.6%

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

      7. *-commutative 90.6%

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

      8. distribute-neg-in 90.6%

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

      9. mul-1-neg 90.6%

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

      10. remove-double-neg 90.6%

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

      11. sub-neg 90.6%

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

      12. *-commutative 90.6%

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

   6. Simplified 90.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-17} \lor \neg \left(b \leq 200000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -51000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.2e+74)
     t_1
     (if (<= y -51000000.0)
       (- (* b (- (+ y t) 2.0)) (* t a))
       (if (<= y 6e+24) (+ x (+ z (* (+ t -2.0) b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.2e+74) {
		tmp = t_1;
	} else if (y <= -51000000.0) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (y <= 6e+24) {
		tmp = x + (z + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-6.2d+74)) then
        tmp = t_1
    else if (y <= (-51000000.0d0)) then
        tmp = (b * ((y + t) - 2.0d0)) - (t * a)
    else if (y <= 6d+24) then
        tmp = x + (z + ((t + (-2.0d0)) * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.2e+74) {
		tmp = t_1;
	} else if (y <= -51000000.0) {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	} else if (y <= 6e+24) {
		tmp = x + (z + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6.2e+74:
		tmp = t_1
	elif y <= -51000000.0:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	elif y <= 6e+24:
		tmp = x + (z + ((t + -2.0) * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.2e+74)
		tmp = t_1;
	elseif (y <= -51000000.0)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	elseif (y <= 6e+24)
		tmp = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.2e+74)
		tmp = t_1;
	elseif (y <= -51000000.0)
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	elseif (y <= 6e+24)
		tmp = x + (z + ((t + -2.0) * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+74], t$95$1, If[LessEqual[y, -51000000.0], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+24], N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000043e74 or 5.9999999999999999e24 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 66.1%

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

   if -6.20000000000000043e74 < y < -5.1e7

   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 t around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

   5. Simplified 80.7%

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

   if -5.1e7 < y < 5.9999999999999999e24

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 71.6%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. associate--l+ 70.4%

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

      2. sub-neg 70.4%

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

      3. metadata-eval 70.4%

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

      4. neg-mul-1 70.4%

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

   6. Simplified 70.4%

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

      1. sub-neg 70.4%

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

      2. add-sqr-sqrt 28.8%

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

      3. sqrt-unprod 51.9%

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

      4. sqr-neg 51.9%

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

      5. sqrt-unprod 34.0%

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

      6. add-sqr-sqrt 56.2%

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

      7. add-sqr-sqrt 22.2%

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

      8. sqrt-unprod 54.1%

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

      9. sqr-neg 54.1%

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

      10. sqrt-unprod 41.5%

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

      11. add-sqr-sqrt 70.4%

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

   8. Applied egg-rr 70.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -51000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+24}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -46000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-283}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -46000000.0)
   (* y b)
   (if (<= y -1.25e-269)
     (+ x z)
     (if (<= y 7.8e-283) (* t b) (if (<= y 1.02e+25) (+ x z) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -46000000.0) {
		tmp = y * b;
	} else if (y <= -1.25e-269) {
		tmp = x + z;
	} else if (y <= 7.8e-283) {
		tmp = t * b;
	} else if (y <= 1.02e+25) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-46000000.0d0)) then
        tmp = y * b
    else if (y <= (-1.25d-269)) then
        tmp = x + z
    else if (y <= 7.8d-283) then
        tmp = t * b
    else if (y <= 1.02d+25) then
        tmp = x + z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -46000000.0) {
		tmp = y * b;
	} else if (y <= -1.25e-269) {
		tmp = x + z;
	} else if (y <= 7.8e-283) {
		tmp = t * b;
	} else if (y <= 1.02e+25) {
		tmp = x + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -46000000.0:
		tmp = y * b
	elif y <= -1.25e-269:
		tmp = x + z
	elif y <= 7.8e-283:
		tmp = t * b
	elif y <= 1.02e+25:
		tmp = x + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -46000000.0)
		tmp = Float64(y * b);
	elseif (y <= -1.25e-269)
		tmp = Float64(x + z);
	elseif (y <= 7.8e-283)
		tmp = Float64(t * b);
	elseif (y <= 1.02e+25)
		tmp = Float64(x + z);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -46000000.0)
		tmp = y * b;
	elseif (y <= -1.25e-269)
		tmp = x + z;
	elseif (y <= 7.8e-283)
		tmp = t * b;
	elseif (y <= 1.02e+25)
		tmp = x + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -46000000.0], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.25e-269], N[(x + z), $MachinePrecision], If[LessEqual[y, 7.8e-283], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.02e+25], N[(x + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6e7 or 1.0199999999999999e25 < y

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 63.3%

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

   4. Taylor expanded in b around inf 37.7%

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

   if -4.6e7 < y < -1.24999999999999995e-269 or 7.8000000000000004e-283 < y < 1.0199999999999999e25

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0 70.9%

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

   4. Taylor expanded in y around 0 69.6%

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

      1. associate--l+ 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. neg-mul-1 69.6%

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

   6. Simplified 69.6%

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

   7. Taylor expanded in b around 0 44.5%

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

   if -1.24999999999999995e-269 < y < 7.8000000000000004e-283

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 60.8%

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

   4. Taylor expanded in b around inf 41.7%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -46000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-283}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+49} \lor \neg \left(b \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e+49) (not (<= b 1.1e+57)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ (- x (* t a)) (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+49) || !(b <= 1.1e+57)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5d+49)) .or. (.not. (b <= 1.1d+57))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x - (t * a)) + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+49) || !(b <= 1.1e+57)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e+49) or not (b <= 1.1e+57):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e+49) || !(b <= 1.1e+57))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x - Float64(t * a)) + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5e+49) || ~((b <= 1.1e+57)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x - (t * a)) + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e+49], N[Not[LessEqual[b, 1.1e+57]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.0000000000000004e49 or 1.1e57 < b

   1. Initial program 92.2%

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

   3. Taylor expanded in a around 0 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 84.7%

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

   if -5.0000000000000004e49 < b < 1.1e57

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 99.3%

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

   4. Taylor expanded in b around 0 86.4%

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

      1. sub-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. *-commutative 86.4%

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

      4. unsub-neg 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

      7. *-commutative 86.4%

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

      8. distribute-neg-in 86.4%

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

      9. mul-1-neg 86.4%

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

      10. remove-double-neg 86.4%

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

      11. sub-neg 86.4%

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

      12. *-commutative 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+49} \lor \neg \left(b \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13200000000 \lor \neg \left(y \leq 1.26 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -13200000000.0) (not (<= y 1.26e+26))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -13200000000.0) || !(y <= 1.26e+26)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-13200000000.0d0)) .or. (.not. (y <= 1.26d+26))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -13200000000.0) || !(y <= 1.26e+26)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -13200000000.0) or not (y <= 1.26e+26):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -13200000000.0) || !(y <= 1.26e+26))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -13200000000.0) || ~((y <= 1.26e+26)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -13200000000.0], N[Not[LessEqual[y, 1.26e+26]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e10 or 1.25999999999999995e26 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 64.3%

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

   4. Taylor expanded in b around inf 38.3%

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

   if -1.32e10 < y < 1.25999999999999995e26

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 27.1%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13200000000 \lor \neg \left(y \leq 1.26 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 18.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+101}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.15e+111) x (if (<= x 7.8e+101) (* -2.0 b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.15e+111) {
		tmp = x;
	} else if (x <= 7.8e+101) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.15d+111)) then
        tmp = x
    else if (x <= 7.8d+101) then
        tmp = (-2.0d0) * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.15e+111) {
		tmp = x;
	} else if (x <= 7.8e+101) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.15e+111:
		tmp = x
	elif x <= 7.8e+101:
		tmp = -2.0 * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.15e+111)
		tmp = x;
	elseif (x <= 7.8e+101)
		tmp = Float64(-2.0 * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.15e+111)
		tmp = x;
	elseif (x <= 7.8e+101)
		tmp = -2.0 * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.15e+111], x, If[LessEqual[x, 7.8e+101], N[(-2.0 * b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999997e111 or 7.8e101 < x

   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 49.1%

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

   if -2.14999999999999997e111 < x < 7.8e101

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-rgt-neg-in 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in t around 0 28.1%

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

   7. Taylor expanded in y around 0 11.5%

      \[\leadsto \color{blue}{-2 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 11.5%

         \[\leadsto \color{blue}{b \cdot -2} \]

   9. Simplified 11.5%

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

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+101}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+154) x (if (<= x 1.8e-142) (* t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+154) {
		tmp = x;
	} else if (x <= 1.8e-142) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.5d+154)) then
        tmp = x
    else if (x <= 1.8d-142) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+154) {
		tmp = x;
	} else if (x <= 1.8e-142) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+154:
		tmp = x
	elif x <= 1.8e-142:
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+154)
		tmp = x;
	elseif (x <= 1.8e-142)
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+154)
		tmp = x;
	elseif (x <= 1.8e-142)
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+154], x, If[LessEqual[x, 1.8e-142], N[(t * b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000001e154 or 1.8e-142 < x

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 33.9%

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

   if -9.5000000000000001e154 < x < 1.8e-142

   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 t around inf 42.1%

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

   4. Taylor expanded in b around inf 22.3%

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

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 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 96.5%

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

3. Taylor expanded in x around inf 19.2%

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

4. Final simplification 19.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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)))