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

Percentage Accurate: 95.2% → 97.4%

Time: 18.5s

Alternatives: 25

Speedup: 0.5×

• 36.1% 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: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 98.4%

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

   3. associate--l+ 98.4%

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

   4. sub-neg 98.4%

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

   5. metadata-eval 98.4%

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

   6. sub-neg 98.4%

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

   7. associate-+l- 98.4%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $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 0 37.5%

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

   4. Taylor expanded in z around 0 62.5%

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

4. Final simplification 98.8%

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

Alternative 3: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -66000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-95}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -66000000.0)
     t_2
     (if (<= y -1.75e-56)
       (+ x z)
       (if (<= y 2e-171)
         t_1
         (if (<= y 1.06e-95) (+ x z) (if (<= y 5000000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -66000000.0) {
		tmp = t_2;
	} else if (y <= -1.75e-56) {
		tmp = x + z;
	} else if (y <= 2e-171) {
		tmp = t_1;
	} else if (y <= 1.06e-95) {
		tmp = x + z;
	} else if (y <= 5000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-66000000.0d0)) then
        tmp = t_2
    else if (y <= (-1.75d-56)) then
        tmp = x + z
    else if (y <= 2d-171) then
        tmp = t_1
    else if (y <= 1.06d-95) then
        tmp = x + z
    else if (y <= 5000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -66000000.0) {
		tmp = t_2;
	} else if (y <= -1.75e-56) {
		tmp = x + z;
	} else if (y <= 2e-171) {
		tmp = t_1;
	} else if (y <= 1.06e-95) {
		tmp = x + z;
	} else if (y <= 5000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -66000000.0:
		tmp = t_2
	elif y <= -1.75e-56:
		tmp = x + z
	elif y <= 2e-171:
		tmp = t_1
	elif y <= 1.06e-95:
		tmp = x + z
	elif y <= 5000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -66000000.0)
		tmp = t_2;
	elseif (y <= -1.75e-56)
		tmp = Float64(x + z);
	elseif (y <= 2e-171)
		tmp = t_1;
	elseif (y <= 1.06e-95)
		tmp = Float64(x + z);
	elseif (y <= 5000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -66000000.0)
		tmp = t_2;
	elseif (y <= -1.75e-56)
		tmp = x + z;
	elseif (y <= 2e-171)
		tmp = t_1;
	elseif (y <= 1.06e-95)
		tmp = x + z;
	elseif (y <= 5000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -66000000.0], t$95$2, If[LessEqual[y, -1.75e-56], N[(x + z), $MachinePrecision], If[LessEqual[y, 2e-171], t$95$1, If[LessEqual[y, 1.06e-95], N[(x + z), $MachinePrecision], If[LessEqual[y, 5000000000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e7 or 5e9 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 67.7%

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

   if -6.6e7 < y < -1.7499999999999999e-56 or 2e-171 < y < 1.06e-95

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 69.4%

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

   4. Taylor expanded in t around 0 65.8%

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

      1. associate--r+ 65.8%

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

      2. sub-neg 65.8%

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

      3. neg-mul-1 65.8%

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

      4. remove-double-neg 65.8%

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

      5. sub-neg 65.8%

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

      6. metadata-eval 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around 0 65.8%

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

      1. sub-neg 65.8%

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

      2. neg-mul-1 65.8%

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

      3. remove-double-neg 65.8%

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

      4. associate-+l+ 65.8%

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

   9. Simplified 65.8%

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

   10. Taylor expanded in a around 0 66.0%

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

   if -1.7499999999999999e-56 < y < 2e-171 or 1.06e-95 < y < 5e9

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf 52.7%

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

Alternative 4: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.02 \cdot 10^{-227}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -8.2e+110)
     t_1
     (if (<= b -5.6e-77)
       (* a (- 1.0 t))
       (if (<= b 2.02e-227)
         (+ a (+ x z))
         (if (<= b 1.75e-28) (* z (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e+110) {
		tmp = t_1;
	} else if (b <= -5.6e-77) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.02e-227) {
		tmp = a + (x + z);
	} else if (b <= 1.75e-28) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-8.2d+110)) then
        tmp = t_1
    else if (b <= (-5.6d-77)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2.02d-227) then
        tmp = a + (x + z)
    else if (b <= 1.75d-28) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e+110) {
		tmp = t_1;
	} else if (b <= -5.6e-77) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.02e-227) {
		tmp = a + (x + z);
	} else if (b <= 1.75e-28) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -8.2e+110:
		tmp = t_1
	elif b <= -5.6e-77:
		tmp = a * (1.0 - t)
	elif b <= 2.02e-227:
		tmp = a + (x + z)
	elif b <= 1.75e-28:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -8.2e+110)
		tmp = t_1;
	elseif (b <= -5.6e-77)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2.02e-227)
		tmp = Float64(a + Float64(x + z));
	elseif (b <= 1.75e-28)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -8.2e+110)
		tmp = t_1;
	elseif (b <= -5.6e-77)
		tmp = a * (1.0 - t);
	elseif (b <= 2.02e-227)
		tmp = a + (x + z);
	elseif (b <= 1.75e-28)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+110], t$95$1, If[LessEqual[b, -5.6e-77], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.02e-227], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-28], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.1999999999999997e110 or 1.75e-28 < b

   1. Initial program 96.6%

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

   3. Taylor expanded in b around inf 74.9%

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

   if -8.1999999999999997e110 < b < -5.5999999999999999e-77

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 45.8%

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

   if -5.5999999999999999e-77 < b < 2.0200000000000001e-227

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.6%

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

   4. Taylor expanded in t around 0 79.3%

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

      1. associate--r+ 79.3%

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

      2. sub-neg 79.3%

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

      3. neg-mul-1 79.3%

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

      4. remove-double-neg 79.3%

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

      5. sub-neg 79.3%

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

      6. metadata-eval 79.3%

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

   6. Simplified 79.3%

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

   7. Taylor expanded in y around 0 57.5%

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

      1. sub-neg 57.5%

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

      2. neg-mul-1 57.5%

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

      3. remove-double-neg 57.5%

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

      4. associate-+l+ 57.5%

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

   9. Simplified 57.5%

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

   if 2.0200000000000001e-227 < b < 1.75e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.02 \cdot 10^{-227}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.6 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+110) (not (<= b 1.6e-28)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))
   (- x (+ (* (+ y -1.0) z) (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.6e-28)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d+110)) .or. (.not. (b <= 1.6d-28))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    else
        tmp = x - (((y + (-1.0d0)) * z) + (a * (t + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.6e-28)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+110) or not (b <= 1.6e-28):
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	else:
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+110) || !(b <= 1.6e-28))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(a * Float64(t + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+110) || ~((b <= 1.6e-28)))
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	else
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+110], N[Not[LessEqual[b, 1.6e-28]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5e110 or 1.59999999999999991e-28 < b

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 93.3%

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

   if -7.5e110 < b < 1.59999999999999991e-28

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 91.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.6 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 2.8 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+110) (not (<= b 2.8e-36)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (- x (+ (* (+ y -1.0) z) (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 2.8e-36)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d+110)) .or. (.not. (b <= 2.8d-36))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = x - (((y + (-1.0d0)) * z) + (a * (t + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 2.8e-36)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+110) or not (b <= 2.8e-36):
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+110) || !(b <= 2.8e-36))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(a * Float64(t + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+110) || ~((b <= 2.8e-36)))
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+110], N[Not[LessEqual[b, 2.8e-36]], $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[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5e110 or 2.8000000000000001e-36 < b

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 88.3%

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

   if -7.5e110 < b < 2.8000000000000001e-36

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 91.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 2.8 \cdot 10^{-36}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+119} \lor \neg \left(b \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.95e+119) (not (<= b 4.2e+22)))
   (+ x (* b (- (+ y t) 2.0)))
   (- x (+ (* (+ y -1.0) z) (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.95e+119) || !(b <= 4.2e+22)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.95d+119)) .or. (.not. (b <= 4.2d+22))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x - (((y + (-1.0d0)) * z) + (a * (t + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.95e+119) || !(b <= 4.2e+22)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.95e+119) or not (b <= 4.2e+22):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.95e+119) || !(b <= 4.2e+22))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(a * Float64(t + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.95e+119) || ~((b <= 4.2e+22)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x - (((y + -1.0) * z) + (a * (t + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.95e+119], N[Not[LessEqual[b, 4.2e+22]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.95e119 or 4.1999999999999996e22 < b

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0 93.3%

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

   4. Taylor expanded in z around 0 87.8%

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

   if -2.95e119 < b < 4.1999999999999996e22

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 89.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+119} \lor \neg \left(b \leq 4.2 \cdot 10^{+22}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + a \cdot \left(t + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+44}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.3e+111)
     t_1
     (if (<= b -2.85e-77)
       (+ x (* a (- 1.0 t)))
       (if (<= b 4.2e+44) (+ x (* z (- 1.0 y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+111) {
		tmp = t_1;
	} else if (b <= -2.85e-77) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.2e+44) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2.3d+111)) then
        tmp = t_1
    else if (b <= (-2.85d-77)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 4.2d+44) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+111) {
		tmp = t_1;
	} else if (b <= -2.85e-77) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.2e+44) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.3e+111:
		tmp = t_1
	elif b <= -2.85e-77:
		tmp = x + (a * (1.0 - t))
	elif b <= 4.2e+44:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+111)
		tmp = t_1;
	elseif (b <= -2.85e-77)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 4.2e+44)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+111)
		tmp = t_1;
	elseif (b <= -2.85e-77)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 4.2e+44)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+111], t$95$1, If[LessEqual[b, -2.85e-77], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+44], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.30000000000000002e111 or 4.19999999999999974e44 < b

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 82.9%

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

   if -2.30000000000000002e111 < b < -2.84999999999999991e-77

   1. Initial program 90.4%

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

   3. Taylor expanded in b around 0 80.6%

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

   4. Taylor expanded in a around inf 51.6%

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

   if -2.84999999999999991e-77 < b < 4.19999999999999974e44

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 91.7%

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

   4. Taylor expanded in a around 0 69.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+44}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.7 \cdot 10^{-28}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+110) (not (<= b 1.7e-28)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (- (* a (- 1.0 t)) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.7e-28)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d+110)) .or. (.not. (b <= 1.7d-28))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.7e-28)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+110) or not (b <= 1.7e-28):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+110) || !(b <= 1.7e-28))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+110) || ~((b <= 1.7e-28)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+110], N[Not[LessEqual[b, 1.7e-28]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5e110 or 1.7e-28 < b

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 93.3%

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

   4. Taylor expanded in z around 0 84.7%

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

   if -7.5e110 < b < 1.7e-28

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 91.4%

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

   4. Taylor expanded in y around inf 79.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.7 \cdot 10^{-28}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-95}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;y \leq 66000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1100000000.0)
     t_1
     (if (<= y 2.25e-95)
       (+ a (+ x z))
       (if (<= y 66000000.0) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1100000000.0) {
		tmp = t_1;
	} else if (y <= 2.25e-95) {
		tmp = a + (x + z);
	} else if (y <= 66000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1100000000.0d0)) then
        tmp = t_1
    else if (y <= 2.25d-95) then
        tmp = a + (x + z)
    else if (y <= 66000000.0d0) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1100000000.0) {
		tmp = t_1;
	} else if (y <= 2.25e-95) {
		tmp = a + (x + z);
	} else if (y <= 66000000.0) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1100000000.0:
		tmp = t_1
	elif y <= 2.25e-95:
		tmp = a + (x + z)
	elif y <= 66000000.0:
		tmp = t * (b - a)
	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 <= -1100000000.0)
		tmp = t_1;
	elseif (y <= 2.25e-95)
		tmp = Float64(a + Float64(x + z));
	elseif (y <= 66000000.0)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1100000000.0)
		tmp = t_1;
	elseif (y <= 2.25e-95)
		tmp = a + (x + z);
	elseif (y <= 66000000.0)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1100000000.0], t$95$1, If[LessEqual[y, 2.25e-95], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 66000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e9 or 6.6e7 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 67.7%

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

   if -1.1e9 < y < 2.25e-95

   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 b around 0 66.6%

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

   4. Taylor expanded in t around 0 48.1%

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

      1. associate--r+ 48.1%

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

      2. sub-neg 48.1%

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

      3. neg-mul-1 48.1%

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

      4. remove-double-neg 48.1%

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

      5. sub-neg 48.1%

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

      6. metadata-eval 48.1%

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

   6. Simplified 48.1%

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

   7. Taylor expanded in y around 0 48.1%

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

      1. sub-neg 48.1%

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

      2. neg-mul-1 48.1%

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

      3. remove-double-neg 48.1%

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

      4. associate-+l+ 48.1%

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

   9. Simplified 48.1%

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

   if 2.25e-95 < y < 6.6e7

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 58.6%

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

Alternative 11: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -120000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 0.058:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -120000.0)
     t_1
     (if (<= t -1.1e-121) (+ x a) (if (<= t 0.058) (* b (- y 2.0)) 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 <= -120000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-121) {
		tmp = x + a;
	} else if (t <= 0.058) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-120000.0d0)) then
        tmp = t_1
    else if (t <= (-1.1d-121)) then
        tmp = x + a
    else if (t <= 0.058d0) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -120000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-121) {
		tmp = x + a;
	} else if (t <= 0.058) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -120000.0:
		tmp = t_1
	elif t <= -1.1e-121:
		tmp = x + a
	elif t <= 0.058:
		tmp = b * (y - 2.0)
	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 <= -120000.0)
		tmp = t_1;
	elseif (t <= -1.1e-121)
		tmp = Float64(x + a);
	elseif (t <= 0.058)
		tmp = Float64(b * Float64(y - 2.0));
	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 <= -120000.0)
		tmp = t_1;
	elseif (t <= -1.1e-121)
		tmp = x + a;
	elseif (t <= 0.058)
		tmp = b * (y - 2.0);
	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, -120000.0], t$95$1, If[LessEqual[t, -1.1e-121], N[(x + a), $MachinePrecision], If[LessEqual[t, 0.058], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e5 or 0.0580000000000000029 < t

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 57.8%

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

   if -1.2e5 < t < -1.10000000000000011e-121

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0 85.5%

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

   4. Taylor expanded in t around 0 85.5%

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

      1. associate--r+ 85.5%

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

      2. sub-neg 85.5%

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

      3. neg-mul-1 85.5%

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

      4. remove-double-neg 85.5%

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

      5. sub-neg 85.5%

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

      6. metadata-eval 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in y around 0 55.7%

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

      1. sub-neg 55.7%

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

      2. neg-mul-1 55.7%

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

      3. remove-double-neg 55.7%

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

      4. associate-+l+ 55.7%

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

   9. Simplified 55.7%

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

   10. Taylor expanded in z around 0 48.4%

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

   if -1.10000000000000011e-121 < t < 0.0580000000000000029

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 43.7%

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

   4. Taylor expanded in t around 0 43.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -120000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 0.058:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+45}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8e+114)
   (* b (- y 2.0))
   (if (<= b -3.4e-98)
     (* a (- 1.0 t))
     (if (<= b 1.4e+45) (+ x z) (* b (- t 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+114) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.4e-98) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.4e+45) {
		tmp = x + z;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8d+114)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-3.4d-98)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.4d+45) then
        tmp = x + z
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8e+114) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.4e-98) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.4e+45) {
		tmp = x + z;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8e+114:
		tmp = b * (y - 2.0)
	elif b <= -3.4e-98:
		tmp = a * (1.0 - t)
	elif b <= 1.4e+45:
		tmp = x + z
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8e+114)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -3.4e-98)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.4e+45)
		tmp = Float64(x + z);
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8e+114)
		tmp = b * (y - 2.0);
	elseif (b <= -3.4e-98)
		tmp = a * (1.0 - t);
	elseif (b <= 1.4e+45)
		tmp = x + z;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8e+114], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-98], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+45], N[(x + z), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8e114

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 88.2%

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

   4. Taylor expanded in t around 0 58.2%

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

   if -8e114 < b < -3.4000000000000001e-98

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 45.3%

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

   if -3.4000000000000001e-98 < b < 1.4e45

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 91.3%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. associate--r+ 76.8%

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

      2. sub-neg 76.8%

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

      3. neg-mul-1 76.8%

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

      4. remove-double-neg 76.8%

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

      5. sub-neg 76.8%

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

      6. metadata-eval 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 49.6%

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

      1. sub-neg 49.6%

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

      2. neg-mul-1 49.6%

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

      3. remove-double-neg 49.6%

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

      4. associate-+l+ 49.6%

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

   9. Simplified 49.6%

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

   10. Taylor expanded in a around 0 43.2%

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

   if 1.4e45 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in b around inf 80.0%

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

   4. Taylor expanded in y around 0 54.1%

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

Alternative 13: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+48}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -1.8e+111)
     t_1
     (if (<= b -1.05e-97) (* a (- 1.0 t)) (if (<= b 1.25e+48) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.8e+111) {
		tmp = t_1;
	} else if (b <= -1.05e-97) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.25e+48) {
		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 = b * (t - 2.0d0)
    if (b <= (-1.8d+111)) then
        tmp = t_1
    else if (b <= (-1.05d-97)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.25d+48) 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 = b * (t - 2.0);
	double tmp;
	if (b <= -1.8e+111) {
		tmp = t_1;
	} else if (b <= -1.05e-97) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.25e+48) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -1.8e+111:
		tmp = t_1
	elif b <= -1.05e-97:
		tmp = a * (1.0 - t)
	elif b <= 1.25e+48:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -1.8e+111)
		tmp = t_1;
	elseif (b <= -1.05e-97)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.25e+48)
		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 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -1.8e+111)
		tmp = t_1;
	elseif (b <= -1.05e-97)
		tmp = a * (1.0 - t);
	elseif (b <= 1.25e+48)
		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[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+111], t$95$1, If[LessEqual[b, -1.05e-97], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+48], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000001e111 or 1.24999999999999993e48 < b

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 82.9%

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

   4. Taylor expanded in y around 0 53.2%

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

   if -1.8000000000000001e111 < b < -1.0500000000000001e-97

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 45.3%

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

   if -1.0500000000000001e-97 < b < 1.24999999999999993e48

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 91.3%

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

   4. Taylor expanded in t around 0 76.8%

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

      1. associate--r+ 76.8%

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

      2. sub-neg 76.8%

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

      3. neg-mul-1 76.8%

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

      4. remove-double-neg 76.8%

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

      5. sub-neg 76.8%

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

      6. metadata-eval 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 49.6%

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

      1. sub-neg 49.6%

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

      2. neg-mul-1 49.6%

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

      3. remove-double-neg 49.6%

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

      4. associate-+l+ 49.6%

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

   9. Simplified 49.6%

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

   10. Taylor expanded in a around 0 43.2%

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

Alternative 14: 36.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+132}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+35} \lor \neg \left(y \leq 1.15 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.2e+132)
   (* y b)
   (if (or (<= y -4.8e+35) (not (<= y 1.15e+19))) (* y (- z)) (+ x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+132) {
		tmp = y * b;
	} else if ((y <= -4.8e+35) || !(y <= 1.15e+19)) {
		tmp = y * -z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.2d+132)) then
        tmp = y * b
    else if ((y <= (-4.8d+35)) .or. (.not. (y <= 1.15d+19))) then
        tmp = y * -z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.2e+132) {
		tmp = y * b;
	} else if ((y <= -4.8e+35) || !(y <= 1.15e+19)) {
		tmp = y * -z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.2e+132:
		tmp = y * b
	elif (y <= -4.8e+35) or not (y <= 1.15e+19):
		tmp = y * -z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.2e+132)
		tmp = Float64(y * b);
	elseif ((y <= -4.8e+35) || !(y <= 1.15e+19))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.2e+132)
		tmp = y * b;
	elseif ((y <= -4.8e+35) || ~((y <= 1.15e+19)))
		tmp = y * -z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.2e+132], N[(y * b), $MachinePrecision], If[Or[LessEqual[y, -4.8e+35], N[Not[LessEqual[y, 1.15e+19]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000006e132

   1. Initial program 91.2%

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

   3. Taylor expanded in b around inf 54.3%

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

   4. Taylor expanded in y around inf 52.8%

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

   if -9.2000000000000006e132 < y < -4.80000000000000029e35 or 1.15e19 < y

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 48.0%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. associate-*r* 48.0%

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

      2. neg-mul-1 48.0%

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

   6. Simplified 48.0%

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

   if -4.80000000000000029e35 < y < 1.15e19

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 62.7%

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

   4. Taylor expanded in t around 0 44.3%

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

      1. associate--r+ 44.3%

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

      2. sub-neg 44.3%

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

      3. neg-mul-1 44.3%

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

      4. remove-double-neg 44.3%

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

      5. sub-neg 44.3%

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

      6. metadata-eval 44.3%

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

   6. Simplified 44.3%

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

   7. Taylor expanded in y around 0 42.8%

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

      1. sub-neg 42.8%

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

      2. neg-mul-1 42.8%

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

      3. remove-double-neg 42.8%

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

      4. associate-+l+ 42.8%

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

   9. Simplified 42.8%

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

   10. Taylor expanded in a around 0 38.3%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+132}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+35} \lor \neg \left(y \leq 1.15 \cdot 10^{+19}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+69} \lor \neg \left(b \leq 1.8 \cdot 10^{+21}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.32e+69) (not (<= b 1.8e+21)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ (+ x a) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.32e+69) || !(b <= 1.8e+21)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + 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 <= (-1.32d+69)) .or. (.not. (b <= 1.8d+21))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + 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 <= -1.32e+69) || !(b <= 1.8e+21)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.32e+69) or not (b <= 1.8e+21):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + a) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.32e+69) || !(b <= 1.8e+21))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + 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 <= -1.32e+69) || ~((b <= 1.8e+21)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + a) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.32e+69], N[Not[LessEqual[b, 1.8e+21]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.32e69 or 1.8e21 < b

   1. Initial program 95.5%

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

   3. Taylor expanded in a around 0 92.0%

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

   4. Taylor expanded in z around 0 86.0%

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

   if -1.32e69 < b < 1.8e21

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 89.7%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. associate--r+ 71.3%

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

      2. sub-neg 71.3%

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

      3. neg-mul-1 71.3%

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

      4. remove-double-neg 71.3%

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

      5. sub-neg 71.3%

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

      6. metadata-eval 71.3%

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

   6. Simplified 71.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+69} \lor \neg \left(b \leq 1.8 \cdot 10^{+21}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+69} \lor \neg \left(b \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.45e+69) (not (<= b 1.55e-28)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.45e+69) || !(b <= 1.55e-28)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + (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 <= (-1.45d+69)) .or. (.not. (b <= 1.55d-28))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + (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 <= -1.45e+69) || !(b <= 1.55e-28)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.45e+69) or not (b <= 1.55e-28):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.45e+69) || !(b <= 1.55e-28))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + 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 <= -1.45e+69) || ~((b <= 1.55e-28)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.45e+69], N[Not[LessEqual[b, 1.55e-28]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.4499999999999999e69 or 1.54999999999999996e-28 < b

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 92.1%

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

   4. Taylor expanded in z around 0 83.3%

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

   if -1.4499999999999999e69 < b < 1.54999999999999996e-28

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 92.3%

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

   4. Taylor expanded in a around 0 63.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+69} \lor \neg \left(b \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.02e+123)
   (* y b)
   (if (<= b -4.2e-77) (* t (- a)) (if (<= b 4.4e+44) (+ x z) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.02e+123) {
		tmp = y * b;
	} else if (b <= -4.2e-77) {
		tmp = t * -a;
	} else if (b <= 4.4e+44) {
		tmp = x + z;
	} else {
		tmp = t * 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 (b <= (-1.02d+123)) then
        tmp = y * b
    else if (b <= (-4.2d-77)) then
        tmp = t * -a
    else if (b <= 4.4d+44) then
        tmp = x + z
    else
        tmp = t * 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 (b <= -1.02e+123) {
		tmp = y * b;
	} else if (b <= -4.2e-77) {
		tmp = t * -a;
	} else if (b <= 4.4e+44) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.02e+123:
		tmp = y * b
	elif b <= -4.2e-77:
		tmp = t * -a
	elif b <= 4.4e+44:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.02e+123)
		tmp = Float64(y * b);
	elseif (b <= -4.2e-77)
		tmp = Float64(t * Float64(-a));
	elseif (b <= 4.4e+44)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.02e+123)
		tmp = y * b;
	elseif (b <= -4.2e-77)
		tmp = t * -a;
	elseif (b <= 4.4e+44)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.02e+123], N[(y * b), $MachinePrecision], If[LessEqual[b, -4.2e-77], N[(t * (-a)), $MachinePrecision], If[LessEqual[b, 4.4e+44], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.02e123

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 88.2%

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

   4. Taylor expanded in y around inf 44.1%

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

   if -1.02e123 < b < -4.20000000000000031e-77

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf 37.7%

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

   4. Taylor expanded in b around 0 33.5%

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

      1. associate-*r* 33.5%

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

      2. neg-mul-1 33.5%

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

   6. Simplified 33.5%

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

   if -4.20000000000000031e-77 < b < 4.39999999999999991e44

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 91.7%

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

   4. Taylor expanded in t around 0 77.0%

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

      1. associate--r+ 77.0%

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

      2. sub-neg 77.0%

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

      3. neg-mul-1 77.0%

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

      4. remove-double-neg 77.0%

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

      5. sub-neg 77.0%

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

      6. metadata-eval 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in y around 0 49.2%

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

      1. sub-neg 49.2%

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

      2. neg-mul-1 49.2%

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

      3. remove-double-neg 49.2%

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

      4. associate-+l+ 49.2%

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

   9. Simplified 49.2%

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

   10. Taylor expanded in a around 0 42.4%

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

   if 4.39999999999999991e44 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf 42.9%

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

   4. Taylor expanded in b around inf 40.0%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+123}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.32e+69)
   (* y b)
   (if (<= b -2.65e-129) z (if (<= b 1.2e+45) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.32e+69) {
		tmp = y * b;
	} else if (b <= -2.65e-129) {
		tmp = z;
	} else if (b <= 1.2e+45) {
		tmp = x;
	} else {
		tmp = t * 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 (b <= (-1.32d+69)) then
        tmp = y * b
    else if (b <= (-2.65d-129)) then
        tmp = z
    else if (b <= 1.2d+45) then
        tmp = x
    else
        tmp = t * 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 (b <= -1.32e+69) {
		tmp = y * b;
	} else if (b <= -2.65e-129) {
		tmp = z;
	} else if (b <= 1.2e+45) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.32e+69:
		tmp = y * b
	elif b <= -2.65e-129:
		tmp = z
	elif b <= 1.2e+45:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.32e+69)
		tmp = Float64(y * b);
	elseif (b <= -2.65e-129)
		tmp = z;
	elseif (b <= 1.2e+45)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.32e+69)
		tmp = y * b;
	elseif (b <= -2.65e-129)
		tmp = z;
	elseif (b <= 1.2e+45)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.32e+69], N[(y * b), $MachinePrecision], If[LessEqual[b, -2.65e-129], z, If[LessEqual[b, 1.2e+45], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.32e69

   1. Initial program 95.3%

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

   3. Taylor expanded in b around inf 78.9%

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

   4. Taylor expanded in y around inf 38.4%

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

   if -1.32e69 < b < -2.64999999999999987e-129

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 41.1%

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

   4. Taylor expanded in y around 0 20.5%

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

   if -2.64999999999999987e-129 < b < 1.19999999999999995e45

   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 33.8%

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

   if 1.19999999999999995e45 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf 42.9%

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

   4. Taylor expanded in b around inf 40.0%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-129}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-128}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e+69)
   (* y b)
   (if (<= b -1.55e-128) z (if (<= b 4.3e+51) x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e+69) {
		tmp = y * b;
	} else if (b <= -1.55e-128) {
		tmp = z;
	} else if (b <= 4.3e+51) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.45d+69)) then
        tmp = y * b
    else if (b <= (-1.55d-128)) then
        tmp = z
    else if (b <= 4.3d+51) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e+69) {
		tmp = y * b;
	} else if (b <= -1.55e-128) {
		tmp = z;
	} else if (b <= 4.3e+51) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e+69:
		tmp = y * b
	elif b <= -1.55e-128:
		tmp = z
	elif b <= 4.3e+51:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e+69)
		tmp = Float64(y * b);
	elseif (b <= -1.55e-128)
		tmp = z;
	elseif (b <= 4.3e+51)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e+69)
		tmp = y * b;
	elseif (b <= -1.55e-128)
		tmp = z;
	elseif (b <= 4.3e+51)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e+69], N[(y * b), $MachinePrecision], If[LessEqual[b, -1.55e-128], z, If[LessEqual[b, 4.3e+51], x, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4499999999999999e69 or 4.2999999999999997e51 < b

   1. Initial program 95.3%

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

   3. Taylor expanded in b around inf 79.6%

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

   4. Taylor expanded in y around inf 36.5%

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

   if -1.4499999999999999e69 < b < -1.55000000000000001e-128

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 41.1%

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

   4. Taylor expanded in y around 0 20.5%

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

   if -1.55000000000000001e-128 < b < 4.2999999999999997e51

   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 33.8%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-128}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.15 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+110) (not (<= b 1.15e+47)))
   (* b (- (+ y t) 2.0))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.15e+47)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.5d+110)) .or. (.not. (b <= 1.15d+47))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+110) || !(b <= 1.15e+47)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+110) or not (b <= 1.15e+47):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+110) || !(b <= 1.15e+47))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+110) || ~((b <= 1.15e+47)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+110], N[Not[LessEqual[b, 1.15e+47]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5e110 or 1.1499999999999999e47 < b

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 82.9%

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

   if -7.5e110 < b < 1.1499999999999999e47

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 88.7%

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

   4. Taylor expanded in a around inf 54.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110} \lor \neg \left(b \leq 1.15 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+110) (* y b) (if (<= b 7.2e+51) (+ x z) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+110) {
		tmp = y * b;
	} else if (b <= 7.2e+51) {
		tmp = x + z;
	} else {
		tmp = t * 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 (b <= (-7.5d+110)) then
        tmp = y * b
    else if (b <= 7.2d+51) then
        tmp = x + z
    else
        tmp = t * 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 (b <= -7.5e+110) {
		tmp = y * b;
	} else if (b <= 7.2e+51) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+110:
		tmp = y * b
	elif b <= 7.2e+51:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+110)
		tmp = Float64(y * b);
	elseif (b <= 7.2e+51)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+110)
		tmp = y * b;
	elseif (b <= 7.2e+51)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+110], N[(y * b), $MachinePrecision], If[LessEqual[b, 7.2e+51], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5e110

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 88.2%

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

   4. Taylor expanded in y around inf 44.1%

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

   if -7.5e110 < b < 7.20000000000000022e51

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 88.7%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. associate--r+ 70.1%

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

      2. sub-neg 70.1%

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

      3. neg-mul-1 70.1%

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

      4. remove-double-neg 70.1%

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

      5. sub-neg 70.1%

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

      6. metadata-eval 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in y around 0 44.4%

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

      1. sub-neg 44.4%

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

      2. neg-mul-1 44.4%

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

      3. remove-double-neg 44.4%

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

      4. associate-+l+ 44.4%

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

   9. Simplified 44.4%

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

   10. Taylor expanded in a around 0 36.4%

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

   if 7.20000000000000022e51 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf 42.9%

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

   4. Taylor expanded in b around inf 40.0%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+116}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.6e+116) (* y b) (if (<= b 2.6e+51) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.6e+116) {
		tmp = y * b;
	} else if (b <= 2.6e+51) {
		tmp = x + a;
	} else {
		tmp = t * 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 (b <= (-2.6d+116)) then
        tmp = y * b
    else if (b <= 2.6d+51) then
        tmp = x + a
    else
        tmp = t * 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 (b <= -2.6e+116) {
		tmp = y * b;
	} else if (b <= 2.6e+51) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.6e+116:
		tmp = y * b
	elif b <= 2.6e+51:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.6e+116)
		tmp = Float64(y * b);
	elseif (b <= 2.6e+51)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.6e+116)
		tmp = y * b;
	elseif (b <= 2.6e+51)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.6e+116], N[(y * b), $MachinePrecision], If[LessEqual[b, 2.6e+51], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.59999999999999987e116

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 88.2%

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

   4. Taylor expanded in y around inf 44.1%

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

   if -2.59999999999999987e116 < b < 2.6000000000000001e51

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 88.7%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. associate--r+ 70.1%

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

      2. sub-neg 70.1%

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

      3. neg-mul-1 70.1%

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

      4. remove-double-neg 70.1%

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

      5. sub-neg 70.1%

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

      6. metadata-eval 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in y around 0 44.4%

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

      1. sub-neg 44.4%

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

      2. neg-mul-1 44.4%

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

      3. remove-double-neg 44.4%

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

      4. associate-+l+ 44.4%

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

   9. Simplified 44.4%

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

   10. Taylor expanded in z around 0 33.9%

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

   if 2.6000000000000001e51 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf 42.9%

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

   4. Taylor expanded in b around inf 40.0%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+116}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+51}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.95 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8e+79) x (if (<= x 3.95e-17) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+79) {
		tmp = x;
	} else if (x <= 3.95e-17) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8d+79)) then
        tmp = x
    else if (x <= 3.95d-17) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+79) {
		tmp = x;
	} else if (x <= 3.95e-17) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+79:
		tmp = x
	elif x <= 3.95e-17:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+79)
		tmp = x;
	elseif (x <= 3.95e-17)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8e+79)
		tmp = x;
	elseif (x <= 3.95e-17)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8e+79], x, If[LessEqual[x, 3.95e-17], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999974e79 or 3.9500000000000001e-17 < x

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 36.4%

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

   if -7.99999999999999974e79 < x < 3.9500000000000001e-17

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 39.0%

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

   4. Taylor expanded in y around 0 14.3%

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

Alternative 24: 20.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.9e-27) x (if (<= x 4.2e-19) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.9e-27) {
		tmp = x;
	} else if (x <= 4.2e-19) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.9d-27)) then
        tmp = x
    else if (x <= 4.2d-19) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.9e-27) {
		tmp = x;
	} else if (x <= 4.2e-19) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.9e-27:
		tmp = x
	elif x <= 4.2e-19:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.9e-27)
		tmp = x;
	elseif (x <= 4.2e-19)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.9e-27)
		tmp = x;
	elseif (x <= 4.2e-19)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.9e-27], x, If[LessEqual[x, 4.2e-19], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e-27 or 4.1999999999999998e-19 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 31.6%

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

   if -1.9e-27 < x < 4.1999999999999998e-19

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 30.1%

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

   4. Taylor expanded in t around 0 10.2%

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

Alternative 25: 11.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in a around inf 23.9%

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

4. Taylor expanded in t around 0 7.5%

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

Reproduce

herbie shell --seed 2024132 
(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)))