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

Percentage Accurate: 95.2% → 98.0%

Time: 12.2s

Alternatives: 23

Speedup: 0.5×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   3. Taylor expanded in z around 0 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 66.7%

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

4. Final simplification 99.2%

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

Alternative 2: 97.5% 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 97.6%

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

   1. +-commutative 97.6%

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

   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. fmm-def 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + 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(t * Float64(b - a));
	end
	return tmp
end

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 66.7%

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

4. Final simplification 99.2%

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

Alternative 4: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+58} \lor \neg \left(y \leq 5.4 \cdot 10^{-31}\right):\\ \;\;\;\;\left(x + y \cdot \left(b - z\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z\right) + \left(t + -2\right) \cdot b\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= y -2.45e+58) (not (<= y 5.4e-31)))
     (+ (+ x (* y (- b z))) t_1)
     (+ (+ (+ x z) (* (+ t -2.0) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((y <= -2.45e+58) || !(y <= 5.4e-31)) {
		tmp = (x + (y * (b - z))) + t_1;
	} else {
		tmp = ((x + z) + ((t + -2.0) * b)) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((y <= (-2.45d+58)) .or. (.not. (y <= 5.4d-31))) then
        tmp = (x + (y * (b - z))) + t_1
    else
        tmp = ((x + z) + ((t + (-2.0d0)) * b)) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((y <= -2.45e+58) || !(y <= 5.4e-31)) {
		tmp = (x + (y * (b - z))) + t_1;
	} else {
		tmp = ((x + z) + ((t + -2.0) * b)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (y <= -2.45e+58) or not (y <= 5.4e-31):
		tmp = (x + (y * (b - z))) + t_1
	else:
		tmp = ((x + z) + ((t + -2.0) * b)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((y <= -2.45e+58) || !(y <= 5.4e-31))
		tmp = Float64(Float64(x + Float64(y * Float64(b - z))) + t_1);
	else
		tmp = Float64(Float64(Float64(x + z) + Float64(Float64(t + -2.0) * b)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((y <= -2.45e+58) || ~((y <= 5.4e-31)))
		tmp = (x + (y * (b - z))) + t_1;
	else
		tmp = ((x + z) + ((t + -2.0) * b)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -2.45e+58], N[Not[LessEqual[y, 5.4e-31]], $MachinePrecision]], N[(N[(x + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x + z), $MachinePrecision] + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45000000000000009e58 or 5.40000000000000027e-31 < y

   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 z around 0 96.4%

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

   4. Taylor expanded in y around inf 96.5%

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

      1. neg-mul-1 96.5%

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

      2. unsub-neg 96.5%

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

   6. Simplified 96.5%

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

   if -2.45000000000000009e58 < y < 5.40000000000000027e-31

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 98.6%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. associate-+r+ 95.4%

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

      2. sub-neg 95.4%

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

      3. metadata-eval 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

   6. Simplified 95.4%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+58} \lor \neg \left(y \leq 5.4 \cdot 10^{-31}\right):\\ \;\;\;\;\left(x + y \cdot \left(b - z\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z\right) + \left(t + -2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+175} \lor \neg \left(a \leq 1.7 \cdot 10^{+101}\right):\\ \;\;\;\;\left(x + y \cdot \left(b - z\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.15e+175) (not (<= a 1.7e+101)))
   (+ (+ x (* y (- b z))) (* a (- 1.0 t)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e+175) || !(a <= 1.7e+101)) {
		tmp = (x + (y * (b - z))) + (a * (1.0 - t));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (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 ((a <= (-2.15d+175)) .or. (.not. (a <= 1.7d+101))) then
        tmp = (x + (y * (b - z))) + (a * (1.0d0 - t))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + (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 ((a <= -2.15e+175) || !(a <= 1.7e+101)) {
		tmp = (x + (y * (b - z))) + (a * (1.0 - t));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.15e+175) or not (a <= 1.7e+101):
		tmp = (x + (y * (b - z))) + (a * (1.0 - t))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.15e+175) || !(a <= 1.7e+101))
		tmp = Float64(Float64(x + Float64(y * Float64(b - z))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + 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 ((a <= -2.15e+175) || ~((a <= 1.7e+101)))
		tmp = (x + (y * (b - z))) + (a * (1.0 - t));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.15e+175], N[Not[LessEqual[a, 1.7e+101]], $MachinePrecision]], N[(N[(x + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $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]]

Derivation

1. Split input into 2 regimes

2. if a < -2.14999999999999992e175 or 1.70000000000000009e101 < a

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 97.2%

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

   4. Taylor expanded in y around inf 94.0%

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

      1. neg-mul-1 94.0%

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

      2. unsub-neg 94.0%

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

   6. Simplified 94.0%

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

   if -2.14999999999999992e175 < a < 1.70000000000000009e101

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 90.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+175} \lor \neg \left(a \leq 1.7 \cdot 10^{+101}\right):\\ \;\;\;\;\left(x + y \cdot \left(b - z\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -5.5e+21)
     t_1
     (if (<= b 2.1e-28)
       (- (+ x a) (* (+ y -1.0) z))
       (if (<= b 3.3e+38) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -5.5e+21) {
		tmp = t_1;
	} else if (b <= 2.1e-28) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else if (b <= 3.3e+38) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-5.5d+21)) then
        tmp = t_1
    else if (b <= 2.1d-28) then
        tmp = (x + a) - ((y + (-1.0d0)) * z)
    else if (b <= 3.3d+38) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -5.5e+21) {
		tmp = t_1;
	} else if (b <= 2.1e-28) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else if (b <= 3.3e+38) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -5.5e+21:
		tmp = t_1
	elif b <= 2.1e-28:
		tmp = (x + a) - ((y + -1.0) * z)
	elif b <= 3.3e+38:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -5.5e+21)
		tmp = t_1;
	elseif (b <= 2.1e-28)
		tmp = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z));
	elseif (b <= 3.3e+38)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -5.5e+21)
		tmp = t_1;
	elseif (b <= 2.1e-28)
		tmp = (x + a) - ((y + -1.0) * z);
	elseif (b <= 3.3e+38)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+21], t$95$1, If[LessEqual[b, 2.1e-28], N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+38], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5e21 or 3.2999999999999999e38 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in x around -inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. sub-neg 76.9%

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

      3. sub-neg 76.9%

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

      4. metadata-eval 76.9%

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

      5. +-commutative 76.9%

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

      6. sub-neg 76.9%

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

      7. metadata-eval 76.9%

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

      8. associate-/l* 74.1%

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

      9. +-commutative 74.1%

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

      10. metadata-eval 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x around inf 79.6%

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

      1. neg-mul-1 79.6%

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

   8. Simplified 79.6%

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

   if -5.5e21 < b < 2.10000000000000006e-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 b around 0 90.5%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. neg-mul-1 70.7%

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

      2. associate--r+ 70.7%

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

      3. sub-neg 70.7%

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

      4. remove-double-neg 70.7%

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

      5. sub-neg 70.7%

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

      6. metadata-eval 70.7%

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

   6. Simplified 70.7%

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

   if 2.10000000000000006e-28 < b < 3.2999999999999999e38

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 89.4%

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

   4. Taylor expanded in a around inf 83.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-28}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+38}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+22} \lor \neg \left(b \leq 1.15 \cdot 10^{+80}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.3e+22) (not (<= b 1.15e+80)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (- (* a (- 1.0 t)) (* (+ y -1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.3e+22) || !(b <= 1.15e+80)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * 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 <= (-4.3d+22)) .or. (.not. (b <= 1.15d+80))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) - ((y + (-1.0d0)) * 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 <= -4.3e+22) || !(b <= 1.15e+80)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.3e+22) or not (b <= 1.15e+80):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.3e+22) || !(b <= 1.15e+80))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.3e+22) || ~((b <= 1.15e+80)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.3e+22], N[Not[LessEqual[b, 1.15e+80]], $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[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.3000000000000002e22 or 1.15000000000000002e80 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in x around -inf 77.3%

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

      1. mul-1-neg 77.3%

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

      2. sub-neg 77.3%

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

      3. sub-neg 77.3%

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

      4. metadata-eval 77.3%

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

      5. +-commutative 77.3%

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

      6. sub-neg 77.3%

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

      7. metadata-eval 77.3%

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

      8. associate-/l* 74.4%

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

      9. +-commutative 74.4%

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

      10. metadata-eval 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in x around inf 82.5%

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

      1. neg-mul-1 82.5%

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

   8. Simplified 82.5%

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

   if -4.3000000000000002e22 < b < 1.15000000000000002e80

   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 88.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+22} \lor \neg \left(b \leq 1.15 \cdot 10^{+80}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+110}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.6e+63)
     t_1
     (if (<= b 4.9e-29)
       (- (+ x a) (* (+ y -1.0) z))
       (if (<= b 1.8e+110) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.6e+63) {
		tmp = t_1;
	} else if (b <= 4.9e-29) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else if (b <= 1.8e+110) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2.6d+63)) then
        tmp = t_1
    else if (b <= 4.9d-29) then
        tmp = (x + a) - ((y + (-1.0d0)) * z)
    else if (b <= 1.8d+110) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.6e+63) {
		tmp = t_1;
	} else if (b <= 4.9e-29) {
		tmp = (x + a) - ((y + -1.0) * z);
	} else if (b <= 1.8e+110) {
		tmp = x + (a * (1.0 - t));
	} 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 <= -2.6e+63:
		tmp = t_1
	elif b <= 4.9e-29:
		tmp = (x + a) - ((y + -1.0) * z)
	elif b <= 1.8e+110:
		tmp = x + (a * (1.0 - t))
	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 <= -2.6e+63)
		tmp = t_1;
	elseif (b <= 4.9e-29)
		tmp = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z));
	elseif (b <= 1.8e+110)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.6e+63)
		tmp = t_1;
	elseif (b <= 4.9e-29)
		tmp = (x + a) - ((y + -1.0) * z);
	elseif (b <= 1.8e+110)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+63], t$95$1, If[LessEqual[b, 4.9e-29], N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+110], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000001e63 or 1.7999999999999998e110 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -2.6000000000000001e63 < b < 4.8999999999999998e-29

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 87.8%

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

   4. Taylor expanded in t around 0 69.6%

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

      1. neg-mul-1 69.6%

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

      2. associate--r+ 69.6%

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

      3. sub-neg 69.6%

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

      4. remove-double-neg 69.6%

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

      5. sub-neg 69.6%

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

      6. metadata-eval 69.6%

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

   6. Simplified 69.6%

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

   if 4.8999999999999998e-29 < b < 1.7999999999999998e110

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 74.1%

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

   4. Taylor expanded in a around inf 65.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-29}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+110}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-28}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -3.5e+63)
     t_1
     (if (<= b 1.65e-28)
       (- x (* (+ y -1.0) z))
       (if (<= b 1.35e+111) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.5e+63) {
		tmp = t_1;
	} else if (b <= 1.65e-28) {
		tmp = x - ((y + -1.0) * z);
	} else if (b <= 1.35e+111) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-3.5d+63)) then
        tmp = t_1
    else if (b <= 1.65d-28) then
        tmp = x - ((y + (-1.0d0)) * z)
    else if (b <= 1.35d+111) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.5e+63) {
		tmp = t_1;
	} else if (b <= 1.65e-28) {
		tmp = x - ((y + -1.0) * z);
	} else if (b <= 1.35e+111) {
		tmp = x + (a * (1.0 - t));
	} 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 <= -3.5e+63:
		tmp = t_1
	elif b <= 1.65e-28:
		tmp = x - ((y + -1.0) * z)
	elif b <= 1.35e+111:
		tmp = x + (a * (1.0 - t))
	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 <= -3.5e+63)
		tmp = t_1;
	elseif (b <= 1.65e-28)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	elseif (b <= 1.35e+111)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -3.5e+63)
		tmp = t_1;
	elseif (b <= 1.65e-28)
		tmp = x - ((y + -1.0) * z);
	elseif (b <= 1.35e+111)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+63], t$95$1, If[LessEqual[b, 1.65e-28], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+111], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.50000000000000029e63 or 1.3499999999999999e111 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -3.50000000000000029e63 < b < 1.6500000000000001e-28

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 87.8%

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

   4. Taylor expanded in a around 0 59.7%

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

   if 1.6500000000000001e-28 < b < 1.3499999999999999e111

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 74.1%

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

   4. Taylor expanded in a around inf 65.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-28}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+47}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -7.5e+72)
     t_1
     (if (<= y 1.4e-245) (* t (- b a)) (if (<= y 7.5e+47) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.5e+72) {
		tmp = t_1;
	} else if (y <= 1.4e-245) {
		tmp = t * (b - a);
	} else if (y <= 7.5e+47) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-7.5d+72)) then
        tmp = t_1
    else if (y <= 1.4d-245) then
        tmp = t * (b - a)
    else if (y <= 7.5d+47) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.5e+72) {
		tmp = t_1;
	} else if (y <= 1.4e-245) {
		tmp = t * (b - a);
	} else if (y <= 7.5e+47) {
		tmp = x + 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 <= -7.5e+72:
		tmp = t_1
	elif y <= 1.4e-245:
		tmp = t * (b - a)
	elif y <= 7.5e+47:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.5e+72)
		tmp = t_1;
	elseif (y <= 1.4e-245)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 7.5e+47)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.5e+72)
		tmp = t_1;
	elseif (y <= 1.4e-245)
		tmp = t * (b - a);
	elseif (y <= 7.5e+47)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+72], t$95$1, If[LessEqual[y, 1.4e-245], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+47], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000027e72 or 7.4999999999999999e47 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 72.9%

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

   if -7.50000000000000027e72 < y < 1.4000000000000001e-245

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 45.2%

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

   if 1.4000000000000001e-245 < y < 7.4999999999999999e47

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 80.5%

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

   4. Taylor expanded in t around 0 62.8%

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

      1. neg-mul-1 62.8%

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

      2. associate--r+ 62.8%

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

      3. sub-neg 62.8%

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

      4. remove-double-neg 62.8%

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

      5. sub-neg 62.8%

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

      6. metadata-eval 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in y around inf 48.8%

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

   8. Taylor expanded in y around 0 46.0%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+47}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -3.1e+227)
     t_1
     (if (<= b -1.65e-25)
       (* b (- t 2.0))
       (if (<= b 2e+88) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -3.1e+227) {
		tmp = t_1;
	} else if (b <= -1.65e-25) {
		tmp = b * (t - 2.0);
	} else if (b <= 2e+88) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    if (b <= (-3.1d+227)) then
        tmp = t_1
    else if (b <= (-1.65d-25)) then
        tmp = b * (t - 2.0d0)
    else if (b <= 2d+88) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -3.1e+227) {
		tmp = t_1;
	} else if (b <= -1.65e-25) {
		tmp = b * (t - 2.0);
	} else if (b <= 2e+88) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -3.1e+227:
		tmp = t_1
	elif b <= -1.65e-25:
		tmp = b * (t - 2.0)
	elif b <= 2e+88:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -3.1e+227)
		tmp = t_1;
	elseif (b <= -1.65e-25)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (b <= 2e+88)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -3.1e+227)
		tmp = t_1;
	elseif (b <= -1.65e-25)
		tmp = b * (t - 2.0);
	elseif (b <= 2e+88)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+227], t$95$1, If[LessEqual[b, -1.65e-25], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+88], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0999999999999999e227 or 1.99999999999999992e88 < b

   1. Initial program 95.0%

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

   3. Taylor expanded in b around inf 74.5%

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

   4. Taylor expanded in t around 0 55.3%

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

   if -3.0999999999999999e227 < b < -1.6499999999999999e-25

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 60.1%

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

   4. Taylor expanded in y around 0 52.0%

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

   if -1.6499999999999999e-25 < b < 1.99999999999999992e88

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 36.3%

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

Alternative 12: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 10^{-73}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -2.7e+98)
     t_1
     (if (<= a -8e-250) (* b (- t 2.0)) (if (<= a 1e-73) (* y (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.7e+98) {
		tmp = t_1;
	} else if (a <= -8e-250) {
		tmp = b * (t - 2.0);
	} else if (a <= 1e-73) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-2.7d+98)) then
        tmp = t_1
    else if (a <= (-8d-250)) then
        tmp = b * (t - 2.0d0)
    else if (a <= 1d-73) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.7e+98) {
		tmp = t_1;
	} else if (a <= -8e-250) {
		tmp = b * (t - 2.0);
	} else if (a <= 1e-73) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -2.7e+98:
		tmp = t_1
	elif a <= -8e-250:
		tmp = b * (t - 2.0)
	elif a <= 1e-73:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.7e+98)
		tmp = t_1;
	elseif (a <= -8e-250)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (a <= 1e-73)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.7e+98)
		tmp = t_1;
	elseif (a <= -8e-250)
		tmp = b * (t - 2.0);
	elseif (a <= 1e-73)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+98], t$95$1, If[LessEqual[a, -8e-250], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-73], N[(y * (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e98 or 9.99999999999999997e-74 < a

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 58.6%

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

   if -2.7e98 < a < -8.0000000000000004e-250

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 46.8%

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

   4. Taylor expanded in y around 0 34.5%

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

   if -8.0000000000000004e-250 < a < 9.99999999999999997e-74

   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 z around inf 42.1%

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

   4. Taylor expanded in y around inf 30.8%

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

      1. associate-*r* 30.8%

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

      2. neg-mul-1 30.8%

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

      3. *-commutative 30.8%

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

   6. Simplified 30.8%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 10^{-73}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-155}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -5.1e+125)
     t_1
     (if (<= a -2.4e-155) (+ x a) (if (<= a 8.2e-74) (* y (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -5.1e+125) {
		tmp = t_1;
	} else if (a <= -2.4e-155) {
		tmp = x + a;
	} else if (a <= 8.2e-74) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-5.1d+125)) then
        tmp = t_1
    else if (a <= (-2.4d-155)) then
        tmp = x + a
    else if (a <= 8.2d-74) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -5.1e+125) {
		tmp = t_1;
	} else if (a <= -2.4e-155) {
		tmp = x + a;
	} else if (a <= 8.2e-74) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -5.1e+125:
		tmp = t_1
	elif a <= -2.4e-155:
		tmp = x + a
	elif a <= 8.2e-74:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -5.1e+125)
		tmp = t_1;
	elseif (a <= -2.4e-155)
		tmp = Float64(x + a);
	elseif (a <= 8.2e-74)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -5.1e+125)
		tmp = t_1;
	elseif (a <= -2.4e-155)
		tmp = x + a;
	elseif (a <= 8.2e-74)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+125], t$95$1, If[LessEqual[a, -2.4e-155], N[(x + a), $MachinePrecision], If[LessEqual[a, 8.2e-74], N[(y * (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.0999999999999998e125 or 8.20000000000000063e-74 < a

   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 a around inf 59.2%

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

   if -5.0999999999999998e125 < a < -2.4e-155

   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 62.5%

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

   4. Taylor expanded in t around 0 56.7%

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

      1. neg-mul-1 56.7%

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

      2. associate--r+ 56.7%

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

      3. sub-neg 56.7%

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

      4. remove-double-neg 56.7%

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

      5. sub-neg 56.7%

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

      6. metadata-eval 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in y around inf 46.5%

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

   8. Taylor expanded in y around 0 30.0%

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

   if -2.4e-155 < a < 8.20000000000000063e-74

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 38.9%

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

   4. Taylor expanded in y around inf 30.1%

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

      1. associate-*r* 30.1%

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

      2. neg-mul-1 30.1%

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

      3. *-commutative 30.1%

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

   6. Simplified 30.1%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-155}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 75000000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -1.1e+107)
     t_1
     (if (<= t 75000000000000.0) (+ x a) (if (<= t 8.8e+240) t_1 (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.1e+107) {
		tmp = t_1;
	} else if (t <= 75000000000000.0) {
		tmp = x + a;
	} else if (t <= 8.8e+240) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-1.1d+107)) then
        tmp = t_1
    else if (t <= 75000000000000.0d0) then
        tmp = x + a
    else if (t <= 8.8d+240) then
        tmp = t_1
    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 t_1 = t * -a;
	double tmp;
	if (t <= -1.1e+107) {
		tmp = t_1;
	} else if (t <= 75000000000000.0) {
		tmp = x + a;
	} else if (t <= 8.8e+240) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -1.1e+107:
		tmp = t_1
	elif t <= 75000000000000.0:
		tmp = x + a
	elif t <= 8.8e+240:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.1e+107)
		tmp = t_1;
	elseif (t <= 75000000000000.0)
		tmp = Float64(x + a);
	elseif (t <= 8.8e+240)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -1.1e+107)
		tmp = t_1;
	elseif (t <= 75000000000000.0)
		tmp = x + a;
	elseif (t <= 8.8e+240)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.1e+107], t$95$1, If[LessEqual[t, 75000000000000.0], N[(x + a), $MachinePrecision], If[LessEqual[t, 8.8e+240], t$95$1, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e107 or 7.5e13 < t < 8.8000000000000006e240

   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 t around inf 63.6%

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

   4. Taylor expanded in b around 0 40.7%

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

      1. associate-*r* 40.7%

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

      2. neg-mul-1 40.7%

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

      3. *-commutative 40.7%

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

   6. Simplified 40.7%

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

   if -1.1e107 < t < 7.5e13

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 71.5%

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

   4. Taylor expanded in t around 0 69.3%

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

      1. neg-mul-1 69.3%

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

      2. associate--r+ 69.3%

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

      3. sub-neg 69.3%

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

      4. remove-double-neg 69.3%

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

      5. sub-neg 69.3%

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

      6. metadata-eval 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around inf 57.0%

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

   8. Taylor expanded in y around 0 38.7%

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

   if 8.8000000000000006e240 < t

   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 t around inf 82.8%

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

   4. Taylor expanded in b around inf 70.2%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 75000000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+240}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-250}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4e+73)
   (* y b)
   (if (<= y 2e-250) (* t b) (if (<= y 6.5e+47) x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4e+73) {
		tmp = y * b;
	} else if (y <= 2e-250) {
		tmp = t * b;
	} else if (y <= 6.5e+47) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4d+73)) then
        tmp = y * b
    else if (y <= 2d-250) then
        tmp = t * b
    else if (y <= 6.5d+47) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4e+73) {
		tmp = y * b;
	} else if (y <= 2e-250) {
		tmp = t * b;
	} else if (y <= 6.5e+47) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4e+73:
		tmp = y * b
	elif y <= 2e-250:
		tmp = t * b
	elif y <= 6.5e+47:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4e+73)
		tmp = Float64(y * b);
	elseif (y <= 2e-250)
		tmp = Float64(t * b);
	elseif (y <= 6.5e+47)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4e+73)
		tmp = y * b;
	elseif (y <= 2e-250)
		tmp = t * b;
	elseif (y <= 6.5e+47)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4e+73], N[(y * b), $MachinePrecision], If[LessEqual[y, 2e-250], N[(t * b), $MachinePrecision], If[LessEqual[y, 6.5e+47], x, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999993e73 or 6.49999999999999988e47 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 42.8%

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

   4. Taylor expanded in y around inf 38.6%

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

   if -3.99999999999999993e73 < y < 2.0000000000000001e-250

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf 44.6%

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

   4. Taylor expanded in b around inf 29.6%

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

   if 2.0000000000000001e-250 < y < 6.49999999999999988e47

   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 x around inf 30.6%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-250}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-28} \lor \neg \left(b \leq 1.8 \cdot 10^{+110}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.7e-28) (not (<= b 1.8e+110)))
   (* 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 <= -2.7e-28) || !(b <= 1.8e+110)) {
		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 <= (-2.7d-28)) .or. (.not. (b <= 1.8d+110))) 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 <= -2.7e-28) || !(b <= 1.8e+110)) {
		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 <= -2.7e-28) or not (b <= 1.8e+110):
		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 <= -2.7e-28) || !(b <= 1.8e+110))
		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 <= -2.7e-28) || ~((b <= 1.8e+110)))
		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, -2.7e-28], N[Not[LessEqual[b, 1.8e+110]], $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 < -2.6999999999999999e-28 or 1.7999999999999998e110 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf 69.7%

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

   if -2.6999999999999999e-28 < b < 1.7999999999999998e110

   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 88.5%

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

   4. Taylor expanded in a around inf 56.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-28} \lor \neg \left(b \leq 1.8 \cdot 10^{+110}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+42} \lor \neg \left(y \leq 2.8 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.8e+42) (not (<= y 2.8e+47))) (* y (- b z)) (+ a (+ x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e+42) || !(y <= 2.8e+47)) {
		tmp = y * (b - z);
	} else {
		tmp = a + (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 <= (-2.8d+42)) .or. (.not. (y <= 2.8d+47))) then
        tmp = y * (b - z)
    else
        tmp = a + (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 <= -2.8e+42) || !(y <= 2.8e+47)) {
		tmp = y * (b - z);
	} else {
		tmp = a + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.8e+42) or not (y <= 2.8e+47):
		tmp = y * (b - z)
	else:
		tmp = a + (x + z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.8e+42) || !(y <= 2.8e+47))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(a + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.8e+42) || ~((y <= 2.8e+47)))
		tmp = y * (b - z);
	else
		tmp = a + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.8e+42], N[Not[LessEqual[y, 2.8e+47]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e42 or 2.79999999999999988e47 < y

   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 y around inf 69.8%

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

   if -2.7999999999999999e42 < y < 2.79999999999999988e47

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 71.9%

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

   4. Taylor expanded in t around 0 53.9%

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

      1. neg-mul-1 53.9%

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

      2. associate--r+ 53.9%

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

      3. sub-neg 53.9%

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

      4. remove-double-neg 53.9%

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

      5. sub-neg 53.9%

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

      6. metadata-eval 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around 0 51.3%

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

      1. neg-mul-1 51.3%

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

      2. associate--l+ 51.3%

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

      3. sub-neg 51.3%

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

      4. remove-double-neg 51.3%

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

   9. Simplified 51.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+42} \lor \neg \left(y \leq 2.8 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.19 \lor \neg \left(t \leq 60000000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -0.19) (not (<= t 60000000000000.0))) (* t (- b a)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.19) || !(t <= 60000000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-0.19d0)) .or. (.not. (t <= 60000000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.19) || !(t <= 60000000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -0.19) or not (t <= 60000000000000.0):
		tmp = t * (b - a)
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -0.19) || !(t <= 60000000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -0.19) || ~((t <= 60000000000000.0)))
		tmp = t * (b - a);
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -0.19], N[Not[LessEqual[t, 60000000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.19 or 6e13 < t

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf 59.2%

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

   if -0.19 < t < 6e13

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 74.1%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. neg-mul-1 73.7%

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

      2. associate--r+ 73.7%

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

      3. sub-neg 73.7%

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

      4. remove-double-neg 73.7%

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

      5. sub-neg 73.7%

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

      6. metadata-eval 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around inf 62.5%

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

   8. Taylor expanded in y around 0 43.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.19 \lor \neg \left(t \leq 60000000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+115} \lor \neg \left(t \leq 7.5 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.9e+115) (not (<= t 7.5e+49))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.9e+115) || !(t <= 7.5e+49)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.9d+115)) .or. (.not. (t <= 7.5d+49))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.9e+115) || !(t <= 7.5e+49)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.9e+115) or not (t <= 7.5e+49):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.9e+115) || !(t <= 7.5e+49))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.9e+115) || ~((t <= 7.5e+49)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.9e+115], N[Not[LessEqual[t, 7.5e+49]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9e115 or 7.4999999999999995e49 < t

   1. Initial program 95.1%

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

   3. Taylor expanded in t around inf 69.1%

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

   4. Taylor expanded in b around inf 36.1%

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

   if -1.9e115 < t < 7.4999999999999995e49

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 72.9%

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

   4. Taylor expanded in t around 0 69.0%

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

      1. neg-mul-1 69.0%

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

      2. associate--r+ 69.0%

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

      3. sub-neg 69.0%

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

      4. remove-double-neg 69.0%

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

      5. sub-neg 69.0%

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

      6. metadata-eval 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in y around inf 56.4%

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

   8. Taylor expanded in y around 0 37.4%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+115} \lor \neg \left(t \leq 7.5 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+73} \lor \neg \left(y \leq 5.6 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+73) (not (<= y 5.6e+47))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+73) || !(y <= 5.6e+47)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d+73)) .or. (.not. (y <= 5.6d+47))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+73) || !(y <= 5.6e+47)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e+73) or not (y <= 5.6e+47):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+73) || !(y <= 5.6e+47))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e+73) || ~((y <= 5.6e+47)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+73], N[Not[LessEqual[y, 5.6e+47]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e73 or 5.59999999999999976e47 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 42.8%

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

   4. Taylor expanded in y around inf 38.6%

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

   if -3.5999999999999999e73 < y < 5.59999999999999976e47

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 24.2%

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

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+73} \lor \neg \left(y \leq 5.6 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+121}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.2e+54) x (if (<= x 3.2e+121) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.2e+54) {
		tmp = x;
	} else if (x <= 3.2e+121) {
		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 <= (-4.2d+54)) then
        tmp = x
    else if (x <= 3.2d+121) 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 <= -4.2e+54) {
		tmp = x;
	} else if (x <= 3.2e+121) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.2e+54:
		tmp = x
	elif x <= 3.2e+121:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.2e+54)
		tmp = x;
	elseif (x <= 3.2e+121)
		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 <= -4.2e+54)
		tmp = x;
	elseif (x <= 3.2e+121)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.2e+54], x, If[LessEqual[x, 3.2e+121], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999972e54 or 3.1999999999999999e121 < x

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 44.0%

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

   if -4.19999999999999972e54 < x < 3.1999999999999999e121

   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 z around inf 32.1%

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

   4. Taylor expanded in y around 0 13.9%

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

Alternative 22: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+108}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9500000000.0) x (if (<= x 1.7e+108) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9500000000.0) {
		tmp = x;
	} else if (x <= 1.7e+108) {
		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 <= (-9500000000.0d0)) then
        tmp = x
    else if (x <= 1.7d+108) 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 <= -9500000000.0) {
		tmp = x;
	} else if (x <= 1.7e+108) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9500000000.0:
		tmp = x
	elif x <= 1.7e+108:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9500000000.0)
		tmp = x;
	elseif (x <= 1.7e+108)
		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 <= -9500000000.0)
		tmp = x;
	elseif (x <= 1.7e+108)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9500000000.0], x, If[LessEqual[x, 1.7e+108], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e9 or 1.69999999999999998e108 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 40.9%

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

   if -9.5e9 < x < 1.69999999999999998e108

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 32.3%

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

   4. Taylor expanded in t around 0 13.0%

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

Alternative 23: 11.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in a around inf 28.7%

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

4. Taylor expanded in t around 0 10.9%

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

Reproduce

herbie shell --seed 2024170 
(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)))