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

Percentage Accurate: 95.5% → 98.1%

Time: 19.9s

Alternatives: 23

Speedup: 0.5×

• 34.8% 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: 95.5% 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0))) <= Inf)
		tmp = Float64(t_1 - Float64(Float64(a * Float64(t + -1.0)) - Float64(b * Float64(t + Float64(y + -2.0)))));
	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);
	tmp = 0.0;
	if (((t_1 + (a * (1.0 - t))) + (b * ((y + t) - 2.0))) <= Inf)
		tmp = t_1 - ((a * (t + -1.0)) - (b * (t + (y + -2.0))));
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. sub-neg 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-+r+ 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

   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 78.0%

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

4. Final simplification 99.2%

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

Alternative 2: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.6%

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

   3. associate--l+ 97.6%

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

   4. sub-neg 97.6%

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

   5. metadata-eval 97.6%

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

   6. sub-neg 97.6%

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

   7. associate-+l- 97.6%

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

   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: 98.1% 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 78.0%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
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: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-246}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 0.00055:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- x (* (+ y -1.0) z)) (* y b))))
   (if (<= y -2.85e+57)
     t_1
     (if (<= y -1.4e-246)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= y 0.00055) (+ x (- z (* b (- 2.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - ((y + -1.0) * z)) + (y * b);
	double tmp;
	if (y <= -2.85e+57) {
		tmp = t_1;
	} else if (y <= -1.4e-246) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 0.00055) {
		tmp = x + (z - (b * (2.0 - 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 - ((y + (-1.0d0)) * z)) + (y * b)
    if (y <= (-2.85d+57)) then
        tmp = t_1
    else if (y <= (-1.4d-246)) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (y <= 0.00055d0) then
        tmp = x + (z - (b * (2.0d0 - 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 - ((y + -1.0) * z)) + (y * b);
	double tmp;
	if (y <= -2.85e+57) {
		tmp = t_1;
	} else if (y <= -1.4e-246) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (y <= 0.00055) {
		tmp = x + (z - (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x - ((y + -1.0) * z)) + (y * b)
	tmp = 0
	if y <= -2.85e+57:
		tmp = t_1
	elif y <= -1.4e-246:
		tmp = x + (z + (a * (1.0 - t)))
	elif y <= 0.00055:
		tmp = x + (z - (b * (2.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(y * b))
	tmp = 0.0
	if (y <= -2.85e+57)
		tmp = t_1;
	elseif (y <= -1.4e-246)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (y <= 0.00055)
		tmp = Float64(x + Float64(z - Float64(b * Float64(2.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x - ((y + -1.0) * z)) + (y * b);
	tmp = 0.0;
	if (y <= -2.85e+57)
		tmp = t_1;
	elseif (y <= -1.4e-246)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (y <= 0.00055)
		tmp = x + (z - (b * (2.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.85e+57], t$95$1, If[LessEqual[y, -1.4e-246], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00055], N[(x + N[(z - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8499999999999999e57 or 5.50000000000000033e-4 < y

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. metadata-eval 93.1%

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

      4. *-commutative 93.1%

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

      5. sub-neg 93.1%

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

      6. metadata-eval 93.1%

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

      7. sub-neg 93.1%

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

      8. metadata-eval 93.1%

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

      9. associate-+r+ 93.1%

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

      10. +-commutative 93.1%

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

      11. associate-+l+ 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-rgt-neg-in 75.7%

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

   7. Simplified 75.7%

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

   if -2.8499999999999999e57 < y < -1.4e-246

   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 79.3%

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

   4. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   6. Simplified 77.8%

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

   if -1.4e-246 < y < 5.50000000000000033e-4

   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. Step-by-step derivation

      1. associate-+l- 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. *-commutative 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

      7. sub-neg 97.8%

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

      8. metadata-eval 97.8%

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

      9. associate-+r+ 97.8%

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

      10. +-commutative 97.8%

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

      11. associate-+l+ 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in a around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. associate-+r+ 73.2%

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

      5. distribute-rgt-neg-in 73.2%

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

      6. associate-+r+ 73.2%

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

      7. +-commutative 73.2%

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

      8. +-commutative 73.2%

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

      9. distribute-neg-in 73.2%

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

      10. metadata-eval 73.2%

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

      11. sub-neg 73.2%

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

      12. +-commutative 73.2%

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

      13. associate--r+ 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. neg-mul-1 73.2%

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

      3. unsub-neg 73.2%

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

   10. Simplified 73.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+57}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-246}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;y \leq 0.00055:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1550000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;x + \left(t\_1 - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + \left(t + -2\right)\right) \cdot b + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -1550000000000.0) (not (<= z 5.2e-32)))
     (+ x (- t_1 (* (+ y -1.0) z)))
     (+ x (+ (* (+ y (+ 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 ((z <= -1550000000000.0) || !(z <= 5.2e-32)) {
		tmp = x + (t_1 - ((y + -1.0) * z));
	} else {
		tmp = x + (((y + (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 ((z <= (-1550000000000.0d0)) .or. (.not. (z <= 5.2d-32))) then
        tmp = x + (t_1 - ((y + (-1.0d0)) * z))
    else
        tmp = x + (((y + (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 ((z <= -1550000000000.0) || !(z <= 5.2e-32)) {
		tmp = x + (t_1 - ((y + -1.0) * z));
	} else {
		tmp = x + (((y + (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 (z <= -1550000000000.0) or not (z <= 5.2e-32):
		tmp = x + (t_1 - ((y + -1.0) * z))
	else:
		tmp = x + (((y + (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 ((z <= -1550000000000.0) || !(z <= 5.2e-32))
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + 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 ((z <= -1550000000000.0) || ~((z <= 5.2e-32)))
		tmp = x + (t_1 - ((y + -1.0) * z));
	else
		tmp = x + (((y + (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[z, -1550000000000.0], N[Not[LessEqual[z, 5.2e-32]], $MachinePrecision]], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e12 or 5.1999999999999995e-32 < z

   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 b around 0 82.2%

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

   if -1.55e12 < z < 5.1999999999999995e-32

   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. Step-by-step derivation

      1. associate-+l- 96.1%

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

      2. sub-neg 96.1%

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

      3. metadata-eval 96.1%

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

      4. *-commutative 96.1%

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

      5. sub-neg 96.1%

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

      6. metadata-eval 96.1%

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

      7. sub-neg 96.1%

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

      8. metadata-eval 96.1%

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

      9. associate-+r+ 96.1%

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

      10. +-commutative 96.1%

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

      11. associate-+l+ 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in z around 0 94.0%

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

      1. associate--l+ 94.0%

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

      2. sub-neg 94.0%

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

      3. +-commutative 94.0%

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

      4. metadata-eval 94.0%

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

      5. associate-+l+ 94.0%

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

      6. sub-neg 94.0%

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

      7. metadata-eval 94.0%

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

      8. +-commutative 94.0%

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

   7. Simplified 94.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1550000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + \left(t + -2\right)\right) \cdot b + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + \left(\left(y + \left(t + -2\right)\right) \cdot b + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= z -2.4e+85)
     (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))
     (if (<= z 5.2e-32)
       (+ x (+ (* (+ y (+ t -2.0)) b) t_1))
       (+ x (- t_1 (* (+ y -1.0) z)))))))

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 (z <= -2.4e+85) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else if (z <= 5.2e-32) {
		tmp = x + (((y + (t + -2.0)) * b) + t_1);
	} else {
		tmp = x + (t_1 - ((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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (z <= (-2.4d+85)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    else if (z <= 5.2d-32) then
        tmp = x + (((y + (t + (-2.0d0))) * b) + t_1)
    else
        tmp = x + (t_1 - ((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 t_1 = a * (1.0 - t);
	double tmp;
	if (z <= -2.4e+85) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else if (z <= 5.2e-32) {
		tmp = x + (((y + (t + -2.0)) * b) + t_1);
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if z <= -2.4e+85:
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	elif z <= 5.2e-32:
		tmp = x + (((y + (t + -2.0)) * b) + t_1)
	else:
		tmp = x + (t_1 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (z <= -2.4e+85)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	elseif (z <= 5.2e-32)
		tmp = Float64(x + Float64(Float64(Float64(y + Float64(t + -2.0)) * b) + t_1));
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	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 (z <= -2.4e+85)
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	elseif (z <= 5.2e-32)
		tmp = x + (((y + (t + -2.0)) * b) + t_1);
	else
		tmp = x + (t_1 - ((y + -1.0) * z));
	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[z, -2.4e+85], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-32], N[(x + N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999997e85

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0 90.3%

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

   if -2.39999999999999997e85 < z < 5.1999999999999995e-32

   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. Step-by-step derivation

      1. associate-+l- 95.9%

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

      2. sub-neg 95.9%

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

      3. metadata-eval 95.9%

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

      4. *-commutative 95.9%

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

      5. sub-neg 95.9%

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

      6. metadata-eval 95.9%

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

      7. sub-neg 95.9%

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

      8. metadata-eval 95.9%

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

      9. associate-+r+ 95.9%

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

      10. +-commutative 95.9%

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

      11. associate-+l+ 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. associate--l+ 92.0%

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

      2. sub-neg 92.0%

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

      3. +-commutative 92.0%

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

      4. metadata-eval 92.0%

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

      5. associate-+l+ 92.0%

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

      6. sub-neg 92.0%

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

      7. metadata-eval 92.0%

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

      8. +-commutative 92.0%

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

   7. Simplified 92.0%

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

   if 5.1999999999999995e-32 < z

   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 0 84.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + \left(\left(y + \left(t + -2\right)\right) \cdot b + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -7.6e+55)
     t_1
     (if (<= y -3.5e-24)
       (+ x (* a (- 1.0 t)))
       (if (<= y 1.35e+65) (+ x (- z (* b (- 2.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.6e+55) {
		tmp = t_1;
	} else if (y <= -3.5e-24) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 1.35e+65) {
		tmp = x + (z - (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-7.6d+55)) then
        tmp = t_1
    else if (y <= (-3.5d-24)) then
        tmp = x + (a * (1.0d0 - t))
    else if (y <= 1.35d+65) then
        tmp = x + (z - (b * (2.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7.6e+55) {
		tmp = t_1;
	} else if (y <= -3.5e-24) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 1.35e+65) {
		tmp = x + (z - (b * (2.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -7.6e+55:
		tmp = t_1
	elif y <= -3.5e-24:
		tmp = x + (a * (1.0 - t))
	elif y <= 1.35e+65:
		tmp = x + (z - (b * (2.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.6e+55)
		tmp = t_1;
	elseif (y <= -3.5e-24)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (y <= 1.35e+65)
		tmp = Float64(x + Float64(z - Float64(b * Float64(2.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.6e+55)
		tmp = t_1;
	elseif (y <= -3.5e-24)
		tmp = x + (a * (1.0 - t));
	elseif (y <= 1.35e+65)
		tmp = x + (z - (b * (2.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+55], t$95$1, If[LessEqual[y, -3.5e-24], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+65], N[(x + N[(z - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5999999999999999e55 or 1.35000000000000009e65 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 72.4%

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

   if -7.5999999999999999e55 < y < -3.4999999999999996e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 78.9%

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

   4. Taylor expanded in a around inf 73.0%

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

   if -3.4999999999999996e-24 < y < 1.35000000000000009e65

   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. Step-by-step derivation

      1. associate-+l- 98.6%

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

      2. sub-neg 98.6%

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

      3. metadata-eval 98.6%

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

      4. *-commutative 98.6%

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

      5. sub-neg 98.6%

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

      6. metadata-eval 98.6%

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

      7. sub-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. associate-+r+ 98.6%

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

      10. +-commutative 98.6%

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

      11. associate-+l+ 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in a around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. sub-neg 72.1%

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

      3. metadata-eval 72.1%

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

      4. associate-+r+ 72.1%

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

      5. distribute-rgt-neg-in 72.1%

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

      6. associate-+r+ 72.1%

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

      7. +-commutative 72.1%

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

      8. +-commutative 72.1%

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

      9. distribute-neg-in 72.1%

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

      10. metadata-eval 72.1%

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

      11. sub-neg 72.1%

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

      12. +-commutative 72.1%

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

      13. associate--r+ 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in y around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. neg-mul-1 69.5%

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

      3. unsub-neg 69.5%

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

   10. Simplified 69.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-72}:\\ \;\;\;\;x - \left(t \cdot a - a\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))))
   (if (<= z -1.8e+82)
     t_1
     (if (<= z -3.4e-72)
       (- x (- (* t a) a))
       (if (<= z 5.2e-32) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -1.8e+82) {
		tmp = t_1;
	} else if (z <= -3.4e-72) {
		tmp = x - ((t * a) - a);
	} else if (z <= 5.2e-32) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y + (-1.0d0)) * z)
    if (z <= (-1.8d+82)) then
        tmp = t_1
    else if (z <= (-3.4d-72)) then
        tmp = x - ((t * a) - a)
    else if (z <= 5.2d-32) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -1.8e+82) {
		tmp = t_1;
	} else if (z <= -3.4e-72) {
		tmp = x - ((t * a) - a);
	} else if (z <= 5.2e-32) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	tmp = 0
	if z <= -1.8e+82:
		tmp = t_1
	elif z <= -3.4e-72:
		tmp = x - ((t * a) - a)
	elif z <= 5.2e-32:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (z <= -1.8e+82)
		tmp = t_1;
	elseif (z <= -3.4e-72)
		tmp = Float64(x - Float64(Float64(t * a) - a));
	elseif (z <= 5.2e-32)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (z <= -1.8e+82)
		tmp = t_1;
	elseif (z <= -3.4e-72)
		tmp = x - ((t * a) - a);
	elseif (z <= 5.2e-32)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+82], t$95$1, If[LessEqual[z, -3.4e-72], N[(x - N[(N[(t * a), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-32], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000007e82 or 5.1999999999999995e-32 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 82.1%

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

   4. Taylor expanded in a around 0 68.4%

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

   if -1.80000000000000007e82 < z < -3.3999999999999998e-72

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 81.9%

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

   4. Taylor expanded in a around inf 74.1%

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

   5. Taylor expanded in t around 0 74.1%

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

   if -3.3999999999999998e-72 < z < 5.1999999999999995e-32

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. sub-neg 95.3%

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

      3. metadata-eval 95.3%

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

      4. *-commutative 95.3%

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

      5. sub-neg 95.3%

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

      6. metadata-eval 95.3%

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

      7. sub-neg 95.3%

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

      8. metadata-eval 95.3%

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

      9. associate-+r+ 95.3%

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

      10. +-commutative 95.3%

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

      11. associate-+l+ 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in a around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. sub-neg 69.8%

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

      3. metadata-eval 69.8%

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

      4. associate-+r+ 69.8%

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

      5. distribute-rgt-neg-in 69.8%

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

      6. associate-+r+ 69.8%

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

      7. +-commutative 69.8%

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

      8. +-commutative 69.8%

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

      9. distribute-neg-in 69.8%

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

      10. metadata-eval 69.8%

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

      11. sub-neg 69.8%

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

      12. +-commutative 69.8%

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

      13. associate--r+ 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in z around 0 68.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-72}:\\ \;\;\;\;x - \left(t \cdot a - a\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;z \leq -5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-71}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))))
   (if (<= z -5e+81)
     t_1
     (if (<= z -5.6e-71)
       (+ x (* a (- 1.0 t)))
       (if (<= z 5.2e-32) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -5e+81) {
		tmp = t_1;
	} else if (z <= -5.6e-71) {
		tmp = x + (a * (1.0 - t));
	} else if (z <= 5.2e-32) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y + (-1.0d0)) * z)
    if (z <= (-5d+81)) then
        tmp = t_1
    else if (z <= (-5.6d-71)) then
        tmp = x + (a * (1.0d0 - t))
    else if (z <= 5.2d-32) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double tmp;
	if (z <= -5e+81) {
		tmp = t_1;
	} else if (z <= -5.6e-71) {
		tmp = x + (a * (1.0 - t));
	} else if (z <= 5.2e-32) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	tmp = 0
	if z <= -5e+81:
		tmp = t_1
	elif z <= -5.6e-71:
		tmp = x + (a * (1.0 - t))
	elif z <= 5.2e-32:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (z <= -5e+81)
		tmp = t_1;
	elseif (z <= -5.6e-71)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (z <= 5.2e-32)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (z <= -5e+81)
		tmp = t_1;
	elseif (z <= -5.6e-71)
		tmp = x + (a * (1.0 - t));
	elseif (z <= 5.2e-32)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+81], t$95$1, If[LessEqual[z, -5.6e-71], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-32], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999998e81 or 5.1999999999999995e-32 < z

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 82.1%

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

   4. Taylor expanded in a around 0 68.4%

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

   if -4.9999999999999998e81 < z < -5.60000000000000001e-71

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 81.9%

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

   4. Taylor expanded in a around inf 74.1%

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

   if -5.60000000000000001e-71 < z < 5.1999999999999995e-32

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. sub-neg 95.3%

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

      3. metadata-eval 95.3%

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

      4. *-commutative 95.3%

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

      5. sub-neg 95.3%

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

      6. metadata-eval 95.3%

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

      7. sub-neg 95.3%

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

      8. metadata-eval 95.3%

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

      9. associate-+r+ 95.3%

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

      10. +-commutative 95.3%

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

      11. associate-+l+ 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in a around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. sub-neg 69.8%

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

      3. metadata-eval 69.8%

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

      4. associate-+r+ 69.8%

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

      5. distribute-rgt-neg-in 69.8%

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

      6. associate-+r+ 69.8%

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

      7. +-commutative 69.8%

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

      8. +-commutative 69.8%

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

      9. distribute-neg-in 69.8%

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

      10. metadata-eval 69.8%

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

      11. sub-neg 69.8%

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

      12. +-commutative 69.8%

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

      13. associate--r+ 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in z around 0 68.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+81}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-71}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-32}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+83} \lor \neg \left(b \leq 7 \cdot 10^{+101}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+83) (not (<= b 7e+101)))
   (+ 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 <= -1.9e+83) || !(b <= 7e+101)) {
		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 <= (-1.9d+83)) .or. (.not. (b <= 7d+101))) 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 <= -1.9e+83) || !(b <= 7e+101)) {
		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 <= -1.9e+83) or not (b <= 7e+101):
		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 <= -1.9e+83) || !(b <= 7e+101))
		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 <= -1.9e+83) || ~((b <= 7e+101)))
		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, -1.9e+83], N[Not[LessEqual[b, 7e+101]], $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 < -1.9000000000000001e83 or 7.00000000000000046e101 < b

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. sub-neg 91.7%

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

      3. metadata-eval 91.7%

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

      4. *-commutative 91.7%

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

      5. sub-neg 91.7%

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

      6. metadata-eval 91.7%

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

      7. sub-neg 91.7%

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

      8. metadata-eval 91.7%

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

      9. associate-+r+ 91.7%

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

      10. +-commutative 91.7%

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

      11. associate-+l+ 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in a around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. sub-neg 86.9%

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

      3. metadata-eval 86.9%

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

      4. associate-+r+ 86.9%

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

      5. distribute-rgt-neg-in 86.9%

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

      6. associate-+r+ 86.9%

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

      7. +-commutative 86.9%

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

      8. +-commutative 86.9%

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

      9. distribute-neg-in 86.9%

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

      10. metadata-eval 86.9%

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

      11. sub-neg 86.9%

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

      12. +-commutative 86.9%

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

      13. associate--r+ 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in z around 0 80.2%

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

   if -1.9000000000000001e83 < b < 7.00000000000000046e101

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 86.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+83} \lor \neg \left(b \leq 7 \cdot 10^{+101}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-120}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.3e+17)
     t_1
     (if (<= y 6.2e-120) (+ x a) (if (<= y 5.7e+66) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.3e+17) {
		tmp = t_1;
	} else if (y <= 6.2e-120) {
		tmp = x + a;
	} else if (y <= 5.7e+66) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.3d+17)) then
        tmp = t_1
    else if (y <= 6.2d-120) then
        tmp = x + a
    else if (y <= 5.7d+66) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.3e+17) {
		tmp = t_1;
	} else if (y <= 6.2e-120) {
		tmp = x + a;
	} else if (y <= 5.7e+66) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.3e+17:
		tmp = t_1
	elif y <= 6.2e-120:
		tmp = x + a
	elif y <= 5.7e+66:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.3e+17)
		tmp = t_1;
	elseif (y <= 6.2e-120)
		tmp = Float64(x + a);
	elseif (y <= 5.7e+66)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.3e+17)
		tmp = t_1;
	elseif (y <= 6.2e-120)
		tmp = x + a;
	elseif (y <= 5.7e+66)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+17], t$95$1, If[LessEqual[y, 6.2e-120], N[(x + a), $MachinePrecision], If[LessEqual[y, 5.7e+66], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e17 or 5.7000000000000003e66 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 69.3%

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

   if -2.3e17 < y < 6.20000000000000038e-120

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 72.4%

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

   4. Taylor expanded in a around inf 55.2%

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

   5. Taylor expanded in t around 0 41.2%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. sub-neg 41.2%

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

      2. neg-mul-1 41.2%

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

      3. remove-double-neg 41.2%

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

      4. +-commutative 41.2%

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

   7. Simplified 41.2%

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

   if 6.20000000000000038e-120 < y < 5.7000000000000003e66

   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 t around inf 43.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-120}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -25500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -25500.0)
     t_1
     (if (<= t -1.85e-53) (* b (- y 2.0)) (if (<= t 4e+37) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -25500.0) {
		tmp = t_1;
	} else if (t <= -1.85e-53) {
		tmp = b * (y - 2.0);
	} else if (t <= 4e+37) {
		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 = t * (b - a)
    if (t <= (-25500.0d0)) then
        tmp = t_1
    else if (t <= (-1.85d-53)) then
        tmp = b * (y - 2.0d0)
    else if (t <= 4d+37) 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 = t * (b - a);
	double tmp;
	if (t <= -25500.0) {
		tmp = t_1;
	} else if (t <= -1.85e-53) {
		tmp = b * (y - 2.0);
	} else if (t <= 4e+37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -25500.0:
		tmp = t_1
	elif t <= -1.85e-53:
		tmp = b * (y - 2.0)
	elif t <= 4e+37:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -25500.0)
		tmp = t_1;
	elseif (t <= -1.85e-53)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 4e+37)
		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 = t * (b - a);
	tmp = 0.0;
	if (t <= -25500.0)
		tmp = t_1;
	elseif (t <= -1.85e-53)
		tmp = b * (y - 2.0);
	elseif (t <= 4e+37)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -25500.0], t$95$1, If[LessEqual[t, -1.85e-53], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+37], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -25500 or 3.99999999999999982e37 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in t around inf 63.9%

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

   if -25500 < t < -1.84999999999999991e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 60.0%

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

   4. Taylor expanded in t around 0 56.0%

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

   if -1.84999999999999991e-53 < t < 3.99999999999999982e37

   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 76.1%

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

   4. Taylor expanded in a around inf 43.3%

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

   5. Taylor expanded in t around 0 41.9%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. sub-neg 41.9%

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

      2. neg-mul-1 41.9%

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

      3. remove-double-neg 41.9%

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

      4. +-commutative 41.9%

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

   7. Simplified 41.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -25500:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+53} \lor \neg \left(b \leq 2.6 \cdot 10^{+101}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.25e+53) (not (<= b 2.6e+101)))
   (+ x (* b (- (+ y t) 2.0)))
   (- (+ x a) (* (+ y -1.0) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.25e+53) || !(b <= 2.6e+101)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - ((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 <= (-1.25d+53)) .or. (.not. (b <= 2.6d+101))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + a) - ((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 <= -1.25e+53) || !(b <= 2.6e+101)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - ((y + -1.0) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.25e+53) or not (b <= 2.6e+101):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + a) - ((y + -1.0) * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.25e+53) || !(b <= 2.6e+101))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + a) - 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 <= -1.25e+53) || ~((b <= 2.6e+101)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + a) - ((y + -1.0) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.25e+53], N[Not[LessEqual[b, 2.6e+101]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2500000000000001e53 or 2.6e101 < b

   1. Initial program 92.7%

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

      1. associate-+l- 92.7%

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

      2. sub-neg 92.7%

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

      3. metadata-eval 92.7%

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

      4. *-commutative 92.7%

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

      5. sub-neg 92.7%

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

      6. metadata-eval 92.7%

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

      7. sub-neg 92.7%

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

      8. metadata-eval 92.7%

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

      9. associate-+r+ 92.7%

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

      10. +-commutative 92.7%

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

      11. associate-+l+ 92.7%

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

   4. Applied egg-rr 92.7%

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

   5. Taylor expanded in a around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. sub-neg 86.0%

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

      3. metadata-eval 86.0%

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

      4. associate-+r+ 86.0%

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

      5. distribute-rgt-neg-in 86.0%

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

      6. associate-+r+ 86.0%

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

      7. +-commutative 86.0%

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

      8. +-commutative 86.0%

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

      9. distribute-neg-in 86.0%

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

      10. metadata-eval 86.0%

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

      11. sub-neg 86.0%

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

      12. +-commutative 86.0%

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

      13. associate--r+ 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in z around 0 76.8%

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

   if -1.2500000000000001e53 < b < 2.6e101

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0 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. associate--r+ 69.6%

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

      2. sub-neg 69.6%

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

      3. metadata-eval 69.6%

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

      4. sub-neg 69.6%

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

      5. neg-mul-1 69.6%

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

      6. remove-double-neg 69.6%

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

   6. Simplified 69.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+53} \lor \neg \left(b \leq 2.6 \cdot 10^{+101}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-270}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.8e+96)
   x
   (if (<= x 5.4e-270) (* t b) (if (<= x 1.22e+47) (* -2.0 b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+96) {
		tmp = x;
	} else if (x <= 5.4e-270) {
		tmp = t * b;
	} else if (x <= 1.22e+47) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.8d+96)) then
        tmp = x
    else if (x <= 5.4d-270) then
        tmp = t * b
    else if (x <= 1.22d+47) then
        tmp = (-2.0d0) * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+96) {
		tmp = x;
	} else if (x <= 5.4e-270) {
		tmp = t * b;
	} else if (x <= 1.22e+47) {
		tmp = -2.0 * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+96:
		tmp = x
	elif x <= 5.4e-270:
		tmp = t * b
	elif x <= 1.22e+47:
		tmp = -2.0 * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+96)
		tmp = x;
	elseif (x <= 5.4e-270)
		tmp = Float64(t * b);
	elseif (x <= 1.22e+47)
		tmp = Float64(-2.0 * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.8e+96)
		tmp = x;
	elseif (x <= 5.4e-270)
		tmp = t * b;
	elseif (x <= 1.22e+47)
		tmp = -2.0 * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+96], x, If[LessEqual[x, 5.4e-270], N[(t * b), $MachinePrecision], If[LessEqual[x, 1.22e+47], N[(-2.0 * b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000007e96 or 1.22e47 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 41.3%

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

   if -1.80000000000000007e96 < x < 5.40000000000000014e-270

   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 t around inf 31.8%

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

   4. Taylor expanded in b around inf 19.3%

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

   if 5.40000000000000014e-270 < x < 1.22e47

   1. Initial program 95.4%

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

   3. Taylor expanded in b around inf 40.4%

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

   4. Taylor expanded in y around 0 27.2%

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

   5. Taylor expanded in t around 0 19.9%

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

      1. *-commutative 19.9%

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

   7. Simplified 19.9%

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

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-270}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+81} \lor \neg \left(z \leq 3.6 \cdot 10^{+18}\right):\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+81) (not (<= z 3.6e+18)))
   (- x (* (+ y -1.0) z))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+81) || !(z <= 3.6e+18)) {
		tmp = x - ((y + -1.0) * z);
	} 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 ((z <= (-3.6d+81)) .or. (.not. (z <= 3.6d+18))) then
        tmp = x - ((y + (-1.0d0)) * z)
    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 ((z <= -3.6e+81) || !(z <= 3.6e+18)) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.6e+81) or not (z <= 3.6e+18):
		tmp = x - ((y + -1.0) * z)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+81) || !(z <= 3.6e+18))
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	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 ((z <= -3.6e+81) || ~((z <= 3.6e+18)))
		tmp = x - ((y + -1.0) * z);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+81], N[Not[LessEqual[z, 3.6e+18]], $MachinePrecision]], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000005e81 or 3.6e18 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in b around 0 81.3%

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

   4. Taylor expanded in a around 0 71.0%

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

   if -3.60000000000000005e81 < z < 3.6e18

   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 b around 0 63.5%

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

   4. Taylor expanded in a around inf 58.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+81} \lor \neg \left(z \leq 3.6 \cdot 10^{+18}\right):\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+97} \lor \neg \left(z \leq 1.2 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+97) (not (<= z 1.2e+105)))
   (* z (- 1.0 y))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+97) || !(z <= 1.2e+105)) {
		tmp = z * (1.0 - y);
	} 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 ((z <= (-1d+97)) .or. (.not. (z <= 1.2d+105))) then
        tmp = z * (1.0d0 - y)
    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 ((z <= -1e+97) || !(z <= 1.2e+105)) {
		tmp = z * (1.0 - y);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+97) or not (z <= 1.2e+105):
		tmp = z * (1.0 - y)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+97) || !(z <= 1.2e+105))
		tmp = Float64(z * Float64(1.0 - y));
	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 ((z <= -1e+97) || ~((z <= 1.2e+105)))
		tmp = z * (1.0 - y);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+97], N[Not[LessEqual[z, 1.2e+105]], $MachinePrecision]], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0000000000000001e97 or 1.19999999999999987e105 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 69.6%

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

   if -1.0000000000000001e97 < z < 1.19999999999999987e105

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0 64.9%

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

   4. Taylor expanded in a around inf 57.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+97} \lor \neg \left(z \leq 1.2 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+17} \lor \neg \left(y \leq 6.2 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+17) (not (<= y 6.2e+64))) (* 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 <= -4.1e+17) || !(y <= 6.2e+64)) {
		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 <= (-4.1d+17)) .or. (.not. (y <= 6.2d+64))) 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 <= -4.1e+17) || !(y <= 6.2e+64)) {
		tmp = y * (b - z);
	} else {
		tmp = a + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.1e+17) or not (y <= 6.2e+64):
		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 <= -4.1e+17) || !(y <= 6.2e+64))
		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 <= -4.1e+17) || ~((y <= 6.2e+64)))
		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, -4.1e+17], N[Not[LessEqual[y, 6.2e+64]], $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 < -4.1e17 or 6.1999999999999998e64 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 69.3%

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

   if -4.1e17 < y < 6.1999999999999998e64

   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 71.2%

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

   4. Taylor expanded in t around 0 55.9%

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

      1. associate--r+ 55.9%

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

      2. sub-neg 55.9%

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

      3. metadata-eval 55.9%

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

      4. sub-neg 55.9%

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

      5. neg-mul-1 55.9%

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

      6. remove-double-neg 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in y around 0 54.2%

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

      1. neg-mul-1 54.2%

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

      2. associate--l+ 54.2%

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

      3. sub-neg 54.2%

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

      4. remove-double-neg 54.2%

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

   9. Simplified 54.2%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+17} \lor \neg \left(y \leq 6.2 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+121}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+73}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.3e+121) (* y b) (if (<= y 8e+73) (+ x a) (* y (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.3e+121) {
		tmp = y * b;
	} else if (y <= 8e+73) {
		tmp = x + a;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.3d+121)) then
        tmp = y * b
    else if (y <= 8d+73) then
        tmp = x + a
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.3e+121) {
		tmp = y * b;
	} else if (y <= 8e+73) {
		tmp = x + a;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.3e+121:
		tmp = y * b
	elif y <= 8e+73:
		tmp = x + a
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.3e+121)
		tmp = Float64(y * b);
	elseif (y <= 8e+73)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.3e+121)
		tmp = y * b;
	elseif (y <= 8e+73)
		tmp = x + a;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.3e+121], N[(y * b), $MachinePrecision], If[LessEqual[y, 8e+73], N[(x + a), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.30000000000000009e121

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf 44.3%

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

   4. Taylor expanded in y around inf 42.0%

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

      1. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -5.30000000000000009e121 < y < 7.99999999999999986e73

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 71.7%

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

   4. Taylor expanded in a around inf 52.5%

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

   5. Taylor expanded in t around 0 37.0%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. sub-neg 37.0%

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

      2. neg-mul-1 37.0%

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

      3. remove-double-neg 37.0%

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

      4. +-commutative 37.0%

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

   7. Simplified 37.0%

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

   if 7.99999999999999986e73 < y

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 65.0%

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

   4. Taylor expanded in y around inf 65.0%

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

      1. associate-*r* 65.0%

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

      2. neg-mul-1 65.0%

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

   6. Simplified 65.0%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+121}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+73}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.8e+65) (* t b) (if (<= t 1.95e+38) (+ x a) (* t (- a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e+65) {
		tmp = t * b;
	} else if (t <= 1.95e+38) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.8d+65)) then
        tmp = t * b
    else if (t <= 1.95d+38) then
        tmp = x + a
    else
        tmp = t * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e+65) {
		tmp = t * b;
	} else if (t <= 1.95e+38) {
		tmp = x + a;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.8e+65:
		tmp = t * b
	elif t <= 1.95e+38:
		tmp = x + a
	else:
		tmp = t * -a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.8e+65)
		tmp = Float64(t * b);
	elseif (t <= 1.95e+38)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.8e+65)
		tmp = t * b;
	elseif (t <= 1.95e+38)
		tmp = x + a;
	else
		tmp = t * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.8e+65], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.95e+38], N[(x + a), $MachinePrecision], N[(t * (-a)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999999e65

   1. Initial program 92.1%

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

   3. Taylor expanded in t around inf 69.9%

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

   4. Taylor expanded in b around inf 41.8%

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

   if -6.7999999999999999e65 < t < 1.95000000000000012e38

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 74.8%

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

   4. Taylor expanded in a around inf 42.5%

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

   5. Taylor expanded in t around 0 38.6%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. sub-neg 38.6%

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

      2. neg-mul-1 38.6%

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

      3. remove-double-neg 38.6%

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

      4. +-commutative 38.6%

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

   7. Simplified 38.6%

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

   if 1.95000000000000012e38 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 66.3%

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

   4. Taylor expanded in b around 0 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

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

   6. Simplified 44.4%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+60} \lor \neg \left(t \leq 7.8 \cdot 10^{+207}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.6e+60) (not (<= t 7.8e+207))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.6e+60) || !(t <= 7.8e+207)) {
		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 <= (-6.6d+60)) .or. (.not. (t <= 7.8d+207))) 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 <= -6.6e+60) || !(t <= 7.8e+207)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.6e+60) or not (t <= 7.8e+207):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.6e+60) || !(t <= 7.8e+207))
		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 <= -6.6e+60) || ~((t <= 7.8e+207)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.6e+60], N[Not[LessEqual[t, 7.8e+207]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5999999999999995e60 or 7.79999999999999945e207 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in t around inf 73.3%

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

   4. Taylor expanded in b around inf 40.0%

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

   if -6.5999999999999995e60 < t < 7.79999999999999945e207

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 75.2%

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

   4. Taylor expanded in a around inf 44.7%

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

   5. Taylor expanded in t around 0 35.7%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   6. Step-by-step derivation

      1. sub-neg 35.7%

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

      2. neg-mul-1 35.7%

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

      3. remove-double-neg 35.7%

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

      4. +-commutative 35.7%

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

   7. Simplified 35.7%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+60} \lor \neg \left(t \leq 7.8 \cdot 10^{+207}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+18} \lor \neg \left(y \leq 2.3 \cdot 10^{+138}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+18) (not (<= y 2.3e+138))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+18) || !(y <= 2.3e+138)) {
		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 <= (-4.2d+18)) .or. (.not. (y <= 2.3d+138))) 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 <= -4.2e+18) || !(y <= 2.3e+138)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e+18) or not (y <= 2.3e+138):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e+18) || !(y <= 2.3e+138))
		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 <= -4.2e+18) || ~((y <= 2.3e+138)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e+18], N[Not[LessEqual[y, 2.3e+138]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e18 or 2.30000000000000008e138 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in b around inf 39.6%

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

   4. Taylor expanded in y around inf 35.9%

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

      1. *-commutative 35.9%

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

   6. Simplified 35.9%

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

   if -4.2e18 < y < 2.30000000000000008e138

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 22.2%

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

4. Final simplification 26.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+18} \lor \neg \left(y \leq 2.3 \cdot 10^{+138}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+154}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e+154) z (if (<= z 2.1e+48) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+154) {
		tmp = z;
	} else if (z <= 2.1e+48) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.5d+154)) then
        tmp = z
    else if (z <= 2.1d+48) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+154) {
		tmp = z;
	} else if (z <= 2.1e+48) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.5e+154:
		tmp = z
	elif z <= 2.1e+48:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e+154)
		tmp = z;
	elseif (z <= 2.1e+48)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.5e+154)
		tmp = z;
	elseif (z <= 2.1e+48)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e+154], z, If[LessEqual[z, 2.1e+48], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000006e154 or 2.0999999999999998e48 < z

   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 z around inf 64.6%

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

   4. Taylor expanded in y around 0 32.1%

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

   if -5.5000000000000006e154 < z < 2.0999999999999998e48

   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 x around inf 23.6%

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

Alternative 23: 16.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in x around inf 18.4%

   \[\leadsto \color{blue}{x} \]
4. 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)))