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

Percentage Accurate: 95.2% → 98.1%

Time: 17.2s

Alternatives: 23

Speedup: 0.5×

• 35.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 70.2%

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

4. Final simplification 98.8%

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

Alternative 2: 97.6% 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 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-def 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fma-neg 97.6%

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

   9. sub-neg 97.6%

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

   10. metadata-eval 97.6%

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

   11. remove-double-neg 97.6%

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

   12. sub-neg 97.6%

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

   13. metadata-eval 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 36.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+182}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -280000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 0.061:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- y 2.0))))
   (if (<= b -5.8e+182)
     (* t b)
     (if (<= b -280000000000.0)
       t_2
       (if (<= b 3.4e-271)
         t_1
         (if (<= b 6.5e-238)
           x
           (if (<= b 0.061)
             t_1
             (if (<= b 1.1e+38)
               (* t b)
               (if (<= b 1.1e+149)
                 t_1
                 (if (<= b 5.2e+207) (* t b) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -5.8e+182) {
		tmp = t * b;
	} else if (b <= -280000000000.0) {
		tmp = t_2;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 0.061) {
		tmp = t_1;
	} else if (b <= 1.1e+38) {
		tmp = t * b;
	} else if (b <= 1.1e+149) {
		tmp = t_1;
	} else if (b <= 5.2e+207) {
		tmp = t * b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (y - 2.0d0)
    if (b <= (-5.8d+182)) then
        tmp = t * b
    else if (b <= (-280000000000.0d0)) then
        tmp = t_2
    else if (b <= 3.4d-271) then
        tmp = t_1
    else if (b <= 6.5d-238) then
        tmp = x
    else if (b <= 0.061d0) then
        tmp = t_1
    else if (b <= 1.1d+38) then
        tmp = t * b
    else if (b <= 1.1d+149) then
        tmp = t_1
    else if (b <= 5.2d+207) then
        tmp = t * b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -5.8e+182) {
		tmp = t * b;
	} else if (b <= -280000000000.0) {
		tmp = t_2;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 0.061) {
		tmp = t_1;
	} else if (b <= 1.1e+38) {
		tmp = t * b;
	} else if (b <= 1.1e+149) {
		tmp = t_1;
	} else if (b <= 5.2e+207) {
		tmp = t * b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -5.8e+182:
		tmp = t * b
	elif b <= -280000000000.0:
		tmp = t_2
	elif b <= 3.4e-271:
		tmp = t_1
	elif b <= 6.5e-238:
		tmp = x
	elif b <= 0.061:
		tmp = t_1
	elif b <= 1.1e+38:
		tmp = t * b
	elif b <= 1.1e+149:
		tmp = t_1
	elif b <= 5.2e+207:
		tmp = t * b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -5.8e+182)
		tmp = Float64(t * b);
	elseif (b <= -280000000000.0)
		tmp = t_2;
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 0.061)
		tmp = t_1;
	elseif (b <= 1.1e+38)
		tmp = Float64(t * b);
	elseif (b <= 1.1e+149)
		tmp = t_1;
	elseif (b <= 5.2e+207)
		tmp = Float64(t * b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -5.8e+182)
		tmp = t * b;
	elseif (b <= -280000000000.0)
		tmp = t_2;
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 0.061)
		tmp = t_1;
	elseif (b <= 1.1e+38)
		tmp = t * b;
	elseif (b <= 1.1e+149)
		tmp = t_1;
	elseif (b <= 5.2e+207)
		tmp = t * b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+182], N[(t * b), $MachinePrecision], If[LessEqual[b, -280000000000.0], t$95$2, If[LessEqual[b, 3.4e-271], t$95$1, If[LessEqual[b, 6.5e-238], x, If[LessEqual[b, 0.061], t$95$1, If[LessEqual[b, 1.1e+38], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.1e+149], t$95$1, If[LessEqual[b, 5.2e+207], N[(t * b), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.7999999999999997e182 or 0.060999999999999999 < b < 1.10000000000000003e38 or 1.1e149 < b < 5.1999999999999996e207

   1. Initial program 94.3%

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

   3. Taylor expanded in a around 0 96.2%

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

   4. Taylor expanded in t around inf 61.5%

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

   if -5.7999999999999997e182 < b < -2.8e11 or 5.1999999999999996e207 < b

   1. Initial program 92.8%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0 51.9%

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

   if -2.8e11 < b < 3.4000000000000001e-271 or 6.5000000000000006e-238 < b < 0.060999999999999999 or 1.10000000000000003e38 < b < 1.1e149

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 47.5%

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

   if 3.4000000000000001e-271 < b < 6.5000000000000006e-238

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+182}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -280000000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 0.061:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+149}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot b\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := y \cdot \left(b - z\right)\\ t_4 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{+32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-290}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-281}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t b)))
        (t_2 (* t (- b a)))
        (t_3 (* y (- b z)))
        (t_4 (* a (- 1.0 t))))
   (if (<= y -2.85e+32)
     t_3
     (if (<= y -2.4e-96)
       t_1
       (if (<= y -1.05e-284)
         t_2
         (if (<= y 9.5e-290)
           t_4
           (if (<= y 2.6e-281)
             (* -2.0 b)
             (if (<= y 2.95e-162)
               t_2
               (if (<= y 1.7e-126) t_4 (if (<= y 5.6e+36) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double t_4 = a * (1.0 - t);
	double tmp;
	if (y <= -2.85e+32) {
		tmp = t_3;
	} else if (y <= -2.4e-96) {
		tmp = t_1;
	} else if (y <= -1.05e-284) {
		tmp = t_2;
	} else if (y <= 9.5e-290) {
		tmp = t_4;
	} else if (y <= 2.6e-281) {
		tmp = -2.0 * b;
	} else if (y <= 2.95e-162) {
		tmp = t_2;
	} else if (y <= 1.7e-126) {
		tmp = t_4;
	} else if (y <= 5.6e+36) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (t * b)
    t_2 = t * (b - a)
    t_3 = y * (b - z)
    t_4 = a * (1.0d0 - t)
    if (y <= (-2.85d+32)) then
        tmp = t_3
    else if (y <= (-2.4d-96)) then
        tmp = t_1
    else if (y <= (-1.05d-284)) then
        tmp = t_2
    else if (y <= 9.5d-290) then
        tmp = t_4
    else if (y <= 2.6d-281) then
        tmp = (-2.0d0) * b
    else if (y <= 2.95d-162) then
        tmp = t_2
    else if (y <= 1.7d-126) then
        tmp = t_4
    else if (y <= 5.6d+36) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double t_4 = a * (1.0 - t);
	double tmp;
	if (y <= -2.85e+32) {
		tmp = t_3;
	} else if (y <= -2.4e-96) {
		tmp = t_1;
	} else if (y <= -1.05e-284) {
		tmp = t_2;
	} else if (y <= 9.5e-290) {
		tmp = t_4;
	} else if (y <= 2.6e-281) {
		tmp = -2.0 * b;
	} else if (y <= 2.95e-162) {
		tmp = t_2;
	} else if (y <= 1.7e-126) {
		tmp = t_4;
	} else if (y <= 5.6e+36) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * b)
	t_2 = t * (b - a)
	t_3 = y * (b - z)
	t_4 = a * (1.0 - t)
	tmp = 0
	if y <= -2.85e+32:
		tmp = t_3
	elif y <= -2.4e-96:
		tmp = t_1
	elif y <= -1.05e-284:
		tmp = t_2
	elif y <= 9.5e-290:
		tmp = t_4
	elif y <= 2.6e-281:
		tmp = -2.0 * b
	elif y <= 2.95e-162:
		tmp = t_2
	elif y <= 1.7e-126:
		tmp = t_4
	elif y <= 5.6e+36:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * b))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(y * Float64(b - z))
	t_4 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (y <= -2.85e+32)
		tmp = t_3;
	elseif (y <= -2.4e-96)
		tmp = t_1;
	elseif (y <= -1.05e-284)
		tmp = t_2;
	elseif (y <= 9.5e-290)
		tmp = t_4;
	elseif (y <= 2.6e-281)
		tmp = Float64(-2.0 * b);
	elseif (y <= 2.95e-162)
		tmp = t_2;
	elseif (y <= 1.7e-126)
		tmp = t_4;
	elseif (y <= 5.6e+36)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * b);
	t_2 = t * (b - a);
	t_3 = y * (b - z);
	t_4 = a * (1.0 - t);
	tmp = 0.0;
	if (y <= -2.85e+32)
		tmp = t_3;
	elseif (y <= -2.4e-96)
		tmp = t_1;
	elseif (y <= -1.05e-284)
		tmp = t_2;
	elseif (y <= 9.5e-290)
		tmp = t_4;
	elseif (y <= 2.6e-281)
		tmp = -2.0 * b;
	elseif (y <= 2.95e-162)
		tmp = t_2;
	elseif (y <= 1.7e-126)
		tmp = t_4;
	elseif (y <= 5.6e+36)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.85e+32], t$95$3, If[LessEqual[y, -2.4e-96], t$95$1, If[LessEqual[y, -1.05e-284], t$95$2, If[LessEqual[y, 9.5e-290], t$95$4, If[LessEqual[y, 2.6e-281], N[(-2.0 * b), $MachinePrecision], If[LessEqual[y, 2.95e-162], t$95$2, If[LessEqual[y, 1.7e-126], t$95$4, If[LessEqual[y, 5.6e+36], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.85e32 or 5.6000000000000001e36 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 64.3%

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

   if -2.85e32 < y < -2.40000000000000019e-96 or 1.7e-126 < y < 5.6000000000000001e36

   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 z around 0 86.1%

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

   4. Taylor expanded in a around 0 67.9%

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

   5. Taylor expanded in t around inf 57.4%

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

   if -2.40000000000000019e-96 < y < -1.04999999999999996e-284 or 2.60000000000000005e-281 < y < 2.9499999999999998e-162

   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 t around inf 58.0%

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

   if -1.04999999999999996e-284 < y < 9.50000000000000023e-290 or 2.9499999999999998e-162 < y < 1.7e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 62.5%

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

   if 9.50000000000000023e-290 < y < 2.60000000000000005e-281

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-rgt-neg-in 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in t around 0 61.2%

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

   7. Taylor expanded in y around 0 61.2%

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

      1. *-commutative 61.2%

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

   9. Simplified 61.2%

      \[\leadsto \color{blue}{b \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-96}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-284}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-281}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+36}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -66000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+63}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (* a (- 1.0 t)))
        (t_3 (* b (- (+ y t) 2.0))))
   (if (<= b -66000000000.0)
     t_3
     (if (<= b 3.4e-271)
       t_2
       (if (<= b 6.5e-238)
         x
         (if (<= b 2.7e-140)
           t_2
           (if (<= b 9e-77)
             t_1
             (if (<= b 1.15e+63)
               (+ x (* t b))
               (if (<= b 4.6e+115) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -66000000000.0) {
		tmp = t_3;
	} else if (b <= 3.4e-271) {
		tmp = t_2;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 2.7e-140) {
		tmp = t_2;
	} else if (b <= 9e-77) {
		tmp = t_1;
	} else if (b <= 1.15e+63) {
		tmp = x + (t * b);
	} else if (b <= 4.6e+115) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = a * (1.0d0 - t)
    t_3 = b * ((y + t) - 2.0d0)
    if (b <= (-66000000000.0d0)) then
        tmp = t_3
    else if (b <= 3.4d-271) then
        tmp = t_2
    else if (b <= 6.5d-238) then
        tmp = x
    else if (b <= 2.7d-140) then
        tmp = t_2
    else if (b <= 9d-77) then
        tmp = t_1
    else if (b <= 1.15d+63) then
        tmp = x + (t * b)
    else if (b <= 4.6d+115) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -66000000000.0) {
		tmp = t_3;
	} else if (b <= 3.4e-271) {
		tmp = t_2;
	} else if (b <= 6.5e-238) {
		tmp = x;
	} else if (b <= 2.7e-140) {
		tmp = t_2;
	} else if (b <= 9e-77) {
		tmp = t_1;
	} else if (b <= 1.15e+63) {
		tmp = x + (t * b);
	} else if (b <= 4.6e+115) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = a * (1.0 - t)
	t_3 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -66000000000.0:
		tmp = t_3
	elif b <= 3.4e-271:
		tmp = t_2
	elif b <= 6.5e-238:
		tmp = x
	elif b <= 2.7e-140:
		tmp = t_2
	elif b <= 9e-77:
		tmp = t_1
	elif b <= 1.15e+63:
		tmp = x + (t * b)
	elif b <= 4.6e+115:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -66000000000.0)
		tmp = t_3;
	elseif (b <= 3.4e-271)
		tmp = t_2;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 2.7e-140)
		tmp = t_2;
	elseif (b <= 9e-77)
		tmp = t_1;
	elseif (b <= 1.15e+63)
		tmp = Float64(x + Float64(t * b));
	elseif (b <= 4.6e+115)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = a * (1.0 - t);
	t_3 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -66000000000.0)
		tmp = t_3;
	elseif (b <= 3.4e-271)
		tmp = t_2;
	elseif (b <= 6.5e-238)
		tmp = x;
	elseif (b <= 2.7e-140)
		tmp = t_2;
	elseif (b <= 9e-77)
		tmp = t_1;
	elseif (b <= 1.15e+63)
		tmp = x + (t * b);
	elseif (b <= 4.6e+115)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -66000000000.0], t$95$3, If[LessEqual[b, 3.4e-271], t$95$2, If[LessEqual[b, 6.5e-238], x, If[LessEqual[b, 2.7e-140], t$95$2, If[LessEqual[b, 9e-77], t$95$1, If[LessEqual[b, 1.15e+63], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+115], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.6e10 or 4.60000000000000007e115 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf 74.6%

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

   if -6.6e10 < b < 3.4000000000000001e-271 or 6.5000000000000006e-238 < b < 2.7e-140

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 55.7%

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

   if 3.4000000000000001e-271 < b < 6.5000000000000006e-238

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

   if 2.7e-140 < b < 9.0000000000000001e-77 or 1.14999999999999997e63 < b < 4.60000000000000007e115

   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 z around inf 64.6%

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

   if 9.0000000000000001e-77 < b < 1.14999999999999997e63

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in a around 0 67.8%

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

   5. Taylor expanded in t around inf 58.2%

      \[\leadsto x + \color{blue}{b \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -66000000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+63}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(t - 2\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 0.17:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+204}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* b (- t 2.0))))
        (t_3 (* b (- (+ y t) 2.0)))
        (t_4 (* z (- 1.0 y))))
   (if (<= b -3e+16)
     t_3
     (if (<= b 4.8e-140)
       t_1
       (if (<= b 3.2e-75)
         t_4
         (if (<= b 0.17)
           t_1
           (if (<= b 7.2e+56)
             t_2
             (if (<= b 4.6e+115) t_4 (if (<= b 4.8e+204) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * (t - 2.0));
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -3e+16) {
		tmp = t_3;
	} else if (b <= 4.8e-140) {
		tmp = t_1;
	} else if (b <= 3.2e-75) {
		tmp = t_4;
	} else if (b <= 0.17) {
		tmp = t_1;
	} else if (b <= 7.2e+56) {
		tmp = t_2;
	} else if (b <= 4.6e+115) {
		tmp = t_4;
	} else if (b <= 4.8e+204) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * (t - 2.0d0))
    t_3 = b * ((y + t) - 2.0d0)
    t_4 = z * (1.0d0 - y)
    if (b <= (-3d+16)) then
        tmp = t_3
    else if (b <= 4.8d-140) then
        tmp = t_1
    else if (b <= 3.2d-75) then
        tmp = t_4
    else if (b <= 0.17d0) then
        tmp = t_1
    else if (b <= 7.2d+56) then
        tmp = t_2
    else if (b <= 4.6d+115) then
        tmp = t_4
    else if (b <= 4.8d+204) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * (t - 2.0));
	double t_3 = b * ((y + t) - 2.0);
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -3e+16) {
		tmp = t_3;
	} else if (b <= 4.8e-140) {
		tmp = t_1;
	} else if (b <= 3.2e-75) {
		tmp = t_4;
	} else if (b <= 0.17) {
		tmp = t_1;
	} else if (b <= 7.2e+56) {
		tmp = t_2;
	} else if (b <= 4.6e+115) {
		tmp = t_4;
	} else if (b <= 4.8e+204) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * (t - 2.0))
	t_3 = b * ((y + t) - 2.0)
	t_4 = z * (1.0 - y)
	tmp = 0
	if b <= -3e+16:
		tmp = t_3
	elif b <= 4.8e-140:
		tmp = t_1
	elif b <= 3.2e-75:
		tmp = t_4
	elif b <= 0.17:
		tmp = t_1
	elif b <= 7.2e+56:
		tmp = t_2
	elif b <= 4.6e+115:
		tmp = t_4
	elif b <= 4.8e+204:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(t - 2.0)))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_4 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -3e+16)
		tmp = t_3;
	elseif (b <= 4.8e-140)
		tmp = t_1;
	elseif (b <= 3.2e-75)
		tmp = t_4;
	elseif (b <= 0.17)
		tmp = t_1;
	elseif (b <= 7.2e+56)
		tmp = t_2;
	elseif (b <= 4.6e+115)
		tmp = t_4;
	elseif (b <= 4.8e+204)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (b * (t - 2.0));
	t_3 = b * ((y + t) - 2.0);
	t_4 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -3e+16)
		tmp = t_3;
	elseif (b <= 4.8e-140)
		tmp = t_1;
	elseif (b <= 3.2e-75)
		tmp = t_4;
	elseif (b <= 0.17)
		tmp = t_1;
	elseif (b <= 7.2e+56)
		tmp = t_2;
	elseif (b <= 4.6e+115)
		tmp = t_4;
	elseif (b <= 4.8e+204)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+16], t$95$3, If[LessEqual[b, 4.8e-140], t$95$1, If[LessEqual[b, 3.2e-75], t$95$4, If[LessEqual[b, 0.17], t$95$1, If[LessEqual[b, 7.2e+56], t$95$2, If[LessEqual[b, 4.6e+115], t$95$4, If[LessEqual[b, 4.8e+204], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3e16 or 4.7999999999999999e204 < b

   1. Initial program 93.2%

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

   3. Taylor expanded in b around inf 79.3%

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

   if -3e16 < b < 4.79999999999999973e-140 or 3.19999999999999977e-75 < b < 0.170000000000000012

   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 z around 0 72.9%

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

   4. Taylor expanded in b around 0 69.3%

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

   if 4.79999999999999973e-140 < b < 3.19999999999999977e-75 or 7.19999999999999996e56 < b < 4.60000000000000007e115

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf 63.4%

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

   if 0.170000000000000012 < b < 7.19999999999999996e56 or 4.60000000000000007e115 < b < 4.7999999999999999e204

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 90.2%

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

   4. Taylor expanded in a around 0 81.9%

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

   5. Taylor expanded in y around 0 73.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-75}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 0.17:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+204}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 0.011:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+80}:\\ \;\;\;\;x + t\_3\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+204}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -1.45e+16)
     t_2
     (if (<= b 4.8e-140)
       t_1
       (if (<= b 4e-77)
         t_3
         (if (<= b 0.011)
           t_1
           (if (<= b 2e+50)
             t_2
             (if (<= b 6.5e+80)
               (+ x t_3)
               (if (<= b 1.65e+204) (+ x (* b (- t 2.0))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_2;
	} else if (b <= 4.8e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 0.011) {
		tmp = t_1;
	} else if (b <= 2e+50) {
		tmp = t_2;
	} else if (b <= 6.5e+80) {
		tmp = x + t_3;
	} else if (b <= 1.65e+204) {
		tmp = x + (b * (t - 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = z * (1.0d0 - y)
    if (b <= (-1.45d+16)) then
        tmp = t_2
    else if (b <= 4.8d-140) then
        tmp = t_1
    else if (b <= 4d-77) then
        tmp = t_3
    else if (b <= 0.011d0) then
        tmp = t_1
    else if (b <= 2d+50) then
        tmp = t_2
    else if (b <= 6.5d+80) then
        tmp = x + t_3
    else if (b <= 1.65d+204) then
        tmp = x + (b * (t - 2.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_2;
	} else if (b <= 4.8e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 0.011) {
		tmp = t_1;
	} else if (b <= 2e+50) {
		tmp = t_2;
	} else if (b <= 6.5e+80) {
		tmp = x + t_3;
	} else if (b <= 1.65e+204) {
		tmp = x + (b * (t - 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -1.45e+16:
		tmp = t_2
	elif b <= 4.8e-140:
		tmp = t_1
	elif b <= 4e-77:
		tmp = t_3
	elif b <= 0.011:
		tmp = t_1
	elif b <= 2e+50:
		tmp = t_2
	elif b <= 6.5e+80:
		tmp = x + t_3
	elif b <= 1.65e+204:
		tmp = x + (b * (t - 2.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -1.45e+16)
		tmp = t_2;
	elseif (b <= 4.8e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 0.011)
		tmp = t_1;
	elseif (b <= 2e+50)
		tmp = t_2;
	elseif (b <= 6.5e+80)
		tmp = Float64(x + t_3);
	elseif (b <= 1.65e+204)
		tmp = Float64(x + Float64(b * Float64(t - 2.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -1.45e+16)
		tmp = t_2;
	elseif (b <= 4.8e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 0.011)
		tmp = t_1;
	elseif (b <= 2e+50)
		tmp = t_2;
	elseif (b <= 6.5e+80)
		tmp = x + t_3;
	elseif (b <= 1.65e+204)
		tmp = x + (b * (t - 2.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+16], t$95$2, If[LessEqual[b, 4.8e-140], t$95$1, If[LessEqual[b, 4e-77], t$95$3, If[LessEqual[b, 0.011], t$95$1, If[LessEqual[b, 2e+50], t$95$2, If[LessEqual[b, 6.5e+80], N[(x + t$95$3), $MachinePrecision], If[LessEqual[b, 1.65e+204], N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.45e16 or 0.010999999999999999 < b < 2.0000000000000002e50 or 1.6499999999999999e204 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf 78.3%

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

   if -1.45e16 < b < 4.79999999999999973e-140 or 3.9999999999999997e-77 < b < 0.010999999999999999

   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 z around 0 72.9%

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

   4. Taylor expanded in b around 0 69.3%

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

   if 4.79999999999999973e-140 < b < 3.9999999999999997e-77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.0%

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

   if 2.0000000000000002e50 < b < 6.4999999999999998e80

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 70.8%

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

   4. Taylor expanded in b around 0 69.5%

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

   if 6.4999999999999998e80 < b < 1.6499999999999999e204

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 79.4%

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

   4. Taylor expanded in a around 0 75.7%

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

   5. Taylor expanded in y around 0 68.2%

      \[\leadsto x + \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-140}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 0.011:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+80}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+204}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 360000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -9.5e+57)
     t_2
     (if (<= t -3.1e-89)
       t_1
       (if (<= t -1.56e-134)
         x
         (if (<= t -1.55e-290)
           (* a (- 1.0 t))
           (if (<= t 2.4e-93)
             t_1
             (if (<= t 4.2e-38) x (if (<= t 360000000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9.5e+57) {
		tmp = t_2;
	} else if (t <= -3.1e-89) {
		tmp = t_1;
	} else if (t <= -1.56e-134) {
		tmp = x;
	} else if (t <= -1.55e-290) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-93) {
		tmp = t_1;
	} else if (t <= 4.2e-38) {
		tmp = x;
	} else if (t <= 360000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-9.5d+57)) then
        tmp = t_2
    else if (t <= (-3.1d-89)) then
        tmp = t_1
    else if (t <= (-1.56d-134)) then
        tmp = x
    else if (t <= (-1.55d-290)) then
        tmp = a * (1.0d0 - t)
    else if (t <= 2.4d-93) then
        tmp = t_1
    else if (t <= 4.2d-38) then
        tmp = x
    else if (t <= 360000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9.5e+57) {
		tmp = t_2;
	} else if (t <= -3.1e-89) {
		tmp = t_1;
	} else if (t <= -1.56e-134) {
		tmp = x;
	} else if (t <= -1.55e-290) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-93) {
		tmp = t_1;
	} else if (t <= 4.2e-38) {
		tmp = x;
	} else if (t <= 360000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -9.5e+57:
		tmp = t_2
	elif t <= -3.1e-89:
		tmp = t_1
	elif t <= -1.56e-134:
		tmp = x
	elif t <= -1.55e-290:
		tmp = a * (1.0 - t)
	elif t <= 2.4e-93:
		tmp = t_1
	elif t <= 4.2e-38:
		tmp = x
	elif t <= 360000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9.5e+57)
		tmp = t_2;
	elseif (t <= -3.1e-89)
		tmp = t_1;
	elseif (t <= -1.56e-134)
		tmp = x;
	elseif (t <= -1.55e-290)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 2.4e-93)
		tmp = t_1;
	elseif (t <= 4.2e-38)
		tmp = x;
	elseif (t <= 360000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -9.5e+57)
		tmp = t_2;
	elseif (t <= -3.1e-89)
		tmp = t_1;
	elseif (t <= -1.56e-134)
		tmp = x;
	elseif (t <= -1.55e-290)
		tmp = a * (1.0 - t);
	elseif (t <= 2.4e-93)
		tmp = t_1;
	elseif (t <= 4.2e-38)
		tmp = x;
	elseif (t <= 360000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+57], t$95$2, If[LessEqual[t, -3.1e-89], t$95$1, If[LessEqual[t, -1.56e-134], x, If[LessEqual[t, -1.55e-290], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-93], t$95$1, If[LessEqual[t, 4.2e-38], x, If[LessEqual[t, 360000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.4999999999999997e57 or 3.6e8 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in t around inf 74.5%

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

   if -9.4999999999999997e57 < t < -3.09999999999999996e-89 or -1.54999999999999995e-290 < t < 2.4000000000000001e-93 or 4.20000000000000026e-38 < t < 3.6e8

   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 y around inf 44.6%

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

   if -3.09999999999999996e-89 < t < -1.56000000000000009e-134 or 2.4000000000000001e-93 < t < 4.20000000000000026e-38

   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 x around inf 46.7%

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

   if -1.56000000000000009e-134 < t < -1.54999999999999995e-290

   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 a around inf 42.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 360000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.76 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -8e+57)
     t_2
     (if (<= t -1.65e-90)
       t_1
       (if (<= t -1.95e-134)
         x
         (if (<= t -1.65e-290)
           (* a (- 1.0 t))
           (if (<= t 2.4e-92)
             t_1
             (if (<= t 2.05e-38)
               x
               (if (<= t 2.76e+14) (* z (- 1.0 y)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+57) {
		tmp = t_2;
	} else if (t <= -1.65e-90) {
		tmp = t_1;
	} else if (t <= -1.95e-134) {
		tmp = x;
	} else if (t <= -1.65e-290) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-92) {
		tmp = t_1;
	} else if (t <= 2.05e-38) {
		tmp = x;
	} else if (t <= 2.76e+14) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-8d+57)) then
        tmp = t_2
    else if (t <= (-1.65d-90)) then
        tmp = t_1
    else if (t <= (-1.95d-134)) then
        tmp = x
    else if (t <= (-1.65d-290)) then
        tmp = a * (1.0d0 - t)
    else if (t <= 2.4d-92) then
        tmp = t_1
    else if (t <= 2.05d-38) then
        tmp = x
    else if (t <= 2.76d+14) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+57) {
		tmp = t_2;
	} else if (t <= -1.65e-90) {
		tmp = t_1;
	} else if (t <= -1.95e-134) {
		tmp = x;
	} else if (t <= -1.65e-290) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.4e-92) {
		tmp = t_1;
	} else if (t <= 2.05e-38) {
		tmp = x;
	} else if (t <= 2.76e+14) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8e+57:
		tmp = t_2
	elif t <= -1.65e-90:
		tmp = t_1
	elif t <= -1.95e-134:
		tmp = x
	elif t <= -1.65e-290:
		tmp = a * (1.0 - t)
	elif t <= 2.4e-92:
		tmp = t_1
	elif t <= 2.05e-38:
		tmp = x
	elif t <= 2.76e+14:
		tmp = z * (1.0 - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8e+57)
		tmp = t_2;
	elseif (t <= -1.65e-90)
		tmp = t_1;
	elseif (t <= -1.95e-134)
		tmp = x;
	elseif (t <= -1.65e-290)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 2.4e-92)
		tmp = t_1;
	elseif (t <= 2.05e-38)
		tmp = x;
	elseif (t <= 2.76e+14)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8e+57)
		tmp = t_2;
	elseif (t <= -1.65e-90)
		tmp = t_1;
	elseif (t <= -1.95e-134)
		tmp = x;
	elseif (t <= -1.65e-290)
		tmp = a * (1.0 - t);
	elseif (t <= 2.4e-92)
		tmp = t_1;
	elseif (t <= 2.05e-38)
		tmp = x;
	elseif (t <= 2.76e+14)
		tmp = z * (1.0 - y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+57], t$95$2, If[LessEqual[t, -1.65e-90], t$95$1, If[LessEqual[t, -1.95e-134], x, If[LessEqual[t, -1.65e-290], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-92], t$95$1, If[LessEqual[t, 2.05e-38], x, If[LessEqual[t, 2.76e+14], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.00000000000000039e57 or 2.76e14 < t

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf 75.8%

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

   if -8.00000000000000039e57 < t < -1.65e-90 or -1.64999999999999993e-290 < t < 2.4000000000000001e-92

   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 y around inf 43.9%

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

   if -1.65e-90 < t < -1.95e-134 or 2.4000000000000001e-92 < t < 2.0499999999999999e-38

   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 x around inf 46.7%

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

   if -1.95e-134 < t < -1.64999999999999993e-290

   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 a around inf 42.2%

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

   if 2.0499999999999999e-38 < t < 2.76e14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 45.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.76 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57} \lor \neg \left(b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -2.05e+15)
     t_2
     (if (<= b 4.1e-140)
       t_1
       (if (<= b 4e-77)
         t_3
         (if (<= b 2.65e-5)
           t_1
           (if (or (<= b 1.28e+57) (not (<= b 4.6e+115))) t_2 (+ x t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.05e+15) {
		tmp = t_2;
	} else if (b <= 4.1e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 2.65e-5) {
		tmp = t_1;
	} else if ((b <= 1.28e+57) || !(b <= 4.6e+115)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = z * (1.0d0 - y)
    if (b <= (-2.05d+15)) then
        tmp = t_2
    else if (b <= 4.1d-140) then
        tmp = t_1
    else if (b <= 4d-77) then
        tmp = t_3
    else if (b <= 2.65d-5) then
        tmp = t_1
    else if ((b <= 1.28d+57) .or. (.not. (b <= 4.6d+115))) then
        tmp = t_2
    else
        tmp = x + t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.05e+15) {
		tmp = t_2;
	} else if (b <= 4.1e-140) {
		tmp = t_1;
	} else if (b <= 4e-77) {
		tmp = t_3;
	} else if (b <= 2.65e-5) {
		tmp = t_1;
	} else if ((b <= 1.28e+57) || !(b <= 4.6e+115)) {
		tmp = t_2;
	} else {
		tmp = x + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -2.05e+15:
		tmp = t_2
	elif b <= 4.1e-140:
		tmp = t_1
	elif b <= 4e-77:
		tmp = t_3
	elif b <= 2.65e-5:
		tmp = t_1
	elif (b <= 1.28e+57) or not (b <= 4.6e+115):
		tmp = t_2
	else:
		tmp = x + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -2.05e+15)
		tmp = t_2;
	elseif (b <= 4.1e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 2.65e-5)
		tmp = t_1;
	elseif ((b <= 1.28e+57) || !(b <= 4.6e+115))
		tmp = t_2;
	else
		tmp = Float64(x + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -2.05e+15)
		tmp = t_2;
	elseif (b <= 4.1e-140)
		tmp = t_1;
	elseif (b <= 4e-77)
		tmp = t_3;
	elseif (b <= 2.65e-5)
		tmp = t_1;
	elseif ((b <= 1.28e+57) || ~((b <= 4.6e+115)))
		tmp = t_2;
	else
		tmp = x + t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+15], t$95$2, If[LessEqual[b, 4.1e-140], t$95$1, If[LessEqual[b, 4e-77], t$95$3, If[LessEqual[b, 2.65e-5], t$95$1, If[Or[LessEqual[b, 1.28e+57], N[Not[LessEqual[b, 4.6e+115]], $MachinePrecision]], t$95$2, N[(x + t$95$3), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05e15 or 2.65e-5 < b < 1.28000000000000001e57 or 4.60000000000000007e115 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0 87.9%

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

   4. Taylor expanded in a around 0 83.7%

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

   if -2.05e15 < b < 4.1000000000000001e-140 or 3.9999999999999997e-77 < b < 2.65e-5

   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 z around 0 72.6%

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

   4. Taylor expanded in b around 0 69.1%

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

   if 4.1000000000000001e-140 < b < 3.9999999999999997e-77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.0%

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

   if 1.28000000000000001e57 < b < 4.60000000000000007e115

   1. Initial program 92.3%

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

   3. Taylor expanded in a around 0 77.5%

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

   4. Taylor expanded in b around 0 69.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-140}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57} \lor \neg \left(b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(t - 2\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- t 2.0)))) (t_2 (* y (- b z))))
   (if (<= y -5.2e+36)
     t_2
     (if (<= y 3.1e-282)
       t_1
       (if (<= y 1.2e-166)
         (* t (- b a))
         (if (<= y 6.4e-163)
           t_1
           (if (<= y 5.6e-126) (* a (- 1.0 t)) (if (<= y 6e+37) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -5.2e+36) {
		tmp = t_2;
	} else if (y <= 3.1e-282) {
		tmp = t_1;
	} else if (y <= 1.2e-166) {
		tmp = t * (b - a);
	} else if (y <= 6.4e-163) {
		tmp = t_1;
	} else if (y <= 5.6e-126) {
		tmp = a * (1.0 - t);
	} else if (y <= 6e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * (t - 2.0d0))
    t_2 = y * (b - z)
    if (y <= (-5.2d+36)) then
        tmp = t_2
    else if (y <= 3.1d-282) then
        tmp = t_1
    else if (y <= 1.2d-166) then
        tmp = t * (b - a)
    else if (y <= 6.4d-163) then
        tmp = t_1
    else if (y <= 5.6d-126) then
        tmp = a * (1.0d0 - t)
    else if (y <= 6d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (t - 2.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -5.2e+36) {
		tmp = t_2;
	} else if (y <= 3.1e-282) {
		tmp = t_1;
	} else if (y <= 1.2e-166) {
		tmp = t * (b - a);
	} else if (y <= 6.4e-163) {
		tmp = t_1;
	} else if (y <= 5.6e-126) {
		tmp = a * (1.0 - t);
	} else if (y <= 6e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (t - 2.0))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -5.2e+36:
		tmp = t_2
	elif y <= 3.1e-282:
		tmp = t_1
	elif y <= 1.2e-166:
		tmp = t * (b - a)
	elif y <= 6.4e-163:
		tmp = t_1
	elif y <= 5.6e-126:
		tmp = a * (1.0 - t)
	elif y <= 6e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(t - 2.0)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5.2e+36)
		tmp = t_2;
	elseif (y <= 3.1e-282)
		tmp = t_1;
	elseif (y <= 1.2e-166)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 6.4e-163)
		tmp = t_1;
	elseif (y <= 5.6e-126)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 6e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * (t - 2.0));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -5.2e+36)
		tmp = t_2;
	elseif (y <= 3.1e-282)
		tmp = t_1;
	elseif (y <= 1.2e-166)
		tmp = t * (b - a);
	elseif (y <= 6.4e-163)
		tmp = t_1;
	elseif (y <= 5.6e-126)
		tmp = a * (1.0 - t);
	elseif (y <= 6e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+36], t$95$2, If[LessEqual[y, 3.1e-282], t$95$1, If[LessEqual[y, 1.2e-166], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-163], t$95$1, If[LessEqual[y, 5.6e-126], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+37], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000003e36 or 6.00000000000000043e37 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 64.3%

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

   if -5.2000000000000003e36 < y < 3.10000000000000013e-282 or 1.1999999999999999e-166 < y < 6.39999999999999976e-163 or 5.59999999999999983e-126 < y < 6.00000000000000043e37

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 83.6%

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

   4. Taylor expanded in a around 0 62.6%

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

   5. Taylor expanded in y around 0 61.9%

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

   if 3.10000000000000013e-282 < y < 1.1999999999999999e-166

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 65.9%

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

   if 6.39999999999999976e-163 < y < 5.59999999999999983e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 69.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-282}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-163}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+37}:\\ \;\;\;\;x + b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.6 \lor \neg \left(b \leq 4.9 \cdot 10^{+38}\right) \land b \leq 6.6 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -2.18e+175)
     (* t b)
     (if (<= b 3.4e-271)
       t_1
       (if (<= b 6.2e-238)
         x
         (if (or (<= b 2.6) (and (not (<= b 4.9e+38)) (<= b 6.6e+148)))
           t_1
           (* t b)))))))

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 (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.2e-238) {
		tmp = x;
	} else if ((b <= 2.6) || (!(b <= 4.9e+38) && (b <= 6.6e+148))) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-2.18d+175)) then
        tmp = t * b
    else if (b <= 3.4d-271) then
        tmp = t_1
    else if (b <= 6.2d-238) then
        tmp = x
    else if ((b <= 2.6d0) .or. (.not. (b <= 4.9d+38)) .and. (b <= 6.6d+148)) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= 3.4e-271) {
		tmp = t_1;
	} else if (b <= 6.2e-238) {
		tmp = x;
	} else if ((b <= 2.6) || (!(b <= 4.9e+38) && (b <= 6.6e+148))) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -2.18e+175:
		tmp = t * b
	elif b <= 3.4e-271:
		tmp = t_1
	elif b <= 6.2e-238:
		tmp = x
	elif (b <= 2.6) or (not (b <= 4.9e+38) and (b <= 6.6e+148)):
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.18e+175)
		tmp = Float64(t * b);
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.2e-238)
		tmp = x;
	elseif ((b <= 2.6) || (!(b <= 4.9e+38) && (b <= 6.6e+148)))
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.18e+175)
		tmp = t * b;
	elseif (b <= 3.4e-271)
		tmp = t_1;
	elseif (b <= 6.2e-238)
		tmp = x;
	elseif ((b <= 2.6) || (~((b <= 4.9e+38)) && (b <= 6.6e+148)))
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.18e+175], N[(t * b), $MachinePrecision], If[LessEqual[b, 3.4e-271], t$95$1, If[LessEqual[b, 6.2e-238], x, If[Or[LessEqual[b, 2.6], And[N[Not[LessEqual[b, 4.9e+38]], $MachinePrecision], LessEqual[b, 6.6e+148]]], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1799999999999999e175 or 2.60000000000000009 < b < 4.90000000000000002e38 or 6.60000000000000021e148 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0 95.7%

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

   4. Taylor expanded in t around inf 54.3%

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

   if -2.1799999999999999e175 < b < 3.4000000000000001e-271 or 6.2000000000000002e-238 < b < 2.60000000000000009 or 4.90000000000000002e38 < b < 6.60000000000000021e148

   1. Initial program 98.1%

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

   3. Taylor expanded in a around inf 42.9%

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

   if 3.4000000000000001e-271 < b < 6.2000000000000002e-238

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 63.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.6 \lor \neg \left(b \leq 4.9 \cdot 10^{+38}\right) \land b \leq 6.6 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+50} \lor \neg \left(b \leq 100 \lor \neg \left(b \leq 1.12 \cdot 10^{+38}\right) \land b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+50)
         (not (or (<= b 100.0) (and (not (<= b 1.12e+38)) (<= b 4.6e+115)))))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+50) || !((b <= 100.0) || (!(b <= 1.12e+38) && (b <= 4.6e+115)))) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.6d+50)) .or. (.not. (b <= 100.0d0) .or. (.not. (b <= 1.12d+38)) .and. (b <= 4.6d+115))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+50) || !((b <= 100.0) || (!(b <= 1.12e+38) && (b <= 4.6e+115)))) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+50) or not ((b <= 100.0) or (not (b <= 1.12e+38) and (b <= 4.6e+115))):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+50) || !((b <= 100.0) || (!(b <= 1.12e+38) && (b <= 4.6e+115))))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+50) || ~(((b <= 100.0) || (~((b <= 1.12e+38)) && (b <= 4.6e+115)))))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+50], N[Not[Or[LessEqual[b, 100.0], And[N[Not[LessEqual[b, 1.12e+38]], $MachinePrecision], LessEqual[b, 4.6e+115]]]], $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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.59999999999999986e50 or 100 < b < 1.1199999999999999e38 or 4.60000000000000007e115 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 90.1%

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

   4. Taylor expanded in a around 0 87.3%

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

   if -3.59999999999999986e50 < b < 100 or 1.1199999999999999e38 < b < 4.60000000000000007e115

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 93.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+50} \lor \neg \left(b \leq 100 \lor \neg \left(b \leq 1.12 \cdot 10^{+38}\right) \land b \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := t\_2 + t\_1\\ t_4 := x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;b \leq -5.9 \cdot 10^{+51}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ t_2 t_1))
        (t_4 (+ x (+ t_1 (* z (- 1.0 y))))))
   (if (<= b -5.9e+51)
     t_3
     (if (<= b 3.8e-77)
       t_4
       (if (<= b 1.28e+57) t_3 (if (<= b 1.75e+118) t_4 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -5.9e+51) {
		tmp = t_3;
	} else if (b <= 3.8e-77) {
		tmp = t_4;
	} else if (b <= 1.28e+57) {
		tmp = t_3;
	} else if (b <= 1.75e+118) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = t_2 + t_1
    t_4 = x + (t_1 + (z * (1.0d0 - y)))
    if (b <= (-5.9d+51)) then
        tmp = t_3
    else if (b <= 3.8d-77) then
        tmp = t_4
    else if (b <= 1.28d+57) then
        tmp = t_3
    else if (b <= 1.75d+118) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = t_2 + t_1;
	double t_4 = x + (t_1 + (z * (1.0 - y)));
	double tmp;
	if (b <= -5.9e+51) {
		tmp = t_3;
	} else if (b <= 3.8e-77) {
		tmp = t_4;
	} else if (b <= 1.28e+57) {
		tmp = t_3;
	} else if (b <= 1.75e+118) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = t_2 + t_1
	t_4 = x + (t_1 + (z * (1.0 - y)))
	tmp = 0
	if b <= -5.9e+51:
		tmp = t_3
	elif b <= 3.8e-77:
		tmp = t_4
	elif b <= 1.28e+57:
		tmp = t_3
	elif b <= 1.75e+118:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (b <= -5.9e+51)
		tmp = t_3;
	elseif (b <= 3.8e-77)
		tmp = t_4;
	elseif (b <= 1.28e+57)
		tmp = t_3;
	elseif (b <= 1.75e+118)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = t_2 + t_1;
	t_4 = x + (t_1 + (z * (1.0 - y)));
	tmp = 0.0;
	if (b <= -5.9e+51)
		tmp = t_3;
	elseif (b <= 3.8e-77)
		tmp = t_4;
	elseif (b <= 1.28e+57)
		tmp = t_3;
	elseif (b <= 1.75e+118)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.9e+51], t$95$3, If[LessEqual[b, 3.8e-77], t$95$4, If[LessEqual[b, 1.28e+57], t$95$3, If[LessEqual[b, 1.75e+118], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.89999999999999983e51 or 3.7999999999999999e-77 < b < 1.28000000000000001e57

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 90.0%

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

   if -5.89999999999999983e51 < b < 3.7999999999999999e-77 or 1.28000000000000001e57 < b < 1.75000000000000008e118

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 94.4%

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

   if 1.75000000000000008e118 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 88.8%

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

   4. Taylor expanded in a around 0 90.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+51}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+57}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.72:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= b -2.18e+175)
     (* t b)
     (if (<= b -2.05e+16)
       (* y b)
       (if (<= b 3.3e-271)
         t_1
         (if (<= b 2.75e-219) x (if (<= b 1.72) t_1 (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= -2.05e+16) {
		tmp = y * b;
	} else if (b <= 3.3e-271) {
		tmp = t_1;
	} else if (b <= 2.75e-219) {
		tmp = x;
	} else if (b <= 1.72) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (b <= (-2.18d+175)) then
        tmp = t * b
    else if (b <= (-2.05d+16)) then
        tmp = y * b
    else if (b <= 3.3d-271) then
        tmp = t_1
    else if (b <= 2.75d-219) then
        tmp = x
    else if (b <= 1.72d0) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (b <= -2.18e+175) {
		tmp = t * b;
	} else if (b <= -2.05e+16) {
		tmp = y * b;
	} else if (b <= 3.3e-271) {
		tmp = t_1;
	} else if (b <= 2.75e-219) {
		tmp = x;
	} else if (b <= 1.72) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if b <= -2.18e+175:
		tmp = t * b
	elif b <= -2.05e+16:
		tmp = y * b
	elif b <= 3.3e-271:
		tmp = t_1
	elif b <= 2.75e-219:
		tmp = x
	elif b <= 1.72:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (b <= -2.18e+175)
		tmp = Float64(t * b);
	elseif (b <= -2.05e+16)
		tmp = Float64(y * b);
	elseif (b <= 3.3e-271)
		tmp = t_1;
	elseif (b <= 2.75e-219)
		tmp = x;
	elseif (b <= 1.72)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (b <= -2.18e+175)
		tmp = t * b;
	elseif (b <= -2.05e+16)
		tmp = y * b;
	elseif (b <= 3.3e-271)
		tmp = t_1;
	elseif (b <= 2.75e-219)
		tmp = x;
	elseif (b <= 1.72)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[b, -2.18e+175], N[(t * b), $MachinePrecision], If[LessEqual[b, -2.05e+16], N[(y * b), $MachinePrecision], If[LessEqual[b, 3.3e-271], t$95$1, If[LessEqual[b, 2.75e-219], x, If[LessEqual[b, 1.72], t$95$1, N[(t * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.1799999999999999e175 or 1.71999999999999997 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in a around 0 90.6%

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

   4. Taylor expanded in t around inf 44.6%

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

   if -2.1799999999999999e175 < b < -2.05e16

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 81.7%

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

   4. Taylor expanded in y around inf 36.2%

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

   if -2.05e16 < b < 3.3000000000000002e-271 or 2.75000000000000009e-219 < b < 1.71999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 38.8%

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

   4. Taylor expanded in b around 0 36.1%

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

      1. associate-*r* 36.1%

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

      2. mul-1-neg 36.1%

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

   6. Simplified 36.1%

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

   if 3.3000000000000002e-271 < b < 2.75000000000000009e-219

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 51.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.18 \cdot 10^{+175}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.72:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+34}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+34)
   (* t b)
   (if (<= t -8.5e-88)
     (* y b)
     (if (<= t -1.56e-134)
       x
       (if (<= t 2.35e-267) a (if (<= t 3.8e+18) x (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+34) {
		tmp = t * b;
	} else if (t <= -8.5e-88) {
		tmp = y * b;
	} else if (t <= -1.56e-134) {
		tmp = x;
	} else if (t <= 2.35e-267) {
		tmp = a;
	} else if (t <= 3.8e+18) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.1d+34)) then
        tmp = t * b
    else if (t <= (-8.5d-88)) then
        tmp = y * b
    else if (t <= (-1.56d-134)) then
        tmp = x
    else if (t <= 2.35d-267) then
        tmp = a
    else if (t <= 3.8d+18) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+34) {
		tmp = t * b;
	} else if (t <= -8.5e-88) {
		tmp = y * b;
	} else if (t <= -1.56e-134) {
		tmp = x;
	} else if (t <= 2.35e-267) {
		tmp = a;
	} else if (t <= 3.8e+18) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+34:
		tmp = t * b
	elif t <= -8.5e-88:
		tmp = y * b
	elif t <= -1.56e-134:
		tmp = x
	elif t <= 2.35e-267:
		tmp = a
	elif t <= 3.8e+18:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+34)
		tmp = Float64(t * b);
	elseif (t <= -8.5e-88)
		tmp = Float64(y * b);
	elseif (t <= -1.56e-134)
		tmp = x;
	elseif (t <= 2.35e-267)
		tmp = a;
	elseif (t <= 3.8e+18)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.1e+34)
		tmp = t * b;
	elseif (t <= -8.5e-88)
		tmp = y * b;
	elseif (t <= -1.56e-134)
		tmp = x;
	elseif (t <= 2.35e-267)
		tmp = a;
	elseif (t <= 3.8e+18)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+34], N[(t * b), $MachinePrecision], If[LessEqual[t, -8.5e-88], N[(y * b), $MachinePrecision], If[LessEqual[t, -1.56e-134], x, If[LessEqual[t, 2.35e-267], a, If[LessEqual[t, 3.8e+18], x, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.0999999999999998e34 or 3.8e18 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in a around 0 69.2%

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

   4. Taylor expanded in t around inf 44.8%

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

   if -4.0999999999999998e34 < t < -8.4999999999999996e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.3%

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

   4. Taylor expanded in y around inf 28.2%

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

   if -8.4999999999999996e-88 < t < -1.56000000000000009e-134 or 2.3500000000000001e-267 < t < 3.8e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 32.4%

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

   if -1.56000000000000009e-134 < t < 2.3500000000000001e-267

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf 38.9%

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

   4. Taylor expanded in t around 0 38.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+34}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -11200000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 16000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -11200000.0)
     t_2
     (if (<= t -3.8e-84)
       t_1
       (if (<= t -1.22e-113) x (if (<= t 16000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -11200000.0) {
		tmp = t_2;
	} else if (t <= -3.8e-84) {
		tmp = t_1;
	} else if (t <= -1.22e-113) {
		tmp = x;
	} else if (t <= 16000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-11200000.0d0)) then
        tmp = t_2
    else if (t <= (-3.8d-84)) then
        tmp = t_1
    else if (t <= (-1.22d-113)) then
        tmp = x
    else if (t <= 16000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -11200000.0) {
		tmp = t_2;
	} else if (t <= -3.8e-84) {
		tmp = t_1;
	} else if (t <= -1.22e-113) {
		tmp = x;
	} else if (t <= 16000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -11200000.0:
		tmp = t_2
	elif t <= -3.8e-84:
		tmp = t_1
	elif t <= -1.22e-113:
		tmp = x
	elif t <= 16000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -11200000.0)
		tmp = t_2;
	elseif (t <= -3.8e-84)
		tmp = t_1;
	elseif (t <= -1.22e-113)
		tmp = x;
	elseif (t <= 16000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -11200000.0)
		tmp = t_2;
	elseif (t <= -3.8e-84)
		tmp = t_1;
	elseif (t <= -1.22e-113)
		tmp = x;
	elseif (t <= 16000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -11200000.0], t$95$2, If[LessEqual[t, -3.8e-84], t$95$1, If[LessEqual[t, -1.22e-113], x, If[LessEqual[t, 16000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.12e7 or 1.6e7 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 71.8%

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

   if -1.12e7 < t < -3.79999999999999986e-84 or -1.21999999999999995e-113 < t < 1.6e7

   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 t around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. distribute-rgt-neg-in 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in t around 0 33.4%

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

   if -3.79999999999999986e-84 < t < -1.21999999999999995e-113

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.5%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -11200000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 16000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+43} \lor \neg \left(b \leq 22\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -2.2e+43) (not (<= b 22.0)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.2e+43) || !(b <= 22.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + 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 = z * (1.0d0 - y)
    if ((b <= (-2.2d+43)) .or. (.not. (b <= 22.0d0))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + ((a * (1.0d0 - t)) + 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 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.2e+43) || !(b <= 22.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -2.2e+43) or not (b <= 22.0):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -2.2e+43) || !(b <= 22.0))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -2.2e+43) || ~((b <= 22.0)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.2e+43], N[Not[LessEqual[b, 22.0]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.20000000000000001e43 or 22 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in a around 0 88.6%

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

   if -2.20000000000000001e43 < b < 22

   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 94.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+43} \lor \neg \left(b \leq 22\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -480000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -480000000.0)
   (* t (- b a))
   (if (<= t 3e+14)
     (+ x (+ a (* b (+ y -2.0))))
     (- (* b (- (+ y t) 2.0)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -480000000.0) {
		tmp = t * (b - a);
	} else if (t <= 3e+14) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (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 <= (-480000000.0d0)) then
        tmp = t * (b - a)
    else if (t <= 3d+14) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else
        tmp = (b * ((y + t) - 2.0d0)) - (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 <= -480000000.0) {
		tmp = t * (b - a);
	} else if (t <= 3e+14) {
		tmp = x + (a + (b * (y + -2.0)));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -480000000.0:
		tmp = t * (b - a)
	elif t <= 3e+14:
		tmp = x + (a + (b * (y + -2.0)))
	else:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -480000000.0)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= 3e+14)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -480000000.0)
		tmp = t * (b - a);
	elseif (t <= 3e+14)
		tmp = x + (a + (b * (y + -2.0)));
	else
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -480000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+14], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8e8

   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 71.5%

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

   if -4.8e8 < t < 3e14

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 74.8%

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

   4. Taylor expanded in t around 0 73.9%

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

      1. associate--l+ 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. neg-mul-1 73.9%

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

   6. Simplified 73.9%

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

   if 3e14 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-in 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -480000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+14} \lor \neg \left(t \leq 4.1 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e+14) (not (<= t 4.1e+14)))
   (* t (- b a))
   (+ x (+ a (* b (+ y -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e+14) || !(t <= 4.1e+14)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (b * (y + -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.1d+14)) .or. (.not. (t <= 4.1d+14))) then
        tmp = t * (b - a)
    else
        tmp = x + (a + (b * (y + (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e+14) || !(t <= 4.1e+14)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (b * (y + -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e+14) or not (t <= 4.1e+14):
		tmp = t * (b - a)
	else:
		tmp = x + (a + (b * (y + -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e+14) || !(t <= 4.1e+14))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.1e+14) || ~((t <= 4.1e+14)))
		tmp = t * (b - a);
	else
		tmp = x + (a + (b * (y + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e+14], N[Not[LessEqual[t, 4.1e+14]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e14 or 4.1e14 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf 72.9%

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

   if -3.1e14 < t < 4.1e14

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 74.8%

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

   4. Taylor expanded in t around 0 73.9%

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

      1. associate--l+ 73.9%

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

      2. sub-neg 73.9%

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

      3. metadata-eval 73.9%

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

      4. neg-mul-1 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+14} \lor \neg \left(t \leq 4.1 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+25)
   (* t b)
   (if (<= t 5.8e-267) a (if (<= t 2.1e+18) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+25) {
		tmp = t * b;
	} else if (t <= 5.8e-267) {
		tmp = a;
	} else if (t <= 2.1e+18) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6d+25)) then
        tmp = t * b
    else if (t <= 5.8d-267) then
        tmp = a
    else if (t <= 2.1d+18) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+25) {
		tmp = t * b;
	} else if (t <= 5.8e-267) {
		tmp = a;
	} else if (t <= 2.1e+18) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+25:
		tmp = t * b
	elif t <= 5.8e-267:
		tmp = a
	elif t <= 2.1e+18:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+25)
		tmp = Float64(t * b);
	elseif (t <= 5.8e-267)
		tmp = a;
	elseif (t <= 2.1e+18)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6e+25)
		tmp = t * b;
	elseif (t <= 5.8e-267)
		tmp = a;
	elseif (t <= 2.1e+18)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+25], N[(t * b), $MachinePrecision], If[LessEqual[t, 5.8e-267], a, If[LessEqual[t, 2.1e+18], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000011e25 or 2.1e18 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in a around 0 69.2%

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

   4. Taylor expanded in t around inf 44.8%

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

   if -6.00000000000000011e25 < t < 5.80000000000000043e-267

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf 31.4%

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

   4. Taylor expanded in t around 0 27.6%

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

   if 5.80000000000000043e-267 < t < 2.1e18

   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 x around inf 27.6%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+25}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.9e+40) x (if (<= x 1.55e+45) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.9e+40) {
		tmp = x;
	} else if (x <= 1.55e+45) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.9d+40)) then
        tmp = x
    else if (x <= 1.55d+45) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.9e+40) {
		tmp = x;
	} else if (x <= 1.55e+45) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.9e+40:
		tmp = x
	elif x <= 1.55e+45:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.9e+40)
		tmp = x;
	elseif (x <= 1.55e+45)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.9e+40)
		tmp = x;
	elseif (x <= 1.55e+45)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.9e+40], x, If[LessEqual[x, 1.55e+45], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000001e40 or 1.54999999999999994e45 < x

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 30.8%

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

   if -3.9000000000000001e40 < x < 1.54999999999999994e45

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 37.0%

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

   4. Taylor expanded in t around 0 14.8%

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

4. Final simplification 21.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 11.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in a around inf 32.4%

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

4. Taylor expanded in t around 0 12.1%

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

5. Final simplification 12.1%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))