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

Percentage Accurate: 95.0% → 98.8%

Time: 16.4s

Alternatives: 24

Speedup: 0.5×

• 36.0% 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: 95.0% 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: 98.8% accurate, 0.5× speedup

Math

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

FPCore

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

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 = z + (x + (b * ((y + t) - (2.0 + (y * (z / b))))));
	}
	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 = z + (x + (b * ((y + t) - (2.0 + (y * (z / b))))));
	}
	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 = z + (x + (b * ((y + t) - (2.0 + (y * (z / b))))))
	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(z + Float64(x + Float64(b * Float64(Float64(y + t) - Float64(2.0 + Float64(y * Float64(z / b)))))));
	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 = z + (x + (b * ((y + t) - (2.0 + (y * (z / b))))));
	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[(z + N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - N[(2.0 + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0 41.7%

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

   4. Taylor expanded in b around inf 25.0%

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

      1. sub-neg 25.0%

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

      2. +-commutative 25.0%

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

      3. metadata-eval 25.0%

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

      4. associate-+l+ 25.0%

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

      5. mul-1-neg 25.0%

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

      6. unsub-neg 25.0%

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

      7. associate-/l* 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in a around 0 50.0%

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

   9. Simplified 75.0%

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

4. Final simplification 98.8%

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

Alternative 2: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. fma-define 97.3%

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

   3. associate--l+ 97.3%

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

   4. sub-neg 97.3%

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

   5. metadata-eval 97.3%

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

   6. sub-neg 97.3%

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

   7. associate-+l- 97.3%

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

   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: 49.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -16500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (* z (- 1.0 y)))
        (t_3 (* b (- (+ y t) 2.0))))
   (if (<= b -8.2e+64)
     t_3
     (if (<= b -16500000000000.0)
       t_1
       (if (<= b -4.4e-46)
         (* y (- b z))
         (if (<= b -4.6e-98)
           x
           (if (<= b -1.05e-246)
             t_2
             (if (<= b -5.5e-295) t_1 (if (<= b 1.55e-52) t_2 t_3)))))))))

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 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e+64) {
		tmp = t_3;
	} else if (b <= -16500000000000.0) {
		tmp = t_1;
	} else if (b <= -4.4e-46) {
		tmp = y * (b - z);
	} else if (b <= -4.6e-98) {
		tmp = x;
	} else if (b <= -1.05e-246) {
		tmp = t_2;
	} else if (b <= -5.5e-295) {
		tmp = t_1;
	} else if (b <= 1.55e-52) {
		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) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    t_3 = b * ((y + t) - 2.0d0)
    if (b <= (-8.2d+64)) then
        tmp = t_3
    else if (b <= (-16500000000000.0d0)) then
        tmp = t_1
    else if (b <= (-4.4d-46)) then
        tmp = y * (b - z)
    else if (b <= (-4.6d-98)) then
        tmp = x
    else if (b <= (-1.05d-246)) then
        tmp = t_2
    else if (b <= (-5.5d-295)) then
        tmp = t_1
    else if (b <= 1.55d-52) 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 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double t_3 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8.2e+64) {
		tmp = t_3;
	} else if (b <= -16500000000000.0) {
		tmp = t_1;
	} else if (b <= -4.4e-46) {
		tmp = y * (b - z);
	} else if (b <= -4.6e-98) {
		tmp = x;
	} else if (b <= -1.05e-246) {
		tmp = t_2;
	} else if (b <= -5.5e-295) {
		tmp = t_1;
	} else if (b <= 1.55e-52) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	t_3 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -8.2e+64:
		tmp = t_3
	elif b <= -16500000000000.0:
		tmp = t_1
	elif b <= -4.4e-46:
		tmp = y * (b - z)
	elif b <= -4.6e-98:
		tmp = x
	elif b <= -1.05e-246:
		tmp = t_2
	elif b <= -5.5e-295:
		tmp = t_1
	elif b <= 1.55e-52:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(1.0 - y))
	t_3 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -8.2e+64)
		tmp = t_3;
	elseif (b <= -16500000000000.0)
		tmp = t_1;
	elseif (b <= -4.4e-46)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -4.6e-98)
		tmp = x;
	elseif (b <= -1.05e-246)
		tmp = t_2;
	elseif (b <= -5.5e-295)
		tmp = t_1;
	elseif (b <= 1.55e-52)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	t_3 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -8.2e+64)
		tmp = t_3;
	elseif (b <= -16500000000000.0)
		tmp = t_1;
	elseif (b <= -4.4e-46)
		tmp = y * (b - z);
	elseif (b <= -4.6e-98)
		tmp = x;
	elseif (b <= -1.05e-246)
		tmp = t_2;
	elseif (b <= -5.5e-295)
		tmp = t_1;
	elseif (b <= 1.55e-52)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+64], t$95$3, If[LessEqual[b, -16500000000000.0], t$95$1, If[LessEqual[b, -4.4e-46], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e-98], x, If[LessEqual[b, -1.05e-246], t$95$2, If[LessEqual[b, -5.5e-295], t$95$1, If[LessEqual[b, 1.55e-52], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.19999999999999956e64 or 1.5499999999999999e-52 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in b around inf 64.1%

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

   if -8.19999999999999956e64 < b < -1.65e13 or -1.04999999999999997e-246 < b < -5.5e-295

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 69.2%

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

   if -1.65e13 < b < -4.4000000000000002e-46

   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 58.1%

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

   if -4.4000000000000002e-46 < b < -4.60000000000000001e-98

   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 48.5%

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

   if -4.60000000000000001e-98 < b < -1.04999999999999997e-246 or -5.5e-295 < b < 1.5499999999999999e-52

   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 53.6%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -16500000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := y \cdot \left(-z\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-248}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 280000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* a (- 1.0 t))) (t_3 (* y (- z))))
   (if (<= a -2.3e+58)
     t_2
     (if (<= a -2.95e-12)
       t_1
       (if (<= a -3.1e-21)
         x
         (if (<= a -7.2e-248)
           t_3
           (if (<= a 1.55e-203)
             x
             (if (<= a 2.9e-144) t_3 (if (<= a 280000000.0) 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 = a * (1.0 - t);
	double t_3 = y * -z;
	double tmp;
	if (a <= -2.3e+58) {
		tmp = t_2;
	} else if (a <= -2.95e-12) {
		tmp = t_1;
	} else if (a <= -3.1e-21) {
		tmp = x;
	} else if (a <= -7.2e-248) {
		tmp = t_3;
	} else if (a <= 1.55e-203) {
		tmp = x;
	} else if (a <= 2.9e-144) {
		tmp = t_3;
	} else if (a <= 280000000.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = a * (1.0d0 - t)
    t_3 = y * -z
    if (a <= (-2.3d+58)) then
        tmp = t_2
    else if (a <= (-2.95d-12)) then
        tmp = t_1
    else if (a <= (-3.1d-21)) then
        tmp = x
    else if (a <= (-7.2d-248)) then
        tmp = t_3
    else if (a <= 1.55d-203) then
        tmp = x
    else if (a <= 2.9d-144) then
        tmp = t_3
    else if (a <= 280000000.0d0) 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 = a * (1.0 - t);
	double t_3 = y * -z;
	double tmp;
	if (a <= -2.3e+58) {
		tmp = t_2;
	} else if (a <= -2.95e-12) {
		tmp = t_1;
	} else if (a <= -3.1e-21) {
		tmp = x;
	} else if (a <= -7.2e-248) {
		tmp = t_3;
	} else if (a <= 1.55e-203) {
		tmp = x;
	} else if (a <= 2.9e-144) {
		tmp = t_3;
	} else if (a <= 280000000.0) {
		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 = a * (1.0 - t)
	t_3 = y * -z
	tmp = 0
	if a <= -2.3e+58:
		tmp = t_2
	elif a <= -2.95e-12:
		tmp = t_1
	elif a <= -3.1e-21:
		tmp = x
	elif a <= -7.2e-248:
		tmp = t_3
	elif a <= 1.55e-203:
		tmp = x
	elif a <= 2.9e-144:
		tmp = t_3
	elif a <= 280000000.0:
		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(a * Float64(1.0 - t))
	t_3 = Float64(y * Float64(-z))
	tmp = 0.0
	if (a <= -2.3e+58)
		tmp = t_2;
	elseif (a <= -2.95e-12)
		tmp = t_1;
	elseif (a <= -3.1e-21)
		tmp = x;
	elseif (a <= -7.2e-248)
		tmp = t_3;
	elseif (a <= 1.55e-203)
		tmp = x;
	elseif (a <= 2.9e-144)
		tmp = t_3;
	elseif (a <= 280000000.0)
		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 = a * (1.0 - t);
	t_3 = y * -z;
	tmp = 0.0;
	if (a <= -2.3e+58)
		tmp = t_2;
	elseif (a <= -2.95e-12)
		tmp = t_1;
	elseif (a <= -3.1e-21)
		tmp = x;
	elseif (a <= -7.2e-248)
		tmp = t_3;
	elseif (a <= 1.55e-203)
		tmp = x;
	elseif (a <= 2.9e-144)
		tmp = t_3;
	elseif (a <= 280000000.0)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[a, -2.3e+58], t$95$2, If[LessEqual[a, -2.95e-12], t$95$1, If[LessEqual[a, -3.1e-21], x, If[LessEqual[a, -7.2e-248], t$95$3, If[LessEqual[a, 1.55e-203], x, If[LessEqual[a, 2.9e-144], t$95$3, If[LessEqual[a, 280000000.0], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.30000000000000002e58 or 2.8e8 < a

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf 56.3%

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

   if -2.30000000000000002e58 < a < -2.95e-12 or 2.9000000000000002e-144 < a < 2.8e8

   1. Initial program 95.7%

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

   3. Taylor expanded in t around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-rgt-neg-in 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in t around 0 42.9%

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

   if -2.95e-12 < a < -3.0999999999999998e-21 or -7.19999999999999969e-248 < a < 1.54999999999999989e-203

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 38.4%

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

   if -3.0999999999999998e-21 < a < -7.19999999999999969e-248 or 1.54999999999999989e-203 < a < 2.9000000000000002e-144

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in y around inf 37.6%

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

      1. mul-1-neg 37.6%

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

      2. distribute-rgt-neg-in 37.6%

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

   6. Simplified 37.6%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-203}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 280000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -3.2e+18)
     t_2
     (if (<= t -9e-135)
       t_1
       (if (<= t -1.65e-152)
         (* y (- z))
         (if (<= t -9.8e-166)
           (* y b)
           (if (<= t -2.05e-265) x (if (<= t 3.5e+37) 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 <= -3.2e+18) {
		tmp = t_2;
	} else if (t <= -9e-135) {
		tmp = t_1;
	} else if (t <= -1.65e-152) {
		tmp = y * -z;
	} else if (t <= -9.8e-166) {
		tmp = y * b;
	} else if (t <= -2.05e-265) {
		tmp = x;
	} else if (t <= 3.5e+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 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-3.2d+18)) then
        tmp = t_2
    else if (t <= (-9d-135)) then
        tmp = t_1
    else if (t <= (-1.65d-152)) then
        tmp = y * -z
    else if (t <= (-9.8d-166)) then
        tmp = y * b
    else if (t <= (-2.05d-265)) then
        tmp = x
    else if (t <= 3.5d+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 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.2e+18) {
		tmp = t_2;
	} else if (t <= -9e-135) {
		tmp = t_1;
	} else if (t <= -1.65e-152) {
		tmp = y * -z;
	} else if (t <= -9.8e-166) {
		tmp = y * b;
	} else if (t <= -2.05e-265) {
		tmp = x;
	} else if (t <= 3.5e+37) {
		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 <= -3.2e+18:
		tmp = t_2
	elif t <= -9e-135:
		tmp = t_1
	elif t <= -1.65e-152:
		tmp = y * -z
	elif t <= -9.8e-166:
		tmp = y * b
	elif t <= -2.05e-265:
		tmp = x
	elif t <= 3.5e+37:
		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 <= -3.2e+18)
		tmp = t_2;
	elseif (t <= -9e-135)
		tmp = t_1;
	elseif (t <= -1.65e-152)
		tmp = Float64(y * Float64(-z));
	elseif (t <= -9.8e-166)
		tmp = Float64(y * b);
	elseif (t <= -2.05e-265)
		tmp = x;
	elseif (t <= 3.5e+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 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.2e+18)
		tmp = t_2;
	elseif (t <= -9e-135)
		tmp = t_1;
	elseif (t <= -1.65e-152)
		tmp = y * -z;
	elseif (t <= -9.8e-166)
		tmp = y * b;
	elseif (t <= -2.05e-265)
		tmp = x;
	elseif (t <= 3.5e+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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+18], t$95$2, If[LessEqual[t, -9e-135], t$95$1, If[LessEqual[t, -1.65e-152], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, -9.8e-166], N[(y * b), $MachinePrecision], If[LessEqual[t, -2.05e-265], x, If[LessEqual[t, 3.5e+37], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2e18 or 3.5e37 < t

   1. Initial program 92.8%

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

   3. Taylor expanded in t around inf 66.5%

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

   if -3.2e18 < t < -8.99999999999999975e-135 or -2.05e-265 < t < 3.5e37

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 40.8%

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

      1. mul-1-neg 40.8%

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

      2. distribute-rgt-neg-in 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in t around 0 37.8%

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

   if -8.99999999999999975e-135 < t < -1.64999999999999999e-152

   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 b around 0 100.0%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-rgt-neg-in 63.6%

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

   6. Simplified 63.6%

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

   if -1.64999999999999999e-152 < t < -9.7999999999999998e-166

   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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

   7. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -9.7999999999999998e-166 < t < -2.05e-265

   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 x around inf 38.1%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-135}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-152}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-250}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -1.6e+66)
     t_2
     (if (<= b -1.9e-81)
       t_1
       (if (<= b -8.8e-250)
         t_3
         (if (<= b -5.6e-297) t_1 (if (<= b 1.65e-51) t_3 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 = x - (b * (2.0 - (y + t)));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -1.6e+66) {
		tmp = t_2;
	} else if (b <= -1.9e-81) {
		tmp = t_1;
	} else if (b <= -8.8e-250) {
		tmp = t_3;
	} else if (b <= -5.6e-297) {
		tmp = t_1;
	} else if (b <= 1.65e-51) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-1.6d+66)) then
        tmp = t_2
    else if (b <= (-1.9d-81)) then
        tmp = t_1
    else if (b <= (-8.8d-250)) then
        tmp = t_3
    else if (b <= (-5.6d-297)) then
        tmp = t_1
    else if (b <= 1.65d-51) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -1.6e+66) {
		tmp = t_2;
	} else if (b <= -1.9e-81) {
		tmp = t_1;
	} else if (b <= -8.8e-250) {
		tmp = t_3;
	} else if (b <= -5.6e-297) {
		tmp = t_1;
	} else if (b <= 1.65e-51) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -1.6e+66:
		tmp = t_2
	elif b <= -1.9e-81:
		tmp = t_1
	elif b <= -8.8e-250:
		tmp = t_3
	elif b <= -5.6e-297:
		tmp = t_1
	elif b <= 1.65e-51:
		tmp = t_3
	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(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -1.6e+66)
		tmp = t_2;
	elseif (b <= -1.9e-81)
		tmp = t_1;
	elseif (b <= -8.8e-250)
		tmp = t_3;
	elseif (b <= -5.6e-297)
		tmp = t_1;
	elseif (b <= 1.65e-51)
		tmp = t_3;
	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 = x - (b * (2.0 - (y + t)));
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -1.6e+66)
		tmp = t_2;
	elseif (b <= -1.9e-81)
		tmp = t_1;
	elseif (b <= -8.8e-250)
		tmp = t_3;
	elseif (b <= -5.6e-297)
		tmp = t_1;
	elseif (b <= 1.65e-51)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+66], t$95$2, If[LessEqual[b, -1.9e-81], t$95$1, If[LessEqual[b, -8.8e-250], t$95$3, If[LessEqual[b, -5.6e-297], t$95$1, If[LessEqual[b, 1.65e-51], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6e66 or 1.64999999999999986e-51 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in a around 0 81.6%

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

   4. Taylor expanded in z around 0 69.5%

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

   if -1.6e66 < b < -1.8999999999999999e-81 or -8.8e-250 < b < -5.59999999999999968e-297

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 82.2%

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

   4. Taylor expanded in a around inf 70.7%

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

   if -1.8999999999999999e-81 < b < -8.8e-250 or -5.59999999999999968e-297 < b < 1.64999999999999986e-51

   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 76.9%

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

   4. Taylor expanded in b around 0 73.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+66}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-250}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (+ x (* z (- 1.0 y)))))
   (if (<= b -4.5e+67)
     t_2
     (if (<= b -9e-81)
       t_1
       (if (<= b -8.2e-247)
         t_3
         (if (<= b -2.15e-291) t_1 (if (<= b 1.95e+71) t_3 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 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.5e+67) {
		tmp = t_2;
	} else if (b <= -9e-81) {
		tmp = t_1;
	} else if (b <= -8.2e-247) {
		tmp = t_3;
	} else if (b <= -2.15e-291) {
		tmp = t_1;
	} else if (b <= 1.95e+71) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-4.5d+67)) then
        tmp = t_2
    else if (b <= (-9d-81)) then
        tmp = t_1
    else if (b <= (-8.2d-247)) then
        tmp = t_3
    else if (b <= (-2.15d-291)) then
        tmp = t_1
    else if (b <= 1.95d+71) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.5e+67) {
		tmp = t_2;
	} else if (b <= -9e-81) {
		tmp = t_1;
	} else if (b <= -8.2e-247) {
		tmp = t_3;
	} else if (b <= -2.15e-291) {
		tmp = t_1;
	} else if (b <= 1.95e+71) {
		tmp = t_3;
	} 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 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -4.5e+67:
		tmp = t_2
	elif b <= -9e-81:
		tmp = t_1
	elif b <= -8.2e-247:
		tmp = t_3
	elif b <= -2.15e-291:
		tmp = t_1
	elif b <= 1.95e+71:
		tmp = t_3
	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(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -4.5e+67)
		tmp = t_2;
	elseif (b <= -9e-81)
		tmp = t_1;
	elseif (b <= -8.2e-247)
		tmp = t_3;
	elseif (b <= -2.15e-291)
		tmp = t_1;
	elseif (b <= 1.95e+71)
		tmp = t_3;
	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 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -4.5e+67)
		tmp = t_2;
	elseif (b <= -9e-81)
		tmp = t_1;
	elseif (b <= -8.2e-247)
		tmp = t_3;
	elseif (b <= -2.15e-291)
		tmp = t_1;
	elseif (b <= 1.95e+71)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(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[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+67], t$95$2, If[LessEqual[b, -9e-81], t$95$1, If[LessEqual[b, -8.2e-247], t$95$3, If[LessEqual[b, -2.15e-291], t$95$1, If[LessEqual[b, 1.95e+71], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4999999999999998e67 or 1.9500000000000001e71 < b

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf 73.7%

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

   if -4.4999999999999998e67 < b < -9.000000000000001e-81 or -8.1999999999999997e-247 < b < -2.15000000000000018e-291

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 82.2%

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

   4. Taylor expanded in a around inf 70.7%

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

   if -9.000000000000001e-81 < b < -8.1999999999999997e-247 or -2.15000000000000018e-291 < b < 1.9500000000000001e71

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 75.8%

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

   4. Taylor expanded in b around 0 65.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-81}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-247}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-291}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -2.95e+29)
     t_1
     (if (<= y 1.7e-251)
       (* t b)
       (if (<= y 3e-45)
         x
         (if (<= y 2.7e+78) (* t (- a)) (if (<= y 4e+95) (* t b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.95e+29) {
		tmp = t_1;
	} else if (y <= 1.7e-251) {
		tmp = t * b;
	} else if (y <= 3e-45) {
		tmp = x;
	} else if (y <= 2.7e+78) {
		tmp = t * -a;
	} else if (y <= 4e+95) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-2.95d+29)) then
        tmp = t_1
    else if (y <= 1.7d-251) then
        tmp = t * b
    else if (y <= 3d-45) then
        tmp = x
    else if (y <= 2.7d+78) then
        tmp = t * -a
    else if (y <= 4d+95) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2.95e+29) {
		tmp = t_1;
	} else if (y <= 1.7e-251) {
		tmp = t * b;
	} else if (y <= 3e-45) {
		tmp = x;
	} else if (y <= 2.7e+78) {
		tmp = t * -a;
	} else if (y <= 4e+95) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -2.95e+29:
		tmp = t_1
	elif y <= 1.7e-251:
		tmp = t * b
	elif y <= 3e-45:
		tmp = x
	elif y <= 2.7e+78:
		tmp = t * -a
	elif y <= 4e+95:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -2.95e+29)
		tmp = t_1;
	elseif (y <= 1.7e-251)
		tmp = Float64(t * b);
	elseif (y <= 3e-45)
		tmp = x;
	elseif (y <= 2.7e+78)
		tmp = Float64(t * Float64(-a));
	elseif (y <= 4e+95)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -2.95e+29)
		tmp = t_1;
	elseif (y <= 1.7e-251)
		tmp = t * b;
	elseif (y <= 3e-45)
		tmp = x;
	elseif (y <= 2.7e+78)
		tmp = t * -a;
	elseif (y <= 4e+95)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -2.95e+29], t$95$1, If[LessEqual[y, 1.7e-251], N[(t * b), $MachinePrecision], If[LessEqual[y, 3e-45], x, If[LessEqual[y, 2.7e+78], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, 4e+95], N[(t * b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9499999999999999e29 or 4.00000000000000008e95 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in b around 0 70.1%

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

   4. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-rgt-neg-in 50.1%

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

   6. Simplified 50.1%

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

   if -2.9499999999999999e29 < y < 1.70000000000000008e-251 or 2.70000000000000004e78 < y < 4.00000000000000008e95

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 77.2%

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

   4. Taylor expanded in t around inf 31.2%

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

   if 1.70000000000000008e-251 < y < 3.00000000000000011e-45

   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 36.6%

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

   if 3.00000000000000011e-45 < y < 2.70000000000000004e78

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf 43.4%

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

   4. Taylor expanded in b around 0 33.4%

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

      1. associate-*r* 33.4%

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

      2. mul-1-neg 33.4%

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

   6. Simplified 33.4%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+95}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - z \cdot \left(y + -1\right)\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-292}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* z (+ y -1.0))))) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -3.2e+74)
     t_2
     (if (<= b -5.2e-247)
       t_1
       (if (<= b -1.75e-292)
         (+ x (* a (- 1.0 t)))
         (if (<= b 2.8e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (z * (y + -1.0)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.2e+74) {
		tmp = t_2;
	} else if (b <= -5.2e-247) {
		tmp = t_1;
	} else if (b <= -1.75e-292) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.8e+75) {
		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 + (a - (z * (y + (-1.0d0))))
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-3.2d+74)) then
        tmp = t_2
    else if (b <= (-5.2d-247)) then
        tmp = t_1
    else if (b <= (-1.75d-292)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.8d+75) 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 + (a - (z * (y + -1.0)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.2e+74) {
		tmp = t_2;
	} else if (b <= -5.2e-247) {
		tmp = t_1;
	} else if (b <= -1.75e-292) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.8e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (z * (y + -1.0)))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -3.2e+74:
		tmp = t_2
	elif b <= -5.2e-247:
		tmp = t_1
	elif b <= -1.75e-292:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.8e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(z * Float64(y + -1.0))))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -3.2e+74)
		tmp = t_2;
	elseif (b <= -5.2e-247)
		tmp = t_1;
	elseif (b <= -1.75e-292)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.8e+75)
		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 + (a - (z * (y + -1.0)));
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -3.2e+74)
		tmp = t_2;
	elseif (b <= -5.2e-247)
		tmp = t_1;
	elseif (b <= -1.75e-292)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.8e+75)
		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[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+74], t$95$2, If[LessEqual[b, -5.2e-247], t$95$1, If[LessEqual[b, -1.75e-292], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.19999999999999995e74 or 2.80000000000000012e75 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in a around 0 85.2%

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

   4. Taylor expanded in z around 0 77.6%

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

   if -3.19999999999999995e74 < b < -5.2e-247 or -1.75e-292 < b < 2.80000000000000012e75

   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 b around 0 85.6%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. sub-neg 70.6%

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

      3. metadata-eval 70.6%

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

      4. neg-mul-1 70.6%

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

      5. unsub-neg 70.6%

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

   6. Simplified 70.6%

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

   if -5.2e-247 < b < -1.75e-292

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in a around inf 90.0%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+74}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-247}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-292}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 25.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+123}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-49}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-252}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+123)
   (* y b)
   (if (<= y -2.4e-13)
     a
     (if (<= y -2.85e-49)
       (* -2.0 b)
       (if (<= y 3.6e-252) (* t b) (if (<= y 6.5e+35) x (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+123) {
		tmp = y * b;
	} else if (y <= -2.4e-13) {
		tmp = a;
	} else if (y <= -2.85e-49) {
		tmp = -2.0 * b;
	} else if (y <= 3.6e-252) {
		tmp = t * b;
	} else if (y <= 6.5e+35) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d+123)) then
        tmp = y * b
    else if (y <= (-2.4d-13)) then
        tmp = a
    else if (y <= (-2.85d-49)) then
        tmp = (-2.0d0) * b
    else if (y <= 3.6d-252) then
        tmp = t * b
    else if (y <= 6.5d+35) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+123) {
		tmp = y * b;
	} else if (y <= -2.4e-13) {
		tmp = a;
	} else if (y <= -2.85e-49) {
		tmp = -2.0 * b;
	} else if (y <= 3.6e-252) {
		tmp = t * b;
	} else if (y <= 6.5e+35) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+123:
		tmp = y * b
	elif y <= -2.4e-13:
		tmp = a
	elif y <= -2.85e-49:
		tmp = -2.0 * b
	elif y <= 3.6e-252:
		tmp = t * b
	elif y <= 6.5e+35:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+123)
		tmp = Float64(y * b);
	elseif (y <= -2.4e-13)
		tmp = a;
	elseif (y <= -2.85e-49)
		tmp = Float64(-2.0 * b);
	elseif (y <= 3.6e-252)
		tmp = Float64(t * b);
	elseif (y <= 6.5e+35)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+123)
		tmp = y * b;
	elseif (y <= -2.4e-13)
		tmp = a;
	elseif (y <= -2.85e-49)
		tmp = -2.0 * b;
	elseif (y <= 3.6e-252)
		tmp = t * b;
	elseif (y <= 6.5e+35)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+123], N[(y * b), $MachinePrecision], If[LessEqual[y, -2.4e-13], a, If[LessEqual[y, -2.85e-49], N[(-2.0 * b), $MachinePrecision], If[LessEqual[y, 3.6e-252], N[(t * b), $MachinePrecision], If[LessEqual[y, 6.5e+35], x, N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.99999999999999982e123 or 6.5000000000000003e35 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in t around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-rgt-neg-in 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in t around 0 36.7%

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

   7. Taylor expanded in y around inf 36.7%

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

      1. *-commutative 36.7%

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

   9. Simplified 36.7%

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

   if -7.99999999999999982e123 < y < -2.3999999999999999e-13

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 44.1%

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

   4. Taylor expanded in t around 0 25.2%

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

   if -2.3999999999999999e-13 < y < -2.8500000000000002e-49

   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 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-rgt-neg-in 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in t around 0 52.4%

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

   7. Taylor expanded in y around 0 51.3%

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

      1. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if -2.8500000000000002e-49 < y < 3.60000000000000023e-252

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 72.6%

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

   4. Taylor expanded in t around inf 30.4%

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

   if 3.60000000000000023e-252 < y < 6.5000000000000003e35

   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 31.9%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+123}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-49}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-252}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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))))
   (if (<= b -2.15e+67)
     t_2
     (if (<= b 1.26e-270)
       t_1
       (if (<= b 2e-92) (* z (- 1.0 y)) (if (<= b 5.8e+75) t_1 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 tmp;
	if (b <= -2.15e+67) {
		tmp = t_2;
	} else if (b <= 1.26e-270) {
		tmp = t_1;
	} else if (b <= 2e-92) {
		tmp = z * (1.0 - y);
	} else if (b <= 5.8e+75) {
		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 + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.15d+67)) then
        tmp = t_2
    else if (b <= 1.26d-270) then
        tmp = t_1
    else if (b <= 2d-92) then
        tmp = z * (1.0d0 - y)
    else if (b <= 5.8d+75) 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 + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.15e+67) {
		tmp = t_2;
	} else if (b <= 1.26e-270) {
		tmp = t_1;
	} else if (b <= 2e-92) {
		tmp = z * (1.0 - y);
	} else if (b <= 5.8e+75) {
		tmp = t_1;
	} 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)
	tmp = 0
	if b <= -2.15e+67:
		tmp = t_2
	elif b <= 1.26e-270:
		tmp = t_1
	elif b <= 2e-92:
		tmp = z * (1.0 - y)
	elif b <= 5.8e+75:
		tmp = t_1
	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))
	tmp = 0.0
	if (b <= -2.15e+67)
		tmp = t_2;
	elseif (b <= 1.26e-270)
		tmp = t_1;
	elseif (b <= 2e-92)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 5.8e+75)
		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 + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.15e+67)
		tmp = t_2;
	elseif (b <= 1.26e-270)
		tmp = t_1;
	elseif (b <= 2e-92)
		tmp = z * (1.0 - y);
	elseif (b <= 5.8e+75)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+67], t$95$2, If[LessEqual[b, 1.26e-270], t$95$1, If[LessEqual[b, 2e-92], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1500000000000001e67 or 5.7999999999999997e75 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf 74.4%

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

   if -2.1500000000000001e67 < b < 1.25999999999999994e-270 or 1.99999999999999998e-92 < b < 5.7999999999999997e75

   1. Initial program 98.4%

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

   3. Taylor expanded in b around 0 83.6%

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

   4. Taylor expanded in a around inf 54.3%

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

   if 1.25999999999999994e-270 < b < 1.99999999999999998e-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 z around inf 65.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-270}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{-22}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t\_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-90}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + b \cdot \left(\left(y + t\right) - \left(2 + y \cdot \frac{z}{b}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -4.8e-22)
     (+ (- x (* b (- 2.0 (+ y t)))) t_1)
     (if (<= b 3.9e-90)
       (+ x (+ t_1 (* z (- 1.0 y))))
       (+ z (+ x (* b (- (+ y t) (+ 2.0 (* y (/ z 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 <= -4.8e-22) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else if (b <= 3.9e-90) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = z + (x + (b * ((y + t) - (2.0 + (y * (z / 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 <= (-4.8d-22)) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + t_1
    else if (b <= 3.9d-90) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = z + (x + (b * ((y + t) - (2.0d0 + (y * (z / 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 <= -4.8e-22) {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	} else if (b <= 3.9e-90) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = z + (x + (b * ((y + t) - (2.0 + (y * (z / b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -4.8e-22:
		tmp = (x - (b * (2.0 - (y + t)))) + t_1
	elif b <= 3.9e-90:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = z + (x + (b * ((y + t) - (2.0 + (y * (z / 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 <= -4.8e-22)
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + t_1);
	elseif (b <= 3.9e-90)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(z + Float64(x + Float64(b * Float64(Float64(y + t) - Float64(2.0 + Float64(y * Float64(z / 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 <= -4.8e-22)
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	elseif (b <= 3.9e-90)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = z + (x + (b * ((y + t) - (2.0 + (y * (z / 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, -4.8e-22], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 3.9e-90], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - N[(2.0 + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.80000000000000005e-22

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 87.3%

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

   if -4.80000000000000005e-22 < b < 3.90000000000000005e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 97.1%

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

   if 3.90000000000000005e-90 < b

   1. Initial program 91.7%

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

   3. Taylor expanded in y around 0 92.7%

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

   4. Taylor expanded in b around inf 93.8%

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

      1. sub-neg 93.8%

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

      2. +-commutative 93.8%

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

      3. metadata-eval 93.8%

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

      4. associate-+l+ 93.8%

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

      5. mul-1-neg 93.8%

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

      6. unsub-neg 93.8%

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

      7. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in a around 0 83.7%

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

   9. Simplified 84.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-22}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-90}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + b \cdot \left(\left(y + t\right) - \left(2 + y \cdot \frac{z}{b}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 60000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1e+41)
     t_2
     (if (<= a -4.1e-249)
       t_1
       (if (<= a 7.7e-202) x (if (<= a 60000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1e+41) {
		tmp = t_2;
	} else if (a <= -4.1e-249) {
		tmp = t_1;
	} else if (a <= 7.7e-202) {
		tmp = x;
	} else if (a <= 60000000.0) {
		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 * -z
    t_2 = a * (1.0d0 - t)
    if (a <= (-1d+41)) then
        tmp = t_2
    else if (a <= (-4.1d-249)) then
        tmp = t_1
    else if (a <= 7.7d-202) then
        tmp = x
    else if (a <= 60000000.0d0) 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 * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1e+41) {
		tmp = t_2;
	} else if (a <= -4.1e-249) {
		tmp = t_1;
	} else if (a <= 7.7e-202) {
		tmp = x;
	} else if (a <= 60000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -1e+41:
		tmp = t_2
	elif a <= -4.1e-249:
		tmp = t_1
	elif a <= 7.7e-202:
		tmp = x
	elif a <= 60000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1e+41)
		tmp = t_2;
	elseif (a <= -4.1e-249)
		tmp = t_1;
	elseif (a <= 7.7e-202)
		tmp = x;
	elseif (a <= 60000000.0)
		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 * -z;
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1e+41)
		tmp = t_2;
	elseif (a <= -4.1e-249)
		tmp = t_1;
	elseif (a <= 7.7e-202)
		tmp = x;
	elseif (a <= 60000000.0)
		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 * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+41], t$95$2, If[LessEqual[a, -4.1e-249], t$95$1, If[LessEqual[a, 7.7e-202], x, If[LessEqual[a, 60000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.00000000000000001e41 or 6e7 < a

   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 a around inf 54.8%

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

   if -1.00000000000000001e41 < a < -4.10000000000000004e-249 or 7.6999999999999996e-202 < a < 6e7

   1. Initial program 96.2%

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

   3. Taylor expanded in b around 0 59.9%

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

   4. Taylor expanded in y around inf 30.7%

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

      1. mul-1-neg 30.7%

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

      2. distribute-rgt-neg-in 30.7%

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

   6. Simplified 30.7%

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

   if -4.10000000000000004e-249 < a < 7.6999999999999996e-202

   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 x around inf 37.0%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 60000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.05 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3.05e+88)
     t_2
     (if (<= t -5.6e-206)
       t_1
       (if (<= t 4.6e-271) x (if (<= t 5.2e+139) 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 <= -3.05e+88) {
		tmp = t_2;
	} else if (t <= -5.6e-206) {
		tmp = t_1;
	} else if (t <= 4.6e-271) {
		tmp = x;
	} else if (t <= 5.2e+139) {
		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 <= (-3.05d+88)) then
        tmp = t_2
    else if (t <= (-5.6d-206)) then
        tmp = t_1
    else if (t <= 4.6d-271) then
        tmp = x
    else if (t <= 5.2d+139) 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 <= -3.05e+88) {
		tmp = t_2;
	} else if (t <= -5.6e-206) {
		tmp = t_1;
	} else if (t <= 4.6e-271) {
		tmp = x;
	} else if (t <= 5.2e+139) {
		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 <= -3.05e+88:
		tmp = t_2
	elif t <= -5.6e-206:
		tmp = t_1
	elif t <= 4.6e-271:
		tmp = x
	elif t <= 5.2e+139:
		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 <= -3.05e+88)
		tmp = t_2;
	elseif (t <= -5.6e-206)
		tmp = t_1;
	elseif (t <= 4.6e-271)
		tmp = x;
	elseif (t <= 5.2e+139)
		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 <= -3.05e+88)
		tmp = t_2;
	elseif (t <= -5.6e-206)
		tmp = t_1;
	elseif (t <= 4.6e-271)
		tmp = x;
	elseif (t <= 5.2e+139)
		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, -3.05e+88], t$95$2, If[LessEqual[t, -5.6e-206], t$95$1, If[LessEqual[t, 4.6e-271], x, If[LessEqual[t, 5.2e+139], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0499999999999999e88 or 5.20000000000000044e139 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in t around inf 79.5%

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

   if -3.0499999999999999e88 < t < -5.6000000000000003e-206 or 4.60000000000000017e-271 < t < 5.20000000000000044e139

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf 43.5%

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

   if -5.6000000000000003e-206 < t < 4.60000000000000017e-271

   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 x around inf 38.5%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+131} \lor \neg \left(z \leq 6.6 \cdot 10^{+146}\right):\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -2.6e+131) (not (<= z 6.6e+146)))
     (+ x (+ t_1 (* z (- 1.0 y))))
     (+ (- x (* b (- 2.0 (+ y t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -2.6e+131) || !(z <= 6.6e+146)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x - (b * (2.0 - (y + 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 = a * (1.0d0 - t)
    if ((z <= (-2.6d+131)) .or. (.not. (z <= 6.6d+146))) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x - (b * (2.0d0 - (y + 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 = a * (1.0 - t);
	double tmp;
	if ((z <= -2.6e+131) || !(z <= 6.6e+146)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (z <= -2.6e+131) or not (z <= 6.6e+146):
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x - (b * (2.0 - (y + t)))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((z <= -2.6e+131) || !(z <= 6.6e+146))
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((z <= -2.6e+131) || ~((z <= 6.6e+146)))
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x - (b * (2.0 - (y + t)))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.6e+131], N[Not[LessEqual[z, 6.6e+146]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e131 or 6.60000000000000032e146 < z

   1. Initial program 89.7%

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

   3. Taylor expanded in b around 0 86.4%

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

   if -2.6e131 < z < 6.60000000000000032e146

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 86.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+131} \lor \neg \left(z \leq 6.6 \cdot 10^{+146}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x + \left(t\_1 + t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -2.2e-19)
     (+ t_2 t_1)
     (if (<= b 1.4e-81) (+ x (+ t_1 t_3)) (+ t_2 t_3)))))

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 * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.2e-19) {
		tmp = t_2 + t_1;
	} else if (b <= 1.4e-81) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + 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 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = z * (1.0d0 - y)
    if (b <= (-2.2d-19)) then
        tmp = t_2 + t_1
    else if (b <= 1.4d-81) then
        tmp = x + (t_1 + t_3)
    else
        tmp = t_2 + 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 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -2.2e-19) {
		tmp = t_2 + t_1;
	} else if (b <= 1.4e-81) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -2.2e-19:
		tmp = t_2 + t_1
	elif b <= 1.4e-81:
		tmp = x + (t_1 + t_3)
	else:
		tmp = t_2 + t_3
	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(2.0 - Float64(y + t))))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -2.2e-19)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 1.4e-81)
		tmp = Float64(x + Float64(t_1 + t_3));
	else
		tmp = Float64(t_2 + t_3);
	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 * (2.0 - (y + t)));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -2.2e-19)
		tmp = t_2 + t_1;
	elseif (b <= 1.4e-81)
		tmp = x + (t_1 + t_3);
	else
		tmp = t_2 + t_3;
	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[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e-19], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 1.4e-81], N[(x + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1999999999999998e-19

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 87.3%

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

   if -2.1999999999999998e-19 < b < 1.3999999999999999e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 97.1%

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

   if 1.3999999999999999e-81 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in a around 0 81.2%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+22}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.5e+119)
     t_1
     (if (<= y -1.2e-7)
       (+ x (- a (* z (+ y -1.0))))
       (if (<= y 4e+22) (+ x (+ z (* (+ t -2.0) b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.5e+119) {
		tmp = t_1;
	} else if (y <= -1.2e-7) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (y <= 4e+22) {
		tmp = x + (z + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4.5d+119)) then
        tmp = t_1
    else if (y <= (-1.2d-7)) then
        tmp = x + (a - (z * (y + (-1.0d0))))
    else if (y <= 4d+22) then
        tmp = x + (z + ((t + (-2.0d0)) * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.5e+119) {
		tmp = t_1;
	} else if (y <= -1.2e-7) {
		tmp = x + (a - (z * (y + -1.0)));
	} else if (y <= 4e+22) {
		tmp = x + (z + ((t + -2.0) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4.5e+119:
		tmp = t_1
	elif y <= -1.2e-7:
		tmp = x + (a - (z * (y + -1.0)))
	elif y <= 4e+22:
		tmp = x + (z + ((t + -2.0) * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.5e+119)
		tmp = t_1;
	elseif (y <= -1.2e-7)
		tmp = Float64(x + Float64(a - Float64(z * Float64(y + -1.0))));
	elseif (y <= 4e+22)
		tmp = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.5e+119)
		tmp = t_1;
	elseif (y <= -1.2e-7)
		tmp = x + (a - (z * (y + -1.0)));
	elseif (y <= 4e+22)
		tmp = x + (z + ((t + -2.0) * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+119], t$95$1, If[LessEqual[y, -1.2e-7], N[(x + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+22], N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000002e119 or 4e22 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -4.5000000000000002e119 < y < -1.19999999999999989e-7

   1. Initial program 89.9%

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

   3. Taylor expanded in b around 0 90.1%

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

   4. Taylor expanded in t around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. sub-neg 75.0%

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

      3. metadata-eval 75.0%

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

      4. neg-mul-1 75.0%

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

      5. unsub-neg 75.0%

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

   6. Simplified 75.0%

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

   if -1.19999999999999989e-7 < y < 4e22

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 75.0%

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

   4. Taylor expanded in y around 0 73.5%

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

      1. associate--l+ 73.5%

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

      2. sub-neg 73.5%

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

      3. metadata-eval 73.5%

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

      4. neg-mul-1 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;x + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+22}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+76} \lor \neg \left(b \leq 3 \cdot 10^{+175}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.7e+76) (not (<= b 3e+175)))
   (- x (* b (- 2.0 (+ y t))))
   (+ 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 <= -4.7e+76) || !(b <= 3e+175)) {
		tmp = x - (b * (2.0 - (y + t)));
	} 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 <= (-4.7d+76)) .or. (.not. (b <= 3d+175))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    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 <= -4.7e+76) || !(b <= 3e+175)) {
		tmp = x - (b * (2.0 - (y + t)));
	} 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 <= -4.7e+76) or not (b <= 3e+175):
		tmp = x - (b * (2.0 - (y + t)))
	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 <= -4.7e+76) || !(b <= 3e+175))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	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 <= -4.7e+76) || ~((b <= 3e+175)))
		tmp = x - (b * (2.0 - (y + t)));
	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, -4.7e+76], N[Not[LessEqual[b, 3e+175]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $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 < -4.7000000000000003e76 or 3.0000000000000002e175 < 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 a around 0 85.9%

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

   4. Taylor expanded in z around 0 83.6%

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

   if -4.7000000000000003e76 < b < 3.0000000000000002e175

   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 83.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+76} \lor \neg \left(b \leq 3 \cdot 10^{+175}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-252}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -3.5e+29)
     t_1
     (if (<= y 1.75e-252) (* t b) (if (<= y 7.2e+22) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -3.5e+29) {
		tmp = t_1;
	} else if (y <= 1.75e-252) {
		tmp = t * b;
	} else if (y <= 7.2e+22) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-3.5d+29)) then
        tmp = t_1
    else if (y <= 1.75d-252) then
        tmp = t * b
    else if (y <= 7.2d+22) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -3.5e+29) {
		tmp = t_1;
	} else if (y <= 1.75e-252) {
		tmp = t * b;
	} else if (y <= 7.2e+22) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -3.5e+29:
		tmp = t_1
	elif y <= 1.75e-252:
		tmp = t * b
	elif y <= 7.2e+22:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -3.5e+29)
		tmp = t_1;
	elseif (y <= 1.75e-252)
		tmp = Float64(t * b);
	elseif (y <= 7.2e+22)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -3.5e+29)
		tmp = t_1;
	elseif (y <= 1.75e-252)
		tmp = t * b;
	elseif (y <= 7.2e+22)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.5e+29], t$95$1, If[LessEqual[y, 1.75e-252], N[(t * b), $MachinePrecision], If[LessEqual[y, 7.2e+22], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999979e29 or 7.2e22 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in b around 0 68.7%

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

   4. Taylor expanded in y around inf 47.1%

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

      1. mul-1-neg 47.1%

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

      2. distribute-rgt-neg-in 47.1%

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

   6. Simplified 47.1%

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

   if -3.49999999999999979e29 < y < 1.74999999999999993e-252

   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 a around 0 76.4%

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

   4. Taylor expanded in t around inf 29.9%

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

   if 1.74999999999999993e-252 < y < 7.2e22

   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 31.9%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-252}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 19.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+112}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.4e+78)
   x
   (if (<= x 2.7e-155) (* -2.0 b) (if (<= x 1.1e+112) z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+78) {
		tmp = x;
	} else if (x <= 2.7e-155) {
		tmp = -2.0 * b;
	} else if (x <= 1.1e+112) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.4d+78)) then
        tmp = x
    else if (x <= 2.7d-155) then
        tmp = (-2.0d0) * b
    else if (x <= 1.1d+112) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.4e+78) {
		tmp = x;
	} else if (x <= 2.7e-155) {
		tmp = -2.0 * b;
	} else if (x <= 1.1e+112) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.4e+78:
		tmp = x
	elif x <= 2.7e-155:
		tmp = -2.0 * b
	elif x <= 1.1e+112:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.4e+78)
		tmp = x;
	elseif (x <= 2.7e-155)
		tmp = Float64(-2.0 * b);
	elseif (x <= 1.1e+112)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.4e+78)
		tmp = x;
	elseif (x <= 2.7e-155)
		tmp = -2.0 * b;
	elseif (x <= 1.1e+112)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.4e+78], x, If[LessEqual[x, 2.7e-155], N[(-2.0 * b), $MachinePrecision], If[LessEqual[x, 1.1e+112], z, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.40000000000000028e78 or 1.1e112 < x

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 34.1%

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

   if -4.40000000000000028e78 < x < 2.69999999999999981e-155

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 57.0%

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

      1. mul-1-neg 57.0%

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

      2. distribute-rgt-neg-in 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in t around 0 31.7%

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

   7. Taylor expanded in y around 0 19.2%

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

      1. *-commutative 19.2%

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

   9. Simplified 19.2%

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

   if 2.69999999999999981e-155 < x < 1.1e112

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 36.4%

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

   4. Taylor expanded in y around 0 19.7%

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

4. Final simplification 24.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+112}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+115} \lor \neg \left(b \leq 0.0016\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.3e+115) (not (<= b 0.0016))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e+115) || !(b <= 0.0016)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.3d+115)) .or. (.not. (b <= 0.0016d0))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e+115) || !(b <= 0.0016)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.3e+115) or not (b <= 0.0016):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.3e+115) || !(b <= 0.0016))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.3e+115) || ~((b <= 0.0016)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.3e+115], N[Not[LessEqual[b, 0.0016]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -2.30000000000000004e115 or 0.00160000000000000008 < b

   1. Initial program 89.0%

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

   3. Taylor expanded in a around 0 80.0%

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

   4. Taylor expanded in t around inf 34.6%

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

   if -2.30000000000000004e115 < b < 0.00160000000000000008

   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 23.3%

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

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+115} \lor \neg \left(b \leq 0.0016\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e-7) x (if (<= x 1.25e-49) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e-7) {
		tmp = x;
	} else if (x <= 1.25e-49) {
		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 <= (-4.5d-7)) then
        tmp = x
    else if (x <= 1.25d-49) 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 <= -4.5e-7) {
		tmp = x;
	} else if (x <= 1.25e-49) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e-7:
		tmp = x
	elif x <= 1.25e-49:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e-7)
		tmp = x;
	elseif (x <= 1.25e-49)
		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 <= -4.5e-7)
		tmp = x;
	elseif (x <= 1.25e-49)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e-7], x, If[LessEqual[x, 1.25e-49], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999998e-7 or 1.25e-49 < 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 23.5%

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

   if -4.4999999999999998e-7 < x < 1.25e-49

   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 27.2%

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

   4. Taylor expanded in t around 0 13.0%

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

4. Final simplification 19.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-49}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.9e+76) x (if (<= x 8.8e+111) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+76) {
		tmp = x;
	} else if (x <= 8.8e+111) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.9d+76)) then
        tmp = x
    else if (x <= 8.8d+111) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+76) {
		tmp = x;
	} else if (x <= 8.8e+111) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.9e+76:
		tmp = x
	elif x <= 8.8e+111:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.9e+76)
		tmp = x;
	elseif (x <= 8.8e+111)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.9e+76)
		tmp = x;
	elseif (x <= 8.8e+111)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.9e+76], x, If[LessEqual[x, 8.8e+111], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000002e76 or 8.79999999999999994e111 < x

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 34.1%

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

   if -2.9000000000000002e76 < x < 8.79999999999999994e111

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 35.1%

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

   4. Taylor expanded in y around 0 15.5%

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

4. Final simplification 22.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 10.9% 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 95.3%

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

3. Taylor expanded in a around inf 27.8%

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

4. Taylor expanded in t around 0 9.6%

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

5. Final simplification 9.6%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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)))