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

Percentage Accurate: 94.9% → 98.0%

Time: 16.3s

Alternatives: 28

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * N[(y + -1.0), $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[(N[(b * N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $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 inf 60.0%

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

   4. Taylor expanded in z around -inf 47.3%

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

      1. associate-*r* 47.3%

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

      2. neg-mul-1 47.3%

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

      3. mul-1-neg 47.3%

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

      4. unsub-neg 47.3%

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

      5. associate-/l* 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in z around inf 47.3%

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

      1. associate-*r/ 65.0%

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

      2. +-commutative 65.0%

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

      3. mul-1-neg 65.0%

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

      4. unsub-neg 65.0%

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

   9. Simplified 65.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x - z \cdot \left(y + -1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \frac{y}{z} - y\right)\\ \end{array} \]
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 93.3%

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

   1. +-commutative 93.3%

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

   2. fma-define 96.1%

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

   3. associate--l+ 96.1%

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

   4. sub-neg 96.1%

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

   5. metadata-eval 96.1%

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

   6. sub-neg 96.1%

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

   7. associate-+l- 96.1%

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

   8. fma-neg 96.8%

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

   9. sub-neg 96.8%

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

   10. metadata-eval 96.8%

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

   11. remove-double-neg 96.8%

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

   12. sub-neg 96.8%

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

   13. metadata-eval 96.8%

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

3. Simplified 96.8%

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

5. Final simplification 96.8%

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

Alternative 3: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.00042:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-165}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{-118}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -0.00042)
     t_2
     (if (<= b -2.5e-165)
       (+ x z)
       (if (<= b 2.1e-277)
         t_1
         (if (<= b 1.76e-118)
           (+ x z)
           (if (<= b 1.9e-57)
             t_1
             (if (<= b 3e-16)
               (* t (- b a))
               (if (<= b 8.5e+75)
                 (* y (- b z))
                 (if (<= b 3e+112) (+ x z) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -0.00042) {
		tmp = t_2;
	} else if (b <= -2.5e-165) {
		tmp = x + z;
	} else if (b <= 2.1e-277) {
		tmp = t_1;
	} else if (b <= 1.76e-118) {
		tmp = x + z;
	} else if (b <= 1.9e-57) {
		tmp = t_1;
	} else if (b <= 3e-16) {
		tmp = t * (b - a);
	} else if (b <= 8.5e+75) {
		tmp = y * (b - z);
	} else if (b <= 3e+112) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-0.00042d0)) then
        tmp = t_2
    else if (b <= (-2.5d-165)) then
        tmp = x + z
    else if (b <= 2.1d-277) then
        tmp = t_1
    else if (b <= 1.76d-118) then
        tmp = x + z
    else if (b <= 1.9d-57) then
        tmp = t_1
    else if (b <= 3d-16) then
        tmp = t * (b - a)
    else if (b <= 8.5d+75) then
        tmp = y * (b - z)
    else if (b <= 3d+112) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -0.00042) {
		tmp = t_2;
	} else if (b <= -2.5e-165) {
		tmp = x + z;
	} else if (b <= 2.1e-277) {
		tmp = t_1;
	} else if (b <= 1.76e-118) {
		tmp = x + z;
	} else if (b <= 1.9e-57) {
		tmp = t_1;
	} else if (b <= 3e-16) {
		tmp = t * (b - a);
	} else if (b <= 8.5e+75) {
		tmp = y * (b - z);
	} else if (b <= 3e+112) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -0.00042:
		tmp = t_2
	elif b <= -2.5e-165:
		tmp = x + z
	elif b <= 2.1e-277:
		tmp = t_1
	elif b <= 1.76e-118:
		tmp = x + z
	elif b <= 1.9e-57:
		tmp = t_1
	elif b <= 3e-16:
		tmp = t * (b - a)
	elif b <= 8.5e+75:
		tmp = y * (b - z)
	elif b <= 3e+112:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -0.00042)
		tmp = t_2;
	elseif (b <= -2.5e-165)
		tmp = Float64(x + z);
	elseif (b <= 2.1e-277)
		tmp = t_1;
	elseif (b <= 1.76e-118)
		tmp = Float64(x + z);
	elseif (b <= 1.9e-57)
		tmp = t_1;
	elseif (b <= 3e-16)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 8.5e+75)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 3e+112)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -0.00042)
		tmp = t_2;
	elseif (b <= -2.5e-165)
		tmp = x + z;
	elseif (b <= 2.1e-277)
		tmp = t_1;
	elseif (b <= 1.76e-118)
		tmp = x + z;
	elseif (b <= 1.9e-57)
		tmp = t_1;
	elseif (b <= 3e-16)
		tmp = t * (b - a);
	elseif (b <= 8.5e+75)
		tmp = y * (b - z);
	elseif (b <= 3e+112)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.00042], t$95$2, If[LessEqual[b, -2.5e-165], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.1e-277], t$95$1, If[LessEqual[b, 1.76e-118], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.9e-57], t$95$1, If[LessEqual[b, 3e-16], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+75], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+112], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.2000000000000002e-4 or 2.99999999999999979e112 < b

   1. Initial program 85.8%

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

   3. Taylor expanded in b around inf 78.2%

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

   if -4.2000000000000002e-4 < b < -2.4999999999999999e-165 or 2.09999999999999995e-277 < b < 1.76e-118 or 8.4999999999999993e75 < b < 2.99999999999999979e112

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 98.7%

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

   4. Taylor expanded in a around 0 77.9%

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

   5. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{x} - -1 \cdot z \]

   if -2.4999999999999999e-165 < b < 2.09999999999999995e-277 or 1.76e-118 < b < 1.8999999999999999e-57

   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 60.4%

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

   if 1.8999999999999999e-57 < b < 2.99999999999999994e-16

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 42.4%

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

   if 2.99999999999999994e-16 < b < 8.4999999999999993e75

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 62.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00042:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-165}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.76 \cdot 10^{-118}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{-5}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= b -2.05e-5)
     (* y b)
     (if (<= b -1.2e-66)
       x
       (if (<= b 2.1e-275)
         t_1
         (if (<= b 3.6e-203)
           t_2
           (if (<= b 9.5e-16)
             t_1
             (if (<= b 5.2e+53) t_2 (if (<= b 4.5e+99) t_1 (* y b))))))))))

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 * -y;
	double tmp;
	if (b <= -2.05e-5) {
		tmp = y * b;
	} else if (b <= -1.2e-66) {
		tmp = x;
	} else if (b <= 2.1e-275) {
		tmp = t_1;
	} else if (b <= 3.6e-203) {
		tmp = t_2;
	} else if (b <= 9.5e-16) {
		tmp = t_1;
	} else if (b <= 5.2e+53) {
		tmp = t_2;
	} else if (b <= 4.5e+99) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * -y
    if (b <= (-2.05d-5)) then
        tmp = y * b
    else if (b <= (-1.2d-66)) then
        tmp = x
    else if (b <= 2.1d-275) then
        tmp = t_1
    else if (b <= 3.6d-203) then
        tmp = t_2
    else if (b <= 9.5d-16) then
        tmp = t_1
    else if (b <= 5.2d+53) then
        tmp = t_2
    else if (b <= 4.5d+99) then
        tmp = t_1
    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 t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (b <= -2.05e-5) {
		tmp = y * b;
	} else if (b <= -1.2e-66) {
		tmp = x;
	} else if (b <= 2.1e-275) {
		tmp = t_1;
	} else if (b <= 3.6e-203) {
		tmp = t_2;
	} else if (b <= 9.5e-16) {
		tmp = t_1;
	} else if (b <= 5.2e+53) {
		tmp = t_2;
	} else if (b <= 4.5e+99) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * -y
	tmp = 0
	if b <= -2.05e-5:
		tmp = y * b
	elif b <= -1.2e-66:
		tmp = x
	elif b <= 2.1e-275:
		tmp = t_1
	elif b <= 3.6e-203:
		tmp = t_2
	elif b <= 9.5e-16:
		tmp = t_1
	elif b <= 5.2e+53:
		tmp = t_2
	elif b <= 4.5e+99:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(-y))
	tmp = 0.0
	if (b <= -2.05e-5)
		tmp = Float64(y * b);
	elseif (b <= -1.2e-66)
		tmp = x;
	elseif (b <= 2.1e-275)
		tmp = t_1;
	elseif (b <= 3.6e-203)
		tmp = t_2;
	elseif (b <= 9.5e-16)
		tmp = t_1;
	elseif (b <= 5.2e+53)
		tmp = t_2;
	elseif (b <= 4.5e+99)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * -y;
	tmp = 0.0;
	if (b <= -2.05e-5)
		tmp = y * b;
	elseif (b <= -1.2e-66)
		tmp = x;
	elseif (b <= 2.1e-275)
		tmp = t_1;
	elseif (b <= 3.6e-203)
		tmp = t_2;
	elseif (b <= 9.5e-16)
		tmp = t_1;
	elseif (b <= 5.2e+53)
		tmp = t_2;
	elseif (b <= 4.5e+99)
		tmp = t_1;
	else
		tmp = y * 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]}, Block[{t$95$2 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[b, -2.05e-5], N[(y * b), $MachinePrecision], If[LessEqual[b, -1.2e-66], x, If[LessEqual[b, 2.1e-275], t$95$1, If[LessEqual[b, 3.6e-203], t$95$2, If[LessEqual[b, 9.5e-16], t$95$1, If[LessEqual[b, 5.2e+53], t$95$2, If[LessEqual[b, 4.5e+99], t$95$1, N[(y * b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05000000000000002e-5 or 4.5e99 < b

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf 46.7%

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

   4. Taylor expanded in b around inf 43.1%

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

   if -2.05000000000000002e-5 < b < -1.20000000000000013e-66

   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 51.4%

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

   if -1.20000000000000013e-66 < b < 2.09999999999999988e-275 or 3.59999999999999979e-203 < b < 9.5000000000000005e-16 or 5.19999999999999996e53 < b < 4.5e99

   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 a around inf 44.7%

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

   if 2.09999999999999988e-275 < b < 3.59999999999999979e-203 or 9.5000000000000005e-16 < b < 5.19999999999999996e53

   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 y around inf 63.1%

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

   4. Taylor expanded in z around -inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. mul-1-neg 59.8%

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

      4. unsub-neg 59.8%

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

      5. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in b around 0 44.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-5}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x - z \cdot \left(y + -1\right)\\ \mathbf{if}\;b \leq -0.000205:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;z + \left(t + -2\right) \cdot b\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+115}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (+ y -1.0)))))
   (if (<= b -0.000205)
     t_2
     (if (<= b 1.05e-277)
       t_1
       (if (<= b 5.3e-120)
         t_3
         (if (<= b 2.3e-82)
           t_1
           (if (<= b 1.55e-32)
             (+ z (* (+ t -2.0) b))
             (if (<= b 9.8e+115) 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 * (y + -1.0));
	double tmp;
	if (b <= -0.000205) {
		tmp = t_2;
	} else if (b <= 1.05e-277) {
		tmp = t_1;
	} else if (b <= 5.3e-120) {
		tmp = t_3;
	} else if (b <= 2.3e-82) {
		tmp = t_1;
	} else if (b <= 1.55e-32) {
		tmp = z + ((t + -2.0) * b);
	} else if (b <= 9.8e+115) {
		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 * (y + (-1.0d0)))
    if (b <= (-0.000205d0)) then
        tmp = t_2
    else if (b <= 1.05d-277) then
        tmp = t_1
    else if (b <= 5.3d-120) then
        tmp = t_3
    else if (b <= 2.3d-82) then
        tmp = t_1
    else if (b <= 1.55d-32) then
        tmp = z + ((t + (-2.0d0)) * b)
    else if (b <= 9.8d+115) 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 * (y + -1.0));
	double tmp;
	if (b <= -0.000205) {
		tmp = t_2;
	} else if (b <= 1.05e-277) {
		tmp = t_1;
	} else if (b <= 5.3e-120) {
		tmp = t_3;
	} else if (b <= 2.3e-82) {
		tmp = t_1;
	} else if (b <= 1.55e-32) {
		tmp = z + ((t + -2.0) * b);
	} else if (b <= 9.8e+115) {
		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 * (y + -1.0))
	tmp = 0
	if b <= -0.000205:
		tmp = t_2
	elif b <= 1.05e-277:
		tmp = t_1
	elif b <= 5.3e-120:
		tmp = t_3
	elif b <= 2.3e-82:
		tmp = t_1
	elif b <= 1.55e-32:
		tmp = z + ((t + -2.0) * b)
	elif b <= 9.8e+115:
		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(y + -1.0)))
	tmp = 0.0
	if (b <= -0.000205)
		tmp = t_2;
	elseif (b <= 1.05e-277)
		tmp = t_1;
	elseif (b <= 5.3e-120)
		tmp = t_3;
	elseif (b <= 2.3e-82)
		tmp = t_1;
	elseif (b <= 1.55e-32)
		tmp = Float64(z + Float64(Float64(t + -2.0) * b));
	elseif (b <= 9.8e+115)
		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 * (y + -1.0));
	tmp = 0.0;
	if (b <= -0.000205)
		tmp = t_2;
	elseif (b <= 1.05e-277)
		tmp = t_1;
	elseif (b <= 5.3e-120)
		tmp = t_3;
	elseif (b <= 2.3e-82)
		tmp = t_1;
	elseif (b <= 1.55e-32)
		tmp = z + ((t + -2.0) * b);
	elseif (b <= 9.8e+115)
		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[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.000205], t$95$2, If[LessEqual[b, 1.05e-277], t$95$1, If[LessEqual[b, 5.3e-120], t$95$3, If[LessEqual[b, 2.3e-82], t$95$1, If[LessEqual[b, 1.55e-32], N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e+115], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05e-4 or 9.79999999999999928e115 < b

   1. Initial program 85.8%

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

   3. Taylor expanded in b around inf 78.2%

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

   if -2.05e-4 < b < 1.04999999999999997e-277 or 5.29999999999999997e-120 < b < 2.29999999999999997e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 73.2%

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

   4. Taylor expanded in b around 0 69.4%

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

   if 1.04999999999999997e-277 < b < 5.29999999999999997e-120 or 1.55000000000000005e-32 < b < 9.79999999999999928e115

   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 a around 0 77.0%

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

   4. Taylor expanded in b around 0 63.6%

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

   if 2.29999999999999997e-82 < b < 1.55000000000000005e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 76.1%

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

   4. Taylor expanded in x around 0 75.3%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. sub-neg 60.6%

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

      2. metadata-eval 60.6%

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

      3. neg-mul-1 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.000205:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-277}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;z + \left(t + -2\right) \cdot b\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+115}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x - z \cdot \left(y + -1\right)\\ \mathbf{if}\;b \leq -0.00033:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4500000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (+ y -1.0)))))
   (if (<= b -0.00033)
     t_2
     (if (<= b 2.4e-277)
       t_1
       (if (<= b 7.6e-120)
         t_3
         (if (<= b 1.2e-15)
           t_1
           (if (<= b 4500000.0)
             (* y (- b z))
             (if (<= b 3.4e+112) 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 * (y + -1.0));
	double tmp;
	if (b <= -0.00033) {
		tmp = t_2;
	} else if (b <= 2.4e-277) {
		tmp = t_1;
	} else if (b <= 7.6e-120) {
		tmp = t_3;
	} else if (b <= 1.2e-15) {
		tmp = t_1;
	} else if (b <= 4500000.0) {
		tmp = y * (b - z);
	} else if (b <= 3.4e+112) {
		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 * (y + (-1.0d0)))
    if (b <= (-0.00033d0)) then
        tmp = t_2
    else if (b <= 2.4d-277) then
        tmp = t_1
    else if (b <= 7.6d-120) then
        tmp = t_3
    else if (b <= 1.2d-15) then
        tmp = t_1
    else if (b <= 4500000.0d0) then
        tmp = y * (b - z)
    else if (b <= 3.4d+112) 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 * (y + -1.0));
	double tmp;
	if (b <= -0.00033) {
		tmp = t_2;
	} else if (b <= 2.4e-277) {
		tmp = t_1;
	} else if (b <= 7.6e-120) {
		tmp = t_3;
	} else if (b <= 1.2e-15) {
		tmp = t_1;
	} else if (b <= 4500000.0) {
		tmp = y * (b - z);
	} else if (b <= 3.4e+112) {
		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 * (y + -1.0))
	tmp = 0
	if b <= -0.00033:
		tmp = t_2
	elif b <= 2.4e-277:
		tmp = t_1
	elif b <= 7.6e-120:
		tmp = t_3
	elif b <= 1.2e-15:
		tmp = t_1
	elif b <= 4500000.0:
		tmp = y * (b - z)
	elif b <= 3.4e+112:
		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(y + -1.0)))
	tmp = 0.0
	if (b <= -0.00033)
		tmp = t_2;
	elseif (b <= 2.4e-277)
		tmp = t_1;
	elseif (b <= 7.6e-120)
		tmp = t_3;
	elseif (b <= 1.2e-15)
		tmp = t_1;
	elseif (b <= 4500000.0)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 3.4e+112)
		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 * (y + -1.0));
	tmp = 0.0;
	if (b <= -0.00033)
		tmp = t_2;
	elseif (b <= 2.4e-277)
		tmp = t_1;
	elseif (b <= 7.6e-120)
		tmp = t_3;
	elseif (b <= 1.2e-15)
		tmp = t_1;
	elseif (b <= 4500000.0)
		tmp = y * (b - z);
	elseif (b <= 3.4e+112)
		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[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.00033], t$95$2, If[LessEqual[b, 2.4e-277], t$95$1, If[LessEqual[b, 7.6e-120], t$95$3, If[LessEqual[b, 1.2e-15], t$95$1, If[LessEqual[b, 4500000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+112], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.3e-4 or 3.39999999999999993e112 < b

   1. Initial program 85.8%

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

   3. Taylor expanded in b around inf 78.2%

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

   if -3.3e-4 < b < 2.4e-277 or 7.5999999999999995e-120 < b < 1.19999999999999997e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.0%

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

   4. Taylor expanded in b around 0 64.1%

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

   if 2.4e-277 < b < 7.5999999999999995e-120 or 4.5e6 < b < 3.39999999999999993e112

   1. Initial program 96.4%

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

   3. Taylor expanded in a around 0 76.1%

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

   4. Taylor expanded in b around 0 66.4%

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

   if 1.19999999999999997e-15 < b < 4.5e6

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 99.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00033:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-277}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-120}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4500000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+112}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.00019:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -0.00019)
     t_2
     (if (<= b 8e-236)
       t_1
       (if (<= b 3.45e-203)
         (* z (- 1.0 y))
         (if (<= b 1.5e-15)
           t_1
           (if (<= b 1.08e+48)
             (* y (- b z))
             (if (<= b 2.5e+100) 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 <= -0.00019) {
		tmp = t_2;
	} else if (b <= 8e-236) {
		tmp = t_1;
	} else if (b <= 3.45e-203) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.5e-15) {
		tmp = t_1;
	} else if (b <= 1.08e+48) {
		tmp = y * (b - z);
	} else if (b <= 2.5e+100) {
		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 <= (-0.00019d0)) then
        tmp = t_2
    else if (b <= 8d-236) then
        tmp = t_1
    else if (b <= 3.45d-203) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.5d-15) then
        tmp = t_1
    else if (b <= 1.08d+48) then
        tmp = y * (b - z)
    else if (b <= 2.5d+100) 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 <= -0.00019) {
		tmp = t_2;
	} else if (b <= 8e-236) {
		tmp = t_1;
	} else if (b <= 3.45e-203) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.5e-15) {
		tmp = t_1;
	} else if (b <= 1.08e+48) {
		tmp = y * (b - z);
	} else if (b <= 2.5e+100) {
		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 <= -0.00019:
		tmp = t_2
	elif b <= 8e-236:
		tmp = t_1
	elif b <= 3.45e-203:
		tmp = z * (1.0 - y)
	elif b <= 1.5e-15:
		tmp = t_1
	elif b <= 1.08e+48:
		tmp = y * (b - z)
	elif b <= 2.5e+100:
		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 <= -0.00019)
		tmp = t_2;
	elseif (b <= 8e-236)
		tmp = t_1;
	elseif (b <= 3.45e-203)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.5e-15)
		tmp = t_1;
	elseif (b <= 1.08e+48)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 2.5e+100)
		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 <= -0.00019)
		tmp = t_2;
	elseif (b <= 8e-236)
		tmp = t_1;
	elseif (b <= 3.45e-203)
		tmp = z * (1.0 - y);
	elseif (b <= 1.5e-15)
		tmp = t_1;
	elseif (b <= 1.08e+48)
		tmp = y * (b - z);
	elseif (b <= 2.5e+100)
		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, -0.00019], t$95$2, If[LessEqual[b, 8e-236], t$95$1, If[LessEqual[b, 3.45e-203], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-15], t$95$1, If[LessEqual[b, 1.08e+48], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+100], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9000000000000001e-4 or 2.4999999999999999e100 < b

   1. Initial program 86.2%

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

   3. Taylor expanded in b around inf 76.1%

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

   if -1.9000000000000001e-4 < b < 8.0000000000000004e-236 or 3.45e-203 < b < 1.5e-15 or 1.07999999999999998e48 < b < 2.4999999999999999e100

   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 z around 0 70.7%

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

   4. Taylor expanded in b around 0 63.7%

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

   if 8.0000000000000004e-236 < b < 3.45e-203

   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 84.4%

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

   if 1.5e-15 < b < 1.07999999999999998e48

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 74.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00019:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-236}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-15}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+100}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-178}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-125}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1 - y \cdot z\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+141}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (* t (- b a))))
   (if (<= t -8e+23)
     t_2
     (if (<= t 9e-178)
       (+ x (+ a (* b (+ y -2.0))))
       (if (<= t 7.4e-125)
         (- x (* z (+ y -1.0)))
         (if (<= t 5.5e+27)
           (- t_1 (* y z))
           (if (<= t 1.4e+141) (+ x t_1) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+23) {
		tmp = t_2;
	} else if (t <= 9e-178) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (t <= 7.4e-125) {
		tmp = x - (z * (y + -1.0));
	} else if (t <= 5.5e+27) {
		tmp = t_1 - (y * z);
	} else if (t <= 1.4e+141) {
		tmp = x + 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 + t) - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-8d+23)) then
        tmp = t_2
    else if (t <= 9d-178) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else if (t <= 7.4d-125) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (t <= 5.5d+27) then
        tmp = t_1 - (y * z)
    else if (t <= 1.4d+141) then
        tmp = x + 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 + t) - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8e+23) {
		tmp = t_2;
	} else if (t <= 9e-178) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (t <= 7.4e-125) {
		tmp = x - (z * (y + -1.0));
	} else if (t <= 5.5e+27) {
		tmp = t_1 - (y * z);
	} else if (t <= 1.4e+141) {
		tmp = x + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8e+23:
		tmp = t_2
	elif t <= 9e-178:
		tmp = x + (a + (b * (y + -2.0)))
	elif t <= 7.4e-125:
		tmp = x - (z * (y + -1.0))
	elif t <= 5.5e+27:
		tmp = t_1 - (y * z)
	elif t <= 1.4e+141:
		tmp = x + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8e+23)
		tmp = t_2;
	elseif (t <= 9e-178)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	elseif (t <= 7.4e-125)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (t <= 5.5e+27)
		tmp = Float64(t_1 - Float64(y * z));
	elseif (t <= 1.4e+141)
		tmp = Float64(x + 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 + t) - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8e+23)
		tmp = t_2;
	elseif (t <= 9e-178)
		tmp = x + (a + (b * (y + -2.0)));
	elseif (t <= 7.4e-125)
		tmp = x - (z * (y + -1.0));
	elseif (t <= 5.5e+27)
		tmp = t_1 - (y * z);
	elseif (t <= 1.4e+141)
		tmp = x + 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[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+23], t$95$2, If[LessEqual[t, 9e-178], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e-125], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+27], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+141], N[(x + t$95$1), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.9999999999999993e23 or 1.39999999999999996e141 < t

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf 70.3%

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

   if -7.9999999999999993e23 < t < 8.99999999999999957e-178

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 78.6%

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

   4. Taylor expanded in t around 0 76.7%

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

      1. associate--l+ 76.7%

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

      2. sub-neg 76.7%

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

      3. metadata-eval 76.7%

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

      4. neg-mul-1 76.7%

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

   6. Simplified 76.7%

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

   if 8.99999999999999957e-178 < t < 7.3999999999999998e-125

   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 84.9%

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

   4. Taylor expanded in b around 0 74.1%

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

   if 7.3999999999999998e-125 < t < 5.49999999999999966e27

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   if 5.49999999999999966e27 < t < 1.39999999999999996e141

   1. Initial program 95.8%

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

   3. Taylor expanded in a around 0 79.8%

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

   4. Taylor expanded in z around 0 79.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-178}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-125}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+141}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 - \frac{t\_1}{b}\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-118}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + t\_1\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -1.2e-5)
     (* b (- (+ t (+ y (/ x b))) (- 2.0 (/ t_1 b))))
     (if (<= b 2.5e-118)
       (+ (- x (* y z)) (+ z t_1))
       (if (<= b 5.8e+66)
         (+ (* b (- (+ y t) 2.0)) (+ t_1 (* z (- 1.0 y))))
         (- z (- (+ (* y (- z b)) (* b (- 2.0 t))) x)))))))

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 <= -1.2e-5) {
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	} else if (b <= 2.5e-118) {
		tmp = (x - (y * z)) + (z + t_1);
	} else if (b <= 5.8e+66) {
		tmp = (b * ((y + t) - 2.0)) + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - 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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-1.2d-5)) then
        tmp = b * ((t + (y + (x / b))) - (2.0d0 - (t_1 / b)))
    else if (b <= 2.5d-118) then
        tmp = (x - (y * z)) + (z + t_1)
    else if (b <= 5.8d+66) then
        tmp = (b * ((y + t) - 2.0d0)) + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = z - (((y * (z - b)) + (b * (2.0d0 - t))) - 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 t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.2e-5) {
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	} else if (b <= 2.5e-118) {
		tmp = (x - (y * z)) + (z + t_1);
	} else if (b <= 5.8e+66) {
		tmp = (b * ((y + t) - 2.0)) + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -1.2e-5:
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)))
	elif b <= 2.5e-118:
		tmp = (x - (y * z)) + (z + t_1)
	elif b <= 5.8e+66:
		tmp = (b * ((y + t) - 2.0)) + (t_1 + (z * (1.0 - y)))
	else:
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.2e-5)
		tmp = Float64(b * Float64(Float64(t + Float64(y + Float64(x / b))) - Float64(2.0 - Float64(t_1 / b))));
	elseif (b <= 2.5e-118)
		tmp = Float64(Float64(x - Float64(y * z)) + Float64(z + t_1));
	elseif (b <= 5.8e+66)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(z - Float64(Float64(Float64(y * Float64(z - b)) + Float64(b * Float64(2.0 - t))) - x));
	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 <= -1.2e-5)
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	elseif (b <= 2.5e-118)
		tmp = (x - (y * z)) + (z + t_1);
	elseif (b <= 5.8e+66)
		tmp = (b * ((y + t) - 2.0)) + (t_1 + (z * (1.0 - y)));
	else
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	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, -1.2e-5], N[(b * N[(N[(t + N[(y + N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 - N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-118], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+66], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.2e-5

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in b around inf 88.1%

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

   if -1.2e-5 < b < 2.50000000000000007e-118

   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 0 100.0%

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

   4. Taylor expanded in b around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. distribute-rgt-neg-in 96.4%

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

   6. Simplified 96.4%

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

   if 2.50000000000000007e-118 < b < 5.79999999999999972e66

   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 0 89.9%

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

   if 5.79999999999999972e66 < b

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0 88.4%

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

   4. Taylor expanded in a around 0 87.8%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - -1 \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 - \frac{a \cdot \left(1 - t\right)}{b}\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-118}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+43} \lor \neg \left(b \leq 4.1 \cdot 10^{-44} \lor \neg \left(b \leq 5200000\right) \land b \leq 4.2 \cdot 10^{+99}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -1.5e+43)
           (not
            (or (<= b 4.1e-44) (and (not (<= b 5200000.0)) (<= b 4.2e+99)))))
     (+ (* b (- (+ y t) 2.0)) t_1)
     (+ x (+ (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -1.5e+43) || !((b <= 4.1e-44) || (!(b <= 5200000.0) && (b <= 4.2e+99)))) {
		tmp = (b * ((y + t) - 2.0)) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-1.5d+43)) .or. (.not. (b <= 4.1d-44) .or. (.not. (b <= 5200000.0d0)) .and. (b <= 4.2d+99))) then
        tmp = (b * ((y + t) - 2.0d0)) + t_1
    else
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -1.5e+43) || !((b <= 4.1e-44) || (!(b <= 5200000.0) && (b <= 4.2e+99)))) {
		tmp = (b * ((y + t) - 2.0)) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -1.5e+43) or not ((b <= 4.1e-44) or (not (b <= 5200000.0) and (b <= 4.2e+99))):
		tmp = (b * ((y + t) - 2.0)) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -1.5e+43) || !((b <= 4.1e-44) || (!(b <= 5200000.0) && (b <= 4.2e+99))))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -1.5e+43) || ~(((b <= 4.1e-44) || (~((b <= 5200000.0)) && (b <= 4.2e+99)))))
		tmp = (b * ((y + t) - 2.0)) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.5e+43], N[Not[Or[LessEqual[b, 4.1e-44], And[N[Not[LessEqual[b, 5200000.0]], $MachinePrecision], LessEqual[b, 4.2e+99]]]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.50000000000000008e43 or 4.09999999999999992e-44 < b < 5.2e6 or 4.2000000000000002e99 < b

   1. Initial program 87.0%

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

   3. Taylor expanded in a around 0 85.1%

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

   4. Taylor expanded in x around 0 82.6%

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

   if -1.50000000000000008e43 < b < 4.09999999999999992e-44 or 5.2e6 < b < 4.2000000000000002e99

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0 91.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+43} \lor \neg \left(b \leq 4.1 \cdot 10^{-44} \lor \neg \left(b \leq 5200000\right) \land b \leq 4.2 \cdot 10^{+99}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := t\_1 - \left(b \cdot \left(2 - \left(y + t\right)\right) - x\right)\\ t_4 := x + \left(t\_1 + t\_2\right)\\ \mathbf{if}\;b \leq -0.0003:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 0.9:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (* z (- 1.0 y)))
        (t_3 (- t_1 (- (* b (- 2.0 (+ y t))) x)))
        (t_4 (+ x (+ t_1 t_2))))
   (if (<= b -0.0003)
     t_3
     (if (<= b 1.55e-51)
       t_4
       (if (<= b 0.9)
         t_3
         (if (<= b 1.2e+100) t_4 (+ (* b (- (+ y t) 2.0)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double t_3 = t_1 - ((b * (2.0 - (y + t))) - x);
	double t_4 = x + (t_1 + t_2);
	double tmp;
	if (b <= -0.0003) {
		tmp = t_3;
	} else if (b <= 1.55e-51) {
		tmp = t_4;
	} else if (b <= 0.9) {
		tmp = t_3;
	} else if (b <= 1.2e+100) {
		tmp = t_4;
	} else {
		tmp = (b * ((y + t) - 2.0)) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    t_3 = t_1 - ((b * (2.0d0 - (y + t))) - x)
    t_4 = x + (t_1 + t_2)
    if (b <= (-0.0003d0)) then
        tmp = t_3
    else if (b <= 1.55d-51) then
        tmp = t_4
    else if (b <= 0.9d0) then
        tmp = t_3
    else if (b <= 1.2d+100) then
        tmp = t_4
    else
        tmp = (b * ((y + t) - 2.0d0)) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double t_3 = t_1 - ((b * (2.0 - (y + t))) - x);
	double t_4 = x + (t_1 + t_2);
	double tmp;
	if (b <= -0.0003) {
		tmp = t_3;
	} else if (b <= 1.55e-51) {
		tmp = t_4;
	} else if (b <= 0.9) {
		tmp = t_3;
	} else if (b <= 1.2e+100) {
		tmp = t_4;
	} else {
		tmp = (b * ((y + t) - 2.0)) + t_2;
	}
	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 = t_1 - ((b * (2.0 - (y + t))) - x)
	t_4 = x + (t_1 + t_2)
	tmp = 0
	if b <= -0.0003:
		tmp = t_3
	elif b <= 1.55e-51:
		tmp = t_4
	elif b <= 0.9:
		tmp = t_3
	elif b <= 1.2e+100:
		tmp = t_4
	else:
		tmp = (b * ((y + t) - 2.0)) + t_2
	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(t_1 - Float64(Float64(b * Float64(2.0 - Float64(y + t))) - x))
	t_4 = Float64(x + Float64(t_1 + t_2))
	tmp = 0.0
	if (b <= -0.0003)
		tmp = t_3;
	elseif (b <= 1.55e-51)
		tmp = t_4;
	elseif (b <= 0.9)
		tmp = t_3;
	elseif (b <= 1.2e+100)
		tmp = t_4;
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	t_3 = t_1 - ((b * (2.0 - (y + t))) - x);
	t_4 = x + (t_1 + t_2);
	tmp = 0.0;
	if (b <= -0.0003)
		tmp = t_3;
	elseif (b <= 1.55e-51)
		tmp = t_4;
	elseif (b <= 0.9)
		tmp = t_3;
	elseif (b <= 1.2e+100)
		tmp = t_4;
	else
		tmp = (b * ((y + t) - 2.0)) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.0003], t$95$3, If[LessEqual[b, 1.55e-51], t$95$4, If[LessEqual[b, 0.9], t$95$3, If[LessEqual[b, 1.2e+100], t$95$4, N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999974e-4 or 1.5499999999999999e-51 < b < 0.900000000000000022

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 84.6%

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

   if -2.99999999999999974e-4 < b < 1.5499999999999999e-51 or 0.900000000000000022 < b < 1.20000000000000006e100

   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 92.6%

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

   if 1.20000000000000006e100 < b

   1. Initial program 82.4%

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

   3. Taylor expanded in a around 0 87.4%

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

   4. Taylor expanded in x around 0 87.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0003:\\ \;\;\;\;a \cdot \left(1 - t\right) - \left(b \cdot \left(2 - \left(y + t\right)\right) - x\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 0.9:\\ \;\;\;\;a \cdot \left(1 - t\right) - \left(b \cdot \left(2 - \left(y + t\right)\right) - x\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + t\_2\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 185000000:\\ \;\;\;\;t\_2 - y \cdot z\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x t_2)))
   (if (<= b -7.6e+43)
     t_3
     (if (<= b 1.35e-16)
       t_1
       (if (<= b 185000000.0)
         (- t_2 (* y z))
         (if (<= b 2.55e+116) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (b <= -7.6e+43) {
		tmp = t_3;
	} else if (b <= 1.35e-16) {
		tmp = t_1;
	} else if (b <= 185000000.0) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.55e+116) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + t_2
    if (b <= (-7.6d+43)) then
        tmp = t_3
    else if (b <= 1.35d-16) then
        tmp = t_1
    else if (b <= 185000000.0d0) then
        tmp = t_2 - (y * z)
    else if (b <= 2.55d+116) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + t_2;
	double tmp;
	if (b <= -7.6e+43) {
		tmp = t_3;
	} else if (b <= 1.35e-16) {
		tmp = t_1;
	} else if (b <= 185000000.0) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.55e+116) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + t_2
	tmp = 0
	if b <= -7.6e+43:
		tmp = t_3
	elif b <= 1.35e-16:
		tmp = t_1
	elif b <= 185000000.0:
		tmp = t_2 - (y * z)
	elif b <= 2.55e+116:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + t_2)
	tmp = 0.0
	if (b <= -7.6e+43)
		tmp = t_3;
	elseif (b <= 1.35e-16)
		tmp = t_1;
	elseif (b <= 185000000.0)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 2.55e+116)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + t_2;
	tmp = 0.0;
	if (b <= -7.6e+43)
		tmp = t_3;
	elseif (b <= 1.35e-16)
		tmp = t_1;
	elseif (b <= 185000000.0)
		tmp = t_2 - (y * z);
	elseif (b <= 2.55e+116)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$2), $MachinePrecision]}, If[LessEqual[b, -7.6e+43], t$95$3, If[LessEqual[b, 1.35e-16], t$95$1, If[LessEqual[b, 185000000.0], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+116], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.60000000000000016e43 or 2.55e116 < b

   1. Initial program 86.0%

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

   3. Taylor expanded in a around 0 84.7%

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

   4. Taylor expanded in z around 0 82.7%

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

   if -7.60000000000000016e43 < b < 1.35e-16 or 1.85e8 < b < 2.55e116

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 89.6%

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

   if 1.35e-16 < b < 1.85e8

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 85.7%

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

   4. Taylor expanded in y around inf 90.5%

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

      1. *-commutative 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 185000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+116}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot b\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t b))) (t_2 (* y (- b z))))
   (if (<= y -2.6e+21)
     t_2
     (if (<= y -5e-225)
       (* a (- 1.0 t))
       (if (<= y 1e-304)
         t_1
         (if (<= y 6.4e-49) (+ x z) (if (<= y 9e+26) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.6e+21) {
		tmp = t_2;
	} else if (y <= -5e-225) {
		tmp = a * (1.0 - t);
	} else if (y <= 1e-304) {
		tmp = t_1;
	} else if (y <= 6.4e-49) {
		tmp = x + z;
	} else if (y <= 9e+26) {
		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 + (t * b)
    t_2 = y * (b - z)
    if (y <= (-2.6d+21)) then
        tmp = t_2
    else if (y <= (-5d-225)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1d-304) then
        tmp = t_1
    else if (y <= 6.4d-49) then
        tmp = x + z
    else if (y <= 9d+26) 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 + (t * b);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.6e+21) {
		tmp = t_2;
	} else if (y <= -5e-225) {
		tmp = a * (1.0 - t);
	} else if (y <= 1e-304) {
		tmp = t_1;
	} else if (y <= 6.4e-49) {
		tmp = x + z;
	} else if (y <= 9e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * b)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.6e+21:
		tmp = t_2
	elif y <= -5e-225:
		tmp = a * (1.0 - t)
	elif y <= 1e-304:
		tmp = t_1
	elif y <= 6.4e-49:
		tmp = x + z
	elif y <= 9e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * b))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.6e+21)
		tmp = t_2;
	elseif (y <= -5e-225)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1e-304)
		tmp = t_1;
	elseif (y <= 6.4e-49)
		tmp = Float64(x + z);
	elseif (y <= 9e+26)
		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 + (t * b);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.6e+21)
		tmp = t_2;
	elseif (y <= -5e-225)
		tmp = a * (1.0 - t);
	elseif (y <= 1e-304)
		tmp = t_1;
	elseif (y <= 6.4e-49)
		tmp = x + z;
	elseif (y <= 9e+26)
		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[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+21], t$95$2, If[LessEqual[y, -5e-225], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-304], t$95$1, If[LessEqual[y, 6.4e-49], N[(x + z), $MachinePrecision], If[LessEqual[y, 9e+26], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6e21 or 8.99999999999999957e26 < y

   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 y around inf 63.1%

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

   if -2.6e21 < y < -5.0000000000000001e-225

   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 a around inf 38.6%

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

   if -5.0000000000000001e-225 < y < 9.99999999999999971e-305 or 6.40000000000000005e-49 < y < 8.99999999999999957e26

   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 85.1%

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

   4. Taylor expanded in z around 0 76.1%

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

   5. Taylor expanded in t around inf 66.7%

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

      1. *-commutative 47.2%

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

   7. Simplified 66.7%

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

   if 9.99999999999999971e-305 < y < 6.40000000000000005e-49

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

   4. Taylor expanded in a around 0 73.6%

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

   5. Taylor expanded in x around inf 48.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 10^{-304}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+26}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.9 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= b -9.5e-5)
     (* y b)
     (if (<= b -6.9e-180)
       x
       (if (<= b 1.9e-198)
         t_1
         (if (<= b 1.2e-129) x (if (<= b 5.2e+149) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (b <= -9.5e-5) {
		tmp = y * b;
	} else if (b <= -6.9e-180) {
		tmp = x;
	} else if (b <= 1.9e-198) {
		tmp = t_1;
	} else if (b <= 1.2e-129) {
		tmp = x;
	} else if (b <= 5.2e+149) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (b <= (-9.5d-5)) then
        tmp = y * b
    else if (b <= (-6.9d-180)) then
        tmp = x
    else if (b <= 1.9d-198) then
        tmp = t_1
    else if (b <= 1.2d-129) then
        tmp = x
    else if (b <= 5.2d+149) then
        tmp = t_1
    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 t_1 = z * -y;
	double tmp;
	if (b <= -9.5e-5) {
		tmp = y * b;
	} else if (b <= -6.9e-180) {
		tmp = x;
	} else if (b <= 1.9e-198) {
		tmp = t_1;
	} else if (b <= 1.2e-129) {
		tmp = x;
	} else if (b <= 5.2e+149) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if b <= -9.5e-5:
		tmp = y * b
	elif b <= -6.9e-180:
		tmp = x
	elif b <= 1.9e-198:
		tmp = t_1
	elif b <= 1.2e-129:
		tmp = x
	elif b <= 5.2e+149:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (b <= -9.5e-5)
		tmp = Float64(y * b);
	elseif (b <= -6.9e-180)
		tmp = x;
	elseif (b <= 1.9e-198)
		tmp = t_1;
	elseif (b <= 1.2e-129)
		tmp = x;
	elseif (b <= 5.2e+149)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (b <= -9.5e-5)
		tmp = y * b;
	elseif (b <= -6.9e-180)
		tmp = x;
	elseif (b <= 1.9e-198)
		tmp = t_1;
	elseif (b <= 1.2e-129)
		tmp = x;
	elseif (b <= 5.2e+149)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[b, -9.5e-5], N[(y * b), $MachinePrecision], If[LessEqual[b, -6.9e-180], x, If[LessEqual[b, 1.9e-198], t$95$1, If[LessEqual[b, 1.2e-129], x, If[LessEqual[b, 5.2e+149], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000005e-5 or 5.19999999999999957e149 < b

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 49.2%

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

   4. Taylor expanded in b around inf 45.9%

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

   if -9.5000000000000005e-5 < b < -6.9000000000000003e-180 or 1.9000000000000001e-198 < b < 1.19999999999999994e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 40.4%

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

   if -6.9000000000000003e-180 < b < 1.9000000000000001e-198 or 1.19999999999999994e-129 < b < 5.19999999999999957e149

   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 y around inf 31.2%

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

   4. Taylor expanded in z around -inf 29.5%

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

      1. associate-*r* 29.5%

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

      2. neg-mul-1 29.5%

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

      3. mul-1-neg 29.5%

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

      4. unsub-neg 29.5%

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

      5. associate-/l* 29.3%

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

   6. Simplified 29.3%

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

   7. Taylor expanded in b around 0 24.5%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.9 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + b \cdot \left(y + -2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-149}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* b (+ y -2.0))))) (t_2 (* t (- b a))))
   (if (<= t -2.2e+24)
     t_2
     (if (<= t 9e-178)
       t_1
       (if (<= t 5.8e-149)
         (- x (* z (+ y -1.0)))
         (if (<= t 2.8e+76) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.2e+24) {
		tmp = t_2;
	} else if (t <= 9e-178) {
		tmp = t_1;
	} else if (t <= 5.8e-149) {
		tmp = x - (z * (y + -1.0));
	} else if (t <= 2.8e+76) {
		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 + (b * (y + (-2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-2.2d+24)) then
        tmp = t_2
    else if (t <= 9d-178) then
        tmp = t_1
    else if (t <= 5.8d-149) then
        tmp = x - (z * (y + (-1.0d0)))
    else if (t <= 2.8d+76) 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 + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.2e+24) {
		tmp = t_2;
	} else if (t <= 9e-178) {
		tmp = t_1;
	} else if (t <= 5.8e-149) {
		tmp = x - (z * (y + -1.0));
	} else if (t <= 2.8e+76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (b * (y + -2.0)))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.2e+24:
		tmp = t_2
	elif t <= 9e-178:
		tmp = t_1
	elif t <= 5.8e-149:
		tmp = x - (z * (y + -1.0))
	elif t <= 2.8e+76:
		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(b * Float64(y + -2.0))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.2e+24)
		tmp = t_2;
	elseif (t <= 9e-178)
		tmp = t_1;
	elseif (t <= 5.8e-149)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	elseif (t <= 2.8e+76)
		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 + (b * (y + -2.0)));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.2e+24)
		tmp = t_2;
	elseif (t <= 9e-178)
		tmp = t_1;
	elseif (t <= 5.8e-149)
		tmp = x - (z * (y + -1.0));
	elseif (t <= 2.8e+76)
		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[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+24], t$95$2, If[LessEqual[t, 9e-178], t$95$1, If[LessEqual[t, 5.8e-149], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+76], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000002e24 or 2.7999999999999999e76 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 68.6%

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

   if -2.20000000000000002e24 < t < 8.99999999999999957e-178 or 5.8e-149 < t < 2.7999999999999999e76

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 76.8%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. associate--l+ 72.1%

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

      2. sub-neg 72.1%

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

      3. metadata-eval 72.1%

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

      4. neg-mul-1 72.1%

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

   6. Simplified 72.1%

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

   if 8.99999999999999957e-178 < t < 5.8e-149

   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 91.0%

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

   4. Taylor expanded in b around 0 82.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-178}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-149}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+76}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.72 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -3.4e+16)
     t_2
     (if (<= t -1.5e-105)
       t_1
       (if (<= t -1.72e-152) (* a (- 1.0 t)) (if (<= t 1.7e+58) 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 <= -3.4e+16) {
		tmp = t_2;
	} else if (t <= -1.5e-105) {
		tmp = t_1;
	} else if (t <= -1.72e-152) {
		tmp = a * (1.0 - t);
	} else if (t <= 1.7e+58) {
		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 <= (-3.4d+16)) then
        tmp = t_2
    else if (t <= (-1.5d-105)) then
        tmp = t_1
    else if (t <= (-1.72d-152)) then
        tmp = a * (1.0d0 - t)
    else if (t <= 1.7d+58) 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 <= -3.4e+16) {
		tmp = t_2;
	} else if (t <= -1.5e-105) {
		tmp = t_1;
	} else if (t <= -1.72e-152) {
		tmp = a * (1.0 - t);
	} else if (t <= 1.7e+58) {
		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 <= -3.4e+16:
		tmp = t_2
	elif t <= -1.5e-105:
		tmp = t_1
	elif t <= -1.72e-152:
		tmp = a * (1.0 - t)
	elif t <= 1.7e+58:
		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 <= -3.4e+16)
		tmp = t_2;
	elseif (t <= -1.5e-105)
		tmp = t_1;
	elseif (t <= -1.72e-152)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 1.7e+58)
		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 <= -3.4e+16)
		tmp = t_2;
	elseif (t <= -1.5e-105)
		tmp = t_1;
	elseif (t <= -1.72e-152)
		tmp = a * (1.0 - t);
	elseif (t <= 1.7e+58)
		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, -3.4e+16], t$95$2, If[LessEqual[t, -1.5e-105], t$95$1, If[LessEqual[t, -1.72e-152], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e16 or 1.7e58 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 67.0%

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

   if -3.4e16 < t < -1.5e-105 or -1.72e-152 < t < 1.7e58

   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 y around inf 45.5%

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

   if -1.5e-105 < t < -1.72e-152

   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 48.2%

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

Alternative 17: 46.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.3e+15)
     t_1
     (if (<= t 4.5e-14)
       (* b (- y 2.0))
       (if (<= t 5e+35) x (if (<= t 4.8e+57) (* y b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.3e+15) {
		tmp = t_1;
	} else if (t <= 4.5e-14) {
		tmp = b * (y - 2.0);
	} else if (t <= 5e+35) {
		tmp = x;
	} else if (t <= 4.8e+57) {
		tmp = y * 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 = t * (b - a)
    if (t <= (-4.3d+15)) then
        tmp = t_1
    else if (t <= 4.5d-14) then
        tmp = b * (y - 2.0d0)
    else if (t <= 5d+35) then
        tmp = x
    else if (t <= 4.8d+57) then
        tmp = y * 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 = t * (b - a);
	double tmp;
	if (t <= -4.3e+15) {
		tmp = t_1;
	} else if (t <= 4.5e-14) {
		tmp = b * (y - 2.0);
	} else if (t <= 5e+35) {
		tmp = x;
	} else if (t <= 4.8e+57) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.3e+15:
		tmp = t_1
	elif t <= 4.5e-14:
		tmp = b * (y - 2.0)
	elif t <= 5e+35:
		tmp = x
	elif t <= 4.8e+57:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.3e+15)
		tmp = t_1;
	elseif (t <= 4.5e-14)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 5e+35)
		tmp = x;
	elseif (t <= 4.8e+57)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.3e+15)
		tmp = t_1;
	elseif (t <= 4.5e-14)
		tmp = b * (y - 2.0);
	elseif (t <= 5e+35)
		tmp = x;
	elseif (t <= 4.8e+57)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.3e+15], t$95$1, If[LessEqual[t, 4.5e-14], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+35], x, If[LessEqual[t, 4.8e+57], N[(y * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.3e15 or 4.80000000000000009e57 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 67.0%

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

   if -4.3e15 < t < 4.4999999999999998e-14

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 37.9%

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

   4. Taylor expanded in t around 0 37.9%

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

   if 4.4999999999999998e-14 < t < 5.00000000000000021e35

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 36.9%

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

   if 5.00000000000000021e35 < t < 4.80000000000000009e57

   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 61.4%

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

   4. Taylor expanded in b around inf 61.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+57}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.8e+115)
     t_1
     (if (<= a -2.7e+18)
       (* z (- y))
       (if (<= a -1.45e-122) x (if (<= a 2.35e+76) (* b (- y 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.8e+115) {
		tmp = t_1;
	} else if (a <= -2.7e+18) {
		tmp = z * -y;
	} else if (a <= -1.45e-122) {
		tmp = x;
	} else if (a <= 2.35e+76) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.8d+115)) then
        tmp = t_1
    else if (a <= (-2.7d+18)) then
        tmp = z * -y
    else if (a <= (-1.45d-122)) then
        tmp = x
    else if (a <= 2.35d+76) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.8e+115) {
		tmp = t_1;
	} else if (a <= -2.7e+18) {
		tmp = z * -y;
	} else if (a <= -1.45e-122) {
		tmp = x;
	} else if (a <= 2.35e+76) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.8e+115:
		tmp = t_1
	elif a <= -2.7e+18:
		tmp = z * -y
	elif a <= -1.45e-122:
		tmp = x
	elif a <= 2.35e+76:
		tmp = b * (y - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.8e+115)
		tmp = t_1;
	elseif (a <= -2.7e+18)
		tmp = Float64(z * Float64(-y));
	elseif (a <= -1.45e-122)
		tmp = x;
	elseif (a <= 2.35e+76)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.8e+115)
		tmp = t_1;
	elseif (a <= -2.7e+18)
		tmp = z * -y;
	elseif (a <= -1.45e-122)
		tmp = x;
	elseif (a <= 2.35e+76)
		tmp = b * (y - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+115], t$95$1, If[LessEqual[a, -2.7e+18], N[(z * (-y)), $MachinePrecision], If[LessEqual[a, -1.45e-122], x, If[LessEqual[a, 2.35e+76], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.8000000000000001e115 or 2.3500000000000002e76 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in a around inf 61.1%

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

   if -4.8000000000000001e115 < a < -2.7e18

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 63.3%

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

   4. Taylor expanded in z around -inf 58.1%

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

      1. associate-*r* 58.1%

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

      2. neg-mul-1 58.1%

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

      3. mul-1-neg 58.1%

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

      4. unsub-neg 58.1%

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

      5. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in b around 0 41.8%

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

   if -2.7e18 < a < -1.4500000000000001e-122

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 33.3%

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

   if -1.4500000000000001e-122 < a < 2.3500000000000002e76

   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 b around inf 51.7%

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

   4. Taylor expanded in t around 0 34.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -0.000225:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 - \frac{t\_1}{b}\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -0.000225)
     (* b (- (+ t (+ y (/ x b))) (- 2.0 (/ t_1 b))))
     (if (<= b 1.9e-57)
       (+ (- x (* y z)) (+ z t_1))
       (- z (- (+ (* y (- z b)) (* b (- 2.0 t))) x))))))

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 <= -0.000225) {
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	} else if (b <= 1.9e-57) {
		tmp = (x - (y * z)) + (z + t_1);
	} else {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - 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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-0.000225d0)) then
        tmp = b * ((t + (y + (x / b))) - (2.0d0 - (t_1 / b)))
    else if (b <= 1.9d-57) then
        tmp = (x - (y * z)) + (z + t_1)
    else
        tmp = z - (((y * (z - b)) + (b * (2.0d0 - t))) - 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 t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -0.000225) {
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	} else if (b <= 1.9e-57) {
		tmp = (x - (y * z)) + (z + t_1);
	} else {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -0.000225:
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)))
	elif b <= 1.9e-57:
		tmp = (x - (y * z)) + (z + t_1)
	else:
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -0.000225)
		tmp = Float64(b * Float64(Float64(t + Float64(y + Float64(x / b))) - Float64(2.0 - Float64(t_1 / b))));
	elseif (b <= 1.9e-57)
		tmp = Float64(Float64(x - Float64(y * z)) + Float64(z + t_1));
	else
		tmp = Float64(z - Float64(Float64(Float64(y * Float64(z - b)) + Float64(b * Float64(2.0 - t))) - x));
	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 <= -0.000225)
		tmp = b * ((t + (y + (x / b))) - (2.0 - (t_1 / b)));
	elseif (b <= 1.9e-57)
		tmp = (x - (y * z)) + (z + t_1);
	else
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	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, -0.000225], N[(b * N[(N[(t + N[(y + N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(2.0 - N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-57], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2499999999999999e-4

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 85.2%

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

   4. Taylor expanded in b around inf 88.1%

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

   if -2.2499999999999999e-4 < b < 1.8999999999999999e-57

   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 y around 0 100.0%

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

   4. Taylor expanded in b around 0 95.2%

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

      1. mul-1-neg 95.2%

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

      2. distribute-rgt-neg-in 95.2%

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

   6. Simplified 95.2%

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

   if 1.8999999999999999e-57 < b

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0 91.5%

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

   4. Taylor expanded in a around 0 83.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.000225:\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 - \frac{a \cdot \left(1 - t\right)}{b}\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y \cdot z\right) + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+116}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.55e+116)
   (+ (+ x (* b (- (+ y t) 2.0))) (- a (* t a)))
   (if (<= a 3.4e+109)
     (- z (- (+ (* y (- z b)) (* b (- 2.0 t))) x))
     (+ (* y b) (+ (* 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 (a <= -2.55e+116) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a - (t * a));
	} else if (a <= 3.4e+109) {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	} else {
		tmp = (y * b) + ((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 (a <= (-2.55d+116)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a - (t * a))
    else if (a <= 3.4d+109) then
        tmp = z - (((y * (z - b)) + (b * (2.0d0 - t))) - x)
    else
        tmp = (y * b) + ((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 (a <= -2.55e+116) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a - (t * a));
	} else if (a <= 3.4e+109) {
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	} else {
		tmp = (y * b) + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.55e+116:
		tmp = (x + (b * ((y + t) - 2.0))) + (a - (t * a))
	elif a <= 3.4e+109:
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x)
	else:
		tmp = (y * b) + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.55e+116)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a - Float64(t * a)));
	elseif (a <= 3.4e+109)
		tmp = Float64(z - Float64(Float64(Float64(y * Float64(z - b)) + Float64(b * Float64(2.0 - t))) - x));
	else
		tmp = Float64(Float64(y * b) + 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 (a <= -2.55e+116)
		tmp = (x + (b * ((y + t) - 2.0))) + (a - (t * a));
	elseif (a <= 3.4e+109)
		tmp = z - (((y * (z - b)) + (b * (2.0 - t))) - x);
	else
		tmp = (y * b) + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.55e+116], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+109], N[(z - N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(y * b), $MachinePrecision] + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.55e116

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. sub-neg 87.9%

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

      2. distribute-rgt-in 87.9%

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

      3. metadata-eval 87.9%

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

      4. neg-mul-1 87.9%

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

   5. Applied egg-rr 87.9%

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

   if -2.55e116 < a < 3.40000000000000006e109

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 95.7%

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

   4. Taylor expanded in a around 0 91.0%

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

   if 3.40000000000000006e109 < a

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in y around inf 89.3%

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

      1. *-commutative 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+116}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+109}:\\ \;\;\;\;z - \left(\left(y \cdot \left(z - b\right) + b \cdot \left(2 - t\right)\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+118}:\\ \;\;\;\;t\_2 + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= a -1.75e+118)
     (+ t_2 (- a (* t a)))
     (if (<= a 4e+114) (+ t_2 t_1) (+ (* y b) (+ (* a (- 1.0 t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (a <= -1.75e+118) {
		tmp = t_2 + (a - (t * a));
	} else if (a <= 4e+114) {
		tmp = t_2 + t_1;
	} else {
		tmp = (y * b) + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (a <= (-1.75d+118)) then
        tmp = t_2 + (a - (t * a))
    else if (a <= 4d+114) then
        tmp = t_2 + t_1
    else
        tmp = (y * b) + ((a * (1.0d0 - t)) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (a <= -1.75e+118) {
		tmp = t_2 + (a - (t * a));
	} else if (a <= 4e+114) {
		tmp = t_2 + t_1;
	} else {
		tmp = (y * b) + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if a <= -1.75e+118:
		tmp = t_2 + (a - (t * a))
	elif a <= 4e+114:
		tmp = t_2 + t_1
	else:
		tmp = (y * b) + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (a <= -1.75e+118)
		tmp = Float64(t_2 + Float64(a - Float64(t * a)));
	elseif (a <= 4e+114)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(Float64(y * b) + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (a <= -1.75e+118)
		tmp = t_2 + (a - (t * a));
	elseif (a <= 4e+114)
		tmp = t_2 + t_1;
	else
		tmp = (y * b) + ((a * (1.0 - t)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+118], N[(t$95$2 + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+114], N[(t$95$2 + t$95$1), $MachinePrecision], N[(N[(y * b), $MachinePrecision] + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75000000000000008e118

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. sub-neg 87.9%

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

      2. distribute-rgt-in 87.9%

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

      3. metadata-eval 87.9%

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

      4. neg-mul-1 87.9%

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

   5. Applied egg-rr 87.9%

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

   if -1.75000000000000008e118 < a < 4e114

   1. Initial program 94.5%

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

   3. Taylor expanded in a around 0 90.3%

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

   if 4e114 < a

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in y around inf 89.3%

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

      1. *-commutative 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+118}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+117}:\\ \;\;\;\;t\_1 - \left(b \cdot \left(2 - \left(y + t\right)\right) - x\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+112}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(t\_1 + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- 1.0 y))))
   (if (<= a -2e+117)
     (- t_1 (- (* b (- 2.0 (+ y t))) x))
     (if (<= a 1.55e+112)
       (+ (+ x (* b (- (+ y t) 2.0))) t_2)
       (+ (* y b) (+ t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (a <= -2e+117) {
		tmp = t_1 - ((b * (2.0 - (y + t))) - x);
	} else if (a <= 1.55e+112) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	} else {
		tmp = (y * b) + (t_1 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    if (a <= (-2d+117)) then
        tmp = t_1 - ((b * (2.0d0 - (y + t))) - x)
    else if (a <= 1.55d+112) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_2
    else
        tmp = (y * b) + (t_1 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (a <= -2e+117) {
		tmp = t_1 - ((b * (2.0 - (y + t))) - x);
	} else if (a <= 1.55e+112) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	} else {
		tmp = (y * b) + (t_1 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	tmp = 0
	if a <= -2e+117:
		tmp = t_1 - ((b * (2.0 - (y + t))) - x)
	elif a <= 1.55e+112:
		tmp = (x + (b * ((y + t) - 2.0))) + t_2
	else:
		tmp = (y * b) + (t_1 + t_2)
	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))
	tmp = 0.0
	if (a <= -2e+117)
		tmp = Float64(t_1 - Float64(Float64(b * Float64(2.0 - Float64(y + t))) - x));
	elseif (a <= 1.55e+112)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_2);
	else
		tmp = Float64(Float64(y * b) + Float64(t_1 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -2e+117)
		tmp = t_1 - ((b * (2.0 - (y + t))) - x);
	elseif (a <= 1.55e+112)
		tmp = (x + (b * ((y + t) - 2.0))) + t_2;
	else
		tmp = (y * b) + (t_1 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+117], N[(t$95$1 - N[(N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+112], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(y * b), $MachinePrecision] + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0000000000000001e117

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 87.9%

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

   if -2.0000000000000001e117 < a < 1.54999999999999991e112

   1. Initial program 94.5%

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

   3. Taylor expanded in a around 0 90.3%

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

   if 1.54999999999999991e112 < a

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 84.7%

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

   4. Taylor expanded in y around inf 89.3%

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

      1. *-commutative 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+117}:\\ \;\;\;\;a \cdot \left(1 - t\right) - \left(b \cdot \left(2 - \left(y + t\right)\right) - x\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+112}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))))
   (if (<= a -4.8e+115)
     t_1
     (if (<= a -9.5e+19)
       (- (* t b) (* z (+ y -1.0)))
       (if (<= a 2.2e+81) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -4.8e+115) {
		tmp = t_1;
	} else if (a <= -9.5e+19) {
		tmp = (t * b) - (z * (y + -1.0));
	} else if (a <= 2.2e+81) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    if (a <= (-4.8d+115)) then
        tmp = t_1
    else if (a <= (-9.5d+19)) then
        tmp = (t * b) - (z * (y + (-1.0d0)))
    else if (a <= 2.2d+81) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -4.8e+115) {
		tmp = t_1;
	} else if (a <= -9.5e+19) {
		tmp = (t * b) - (z * (y + -1.0));
	} else if (a <= 2.2e+81) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	tmp = 0
	if a <= -4.8e+115:
		tmp = t_1
	elif a <= -9.5e+19:
		tmp = (t * b) - (z * (y + -1.0))
	elif a <= 2.2e+81:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (a <= -4.8e+115)
		tmp = t_1;
	elseif (a <= -9.5e+19)
		tmp = Float64(Float64(t * b) - Float64(z * Float64(y + -1.0)));
	elseif (a <= 2.2e+81)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (a <= -4.8e+115)
		tmp = t_1;
	elseif (a <= -9.5e+19)
		tmp = (t * b) - (z * (y + -1.0));
	elseif (a <= 2.2e+81)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+115], t$95$1, If[LessEqual[a, -9.5e+19], N[(N[(t * b), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+81], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8000000000000001e115 or 2.19999999999999987e81 < a

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 82.4%

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

   4. Taylor expanded in b around 0 72.3%

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

   if -4.8000000000000001e115 < a < -9.5e19

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0 88.7%

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

   4. Taylor expanded in x around 0 88.7%

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

   5. Taylor expanded in t around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if -9.5e19 < a < 2.19999999999999987e81

   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 a around 0 91.5%

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

   4. Taylor expanded in z around 0 66.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+115}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+82}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))))
   (if (<= a -6.2e+138)
     t_1
     (if (<= a -1.75e+18)
       (* y (- b z))
       (if (<= a 5.3e+82) (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -6.2e+138) {
		tmp = t_1;
	} else if (a <= -1.75e+18) {
		tmp = y * (b - z);
	} else if (a <= 5.3e+82) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    if (a <= (-6.2d+138)) then
        tmp = t_1
    else if (a <= (-1.75d+18)) then
        tmp = y * (b - z)
    else if (a <= 5.3d+82) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -6.2e+138) {
		tmp = t_1;
	} else if (a <= -1.75e+18) {
		tmp = y * (b - z);
	} else if (a <= 5.3e+82) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	tmp = 0
	if a <= -6.2e+138:
		tmp = t_1
	elif a <= -1.75e+18:
		tmp = y * (b - z)
	elif a <= 5.3e+82:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (a <= -6.2e+138)
		tmp = t_1;
	elseif (a <= -1.75e+18)
		tmp = Float64(y * Float64(b - z));
	elseif (a <= 5.3e+82)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (a <= -6.2e+138)
		tmp = t_1;
	elseif (a <= -1.75e+18)
		tmp = y * (b - z);
	elseif (a <= 5.3e+82)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+138], t$95$1, If[LessEqual[a, -1.75e+18], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e+82], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.1999999999999995e138 or 5.29999999999999977e82 < a

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 82.0%

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

   4. Taylor expanded in b around 0 72.8%

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

   if -6.1999999999999995e138 < a < -1.75e18

   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 y around inf 62.1%

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

   if -1.75e18 < a < 5.29999999999999977e82

   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 a around 0 91.5%

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

   4. Taylor expanded in z around 0 66.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+138}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+82}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.9e+20)
     t_1
     (if (<= y -1.3e-223)
       (* a (- 1.0 t))
       (if (<= y 1.3e+28) (+ x (* t 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 <= -1.9e+20) {
		tmp = t_1;
	} else if (y <= -1.3e-223) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.3e+28) {
		tmp = x + (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 * (b - z)
    if (y <= (-1.9d+20)) then
        tmp = t_1
    else if (y <= (-1.3d-223)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.3d+28) then
        tmp = x + (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 * (b - z);
	double tmp;
	if (y <= -1.9e+20) {
		tmp = t_1;
	} else if (y <= -1.3e-223) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.3e+28) {
		tmp = x + (t * 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 <= -1.9e+20:
		tmp = t_1
	elif y <= -1.3e-223:
		tmp = a * (1.0 - t)
	elif y <= 1.3e+28:
		tmp = x + (t * 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 <= -1.9e+20)
		tmp = t_1;
	elseif (y <= -1.3e-223)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.3e+28)
		tmp = Float64(x + 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 * (b - z);
	tmp = 0.0;
	if (y <= -1.9e+20)
		tmp = t_1;
	elseif (y <= -1.3e-223)
		tmp = a * (1.0 - t);
	elseif (y <= 1.3e+28)
		tmp = x + (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 * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+20], t$95$1, If[LessEqual[y, -1.3e-223], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+28], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e20 or 1.3000000000000001e28 < y

   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 y around inf 63.1%

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

   if -1.9e20 < y < -1.3e-223

   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 a around inf 38.6%

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

   if -1.3e-223 < y < 1.3000000000000001e28

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0 78.4%

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

   4. Taylor expanded in z around 0 56.9%

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

   5. Taylor expanded in t around inf 46.3%

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

      1. *-commutative 46.4%

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

   7. Simplified 46.3%

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

Alternative 26: 25.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00041 \lor \neg \left(b \leq 1.25 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.00041) (not (<= b 1.25e-16))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00041) || !(b <= 1.25e-16)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.00041d0)) .or. (.not. (b <= 1.25d-16))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.00041) || !(b <= 1.25e-16)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.00041) or not (b <= 1.25e-16):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.00041) || !(b <= 1.25e-16))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.00041) || ~((b <= 1.25e-16)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.00041], N[Not[LessEqual[b, 1.25e-16]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -4.0999999999999999e-4 or 1.2500000000000001e-16 < b

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 46.3%

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

   4. Taylor expanded in b around inf 37.6%

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

   if -4.0999999999999999e-4 < b < 1.2500000000000001e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 25.2%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00041 \lor \neg \left(b \leq 1.25 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+51}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.8e+51) z (if (<= z 3.7e+139) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.8e+51) {
		tmp = z;
	} else if (z <= 3.7e+139) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.8d+51)) then
        tmp = z
    else if (z <= 3.7d+139) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.8e+51) {
		tmp = z;
	} else if (z <= 3.7e+139) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.8e+51:
		tmp = z
	elif z <= 3.7e+139:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.8e+51)
		tmp = z;
	elseif (z <= 3.7e+139)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.8e+51)
		tmp = z;
	elseif (z <= 3.7e+139)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.8e+51], z, If[LessEqual[z, 3.7e+139], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000005e51 or 3.69999999999999992e139 < z

   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 z around inf 56.9%

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

   4. Taylor expanded in y around 0 24.6%

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

   if -2.80000000000000005e51 < z < 3.69999999999999992e139

   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 x around inf 22.2%

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

Alternative 28: 15.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in x around inf 16.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(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)))