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

Percentage Accurate: 95.0% → 97.8%

Time: 11.3s

Alternatives: 21

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. mul-1-neg 100.0%

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

      10. remove-double-neg 100.0%

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

      11. distribute-lft-neg-in 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   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 73.4%

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

4. Final simplification 98.4%

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

Alternative 2: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -25000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + \left(z + b \cdot \left(y - 2\right)\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x (* (- (+ y t) 2.0) b)) (* a (- 1.0 t)))))
   (if (<= b -25000000.0)
     t_1
     (if (<= b 7e-109)
       (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
       (if (<= b 4.8e+99)
         (- (+ a (+ x (+ z (* b (- y 2.0))))) (* y z))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	double tmp;
	if (b <= -25000000.0) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 4.8e+99) {
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y + t) - 2.0d0) * b)) + (a * (1.0d0 - t))
    if (b <= (-25000000.0d0)) then
        tmp = t_1
    else if (b <= 7d-109) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else if (b <= 4.8d+99) then
        tmp = (a + (x + (z + (b * (y - 2.0d0))))) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	double tmp;
	if (b <= -25000000.0) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 4.8e+99) {
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t))
	tmp = 0
	if b <= -25000000.0:
		tmp = t_1
	elif b <= 7e-109:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	elif b <= 4.8e+99:
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -25000000.0)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	elseif (b <= 4.8e+99)
		tmp = Float64(Float64(a + Float64(x + Float64(z + Float64(b * Float64(y - 2.0))))) - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -25000000.0)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	elseif (b <= 4.8e+99)
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -25000000.0], t$95$1, If[LessEqual[b, 7e-109], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+99], N[(N[(a + N[(x + N[(z + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e7 or 4.8000000000000002e99 < 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 z around 0 89.0%

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

   if -2.5e7 < b < 7e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 97.2%

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

   if 7e-109 < b < 4.8000000000000002e99

   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 y around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. *-commutative 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-neg-in 97.7%

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

      9. mul-1-neg 97.7%

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

      10. remove-double-neg 97.7%

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

      11. distribute-lft-neg-in 97.7%

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

      12. +-commutative 97.7%

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

      13. distribute-neg-in 97.7%

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

      14. metadata-eval 97.7%

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

      15. sub-neg 97.7%

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

      16. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in t around 0 88.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -25000000:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + \left(z + b \cdot \left(y - 2\right)\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;\left(a + \left(x + \left(z + b \cdot \left(y - 2\right)\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -9.5e+68)
     t_1
     (if (<= b 3.5e-109)
       (- (+ x (+ z (* a (- 1.0 t)))) (* y z))
       (if (<= b 1.7e+102)
         (- (+ a (+ x (+ z (* b (- y 2.0))))) (* y z))
         (- t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -9.5e+68) {
		tmp = t_1;
	} else if (b <= 3.5e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 1.7e+102) {
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-9.5d+68)) then
        tmp = t_1
    else if (b <= 3.5d-109) then
        tmp = (x + (z + (a * (1.0d0 - t)))) - (y * z)
    else if (b <= 1.7d+102) then
        tmp = (a + (x + (z + (b * (y - 2.0d0))))) - (y * z)
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -9.5e+68) {
		tmp = t_1;
	} else if (b <= 3.5e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 1.7e+102) {
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -9.5e+68:
		tmp = t_1
	elif b <= 3.5e-109:
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z)
	elif b <= 1.7e+102:
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z)
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -9.5e+68)
		tmp = t_1;
	elseif (b <= 3.5e-109)
		tmp = Float64(Float64(x + Float64(z + Float64(a * Float64(1.0 - t)))) - Float64(y * z));
	elseif (b <= 1.7e+102)
		tmp = Float64(Float64(a + Float64(x + Float64(z + Float64(b * Float64(y - 2.0))))) - Float64(y * z));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -9.5e+68)
		tmp = t_1;
	elseif (b <= 3.5e-109)
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	elseif (b <= 1.7e+102)
		tmp = (a + (x + (z + (b * (y - 2.0))))) - (y * z);
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.5e+68], t$95$1, If[LessEqual[b, 3.5e-109], N[(N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+102], N[(N[(a + N[(x + N[(z + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.50000000000000069e68

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -9.50000000000000069e68 < b < 3.5e-109

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 99.2%

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

      1. sub-neg 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

      5. sub-neg 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. distribute-neg-in 99.2%

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

      9. mul-1-neg 99.2%

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

      10. remove-double-neg 99.2%

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

      11. distribute-lft-neg-in 99.2%

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

      12. +-commutative 99.2%

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

      13. distribute-neg-in 99.2%

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

      14. metadata-eval 99.2%

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

      15. sub-neg 99.2%

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

      16. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in b around 0 94.4%

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

   if 3.5e-109 < b < 1.7e102

   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 0 97.8%

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

      1. sub-neg 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. *-commutative 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

      7. *-commutative 97.8%

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

      8. distribute-neg-in 97.8%

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

      9. mul-1-neg 97.8%

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

      10. remove-double-neg 97.8%

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

      11. distribute-lft-neg-in 97.8%

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

      12. +-commutative 97.8%

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

      13. distribute-neg-in 97.8%

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

      14. metadata-eval 97.8%

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

      15. sub-neg 97.8%

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

      16. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in t around 0 87.1%

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

   if 1.7e102 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf 85.1%

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

      1. associate-*r* 85.1%

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

      2. neg-mul-1 85.1%

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

   5. Simplified 85.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;\left(a + \left(x + \left(z + b \cdot \left(y - 2\right)\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+215}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -3.1e+215)
     (* y b)
     (if (<= y -1.56e+118)
       t_1
       (if (<= y 8.5e-117)
         (* a (- 1.0 t))
         (if (<= y 95000000000.0) x (if (<= y 1.6e+134) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -3.1e+215) {
		tmp = y * b;
	} else if (y <= -1.56e+118) {
		tmp = t_1;
	} else if (y <= 8.5e-117) {
		tmp = a * (1.0 - t);
	} else if (y <= 95000000000.0) {
		tmp = x;
	} else if (y <= 1.6e+134) {
		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 = y * -z
    if (y <= (-3.1d+215)) then
        tmp = y * b
    else if (y <= (-1.56d+118)) then
        tmp = t_1
    else if (y <= 8.5d-117) then
        tmp = a * (1.0d0 - t)
    else if (y <= 95000000000.0d0) then
        tmp = x
    else if (y <= 1.6d+134) 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 = y * -z;
	double tmp;
	if (y <= -3.1e+215) {
		tmp = y * b;
	} else if (y <= -1.56e+118) {
		tmp = t_1;
	} else if (y <= 8.5e-117) {
		tmp = a * (1.0 - t);
	} else if (y <= 95000000000.0) {
		tmp = x;
	} else if (y <= 1.6e+134) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -3.1e+215:
		tmp = y * b
	elif y <= -1.56e+118:
		tmp = t_1
	elif y <= 8.5e-117:
		tmp = a * (1.0 - t)
	elif y <= 95000000000.0:
		tmp = x
	elif y <= 1.6e+134:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -3.1e+215)
		tmp = Float64(y * b);
	elseif (y <= -1.56e+118)
		tmp = t_1;
	elseif (y <= 8.5e-117)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 95000000000.0)
		tmp = x;
	elseif (y <= 1.6e+134)
		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 = y * -z;
	tmp = 0.0;
	if (y <= -3.1e+215)
		tmp = y * b;
	elseif (y <= -1.56e+118)
		tmp = t_1;
	elseif (y <= 8.5e-117)
		tmp = a * (1.0 - t);
	elseif (y <= 95000000000.0)
		tmp = x;
	elseif (y <= 1.6e+134)
		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[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.1e+215], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.56e+118], t$95$1, If[LessEqual[y, 8.5e-117], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 95000000000.0], x, If[LessEqual[y, 1.6e+134], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0999999999999999e215 or 1.6e134 < y

   1. Initial program 81.1%

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

   3. Taylor expanded in b around inf 64.4%

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

   4. Taylor expanded in y around inf 62.5%

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

      1. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   if -3.0999999999999999e215 < y < -1.55999999999999996e118 or 9.5e10 < y < 1.6e134

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 54.1%

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

   4. Taylor expanded in y around inf 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

      3. *-commutative 54.1%

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

   6. Simplified 54.1%

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

   if -1.55999999999999996e118 < y < 8.49999999999999981e-117

   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 a around inf 36.5%

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

   if 8.49999999999999981e-117 < y < 9.5e10

   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 43.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+215}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 27.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-102}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 41000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.2e+214)
     (* y b)
     (if (<= y -1.6e+42)
       t_1
       (if (<= y 1.65e-102)
         (* t b)
         (if (<= y 41000000.0) x (if (<= y 1.66e+134) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.2e+214) {
		tmp = y * b;
	} else if (y <= -1.6e+42) {
		tmp = t_1;
	} else if (y <= 1.65e-102) {
		tmp = t * b;
	} else if (y <= 41000000.0) {
		tmp = x;
	} else if (y <= 1.66e+134) {
		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 = y * -z
    if (y <= (-1.2d+214)) then
        tmp = y * b
    else if (y <= (-1.6d+42)) then
        tmp = t_1
    else if (y <= 1.65d-102) then
        tmp = t * b
    else if (y <= 41000000.0d0) then
        tmp = x
    else if (y <= 1.66d+134) 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 = y * -z;
	double tmp;
	if (y <= -1.2e+214) {
		tmp = y * b;
	} else if (y <= -1.6e+42) {
		tmp = t_1;
	} else if (y <= 1.65e-102) {
		tmp = t * b;
	} else if (y <= 41000000.0) {
		tmp = x;
	} else if (y <= 1.66e+134) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.2e+214:
		tmp = y * b
	elif y <= -1.6e+42:
		tmp = t_1
	elif y <= 1.65e-102:
		tmp = t * b
	elif y <= 41000000.0:
		tmp = x
	elif y <= 1.66e+134:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.2e+214)
		tmp = Float64(y * b);
	elseif (y <= -1.6e+42)
		tmp = t_1;
	elseif (y <= 1.65e-102)
		tmp = Float64(t * b);
	elseif (y <= 41000000.0)
		tmp = x;
	elseif (y <= 1.66e+134)
		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 = y * -z;
	tmp = 0.0;
	if (y <= -1.2e+214)
		tmp = y * b;
	elseif (y <= -1.6e+42)
		tmp = t_1;
	elseif (y <= 1.65e-102)
		tmp = t * b;
	elseif (y <= 41000000.0)
		tmp = x;
	elseif (y <= 1.66e+134)
		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[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.2e+214], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.6e+42], t$95$1, If[LessEqual[y, 1.65e-102], N[(t * b), $MachinePrecision], If[LessEqual[y, 41000000.0], x, If[LessEqual[y, 1.66e+134], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e214 or 1.65999999999999991e134 < y

   1. Initial program 81.1%

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

   3. Taylor expanded in b around inf 64.4%

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

   4. Taylor expanded in y around inf 62.5%

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

      1. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   if -1.2e214 < y < -1.60000000000000001e42 or 4.1e7 < y < 1.65999999999999991e134

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 47.3%

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

   4. Taylor expanded in y around inf 47.3%

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

      1. associate-*r* 47.3%

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

      2. neg-mul-1 47.3%

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

      3. *-commutative 47.3%

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

   6. Simplified 47.3%

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

   if -1.60000000000000001e42 < y < 1.65e-102

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 44.0%

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

   4. Taylor expanded in b around inf 28.7%

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

   if 1.65e-102 < y < 4.1e7

   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 44.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+214}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-102}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 41000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 10^{+102}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -8.2e+68)
     t_1
     (if (<= b 7e-109)
       (- (+ x (+ z (* a (- 1.0 t)))) (* y z))
       (if (<= b 1e+102)
         (- (+ x (+ z (* b (- y 2.0)))) (* y z))
         (- t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.2e+68) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 1e+102) {
		tmp = (x + (z + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-8.2d+68)) then
        tmp = t_1
    else if (b <= 7d-109) then
        tmp = (x + (z + (a * (1.0d0 - t)))) - (y * z)
    else if (b <= 1d+102) then
        tmp = (x + (z + (b * (y - 2.0d0)))) - (y * z)
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.2e+68) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 1e+102) {
		tmp = (x + (z + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -8.2e+68:
		tmp = t_1
	elif b <= 7e-109:
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z)
	elif b <= 1e+102:
		tmp = (x + (z + (b * (y - 2.0)))) - (y * z)
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -8.2e+68)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = Float64(Float64(x + Float64(z + Float64(a * Float64(1.0 - t)))) - Float64(y * z));
	elseif (b <= 1e+102)
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(y - 2.0)))) - Float64(y * z));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -8.2e+68)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	elseif (b <= 1e+102)
		tmp = (x + (z + (b * (y - 2.0)))) - (y * z);
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.2e+68], t$95$1, If[LessEqual[b, 7e-109], N[(N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+102], N[(N[(x + N[(z + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.1999999999999998e68

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -8.1999999999999998e68 < b < 7e-109

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 99.2%

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

      1. sub-neg 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

      5. sub-neg 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. distribute-neg-in 99.2%

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

      9. mul-1-neg 99.2%

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

      10. remove-double-neg 99.2%

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

      11. distribute-lft-neg-in 99.2%

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

      12. +-commutative 99.2%

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

      13. distribute-neg-in 99.2%

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

      14. metadata-eval 99.2%

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

      15. sub-neg 99.2%

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

      16. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in b around 0 94.4%

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

   if 7e-109 < b < 9.99999999999999977e101

   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 0 97.8%

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

      1. sub-neg 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. *-commutative 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

      7. *-commutative 97.8%

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

      8. distribute-neg-in 97.8%

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

      9. mul-1-neg 97.8%

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

      10. remove-double-neg 97.8%

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

      11. distribute-lft-neg-in 97.8%

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

      12. +-commutative 97.8%

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

      13. distribute-neg-in 97.8%

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

      14. metadata-eval 97.8%

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

      15. sub-neg 97.8%

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

      16. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in t around 0 87.1%

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

   7. Taylor expanded in a around 0 80.9%

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

   if 9.99999999999999977e101 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf 85.1%

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

      1. associate-*r* 85.1%

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

      2. neg-mul-1 85.1%

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

   5. Simplified 85.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 10^{+102}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -7e+69)
     t_1
     (if (<= b 7e-109)
       (- (+ x (+ z (* a (- 1.0 t)))) (* y z))
       (if (<= b 2.6e+99)
         (- (+ a (+ x (* b (- y 2.0)))) (* y z))
         (- t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7e+69) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 2.6e+99) {
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-7d+69)) then
        tmp = t_1
    else if (b <= 7d-109) then
        tmp = (x + (z + (a * (1.0d0 - t)))) - (y * z)
    else if (b <= 2.6d+99) then
        tmp = (a + (x + (b * (y - 2.0d0)))) - (y * z)
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7e+69) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	} else if (b <= 2.6e+99) {
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -7e+69:
		tmp = t_1
	elif b <= 7e-109:
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z)
	elif b <= 2.6e+99:
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z)
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -7e+69)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = Float64(Float64(x + Float64(z + Float64(a * Float64(1.0 - t)))) - Float64(y * z));
	elseif (b <= 2.6e+99)
		tmp = Float64(Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))) - Float64(y * z));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -7e+69)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = (x + (z + (a * (1.0 - t)))) - (y * z);
	elseif (b <= 2.6e+99)
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7e+69], t$95$1, If[LessEqual[b, 7e-109], N[(N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+99], N[(N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.99999999999999974e69

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -6.99999999999999974e69 < b < 7e-109

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 99.2%

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

      1. sub-neg 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

      5. sub-neg 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. distribute-neg-in 99.2%

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

      9. mul-1-neg 99.2%

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

      10. remove-double-neg 99.2%

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

      11. distribute-lft-neg-in 99.2%

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

      12. +-commutative 99.2%

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

      13. distribute-neg-in 99.2%

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

      14. metadata-eval 99.2%

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

      15. sub-neg 99.2%

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

      16. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in b around 0 94.4%

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

   if 7e-109 < b < 2.6e99

   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 y around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. *-commutative 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-neg-in 97.7%

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

      9. mul-1-neg 97.7%

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

      10. remove-double-neg 97.7%

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

      11. distribute-lft-neg-in 97.7%

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

      12. +-commutative 97.7%

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

      13. distribute-neg-in 97.7%

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

      14. metadata-eval 97.7%

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

      15. sub-neg 97.7%

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

      16. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in t around 0 88.6%

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

   7. Taylor expanded in z around 0 80.3%

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

   if 2.6e99 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+69}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;\left(x + \left(z + a \cdot \left(1 - t\right)\right)\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.05e+70)
     t_1
     (if (<= b 7e-109)
       (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
       (if (<= b 3.8e+99)
         (- (+ a (+ x (* b (- y 2.0)))) (* y z))
         (- t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.05e+70) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 3.8e+99) {
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-1.05d+70)) then
        tmp = t_1
    else if (b <= 7d-109) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else if (b <= 3.8d+99) then
        tmp = (a + (x + (b * (y - 2.0d0)))) - (y * z)
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.05e+70) {
		tmp = t_1;
	} else if (b <= 7e-109) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 3.8e+99) {
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.05e+70:
		tmp = t_1
	elif b <= 7e-109:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	elif b <= 3.8e+99:
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z)
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.05e+70)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	elseif (b <= 3.8e+99)
		tmp = Float64(Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))) - Float64(y * z));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.05e+70)
		tmp = t_1;
	elseif (b <= 7e-109)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	elseif (b <= 3.8e+99)
		tmp = (a + (x + (b * (y - 2.0)))) - (y * z);
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.05e+70], t$95$1, If[LessEqual[b, 7e-109], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+99], N[(N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.05000000000000004e70

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -1.05000000000000004e70 < b < 7e-109

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 94.3%

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

   if 7e-109 < b < 3.8e99

   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 y around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. *-commutative 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-neg-in 97.7%

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

      9. mul-1-neg 97.7%

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

      10. remove-double-neg 97.7%

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

      11. distribute-lft-neg-in 97.7%

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

      12. +-commutative 97.7%

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

      13. distribute-neg-in 97.7%

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

      14. metadata-eval 97.7%

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

      15. sub-neg 97.7%

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

      16. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in t around 0 88.6%

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

   7. Taylor expanded in z around 0 80.3%

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

   if 3.8e99 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-109}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;\left(a + \left(x + b \cdot \left(y - 2\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-230}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -7.2e-5)
     t_2
     (if (<= b -2.35e-169)
       t_1
       (if (<= b 2.1e-230) (- a (* t a)) (if (<= b 2.9e+17) t_1 t_2))))))

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 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.2e-5) {
		tmp = t_2;
	} else if (b <= -2.35e-169) {
		tmp = t_1;
	} else if (b <= 2.1e-230) {
		tmp = a - (t * a);
	} else if (b <= 2.9e+17) {
		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 = z * (1.0d0 - y)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-7.2d-5)) then
        tmp = t_2
    else if (b <= (-2.35d-169)) then
        tmp = t_1
    else if (b <= 2.1d-230) then
        tmp = a - (t * a)
    else if (b <= 2.9d+17) 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 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.2e-5) {
		tmp = t_2;
	} else if (b <= -2.35e-169) {
		tmp = t_1;
	} else if (b <= 2.1e-230) {
		tmp = a - (t * a);
	} else if (b <= 2.9e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -7.2e-5:
		tmp = t_2
	elif b <= -2.35e-169:
		tmp = t_1
	elif b <= 2.1e-230:
		tmp = a - (t * a)
	elif b <= 2.9e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.2e-5)
		tmp = t_2;
	elseif (b <= -2.35e-169)
		tmp = t_1;
	elseif (b <= 2.1e-230)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 2.9e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -7.2e-5)
		tmp = t_2;
	elseif (b <= -2.35e-169)
		tmp = t_1;
	elseif (b <= 2.1e-230)
		tmp = a - (t * a);
	elseif (b <= 2.9e+17)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.2e-5], t$95$2, If[LessEqual[b, -2.35e-169], t$95$1, If[LessEqual[b, 2.1e-230], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000018e-5 or 2.9e17 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 70.4%

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

   if -7.20000000000000018e-5 < b < -2.34999999999999995e-169 or 2.0999999999999998e-230 < b < 2.9e17

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 49.9%

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

   if -2.34999999999999995e-169 < b < 2.0999999999999998e-230

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.6%

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

   4. Taylor expanded in t around 0 54.6%

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

      1. neg-mul-1 54.6%

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

      2. distribute-lft-neg-in 54.6%

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

   6. Simplified 54.6%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.35 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-230}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4800000000000.0)
     t_1
     (if (<= t -3.5e-289)
       (* b (- y 2.0))
       (if (<= t 8.5e-137) x (if (<= t 1.66e+37) (* y (- z)) 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 <= -4800000000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-289) {
		tmp = b * (y - 2.0);
	} else if (t <= 8.5e-137) {
		tmp = x;
	} else if (t <= 1.66e+37) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-4800000000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.5d-289)) then
        tmp = b * (y - 2.0d0)
    else if (t <= 8.5d-137) then
        tmp = x
    else if (t <= 1.66d+37) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4800000000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-289) {
		tmp = b * (y - 2.0);
	} else if (t <= 8.5e-137) {
		tmp = x;
	} else if (t <= 1.66e+37) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4800000000000.0:
		tmp = t_1
	elif t <= -3.5e-289:
		tmp = b * (y - 2.0)
	elif t <= 8.5e-137:
		tmp = x
	elif t <= 1.66e+37:
		tmp = y * -z
	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 <= -4800000000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-289)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 8.5e-137)
		tmp = x;
	elseif (t <= 1.66e+37)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4800000000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-289)
		tmp = b * (y - 2.0);
	elseif (t <= 8.5e-137)
		tmp = x;
	elseif (t <= 1.66e+37)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4800000000000.0], t$95$1, If[LessEqual[t, -3.5e-289], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-137], x, If[LessEqual[t, 1.66e+37], N[(y * (-z)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.8e12 or 1.66000000000000004e37 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 68.9%

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

   if -4.8e12 < t < -3.4999999999999999e-289

   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 b around inf 41.0%

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

   4. Taylor expanded in t around 0 41.0%

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

   if -3.4999999999999999e-289 < t < 8.5000000000000001e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 36.2%

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

   if 8.5000000000000001e-137 < t < 1.66000000000000004e37

   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 49.7%

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

   4. Taylor expanded in y around inf 39.6%

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

      1. associate-*r* 39.6%

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

      2. neg-mul-1 39.6%

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

      3. *-commutative 39.6%

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

   6. Simplified 39.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4800000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -43000000:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-109}:\\ \;\;\;\;x + \left(t\_2 - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))) (t_2 (* z (- 1.0 y))))
   (if (<= b -43000000.0)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 1.75e-109) (+ x (- t_2 (* (+ t -1.0) a))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (b <= -43000000.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 1.75e-109) {
		tmp = x + (t_2 - ((t + -1.0) * a));
	} else {
		tmp = 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 = x + (((y + t) - 2.0d0) * b)
    t_2 = z * (1.0d0 - y)
    if (b <= (-43000000.0d0)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 1.75d-109) then
        tmp = x + (t_2 - ((t + (-1.0d0)) * a))
    else
        tmp = 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 = x + (((y + t) - 2.0) * b);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (b <= -43000000.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 1.75e-109) {
		tmp = x + (t_2 - ((t + -1.0) * a));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = z * (1.0 - y)
	tmp = 0
	if b <= -43000000.0:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 1.75e-109:
		tmp = x + (t_2 - ((t + -1.0) * a))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -43000000.0)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.75e-109)
		tmp = Float64(x + Float64(t_2 - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -43000000.0)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 1.75e-109)
		tmp = x + (t_2 - ((t + -1.0) * a));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -43000000.0], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-109], N[(x + N[(t$95$2 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.3e7

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0 86.7%

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

   if -4.3e7 < b < 1.75e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 97.2%

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

   if 1.75e-109 < b

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0 87.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -43000000:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-109}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+17}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.1e+70)
     t_1
     (if (<= b 6e+17)
       (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
       (- t_1 (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.1e+70) {
		tmp = t_1;
	} else if (b <= 6e+17) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-1.1d+70)) then
        tmp = t_1
    else if (b <= 6d+17) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.1e+70) {
		tmp = t_1;
	} else if (b <= 6e+17) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.1e+70:
		tmp = t_1
	elif b <= 6e+17:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.1e+70)
		tmp = t_1;
	elseif (b <= 6e+17)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.1e+70)
		tmp = t_1;
	elseif (b <= 6e+17)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.1e+70], t$95$1, If[LessEqual[b, 6e+17], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e70

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -1.1e70 < b < 6e17

   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 90.8%

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

   if 6e17 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. neg-mul-1 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+17}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+17}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -8.6e+68)
     t_1
     (if (<= b 6.5e+17) (- (+ x (+ z a)) (* y z)) (- t_1 (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.6e+68) {
		tmp = t_1;
	} else if (b <= 6.5e+17) {
		tmp = (x + (z + a)) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-8.6d+68)) then
        tmp = t_1
    else if (b <= 6.5d+17) then
        tmp = (x + (z + a)) - (y * z)
    else
        tmp = t_1 - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.6e+68) {
		tmp = t_1;
	} else if (b <= 6.5e+17) {
		tmp = (x + (z + a)) - (y * z);
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -8.6e+68:
		tmp = t_1
	elif b <= 6.5e+17:
		tmp = (x + (z + a)) - (y * z)
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -8.6e+68)
		tmp = t_1;
	elseif (b <= 6.5e+17)
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(y * z));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -8.6e+68)
		tmp = t_1;
	elseif (b <= 6.5e+17)
		tmp = (x + (z + a)) - (y * z);
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.6e+68], t$95$1, If[LessEqual[b, 6.5e+17], N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.6000000000000002e68

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 86.5%

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

   if -8.6000000000000002e68 < b < 6.5e17

   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 y around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

      4. *-commutative 98.6%

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

      5. sub-neg 98.6%

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

      6. metadata-eval 98.6%

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

      7. *-commutative 98.6%

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

      8. distribute-neg-in 98.6%

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

      9. mul-1-neg 98.6%

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

      10. remove-double-neg 98.6%

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

      11. distribute-lft-neg-in 98.6%

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

      12. +-commutative 98.6%

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

      13. distribute-neg-in 98.6%

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

      14. metadata-eval 98.6%

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

      15. sub-neg 98.6%

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

      16. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around 0 76.5%

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

   7. Taylor expanded in b around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-+l+ 70.7%

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

   9. Simplified 70.7%

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

   if 6.5e17 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. neg-mul-1 74.5%

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

   5. Simplified 74.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+68}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+17}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -2e+67)
     t_1
     (if (<= b 2.7e-150)
       (* a (- 1.0 t))
       (if (<= b 4.7e+17) (* y (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -2e+67) {
		tmp = t_1;
	} else if (b <= 2.7e-150) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.7e+17) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    if (b <= (-2d+67)) then
        tmp = t_1
    else if (b <= 2.7d-150) then
        tmp = a * (1.0d0 - t)
    else if (b <= 4.7d+17) then
        tmp = y * -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -2e+67) {
		tmp = t_1;
	} else if (b <= 2.7e-150) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.7e+17) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -2e+67:
		tmp = t_1
	elif b <= 2.7e-150:
		tmp = a * (1.0 - t)
	elif b <= 4.7e+17:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -2e+67)
		tmp = t_1;
	elseif (b <= 2.7e-150)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 4.7e+17)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -2e+67)
		tmp = t_1;
	elseif (b <= 2.7e-150)
		tmp = a * (1.0 - t);
	elseif (b <= 4.7e+17)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+67], t$95$1, If[LessEqual[b, 2.7e-150], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+17], N[(y * (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.99999999999999997e67 or 4.7e17 < b

   1. Initial program 88.1%

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

   3. Taylor expanded in b around inf 78.3%

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

   4. Taylor expanded in t around 0 48.8%

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

   if -1.99999999999999997e67 < b < 2.7000000000000001e-150

   1. Initial program 99.1%

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

   3. Taylor expanded in a around inf 39.9%

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

   if 2.7000000000000001e-150 < b < 4.7e17

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 47.9%

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

   4. Taylor expanded in y around inf 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

      3. *-commutative 43.6%

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

   6. Simplified 43.6%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+68} \lor \neg \left(b \leq 7.2 \cdot 10^{+17}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.3e+68) (not (<= b 7.2e+17)))
   (* (- (+ y t) 2.0) b)
   (- (+ x (+ z a)) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e+68) || !(b <= 7.2e+17)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = (x + (z + a)) - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.3d+68)) .or. (.not. (b <= 7.2d+17))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = (x + (z + a)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e+68) || !(b <= 7.2e+17)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = (x + (z + a)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.3e+68) or not (b <= 7.2e+17):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = (x + (z + a)) - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.3e+68) || !(b <= 7.2e+17))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(Float64(x + Float64(z + a)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.3e+68) || ~((b <= 7.2e+17)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = (x + (z + a)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.3e+68], N[Not[LessEqual[b, 7.2e+17]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3e68 or 7.2e17 < b

   1. Initial program 88.0%

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

   3. Taylor expanded in b around inf 78.1%

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

   if -2.3e68 < b < 7.2e17

   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 y around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

      4. *-commutative 98.6%

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

      5. sub-neg 98.6%

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

      6. metadata-eval 98.6%

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

      7. *-commutative 98.6%

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

      8. distribute-neg-in 98.6%

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

      9. mul-1-neg 98.6%

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

      10. remove-double-neg 98.6%

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

      11. distribute-lft-neg-in 98.6%

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

      12. +-commutative 98.6%

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

      13. distribute-neg-in 98.6%

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

      14. metadata-eval 98.6%

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

      15. sub-neg 98.6%

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

      16. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around 0 76.5%

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

   7. Taylor expanded in b around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-+l+ 70.7%

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

   9. Simplified 70.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+68} \lor \neg \left(b \leq 7.2 \cdot 10^{+17}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + a\right)\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+75}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-258}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.8e+75)
   (* t b)
   (if (<= t -3.4e-258) (* y b) (if (<= t 9.6e+39) x (* t (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e+75) {
		tmp = t * b;
	} else if (t <= -3.4e-258) {
		tmp = y * b;
	} else if (t <= 9.6e+39) {
		tmp = x;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.8d+75)) then
        tmp = t * b
    else if (t <= (-3.4d-258)) then
        tmp = y * b
    else if (t <= 9.6d+39) then
        tmp = x
    else
        tmp = t * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e+75) {
		tmp = t * b;
	} else if (t <= -3.4e-258) {
		tmp = y * b;
	} else if (t <= 9.6e+39) {
		tmp = x;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.8e+75:
		tmp = t * b
	elif t <= -3.4e-258:
		tmp = y * b
	elif t <= 9.6e+39:
		tmp = x
	else:
		tmp = t * -a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.8e+75)
		tmp = Float64(t * b);
	elseif (t <= -3.4e-258)
		tmp = Float64(y * b);
	elseif (t <= 9.6e+39)
		tmp = x;
	else
		tmp = Float64(t * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.8e+75)
		tmp = t * b;
	elseif (t <= -3.4e-258)
		tmp = y * b;
	elseif (t <= 9.6e+39)
		tmp = x;
	else
		tmp = t * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.8e+75], N[(t * b), $MachinePrecision], If[LessEqual[t, -3.4e-258], N[(y * b), $MachinePrecision], If[LessEqual[t, 9.6e+39], x, N[(t * (-a)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.80000000000000012e75

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 72.6%

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

   4. Taylor expanded in b around inf 52.2%

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

   if -2.80000000000000012e75 < t < -3.3999999999999998e-258

   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 b around inf 40.3%

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

   4. Taylor expanded in y around inf 32.3%

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

      1. *-commutative 32.3%

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

   6. Simplified 32.3%

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

   if -3.3999999999999998e-258 < t < 9.6000000000000004e39

   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 27.2%

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

   if 9.6000000000000004e39 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in t around inf 72.9%

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

   4. Taylor expanded in b around 0 47.0%

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

      1. neg-mul-1 47.0%

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

   6. Simplified 47.0%

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

Alternative 17: 26.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-259}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.4e+75)
   (* t b)
   (if (<= t -4.8e-259) (* y b) (if (<= t 1.15e+39) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e+75) {
		tmp = t * b;
	} else if (t <= -4.8e-259) {
		tmp = y * b;
	} else if (t <= 1.15e+39) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.4d+75)) then
        tmp = t * b
    else if (t <= (-4.8d-259)) then
        tmp = y * b
    else if (t <= 1.15d+39) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e+75) {
		tmp = t * b;
	} else if (t <= -4.8e-259) {
		tmp = y * b;
	} else if (t <= 1.15e+39) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.4e+75:
		tmp = t * b
	elif t <= -4.8e-259:
		tmp = y * b
	elif t <= 1.15e+39:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.4e+75)
		tmp = Float64(t * b);
	elseif (t <= -4.8e-259)
		tmp = Float64(y * b);
	elseif (t <= 1.15e+39)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.4e+75)
		tmp = t * b;
	elseif (t <= -4.8e-259)
		tmp = y * b;
	elseif (t <= 1.15e+39)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.4e+75], N[(t * b), $MachinePrecision], If[LessEqual[t, -4.8e-259], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.15e+39], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e75 or 1.15000000000000006e39 < t

   1. Initial program 89.1%

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

   3. Taylor expanded in t around inf 73.1%

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

   4. Taylor expanded in b around inf 46.1%

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

   if -2.4e75 < t < -4.8000000000000001e-259

   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 b around inf 40.3%

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

   4. Taylor expanded in y around inf 32.3%

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

      1. *-commutative 32.3%

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

   6. Simplified 32.3%

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

   if -4.8000000000000001e-259 < t < 1.15000000000000006e39

   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 27.5%

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

Alternative 18: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+100} \lor \neg \left(t \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.1e+100) (not (<= t 4.5e+38))) (* t (- b a)) (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.1e+100) || !(t <= 4.5e+38)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - 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 ((t <= (-2.1d+100)) .or. (.not. (t <= 4.5d+38))) then
        tmp = t * (b - a)
    else
        tmp = y * (b - 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 ((t <= -2.1e+100) || !(t <= 4.5e+38)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.1e+100) or not (t <= 4.5e+38):
		tmp = t * (b - a)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.1e+100) || !(t <= 4.5e+38))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.1e+100) || ~((t <= 4.5e+38)))
		tmp = t * (b - a);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.1e+100], N[Not[LessEqual[t, 4.5e+38]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0999999999999999e100 or 4.4999999999999998e38 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 75.5%

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

   if -2.0999999999999999e100 < t < 4.4999999999999998e38

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 46.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+100} \lor \neg \left(t \leq 4.5 \cdot 10^{+38}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+62} \lor \neg \left(b \leq 1.32 \cdot 10^{+123}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.42e+62) (not (<= b 1.32e+123))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.42e+62) || !(b <= 1.32e+123)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.42d+62)) .or. (.not. (b <= 1.32d+123))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.42e+62) || !(b <= 1.32e+123)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.42e+62) or not (b <= 1.32e+123):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.42e+62) || !(b <= 1.32e+123))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.42e+62) || ~((b <= 1.32e+123)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.42e+62], N[Not[LessEqual[b, 1.32e+123]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -1.42e62 or 1.32e123 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 47.2%

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

   4. Taylor expanded in b around inf 45.3%

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

   if -1.42e62 < b < 1.32e123

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 22.4%

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

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+62} \lor \neg \left(b \leq 1.32 \cdot 10^{+123}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.7e+130) x (if (<= x 2.25e-26) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.7e+130) {
		tmp = x;
	} else if (x <= 2.25e-26) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.7d+130)) then
        tmp = x
    else if (x <= 2.25d-26) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.7e+130) {
		tmp = x;
	} else if (x <= 2.25e-26) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.7e+130:
		tmp = x
	elif x <= 2.25e-26:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.7e+130)
		tmp = x;
	elseif (x <= 2.25e-26)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.7e+130)
		tmp = x;
	elseif (x <= 2.25e-26)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.7e+130], x, If[LessEqual[x, 2.25e-26], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000001e130 or 2.2499999999999999e-26 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 32.7%

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

   if -3.7000000000000001e130 < x < 2.2499999999999999e-26

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 34.5%

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

   4. Taylor expanded in t around 0 16.5%

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

Alternative 21: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in a around inf 26.6%

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

4. Taylor expanded in t around 0 10.5%

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

Reproduce

herbie shell --seed 2024186 
(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)))