Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.8% → 99.8%

Time: 12.3s

Alternatives: 20

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * 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) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * 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) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \left(y + \left(z + \left(-0.5 \cdot b + b \cdot a\right)\right)\right)\right) - z \cdot \log t \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (+ x (+ y (+ z (+ (* -0.5 b) (* b a))))) (* z (log t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + (y + (z + ((-0.5 * b) + (b * a))))) - (z * log(t));
}

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 + (z + (((-0.5d0) * b) + (b * a))))) - (z * log(t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + (y + (z + ((-0.5 * b) + (b * a))))) - (z * Math.log(t));
}

Python

def code(x, y, z, t, a, b):
	return (x + (y + (z + ((-0.5 * b) + (b * a))))) - (z * math.log(t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(y + Float64(z + Float64(Float64(-0.5 * b) + Float64(b * a))))) - Float64(z * log(t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + (y + (z + ((-0.5 * b) + (b * a))))) - (z * log(t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(y + N[(z + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 99.9%

   \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

4. Final simplification 99.9%

   \[\leadsto \left(x + \left(y + \left(z + \left(-0.5 \cdot b + b \cdot a\right)\right)\right)\right) - z \cdot \log t \]
5. Add Preprocessing

Alternative 2: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := z + b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -2 \cdot 10^{-107}:\\ \;\;\;\;\left(x + t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (+ z (* b (- a 0.5)))))
   (if (<= (+ x y) -2e-107) (- (+ x t_2) t_1) (- (+ y t_2) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -2e-107) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = z + (b * (a - 0.5d0))
    if ((x + y) <= (-2d-107)) then
        tmp = (x + t_2) - t_1
    else
        tmp = (y + t_2) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -2e-107) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = z + (b * (a - 0.5))
	tmp = 0
	if (x + y) <= -2e-107:
		tmp = (x + t_2) - t_1
	else:
		tmp = (y + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(z + Float64(b * Float64(a - 0.5)))
	tmp = 0.0
	if (Float64(x + y) <= -2e-107)
		tmp = Float64(Float64(x + t_2) - t_1);
	else
		tmp = Float64(Float64(y + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = z + (b * (a - 0.5));
	tmp = 0.0;
	if ((x + y) <= -2e-107)
		tmp = (x + t_2) - t_1;
	else
		tmp = (y + t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -2e-107], N[(N[(x + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2e-107

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.8%

      \[\leadsto \color{blue}{\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t} \]

   if -2e-107 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\left(y + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + -0.5 \cdot b\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) 2e+28)
     (- (+ x (+ z (* b (- a 0.5)))) t_1)
     (- (+ y (+ z (* -0.5 b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if ((x + y) <= 2e+28) {
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	} else {
		tmp = (y + (z + (-0.5 * b))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if ((x + y) <= 2d+28) then
        tmp = (x + (z + (b * (a - 0.5d0)))) - t_1
    else
        tmp = (y + (z + ((-0.5d0) * b))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double tmp;
	if ((x + y) <= 2e+28) {
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	} else {
		tmp = (y + (z + (-0.5 * b))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= 2e+28:
		tmp = (x + (z + (b * (a - 0.5)))) - t_1
	else:
		tmp = (y + (z + (-0.5 * b))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= 2e+28)
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(a - 0.5)))) - t_1);
	else
		tmp = Float64(Float64(y + Float64(z + Float64(-0.5 * b))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if ((x + y) <= 2e+28)
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	else
		tmp = (y + (z + (-0.5 * b))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 2e+28], N[(N[(x + N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + N[(z + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.99999999999999992e28

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t} \]

   if 1.99999999999999992e28 < (+.f64 x y)

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.3%

      \[\leadsto \color{blue}{\left(y + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in a around 0 57.3%

      \[\leadsto \left(y + \left(z + b \cdot \color{blue}{-0.5}\right)\right) - z \cdot \log t \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + -0.5 \cdot b\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+182}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7e+182)
   (+ (* b (- a 0.5)) (- z (* z (log t))))
   (if (<= z 3.1e+203)
     (+ x (+ y (+ (* -0.5 b) (* b a))))
     (+ (+ x y) (* z (- 1.0 (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+182) {
		tmp = (b * (a - 0.5)) + (z - (z * log(t)));
	} else if (z <= 3.1e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = (x + y) + (z * (1.0 - log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7d+182)) then
        tmp = (b * (a - 0.5d0)) + (z - (z * log(t)))
    else if (z <= 3.1d+203) then
        tmp = x + (y + (((-0.5d0) * b) + (b * a)))
    else
        tmp = (x + y) + (z * (1.0d0 - log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+182) {
		tmp = (b * (a - 0.5)) + (z - (z * Math.log(t)));
	} else if (z <= 3.1e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = (x + y) + (z * (1.0 - Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7e+182:
		tmp = (b * (a - 0.5)) + (z - (z * math.log(t)))
	elif z <= 3.1e+203:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	else:
		tmp = (x + y) + (z * (1.0 - math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7e+182)
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(z - Float64(z * log(t))));
	elseif (z <= 3.1e+203)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	else
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 - log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7e+182)
		tmp = (b * (a - 0.5)) + (z - (z * log(t)));
	elseif (z <= 3.1e+203)
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	else
		tmp = (x + y) + (z * (1.0 - log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7e+182], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+203], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000045e182

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.4%

      \[\leadsto \left(\color{blue}{z} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   if -7.00000000000000045e182 < z < 3.1e203

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 92.7%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

   if 3.1e203 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.6%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.6%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.6%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 96.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+182}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+183}:\\ \;\;\;\;b \cdot a + t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -2.05e+183)
     (+ (* b a) t_1)
     (if (<= z 2.15e+204)
       (+ x (+ y (+ (* -0.5 b) (* b a))))
       (+ (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -2.05e+183) {
		tmp = (b * a) + t_1;
	} else if (z <= 2.15e+204) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-2.05d+183)) then
        tmp = (b * a) + t_1
    else if (z <= 2.15d+204) then
        tmp = x + (y + (((-0.5d0) * b) + (b * a)))
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -2.05e+183) {
		tmp = (b * a) + t_1;
	} else if (z <= 2.15e+204) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -2.05e+183:
		tmp = (b * a) + t_1
	elif z <= 2.15e+204:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -2.05e+183)
		tmp = Float64(Float64(b * a) + t_1);
	elseif (z <= 2.15e+204)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -2.05e+183)
		tmp = (b * a) + t_1;
	elseif (z <= 2.15e+204)
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+183], N[(N[(b * a), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 2.15e+204], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000007e183

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.6%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.6%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 81.0%

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

      1. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   if -2.05000000000000007e183 < z < 2.15e204

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 92.7%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

   if 2.15e204 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.6%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.6%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.6%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 96.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+183}:\\ \;\;\;\;b \cdot a + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+235} \lor \neg \left(z \leq 4.8 \cdot 10^{+204}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+235) (not (<= z 4.8e+204)))
   (+ y (* z (- 1.0 (log t))))
   (+ x (+ y (+ (* -0.5 b) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+235) || !(z <= 4.8e+204)) {
		tmp = y + (z * (1.0 - log(t)));
	} else {
		tmp = x + (y + ((-0.5 * b) + (b * 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 ((z <= (-8.5d+235)) .or. (.not. (z <= 4.8d+204))) then
        tmp = y + (z * (1.0d0 - log(t)))
    else
        tmp = x + (y + (((-0.5d0) * b) + (b * 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 ((z <= -8.5e+235) || !(z <= 4.8e+204)) {
		tmp = y + (z * (1.0 - Math.log(t)));
	} else {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e+235) or not (z <= 4.8e+204):
		tmp = y + (z * (1.0 - math.log(t)))
	else:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+235) || !(z <= 4.8e+204))
		tmp = Float64(y + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e+235) || ~((z <= 4.8e+204)))
		tmp = y + (z * (1.0 - log(t)));
	else
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+235], N[Not[LessEqual[z, 4.8e+204]], $MachinePrecision]], N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000017e235 or 4.7999999999999999e204 < z

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.2%

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

   if -8.50000000000000017e235 < z < 4.7999999999999999e204

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 90.1%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+235} \lor \neg \left(z \leq 4.8 \cdot 10^{+204}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+182}:\\ \;\;\;\;b \cdot a + t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -4.1e+182)
     (+ (* b a) t_1)
     (if (<= z 2.9e+203) (+ x (+ y (+ (* -0.5 b) (* b a)))) (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -4.1e+182) {
		tmp = (b * a) + t_1;
	} else if (z <= 2.9e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-4.1d+182)) then
        tmp = (b * a) + t_1
    else if (z <= 2.9d+203) then
        tmp = x + (y + (((-0.5d0) * b) + (b * a)))
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -4.1e+182) {
		tmp = (b * a) + t_1;
	} else if (z <= 2.9e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -4.1e+182:
		tmp = (b * a) + t_1
	elif z <= 2.9e+203:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -4.1e+182)
		tmp = Float64(Float64(b * a) + t_1);
	elseif (z <= 2.9e+203)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -4.1e+182)
		tmp = (b * a) + t_1;
	elseif (z <= 2.9e+203)
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+182], N[(N[(b * a), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 2.9e+203], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000003e182

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.6%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.6%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.6%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 81.0%

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

      1. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   if -4.10000000000000003e182 < z < 2.90000000000000011e203

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 92.7%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

   if 2.90000000000000011e203 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.6%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.6%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.6%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 87.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+182}:\\ \;\;\;\;b \cdot a + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+236}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+236)
   (- z (* z (log t)))
   (if (<= z 9e+203)
     (+ x (+ y (+ (* -0.5 b) (* b a))))
     (+ x (* z (- 1.0 (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+236) {
		tmp = z - (z * log(t));
	} else if (z <= 9e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = x + (z * (1.0 - log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d+236)) then
        tmp = z - (z * log(t))
    else if (z <= 9d+203) then
        tmp = x + (y + (((-0.5d0) * b) + (b * a)))
    else
        tmp = x + (z * (1.0d0 - log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+236) {
		tmp = z - (z * Math.log(t));
	} else if (z <= 9e+203) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = x + (z * (1.0 - Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e+236:
		tmp = z - (z * math.log(t))
	elif z <= 9e+203:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	else:
		tmp = x + (z * (1.0 - math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+236)
		tmp = Float64(z - Float64(z * log(t)));
	elseif (z <= 9e+203)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	else
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e+236)
		tmp = z - (z * log(t));
	elseif (z <= 9e+203)
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	else
		tmp = x + (z * (1.0 - log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+236], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+203], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e236

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.2%

      \[\leadsto \left(\color{blue}{z} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in b around 0 68.2%

      \[\leadsto \color{blue}{z - z \cdot \log t} \]

   if -2.9000000000000001e236 < z < 9.0000000000000006e203

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 90.1%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

   if 9.0000000000000006e203 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.6%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.6%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.6%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 85.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+236}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+235} \lor \neg \left(z \leq 1.7 \cdot 10^{+205}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+235) (not (<= z 1.7e+205)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (+ (* -0.5 b) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+235) || !(z <= 1.7e+205)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (b * 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 ((z <= (-8.5d+235)) .or. (.not. (z <= 1.7d+205))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + (((-0.5d0) * b) + (b * 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 ((z <= -8.5e+235) || !(z <= 1.7e+205)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e+235) or not (z <= 1.7e+205):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+235) || !(z <= 1.7e+205))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e+235) || ~((z <= 1.7e+205)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+235], N[Not[LessEqual[z, 1.7e+205]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000017e235 or 1.7e205 < z

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.8%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.8%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.9%

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

   6. Taylor expanded in z around inf 73.5%

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

   if -8.50000000000000017e235 < z < 1.7e205

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 90.1%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+235} \lor \neg \left(z \leq 1.7 \cdot 10^{+205}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+236}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.1e+236)
   (- z (* z (log t)))
   (if (<= z 5.6e+204)
     (+ x (+ y (+ (* -0.5 b) (* b a))))
     (* z (- 1.0 (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e+236) {
		tmp = z - (z * log(t));
	} else if (z <= 5.6e+204) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.1d+236)) then
        tmp = z - (z * log(t))
    else if (z <= 5.6d+204) then
        tmp = x + (y + (((-0.5d0) * b) + (b * a)))
    else
        tmp = z * (1.0d0 - log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e+236) {
		tmp = z - (z * Math.log(t));
	} else if (z <= 5.6e+204) {
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.1e+236:
		tmp = z - (z * math.log(t))
	elif z <= 5.6e+204:
		tmp = x + (y + ((-0.5 * b) + (b * a)))
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.1e+236)
		tmp = Float64(z - Float64(z * log(t)));
	elseif (z <= 5.6e+204)
		tmp = Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.1e+236)
		tmp = z - (z * log(t));
	elseif (z <= 5.6e+204)
		tmp = x + (y + ((-0.5 * b) + (b * a)));
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.1e+236], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+204], N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999989e236

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.2%

      \[\leadsto \left(\color{blue}{z} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in b around 0 68.2%

      \[\leadsto \color{blue}{z - z \cdot \log t} \]

   if -1.09999999999999989e236 < z < 5.60000000000000049e204

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 90.1%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

   if 5.60000000000000049e204 < z

   1. Initial program 99.6%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.6%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.6%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.6%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.6%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 85.0%

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

   6. Taylor expanded in z around inf 77.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+236}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+204}:\\ \;\;\;\;x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ z (+ x y)) (* z (log t))) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
}

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 = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * Math.log(t))) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return ((z + (x + y)) - (z * math.log(t))) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \]
4. Add Preprocessing

Alternative 12: 62.0% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0012 \lor \neg \left(b \leq 1.55 \cdot 10^{+82}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.0012) (not (<= b 1.55e+82))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.0012) || !(b <= 1.55e+82)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.0012d0)) .or. (.not. (b <= 1.55d+82))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.0012) || !(b <= 1.55e+82)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.0012) or not (b <= 1.55e+82):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.0012) || !(b <= 1.55e+82))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.0012) || ~((b <= 1.55e+82)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.0012], N[Not[LessEqual[b, 1.55e+82]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.00119999999999999989 or 1.55000000000000016e82 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 83.6%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 83.6%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 83.6%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 83.6%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 83.6%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in x around -inf 69.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y + b \cdot \left(a - 0.5\right)}{x} - 1\right)\right)} \]

   8. Taylor expanded in b around inf 64.9%

      \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(a - 0.5\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \left(a - 0.5\right)\right)} \]

      2. sub-neg 64.9%

         \[\leadsto -1 \cdot \left(-b \cdot \color{blue}{\left(a + \left(-0.5\right)\right)}\right) \]

      3. metadata-eval 64.9%

         \[\leadsto -1 \cdot \left(-b \cdot \left(a + \color{blue}{-0.5}\right)\right) \]

      4. +-commutative 64.9%

         \[\leadsto -1 \cdot \left(-b \cdot \color{blue}{\left(-0.5 + a\right)}\right) \]

      5. distribute-lft-out 64.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(b \cdot -0.5 + b \cdot a\right)}\right) \]

      6. +-commutative 64.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{\left(b \cdot a + b \cdot -0.5\right)}\right) \]

      7. distribute-lft-in 64.9%

         \[\leadsto -1 \cdot \left(-\color{blue}{b \cdot \left(a + -0.5\right)}\right) \]

      8. distribute-rgt-neg-in 64.9%

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-\left(a + -0.5\right)\right)\right)} \]

      9. +-commutative 64.9%

         \[\leadsto -1 \cdot \left(b \cdot \left(-\color{blue}{\left(-0.5 + a\right)}\right)\right) \]

      10. distribute-neg-in 64.9%

          \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(\left(--0.5\right) + \left(-a\right)\right)}\right) \]

      11. metadata-eval 64.9%

          \[\leadsto -1 \cdot \left(b \cdot \left(\color{blue}{0.5} + \left(-a\right)\right)\right) \]

      12. mul-1-neg 64.9%

          \[\leadsto -1 \cdot \left(b \cdot \left(0.5 + \color{blue}{-1 \cdot a}\right)\right) \]

      13. mul-1-neg 64.9%

          \[\leadsto -1 \cdot \left(b \cdot \left(0.5 + \color{blue}{\left(-a\right)}\right)\right) \]

      14. unsub-neg 64.9%

          \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(0.5 - a\right)}\right) \]

   10. Simplified 64.9%

       \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(0.5 - a\right)\right)} \]

   if -0.00119999999999999989 < b < 1.55000000000000016e82

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 72.8%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 72.8%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 72.8%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 72.8%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 72.8%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in b around 0 63.7%

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

      1. +-commutative 63.7%

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

   9. Simplified 63.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0012 \lor \neg \left(b \leq 1.55 \cdot 10^{+82}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-173}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y - b \cdot \left(0.5 - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -4e-173) (+ x (* b (- a 0.5))) (- y (* b (- 0.5 a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e-173) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y - (b * (0.5 - 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 ((x + y) <= (-4d-173)) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y - (b * (0.5d0 - 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 ((x + y) <= -4e-173) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y - (b * (0.5 - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -4e-173:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y - (b * (0.5 - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -4e-173)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y - Float64(b * Float64(0.5 - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -4e-173)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y - (b * (0.5 - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e-173], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(b * N[(0.5 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.0000000000000002e-173

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 80.7%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 80.7%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 80.7%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 80.7%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 80.7%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in y around 0 57.2%

      \[\leadsto \color{blue}{x + b \cdot \left(a - 0.5\right)} \]

   if -4.0000000000000002e-173 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 74.6%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 74.6%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 74.6%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 74.6%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 74.6%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in x around -inf 60.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y + b \cdot \left(a - 0.5\right)}{x} - 1\right)\right)} \]

   8. Taylor expanded in x around 0 53.1%

      \[\leadsto \color{blue}{y + b \cdot \left(a - 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-173}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y - b \cdot \left(0.5 - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+80} \lor \neg \left(b \leq 2.7 \cdot 10^{+100}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e+80) (not (<= b 2.7e+100))) (* b a) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+80) || !(b <= 2.7e+100)) {
		tmp = b * a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5d+80)) .or. (.not. (b <= 2.7d+100))) then
        tmp = b * a
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e+80) || !(b <= 2.7e+100)) {
		tmp = b * a;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e+80) or not (b <= 2.7e+100):
		tmp = b * a
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e+80) || !(b <= 2.7e+100))
		tmp = Float64(b * a);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5e+80) || ~((b <= 2.7e+100)))
		tmp = b * a;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e+80], N[Not[LessEqual[b, 2.7e+100]], $MachinePrecision]], N[(b * a), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999961e80 or 2.69999999999999998e100 < b

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 85.6%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 85.6%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 85.6%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 85.6%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 85.6%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in x around -inf 71.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y + b \cdot \left(a - 0.5\right)}{x} - 1\right)\right)} \]

   8. Taylor expanded in a around inf 44.4%

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

      1. associate-*r* 44.4%

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

      2. mul-1-neg 44.4%

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

   10. Simplified 44.4%

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

   if -4.99999999999999961e80 < b < 2.69999999999999998e100

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 72.9%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 72.9%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 72.9%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 72.9%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 72.9%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in b around 0 60.6%

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

      1. +-commutative 60.6%

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

   9. Simplified 60.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+80} \lor \neg \left(b \leq 2.7 \cdot 10^{+100}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.8% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+86}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 7e+86) (+ x (* b (- a 0.5))) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7e+86) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 7d+86) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7e+86) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 7e+86:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 7e+86)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 7e+86)
		tmp = x + (b * (a - 0.5));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 7e+86], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.00000000000000038e86

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 76.4%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 76.3%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 76.3%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 76.3%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 76.3%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in y around 0 60.6%

      \[\leadsto \color{blue}{x + b \cdot \left(a - 0.5\right)} \]

   if 7.00000000000000038e86 < y

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 82.2%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 82.2%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 82.2%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 82.2%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 82.2%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in b around 0 64.4%

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

      1. +-commutative 64.4%

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

   9. Simplified 64.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+86}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.3% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x (+ y (+ (* -0.5 b) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (y + ((-0.5 * b) + (b * 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 = x + (y + (((-0.5d0) * b) + (b * a)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (y + ((-0.5 * b) + (b * a)));
}

Python

def code(x, y, z, t, a, b):
	return x + (y + ((-0.5 * b) + (b * a)))

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(y + Float64(Float64(-0.5 * b) + Float64(b * a))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (y + ((-0.5 * b) + (b * a)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 99.9%

   \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

4. Taylor expanded in z around 0 77.5%

   \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]

5. Final simplification 77.5%

   \[\leadsto x + \left(y + \left(-0.5 \cdot b + b \cdot a\right)\right) \]
6. Add Preprocessing

Alternative 17: 78.3% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + b \cdot \left(-0.5 + a\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ x y) (* b (+ -0.5 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (-0.5 + 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 = (x + y) + (b * ((-0.5d0) + a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + (b * (-0.5 + a));
}

Python

def code(x, y, z, t, a, b):
	return (x + y) + (b * (-0.5 + a))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + y) + Float64(b * Float64(-0.5 + a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + y) + (b * (-0.5 + a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + N[(b * N[(-0.5 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 99.9%

   \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

4. Taylor expanded in z around 0 77.5%

   \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. distribute-rgt-in 77.5%

      \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

   2. associate-+r+ 77.5%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

   3. +-commutative 77.5%

      \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

6. Simplified 77.5%

   \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

7. Final simplification 77.5%

   \[\leadsto \left(x + y\right) + b \cdot \left(-0.5 + a\right) \]
8. Add Preprocessing

Alternative 18: 28.6% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1.7e+87) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.7e+87) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.7d+87)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.7e+87) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.7e+87:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.7e+87)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.7e+87)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.7e+87], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.7000000000000001e87

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 100.0%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 65.5%

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

   6. Taylor expanded in z around 0 50.8%

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

   if -1.7000000000000001e87 < x

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

      \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

   4. Taylor expanded in z around 0 75.7%

      \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 75.7%

         \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

      2. associate-+r+ 75.7%

         \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

      3. +-commutative 75.7%

         \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

   6. Simplified 75.7%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

   7. Taylor expanded in y around inf 27.8%

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

Alternative 19: 41.7% accurate, 38.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(x + y)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 99.9%

   \[\leadsto \color{blue}{\left(x + \left(y + \left(z + \left(-0.5 \cdot b + a \cdot b\right)\right)\right)\right) - z \cdot \log t} \]

4. Taylor expanded in z around 0 77.5%

   \[\leadsto \color{blue}{x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. distribute-rgt-in 77.5%

      \[\leadsto x + \left(y + \color{blue}{b \cdot \left(-0.5 + a\right)}\right) \]

   2. associate-+r+ 77.5%

      \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(-0.5 + a\right)} \]

   3. +-commutative 77.5%

      \[\leadsto \left(x + y\right) + b \cdot \color{blue}{\left(a + -0.5\right)} \]

6. Simplified 77.5%

   \[\leadsto \color{blue}{\left(x + y\right) + b \cdot \left(a + -0.5\right)} \]

7. Taylor expanded in b around 0 45.1%

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

   1. +-commutative 45.1%

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

9. Simplified 45.1%

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

10. Final simplification 45.1%

    \[\leadsto x + y \]
11. Add Preprocessing

Alternative 20: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

   2. associate--l+ 99.9%

      \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

   3. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

   4. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

   5. *-lft-identity 99.9%

      \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   7. *-commutative 99.9%

      \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   8. distribute-rgt-out-- 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   9. metadata-eval 99.9%

      \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   10. fma-define 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

   11. sub-neg 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

   12. metadata-eval 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 44.3%

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

6. Taylor expanded in z around 0 22.3%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * 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 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * 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 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))