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

Percentage Accurate: 99.9% → 99.9%

Time: 12.2s

Alternatives: 11

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: 99.9% 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: 99.9% 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]

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%

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

Alternative 2: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+120} \lor \neg \left(z \leq 1.06 \cdot 10^{+117}\right):\\ \;\;\;\;t\_1 + \left(x + \left(z - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= z -4.2e+120) (not (<= z 1.06e+117)))
     (+ t_1 (+ x (- z (* z (log t)))))
     (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((z <= -4.2e+120) || !(z <= 1.06e+117)) {
		tmp = t_1 + (x + (z - (z * log(t))));
	} 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 = (a - 0.5d0) * b
    if ((z <= (-4.2d+120)) .or. (.not. (z <= 1.06d+117))) then
        tmp = t_1 + (x + (z - (z * log(t))))
    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 = (a - 0.5) * b;
	double tmp;
	if ((z <= -4.2e+120) || !(z <= 1.06e+117)) {
		tmp = t_1 + (x + (z - (z * Math.log(t))));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (z <= -4.2e+120) or not (z <= 1.06e+117):
		tmp = t_1 + (x + (z - (z * math.log(t))))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((z <= -4.2e+120) || !(z <= 1.06e+117))
		tmp = Float64(t_1 + Float64(x + Float64(z - Float64(z * log(t)))));
	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 = (a - 0.5) * b;
	tmp = 0.0;
	if ((z <= -4.2e+120) || ~((z <= 1.06e+117)))
		tmp = t_1 + (x + (z - (z * log(t))));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[z, -4.2e+120], N[Not[LessEqual[z, 1.06e+117]], $MachinePrecision]], N[(t$95$1 + N[(x + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000001e120 or 1.06e117 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. associate--l+ 91.1%

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

   5. Simplified 91.1%

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

   if -4.2000000000000001e120 < z < 1.06e117

   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 z around 0 95.6%

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

      1. +-commutative 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+120} \lor \neg \left(z \leq 1.06 \cdot 10^{+117}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + \left(z - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+148} \lor \neg \left(z \leq 3.4 \cdot 10^{+153}\right):\\ \;\;\;\;t\_1 + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= z -7.2e+148) (not (<= z 3.4e+153)))
     (+ t_1 (* z (- 1.0 (log t))))
     (+ (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((z <= -7.2e+148) || !(z <= 3.4e+153)) {
		tmp = t_1 + (z * (1.0 - log(t)));
	} 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 = (a - 0.5d0) * b
    if ((z <= (-7.2d+148)) .or. (.not. (z <= 3.4d+153))) then
        tmp = t_1 + (z * (1.0d0 - log(t)))
    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 = (a - 0.5) * b;
	double tmp;
	if ((z <= -7.2e+148) || !(z <= 3.4e+153)) {
		tmp = t_1 + (z * (1.0 - Math.log(t)));
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (z <= -7.2e+148) or not (z <= 3.4e+153):
		tmp = t_1 + (z * (1.0 - math.log(t)))
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((z <= -7.2e+148) || !(z <= 3.4e+153))
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - log(t))));
	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 = (a - 0.5) * b;
	tmp = 0.0;
	if ((z <= -7.2e+148) || ~((z <= 3.4e+153)))
		tmp = t_1 + (z * (1.0 - log(t)));
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[z, -7.2e+148], N[Not[LessEqual[z, 3.4e+153]], $MachinePrecision]], N[(t$95$1 + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000013e148 or 3.3999999999999997e153 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around -inf 87.7%

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

   4. Taylor expanded in t around inf 87.7%

      \[\leadsto \color{blue}{z \cdot \left(1 + \log \left(\frac{1}{t}\right)\right)} + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. log-rec 87.7%

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

      2. sub-neg 87.7%

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

   6. Simplified 87.7%

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

   if -7.20000000000000013e148 < z < 3.3999999999999997e153

   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 z around 0 94.6%

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

      1. +-commutative 94.6%

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

   5. Simplified 94.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+148} \lor \neg \left(z \leq 3.4 \cdot 10^{+153}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+151}:\\ \;\;\;\;t\_1 + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+195}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z - z \cdot \log t\right)\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= z -4.1e+151)
     (+ t_1 (* z (- 1.0 (log t))))
     (if (<= z 4.6e+195)
       (+ (+ x y) t_1)
       (+ (+ x (- z (* z (log t)))) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (z <= -4.1e+151) {
		tmp = t_1 + (z * (1.0 - log(t)));
	} else if (z <= 4.6e+195) {
		tmp = (x + y) + t_1;
	} else {
		tmp = (x + (z - (z * log(t)))) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (z <= (-4.1d+151)) then
        tmp = t_1 + (z * (1.0d0 - log(t)))
    else if (z <= 4.6d+195) then
        tmp = (x + y) + t_1
    else
        tmp = (x + (z - (z * log(t)))) + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (z <= -4.1e+151) {
		tmp = t_1 + (z * (1.0 - Math.log(t)));
	} else if (z <= 4.6e+195) {
		tmp = (x + y) + t_1;
	} else {
		tmp = (x + (z - (z * Math.log(t)))) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if z <= -4.1e+151:
		tmp = t_1 + (z * (1.0 - math.log(t)))
	elif z <= 4.6e+195:
		tmp = (x + y) + t_1
	else:
		tmp = (x + (z - (z * math.log(t)))) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (z <= -4.1e+151)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - log(t))));
	elseif (z <= 4.6e+195)
		tmp = Float64(Float64(x + y) + t_1);
	else
		tmp = Float64(Float64(x + Float64(z - Float64(z * log(t)))) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (z <= -4.1e+151)
		tmp = t_1 + (z * (1.0 - log(t)));
	elseif (z <= 4.6e+195)
		tmp = (x + y) + t_1;
	else
		tmp = (x + (z - (z * log(t)))) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[z, -4.1e+151], N[(t$95$1 + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+195], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999998e151

   1. Initial program 99.7%

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

   3. Taylor expanded in z around -inf 86.7%

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

   4. Taylor expanded in t around inf 86.7%

      \[\leadsto \color{blue}{z \cdot \left(1 + \log \left(\frac{1}{t}\right)\right)} + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. log-rec 86.7%

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

      2. sub-neg 86.7%

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

   6. Simplified 86.7%

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

   if -4.0999999999999998e151 < z < 4.6000000000000002e195

   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 z around 0 93.7%

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

      1. +-commutative 93.7%

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

   5. Simplified 93.7%

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

   if 4.6000000000000002e195 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 93.2%

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

      1. associate--l+ 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in a around inf 90.8%

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

      1. *-commutative 19.0%

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

   8. Simplified 90.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+151}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+195}:\\ \;\;\;\;\left(x + y\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z - z \cdot \log t\right)\right) + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -5 \cdot 10^{+120}:\\ \;\;\;\;\left(z + \left(y - t\_1\right)\right) + a \cdot b\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+195}:\\ \;\;\;\;\left(x + y\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z - t\_1\right)\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= z -5e+120)
     (+ (+ z (- y t_1)) (* a b))
     (if (<= z 4.6e+195)
       (+ (+ x y) (* (- a 0.5) b))
       (+ (+ x (- z t_1)) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if (z <= -5e+120) {
		tmp = (z + (y - t_1)) + (a * b);
	} else if (z <= 4.6e+195) {
		tmp = (x + y) + ((a - 0.5) * b);
	} else {
		tmp = (x + (z - t_1)) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if (z <= (-5d+120)) then
        tmp = (z + (y - t_1)) + (a * b)
    else if (z <= 4.6d+195) then
        tmp = (x + y) + ((a - 0.5d0) * b)
    else
        tmp = (x + (z - t_1)) + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double tmp;
	if (z <= -5e+120) {
		tmp = (z + (y - t_1)) + (a * b);
	} else if (z <= 4.6e+195) {
		tmp = (x + y) + ((a - 0.5) * b);
	} else {
		tmp = (x + (z - t_1)) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if z <= -5e+120:
		tmp = (z + (y - t_1)) + (a * b)
	elif z <= 4.6e+195:
		tmp = (x + y) + ((a - 0.5) * b)
	else:
		tmp = (x + (z - t_1)) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (z <= -5e+120)
		tmp = Float64(Float64(z + Float64(y - t_1)) + Float64(a * b));
	elseif (z <= 4.6e+195)
		tmp = Float64(Float64(x + y) + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(Float64(x + Float64(z - t_1)) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if (z <= -5e+120)
		tmp = (z + (y - t_1)) + (a * b);
	elseif (z <= 4.6e+195)
		tmp = (x + y) + ((a - 0.5) * b);
	else
		tmp = (x + (z - t_1)) + (a * b);
	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[z, -5e+120], N[(N[(z + N[(y - t$95$1), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+195], N[(N[(x + y), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000019e120

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.8%

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

      1. +-commutative 94.8%

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

      2. associate--l+ 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in a around inf 88.3%

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

      1. *-commutative 32.9%

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

   8. Simplified 88.3%

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

   if -5.00000000000000019e120 < z < 4.6000000000000002e195

   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 z around 0 94.3%

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

      1. +-commutative 94.3%

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

   5. Simplified 94.3%

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

   if 4.6000000000000002e195 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 93.2%

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

      1. associate--l+ 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in a around inf 90.8%

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

      1. *-commutative 19.0%

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

   8. Simplified 90.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+120}:\\ \;\;\;\;\left(z + \left(y - z \cdot \log t\right)\right) + a \cdot b\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+195}:\\ \;\;\;\;\left(x + y\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z - z \cdot \log t\right)\right) + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;t\_2 + \left(x + \left(z - t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(z + \left(y - t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* (- a 0.5) b)))
   (if (<= x -1.8e+28) (+ t_2 (+ x (- z t_1))) (+ t_2 (+ z (- y 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 = (a - 0.5) * b;
	double tmp;
	if (x <= -1.8e+28) {
		tmp = t_2 + (x + (z - t_1));
	} else {
		tmp = t_2 + (z + (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) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = (a - 0.5d0) * b
    if (x <= (-1.8d+28)) then
        tmp = t_2 + (x + (z - t_1))
    else
        tmp = t_2 + (z + (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 * Math.log(t);
	double t_2 = (a - 0.5) * b;
	double tmp;
	if (x <= -1.8e+28) {
		tmp = t_2 + (x + (z - t_1));
	} else {
		tmp = t_2 + (z + (y - t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = (a - 0.5) * b
	tmp = 0
	if x <= -1.8e+28:
		tmp = t_2 + (x + (z - t_1))
	else:
		tmp = t_2 + (z + (y - t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (x <= -1.8e+28)
		tmp = Float64(t_2 + Float64(x + Float64(z - t_1)));
	else
		tmp = Float64(t_2 + Float64(z + Float64(y - t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = (a - 0.5) * b;
	tmp = 0.0;
	if (x <= -1.8e+28)
		tmp = t_2 + (x + (z - t_1));
	else
		tmp = t_2 + (z + (y - 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[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[x, -1.8e+28], N[(t$95$2 + N[(x + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(z + N[(y - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e28

   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 86.4%

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

      1. associate--l+ 86.4%

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

   5. Simplified 86.4%

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

   if -1.8e28 < 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 x around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. associate--l+ 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(x + \left(z - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b + \left(z + \left(y - z \cdot \log t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-21} \lor \neg \left(a \leq 3.1 \cdot 10^{+23}\right):\\ \;\;\;\;y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.2e-21) (not (<= a 3.1e+23))) (+ y (* a b)) (+ y (* b -0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.2e-21) || !(a <= 3.1e+23)) {
		tmp = y + (a * b);
	} else {
		tmp = y + (b * -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.2d-21)) .or. (.not. (a <= 3.1d+23))) then
        tmp = y + (a * b)
    else
        tmp = y + (b * (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.2e-21) || !(a <= 3.1e+23)) {
		tmp = y + (a * b);
	} else {
		tmp = y + (b * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.2e-21) or not (a <= 3.1e+23):
		tmp = y + (a * b)
	else:
		tmp = y + (b * -0.5)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.2e-21) || !(a <= 3.1e+23))
		tmp = Float64(y + Float64(a * b));
	else
		tmp = Float64(y + Float64(b * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.2e-21) || ~((a <= 3.1e+23)))
		tmp = y + (a * b);
	else
		tmp = y + (b * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.2e-21], N[Not[LessEqual[a, 3.1e+23]], $MachinePrecision]], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.2000000000000002e-21 or 3.09999999999999971e23 < a

   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 inf 62.8%

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

   4. Taylor expanded in a around inf 62.7%

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

      1. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   if -3.2000000000000002e-21 < a < 3.09999999999999971e23

   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 inf 53.1%

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

   4. Taylor expanded in a around 0 53.1%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-21} \lor \neg \left(a \leq 3.1 \cdot 10^{+23}\right):\\ \;\;\;\;y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot -0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.8% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.48 \cdot 10^{+103}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.48e+103) (+ x (* (- a 0.5) b)) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.48e+103) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.48d+103) then
        tmp = x + ((a - 0.5d0) * b)
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.48e+103) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.48e+103:
		tmp = x + ((a - 0.5) * b)
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.48e+103)
		tmp = Float64(x + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.48e+103)
		tmp = x + ((a - 0.5) * b);
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.48e+103], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.48000000000000009e103

   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 x around inf 61.8%

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

   if 1.48000000000000009e103 < 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 y around inf 71.4%

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

   4. Taylor expanded in a around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.48 \cdot 10^{+103}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b))) (if (<= y 5.2e+14) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (y <= 5.2e+14) {
		tmp = x + t_1;
	} 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 = (a - 0.5d0) * b
    if (y <= 5.2d+14) then
        tmp = x + t_1
    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 = (a - 0.5) * b;
	double tmp;
	if (y <= 5.2e+14) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if y <= 5.2e+14:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (y <= 5.2e+14)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (y <= 5.2e+14)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, 5.2e+14], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 5.2e14

   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 x around inf 63.5%

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

   if 5.2e14 < 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 y around inf 66.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + \left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $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 z around 0 77.6%

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

   1. +-commutative 77.6%

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

5. Simplified 77.6%

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

6. Final simplification 77.6%

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

Alternative 11: 34.2% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ y + b \cdot -0.5 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y + N[(b * -0.5), $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 y around inf 57.7%

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

4. Taylor expanded in a around 0 37.9%

   \[\leadsto y + \color{blue}{-0.5 \cdot b} \]

5. Final simplification 37.9%

   \[\leadsto y + b \cdot -0.5 \]
6. Add Preprocessing

Developer target: 99.5% 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 2024067 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

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

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