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

Percentage Accurate: 99.8% → 99.8%

Time: 2.6s

Alternatives: 10

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

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

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. Add Preprocessing

Alternative 2: 90.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + z\\ t_2 := \left(a - 0.5\right) \cdot b\\ t_3 := \left(t\_1 + t\_2\right) + z\\ \mathbf{if}\;t\_2 \leq -2.3 \cdot 10^{+125}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1 - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) z)) (t_2 (* (- a 0.5) b)) (t_3 (+ (+ t_1 t_2) z)))
   (if (<= t_2 -2.3e+125)
     t_3
     (if (<= t_2 3.6e+44) (- t_1 (* z (log t))) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + z;
	double t_2 = (a - 0.5) * b;
	double t_3 = (t_1 + t_2) + z;
	double tmp;
	if (t_2 <= -2.3e+125) {
		tmp = t_3;
	} else if (t_2 <= 3.6e+44) {
		tmp = t_1 - (z * log(t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + y) + z
    t_2 = (a - 0.5d0) * b
    t_3 = (t_1 + t_2) + z
    if (t_2 <= (-2.3d+125)) then
        tmp = t_3
    else if (t_2 <= 3.6d+44) then
        tmp = t_1 - (z * log(t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + z;
	double t_2 = (a - 0.5) * b;
	double t_3 = (t_1 + t_2) + z;
	double tmp;
	if (t_2 <= -2.3e+125) {
		tmp = t_3;
	} else if (t_2 <= 3.6e+44) {
		tmp = t_1 - (z * Math.log(t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + z
	t_2 = (a - 0.5) * b
	t_3 = (t_1 + t_2) + z
	tmp = 0
	if t_2 <= -2.3e+125:
		tmp = t_3
	elif t_2 <= 3.6e+44:
		tmp = t_1 - (z * math.log(t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + z)
	t_2 = Float64(Float64(a - 0.5) * b)
	t_3 = Float64(Float64(t_1 + t_2) + z)
	tmp = 0.0
	if (t_2 <= -2.3e+125)
		tmp = t_3;
	elseif (t_2 <= 3.6e+44)
		tmp = Float64(t_1 - Float64(z * log(t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + z;
	t_2 = (a - 0.5) * b;
	t_3 = (t_1 + t_2) + z;
	tmp = 0.0;
	if (t_2 <= -2.3e+125)
		tmp = t_3;
	elseif (t_2 <= 3.6e+44)
		tmp = t_1 - (z * log(t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 + t$95$2), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[t$95$2, -2.3e+125], t$95$3, If[LessEqual[t$95$2, 3.6e+44], N[(t$95$1 - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.30000000000000013e125 or 3.6e44 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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 x around 0

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.7%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 91.3%

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

   if -2.30000000000000013e125 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.6e44

   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

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

   5. Applied rewrites 92.7%

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

Alternative 3: 66.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1.42 \cdot 10^{+114}:\\ \;\;\;\;t\_1 + z\\ \mathbf{elif}\;t\_1 \leq 3.5 \cdot 10^{+199}:\\ \;\;\;\;\left(\left(x + y\right) + z\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1.42e+114)
     (+ t_1 z)
     (if (<= t_1 3.5e+199) (+ (+ (+ x y) z) z) 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 (t_1 <= -1.42e+114) {
		tmp = t_1 + z;
	} else if (t_1 <= 3.5e+199) {
		tmp = ((x + y) + z) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-1.42d+114)) then
        tmp = t_1 + z
    else if (t_1 <= 3.5d+199) then
        tmp = ((x + y) + z) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1.42e+114) {
		tmp = t_1 + z;
	} else if (t_1 <= 3.5e+199) {
		tmp = ((x + y) + z) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -1.42e+114:
		tmp = t_1 + z
	elif t_1 <= 3.5e+199:
		tmp = ((x + y) + z) + z
	else:
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = Float64(t_1 + z);
	elseif (t_1 <= 3.5e+199)
		tmp = Float64(Float64(Float64(x + y) + z) + z);
	else
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = t_1 + z;
	elseif (t_1 <= 3.5e+199)
		tmp = ((x + y) + z) + z;
	else
		tmp = 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[t$95$1, -1.42e+114], N[(t$95$1 + z), $MachinePrecision], If[LessEqual[t$95$1, 3.5e+199], N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.4200000000000001e114

   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

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.9%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 88.3%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 74.2%

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

   if -1.4200000000000001e114 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.49999999999999981e199

   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

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 74.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto y + z \]

   14. Applied rewrites 63.3%

       \[\leadsto \left(\left(x + y\right) + z\right) + z \]

   if 3.49999999999999981e199 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   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

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.8%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 86.3%

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

Alternative 4: 66.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1.42 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 3.5 \cdot 10^{+199}:\\ \;\;\;\;\left(\left(x + y\right) + z\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1.42e+114)
     t_1
     (if (<= t_1 3.5e+199) (+ (+ (+ x y) z) z) 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 (t_1 <= -1.42e+114) {
		tmp = t_1;
	} else if (t_1 <= 3.5e+199) {
		tmp = ((x + y) + z) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-1.42d+114)) then
        tmp = t_1
    else if (t_1 <= 3.5d+199) then
        tmp = ((x + y) + z) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1.42e+114) {
		tmp = t_1;
	} else if (t_1 <= 3.5e+199) {
		tmp = ((x + y) + z) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -1.42e+114:
		tmp = t_1
	elif t_1 <= 3.5e+199:
		tmp = ((x + y) + z) + z
	else:
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = t_1;
	elseif (t_1 <= 3.5e+199)
		tmp = Float64(Float64(Float64(x + y) + z) + z);
	else
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = t_1;
	elseif (t_1 <= 3.5e+199)
		tmp = ((x + y) + z) + z;
	else
		tmp = 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[t$95$1, -1.42e+114], t$95$1, If[LessEqual[t$95$1, 3.5e+199], N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.4200000000000001e114 or 3.49999999999999981e199 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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 x around 0

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.0%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 78.5%

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

   if -1.4200000000000001e114 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.49999999999999981e199

   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

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 74.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto y + z \]

   14. Applied rewrites 63.3%

       \[\leadsto \left(\left(x + y\right) + z\right) + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 66.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1.42 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 3.5 \cdot 10^{+199}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1.42e+114) t_1 (if (<= t_1 3.5e+199) (+ (+ x y) z) 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 (t_1 <= -1.42e+114) {
		tmp = t_1;
	} else if (t_1 <= 3.5e+199) {
		tmp = (x + y) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-1.42d+114)) then
        tmp = t_1
    else if (t_1 <= 3.5d+199) then
        tmp = (x + y) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -1.42e+114) {
		tmp = t_1;
	} else if (t_1 <= 3.5e+199) {
		tmp = (x + y) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -1.42e+114:
		tmp = t_1
	elif t_1 <= 3.5e+199:
		tmp = (x + y) + z
	else:
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = t_1;
	elseif (t_1 <= 3.5e+199)
		tmp = Float64(Float64(x + y) + z);
	else
		tmp = 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 (t_1 <= -1.42e+114)
		tmp = t_1;
	elseif (t_1 <= 3.5e+199)
		tmp = (x + y) + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1.42e+114], t$95$1, If[LessEqual[t$95$1, 3.5e+199], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.4200000000000001e114 or 3.49999999999999981e199 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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 x around 0

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.0%

      \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 78.5%

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

   if -1.4200000000000001e114 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.49999999999999981e199

   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

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.3%

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

Alternative 6: 80.4% accurate, 6.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Applied rewrites 81.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 60.2%

   \[\leadsto \left(\left(\left(\left(x + y\right) + z\right) + \left(a - 0.5\right) \cdot b\right) + z\right) + \left(a - 0.5\right) \cdot b \]

9. Taylor expanded in x around 0

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

11. Applied rewrites 81.8%

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

Alternative 7: 80.4% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + z), $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 x around 0

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

5. Applied rewrites 81.8%

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

Alternative 8: 79.5% accurate, 8.4× 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 x around 0

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

5. Applied rewrites 81.1%

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

Alternative 9: 43.7% accurate, 18.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + z \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + z), $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 x around 0

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

5. Applied rewrites 62.1%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 44.5%

   \[\leadsto \left(x + y\right) + \color{blue}{z} \]
9. Add Preprocessing

Alternative 10: 42.7% accurate, 31.5× 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 x around 0

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

5. Applied rewrites 62.1%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 43.7%

   \[\leadsto x + \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 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 2024313 
(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)))