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

Percentage Accurate: 99.8% → 99.8%

Time: 2.4s

Alternatives: 9

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := \left(x + y\right) + z\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+125}:\\ \;\;\;\;t\_2 - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (+ (+ x y) z)) (t_3 (+ t_2 t_1)))
   (if (<= t_1 -5e+96) t_3 (if (<= t_1 2e+125) (- t_2 (* z (log t))) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = (x + y) + z;
	double t_3 = t_2 + t_1;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_3;
	} else if (t_1 <= 2e+125) {
		tmp = t_2 - (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 = (a - 0.5d0) * b
    t_2 = (x + y) + z
    t_3 = t_2 + t_1
    if (t_1 <= (-5d+96)) then
        tmp = t_3
    else if (t_1 <= 2d+125) then
        tmp = t_2 - (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 = (a - 0.5) * b;
	double t_2 = (x + y) + z;
	double t_3 = t_2 + t_1;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_3;
	} else if (t_1 <= 2e+125) {
		tmp = t_2 - (z * Math.log(t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = (x + y) + z
	t_3 = t_2 + t_1
	tmp = 0
	if t_1 <= -5e+96:
		tmp = t_3
	elif t_1 <= 2e+125:
		tmp = t_2 - (z * math.log(t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(Float64(x + y) + z)
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (t_1 <= -5e+96)
		tmp = t_3;
	elseif (t_1 <= 2e+125)
		tmp = Float64(t_2 - 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 = (a - 0.5) * b;
	t_2 = (x + y) + z;
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (t_1 <= -5e+96)
		tmp = t_3;
	elseif (t_1 <= 2e+125)
		tmp = t_2 - (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[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+96], t$95$3, If[LessEqual[t$95$1, 2e+125], N[(t$95$2 - 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) < -5.0000000000000004e96 or 1.9999999999999998e125 < (*.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 93.2%

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

   if -5.0000000000000004e96 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.9999999999999998e125

   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 92.2%

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

Alternative 3: 66.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := \left(t\_1 + z\right) + z\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (+ (+ t_1 z) z)))
   (if (<= t_1 -5e+96) t_2 (if (<= t_1 2e+144) (+ (+ x y) z) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = (t_1 + z) + z;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_2;
	} else if (t_1 <= 2e+144) {
		tmp = (x + y) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = (t_1 + z) + z
    if (t_1 <= (-5d+96)) then
        tmp = t_2
    else if (t_1 <= 2d+144) then
        tmp = (x + y) + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = (t_1 + z) + z;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_2;
	} else if (t_1 <= 2e+144) {
		tmp = (x + y) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = (t_1 + z) + z
	tmp = 0
	if t_1 <= -5e+96:
		tmp = t_2
	elif t_1 <= 2e+144:
		tmp = (x + y) + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(Float64(t_1 + z) + z)
	tmp = 0.0
	if (t_1 <= -5e+96)
		tmp = t_2;
	elseif (t_1 <= 2e+144)
		tmp = Float64(Float64(x + y) + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = (t_1 + z) + z;
	tmp = 0.0;
	if (t_1 <= -5e+96)
		tmp = t_2;
	elseif (t_1 <= 2e+144)
		tmp = (x + y) + z;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(t$95$1 + z), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+96], t$95$2, If[LessEqual[t$95$1, 2e+144], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000004e96 or 2.00000000000000005e144 < (*.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

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

   5. Applied rewrites 22.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 15.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 80.0%

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

   if -5.0000000000000004e96 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000005e144

   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 92.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.9%

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

Alternative 4: 66.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := t\_1 + z\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (+ t_1 z)))
   (if (<= t_1 -5e+96) t_2 (if (<= t_1 2e+144) (+ (+ x y) z) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = t_1 + z;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_2;
	} else if (t_1 <= 2e+144) {
		tmp = (x + y) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = t_1 + z
    if (t_1 <= (-5d+96)) then
        tmp = t_2
    else if (t_1 <= 2d+144) then
        tmp = (x + y) + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = t_1 + z;
	double tmp;
	if (t_1 <= -5e+96) {
		tmp = t_2;
	} else if (t_1 <= 2e+144) {
		tmp = (x + y) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = t_1 + z
	tmp = 0
	if t_1 <= -5e+96:
		tmp = t_2
	elif t_1 <= 2e+144:
		tmp = (x + y) + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(t_1 + z)
	tmp = 0.0
	if (t_1 <= -5e+96)
		tmp = t_2;
	elseif (t_1 <= 2e+144)
		tmp = Float64(Float64(x + y) + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = t_1 + z;
	tmp = 0.0;
	if (t_1 <= -5e+96)
		tmp = t_2;
	elseif (t_1 <= 2e+144)
		tmp = (x + y) + z;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t$95$1 + z), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+96], t$95$2, If[LessEqual[t$95$1, 2e+144], N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000004e96 or 2.00000000000000005e144 < (*.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

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

   5. Applied rewrites 22.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(y + z\right) - z \cdot \log t \]

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 80.0%

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

   if -5.0000000000000004e96 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000005e144

   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 92.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.9%

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

Alternative 5: 66.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+144}:\\ \;\;\;\;\left(x + y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -5e+96) t_1 (if (<= t_1 2e+144) (+ (+ 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 <= -5e+96) {
		tmp = t_1;
	} else if (t_1 <= 2e+144) {
		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 <= (-5d+96)) then
        tmp = t_1
    else if (t_1 <= 2d+144) 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 <= -5e+96) {
		tmp = t_1;
	} else if (t_1 <= 2e+144) {
		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 <= -5e+96:
		tmp = t_1
	elif t_1 <= 2e+144:
		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 <= -5e+96)
		tmp = t_1;
	elseif (t_1 <= 2e+144)
		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 <= -5e+96)
		tmp = t_1;
	elseif (t_1 <= 2e+144)
		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, -5e+96], t$95$1, If[LessEqual[t$95$1, 2e+144], 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) < -5.0000000000000004e96 or 2.00000000000000005e144 < (*.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

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

   5. Applied rewrites 22.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(y + z\right) - z \cdot \log t \]

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 79.4%

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

   if -5.0000000000000004e96 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000005e144

   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 92.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.9%

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

Alternative 6: 79.8% 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 80.1%

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

Alternative 7: 79.0% 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 79.3%

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

Alternative 8: 43.0% 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 63.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 44.3%

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

Alternative 9: 42.1% 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 63.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 43.3%

   \[\leadsto x + \color{blue}{y} \]
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 2024321 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64
  :pre (TRUE)

  :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)))