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

Percentage Accurate: 89.6% → 99.5%

Time: 22.6s

Alternatives: 14

Speedup: 1.9×

Specification

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Initial Program: 89.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return fma(-y, (-1.0 + z), fma((-0.5 * pow(y, 2.0)), (-1.0 + z), (log(y) * (-1.0 + x)))) - t;
}

Julia

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((-0.5 * (pow(y, 2.0) * (-1.0 + z))) + (log(y) * (-1.0 + x))) - (y * (-1.0 + z))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((((-0.5d0) * ((y ** 2.0d0) * ((-1.0d0) + z))) + (log(y) * ((-1.0d0) + x))) - (y * ((-1.0d0) + z))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((-0.5 * (Math.pow(y, 2.0) * (-1.0 + z))) + (Math.log(y) * (-1.0 + x))) - (y * (-1.0 + z))) - t;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\log y, -1 + x, y \cdot \left(\left(-z\right) - -1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (log y) (+ -1.0 x) (* y (- (- z) -1.0))) t))

C

double code(double x, double y, double z, double t) {
	return fma(log(y), (-1.0 + x), (y * (-z - -1.0))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(log(y), Float64(-1.0 + x), Float64(y * Float64(Float64(-z) - -1.0))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision] + N[(y * N[((-z) - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 88.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 + x \leq -1\\ \mathbf{if}\;t_1 \lor \neg t_1:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot \left(-1 + z\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (<= (+ -1.0 x) -1.0)))
   (if (or t_1 (not t_1))
     (- (* (log y) (+ -1.0 x)) t)
     (- (- (- (log y)) (* y (+ -1.0 z))) t))))

C

double code(double x, double y, double z, double t) {
	int t_1 = (-1.0 + x) <= -1.0;
	double tmp;
	if (t_1 || !t_1) {
		tmp = (log(y) * (-1.0 + x)) - t;
	} else {
		tmp = (-log(y) - (y * (-1.0 + z))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    logical :: t_1
    real(8) :: tmp
    t_1 = ((-1.0d0) + x) <= (-1.0d0)
    if (t_1 .or. (.not. t_1)) then
        tmp = (log(y) * ((-1.0d0) + x)) - t
    else
        tmp = (-log(y) - (y * ((-1.0d0) + z))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	boolean t_1 = (-1.0 + x) <= -1.0;
	double tmp;
	if (t_1 || !t_1) {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	} else {
		tmp = (-Math.log(y) - (y * (-1.0 + z))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-1.0 + x) <= -1.0
	tmp = 0
	if t_1 or not t_1:
		tmp = (math.log(y) * (-1.0 + x)) - t
	else:
		tmp = (-math.log(y) - (y * (-1.0 + z))) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-1.0 + x) <= -1.0
	tmp = 0.0
	if (t_1 || !t_1)
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	else
		tmp = Float64(Float64(Float64(-log(y)) - Float64(y * Float64(-1.0 + z))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-1.0 + x) <= -1.0;
	tmp = 0.0;
	if (t_1 || ~(t_1))
		tmp = (log(y) * (-1.0 + x)) - t;
	else
		tmp = (-log(y) - (y * (-1.0 + z))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = LessEqual[N[(-1.0 + x), $MachinePrecision], -1.0]}, If[Or[t$95$1, N[Not[t$95$1], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[Log[y], $MachinePrecision]) - N[(y * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 95.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(-1 + x\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-9}:\\ \;\;\;\;t_1 - t\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+15}:\\ \;\;\;\;t_1 - y \cdot \left(-1 + z\right)\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) (+ -1.0 x))))
   (if (<= t -2.8e-9)
     (- t_1 t)
     (if (<= t 1.08e+15) (- t_1 (* y (+ -1.0 z))) (- (* (log y) x) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * (-1.0 + x);
	double tmp;
	if (t <= -2.8e-9) {
		tmp = t_1 - t;
	} else if (t <= 1.08e+15) {
		tmp = t_1 - (y * (-1.0 + z));
	} else {
		tmp = (log(y) * x) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * ((-1.0d0) + x)
    if (t <= (-2.8d-9)) then
        tmp = t_1 - t
    else if (t <= 1.08d+15) then
        tmp = t_1 - (y * ((-1.0d0) + z))
    else
        tmp = (log(y) * x) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * (-1.0 + x);
	double tmp;
	if (t <= -2.8e-9) {
		tmp = t_1 - t;
	} else if (t <= 1.08e+15) {
		tmp = t_1 - (y * (-1.0 + z));
	} else {
		tmp = (Math.log(y) * x) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * (-1.0 + x)
	tmp = 0
	if t <= -2.8e-9:
		tmp = t_1 - t
	elif t <= 1.08e+15:
		tmp = t_1 - (y * (-1.0 + z))
	else:
		tmp = (math.log(y) * x) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * Float64(-1.0 + x))
	tmp = 0.0
	if (t <= -2.8e-9)
		tmp = Float64(t_1 - t);
	elseif (t <= 1.08e+15)
		tmp = Float64(t_1 - Float64(y * Float64(-1.0 + z)));
	else
		tmp = Float64(Float64(log(y) * x) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * (-1.0 + x);
	tmp = 0.0;
	if (t <= -2.8e-9)
		tmp = t_1 - t;
	elseif (t <= 1.08e+15)
		tmp = t_1 - (y * (-1.0 + z));
	else
		tmp = (log(y) * x) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-9], N[(t$95$1 - t), $MachinePrecision], If[LessEqual[t, 1.08e+15], N[(t$95$1 - N[(y * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 99.1% accurate, 1.9× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (- (* (log y) (+ -1.0 x)) (* y (+ -1.0 z))) t))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return ((Math.log(y) * (-1.0 + x)) - (y * (-1.0 + z))) - t;
}

Python

def code(x, y, z, t):
	return ((math.log(y) * (-1.0 + x)) - (y * (-1.0 + z))) - t

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 87.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (- (* (log y) x) t) (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (log(y) * x) - t;
	} else {
		tmp = -log(y) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (log(y) * x) - t
    else
        tmp = -log(y) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = (Math.log(y) * x) - t;
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = (math.log(y) * x) - t
	else:
		tmp = -math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(Float64(log(y) * x) - t);
	else
		tmp = Float64(Float64(-log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = (log(y) * x) - t;
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 60.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+114} \lor \neg \left(z \leq 1.25 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \left(-z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+114) (not (<= z 1.25e+164)))
   (- (* y (- z)) t)
   (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+114) || !(z <= 1.25e+164)) {
		tmp = (y * -z) - t;
	} else {
		tmp = -log(y) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.5d+114)) .or. (.not. (z <= 1.25d+164))) then
        tmp = (y * -z) - t
    else
        tmp = -log(y) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+114) || !(z <= 1.25e+164)) {
		tmp = (y * -z) - t;
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+114) or not (z <= 1.25e+164):
		tmp = (y * -z) - t
	else:
		tmp = -math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+114) || !(z <= 1.25e+164))
		tmp = Float64(Float64(y * Float64(-z)) - t);
	else
		tmp = Float64(Float64(-log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e+114) || ~((z <= 1.25e+164)))
		tmp = (y * -z) - t;
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+114], N[Not[LessEqual[z, 1.25e+164]], $MachinePrecision]], N[(N[(y * (-z)), $MachinePrecision] - t), $MachinePrecision], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 88.3% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (- (* (log y) (+ -1.0 x)) t))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return (Math.log(y) * (-1.0 + x)) - t;
}

Python

def code(x, y, z, t):
	return (math.log(y) * (-1.0 + x)) - t

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 42.0% accurate, 23.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-9} \lor \neg \left(t \leq 2.4 \cdot 10^{+33}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e-9) (not (<= t 2.4e+33))) (- t) (* y (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-9) || !(t <= 2.4e+33)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.1d-9)) .or. (.not. (t <= 2.4d+33))) then
        tmp = -t
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-9) || !(t <= 2.4e+33)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e-9) or not (t <= 2.4e+33):
		tmp = -t
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e-9) || !(t <= 2.4e+33))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.1e-9) || ~((t <= 2.4e+33)))
		tmp = -t;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e-9], N[Not[LessEqual[t, 2.4e+33]], $MachinePrecision]], (-t), N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 41.9% accurate, 26.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-9} \lor \neg \left(t \leq 6 \cdot 10^{+28}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e-9) (not (<= t 6e+28))) (- t) (* y (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-9) || !(t <= 6e+28)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.1d-9)) .or. (.not. (t <= 6d+28))) then
        tmp = -t
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e-9) || !(t <= 6e+28)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e-9) or not (t <= 6e+28):
		tmp = -t
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e-9) || !(t <= 6e+28))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.1e-9) || ~((t <= 6e+28)))
		tmp = -t;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e-9], N[Not[LessEqual[t, 6e+28]], $MachinePrecision]], (-t), N[(y * (-z)), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 45.8% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(1 - z\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* y (- 1.0 z)) t))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return (y * (1.0 - z)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * Float64(1.0 - z)) - t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 45.6% accurate, 35.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(-z\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* y (- z)) t))

C

double code(double x, double y, double z, double t) {
	return (y * -z) - t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return (y * -z) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * Float64(-z)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * -z) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * (-z)), $MachinePrecision] - t), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 35.6% accurate, 107.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- t))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return -t

Julia

function code(x, y, z, t)
	return Float64(-t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))