Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

Percentage Accurate: 99.4% → 99.4%

Time: 13.7s

Alternatives: 9

Speedup: 1.0×

• 44.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

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 * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

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 * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

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 * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\frac{t \cdot t}{2}}\\ t_2 := \sqrt{z \cdot 2}\\ \mathbf{if}\;t \cdot t \leq 1.08 \cdot 10^{-5}:\\ \;\;\;\;\sqrt{z} \cdot \left(\sqrt{2} \cdot \left(x \cdot 0.5 - y\right)\right)\\ \mathbf{elif}\;t \cdot t \leq 5 \cdot 10^{+259}:\\ \;\;\;\;t_1 \cdot \frac{t_2}{\frac{2}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(y \cdot \left(-t_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (exp (/ (* t t) 2.0))) (t_2 (sqrt (* z 2.0))))
   (if (<= (* t t) 1.08e-5)
     (* (sqrt z) (* (sqrt 2.0) (- (* x 0.5) y)))
     (if (<= (* t t) 5e+259)
       (* t_1 (/ t_2 (/ 2.0 x)))
       (* t_1 (* y (- t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = exp(((t * t) / 2.0));
	double t_2 = sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1.08e-5) {
		tmp = sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
	} else if ((t * t) <= 5e+259) {
		tmp = t_1 * (t_2 / (2.0 / x));
	} else {
		tmp = t_1 * (y * -t_2);
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = exp(((t * t) / 2.0d0))
    t_2 = sqrt((z * 2.0d0))
    if ((t * t) <= 1.08d-5) then
        tmp = sqrt(z) * (sqrt(2.0d0) * ((x * 0.5d0) - y))
    else if ((t * t) <= 5d+259) then
        tmp = t_1 * (t_2 / (2.0d0 / x))
    else
        tmp = t_1 * (y * -t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.exp(((t * t) / 2.0));
	double t_2 = Math.sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1.08e-5) {
		tmp = Math.sqrt(z) * (Math.sqrt(2.0) * ((x * 0.5) - y));
	} else if ((t * t) <= 5e+259) {
		tmp = t_1 * (t_2 / (2.0 / x));
	} else {
		tmp = t_1 * (y * -t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.exp(((t * t) / 2.0))
	t_2 = math.sqrt((z * 2.0))
	tmp = 0
	if (t * t) <= 1.08e-5:
		tmp = math.sqrt(z) * (math.sqrt(2.0) * ((x * 0.5) - y))
	elif (t * t) <= 5e+259:
		tmp = t_1 * (t_2 / (2.0 / x))
	else:
		tmp = t_1 * (y * -t_2)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = exp(Float64(Float64(t * t) / 2.0))
	t_2 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (Float64(t * t) <= 1.08e-5)
		tmp = Float64(sqrt(z) * Float64(sqrt(2.0) * Float64(Float64(x * 0.5) - y)));
	elseif (Float64(t * t) <= 5e+259)
		tmp = Float64(t_1 * Float64(t_2 / Float64(2.0 / x)));
	else
		tmp = Float64(t_1 * Float64(y * Float64(-t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = exp(((t * t) / 2.0));
	t_2 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((t * t) <= 1.08e-5)
		tmp = sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
	elseif ((t * t) <= 5e+259)
		tmp = t_1 * (t_2 / (2.0 / x));
	else
		tmp = t_1 * (y * -t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t * t), $MachinePrecision], 1.08e-5], N[(N[Sqrt[z], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t * t), $MachinePrecision], 5e+259], N[(t$95$1 * N[(t$95$2 / N[(2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(y * (-t$95$2)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \cdot t \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{z} \cdot \left(\sqrt{2} \cdot \left(x \cdot 0.5 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(y \cdot \left(-\sqrt{z \cdot 2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* t t) 8.5e-17)
   (* (sqrt z) (* (sqrt 2.0) (- (* x 0.5) y)))
   (* (exp (/ (* t t) 2.0)) (* y (- (sqrt (* z 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 8.5e-17) {
		tmp = sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
	} else {
		tmp = exp(((t * t) / 2.0)) * (y * -sqrt((z * 2.0)));
	}
	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 * t) <= 8.5d-17) then
        tmp = sqrt(z) * (sqrt(2.0d0) * ((x * 0.5d0) - y))
    else
        tmp = exp(((t * t) / 2.0d0)) * (y * -sqrt((z * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 8.5e-17) {
		tmp = Math.sqrt(z) * (Math.sqrt(2.0) * ((x * 0.5) - y));
	} else {
		tmp = Math.exp(((t * t) / 2.0)) * (y * -Math.sqrt((z * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t * t) <= 8.5e-17:
		tmp = math.sqrt(z) * (math.sqrt(2.0) * ((x * 0.5) - y))
	else:
		tmp = math.exp(((t * t) / 2.0)) * (y * -math.sqrt((z * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t * t) <= 8.5e-17)
		tmp = Float64(sqrt(z) * Float64(sqrt(2.0) * Float64(Float64(x * 0.5) - y)));
	else
		tmp = Float64(exp(Float64(Float64(t * t) / 2.0)) * Float64(y * Float64(-sqrt(Float64(z * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t * t) <= 8.5e-17)
		tmp = sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
	else
		tmp = exp(((t * t) / 2.0)) * (y * -sqrt((z * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t * t), $MachinePrecision], 8.5e-17], N[(N[Sqrt[z], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision] * N[(y * (-N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 42.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+132}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{t_1}{\frac{-1}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(0.5 \cdot {x}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (<= x -9.8e+132)
     (* (* x 0.5) t_1)
     (if (<= x 5.6e+40) (/ t_1 (/ -1.0 y)) (sqrt (* z (* 0.5 (pow x 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if (x <= -9.8e+132) {
		tmp = (x * 0.5) * t_1;
	} else if (x <= 5.6e+40) {
		tmp = t_1 / (-1.0 / y);
	} else {
		tmp = sqrt((z * (0.5 * pow(x, 2.0))));
	}
	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 = sqrt((z * 2.0d0))
    if (x <= (-9.8d+132)) then
        tmp = (x * 0.5d0) * t_1
    else if (x <= 5.6d+40) then
        tmp = t_1 / ((-1.0d0) / y)
    else
        tmp = sqrt((z * (0.5d0 * (x ** 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if (x <= -9.8e+132) {
		tmp = (x * 0.5) * t_1;
	} else if (x <= 5.6e+40) {
		tmp = t_1 / (-1.0 / y);
	} else {
		tmp = Math.sqrt((z * (0.5 * Math.pow(x, 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if x <= -9.8e+132:
		tmp = (x * 0.5) * t_1
	elif x <= 5.6e+40:
		tmp = t_1 / (-1.0 / y)
	else:
		tmp = math.sqrt((z * (0.5 * math.pow(x, 2.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (x <= -9.8e+132)
		tmp = Float64(Float64(x * 0.5) * t_1);
	elseif (x <= 5.6e+40)
		tmp = Float64(t_1 / Float64(-1.0 / y));
	else
		tmp = sqrt(Float64(z * Float64(0.5 * (x ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if (x <= -9.8e+132)
		tmp = (x * 0.5) * t_1;
	elseif (x <= 5.6e+40)
		tmp = t_1 / (-1.0 / y);
	else
		tmp = sqrt((z * (0.5 * (x ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -9.8e+132], N[(N[(x * 0.5), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[x, 5.6e+40], N[(t$95$1 / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(z * N[(0.5 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]

Derivation

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

Alternative 5: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{z} \cdot \left(\sqrt{2} \cdot \left(x \cdot 0.5 - y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (sqrt z) (* (sqrt 2.0) (- (* x 0.5) y))))

C

double code(double x, double y, double z, double t) {
	return sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
}

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 = sqrt(z) * (sqrt(2.0d0) * ((x * 0.5d0) - y))
end function

Java

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

Python

def code(x, y, z, t):
	return math.sqrt(z) * (math.sqrt(2.0) * ((x * 0.5) - y))

Julia

function code(x, y, z, t)
	return Float64(sqrt(z) * Float64(sqrt(2.0) * Float64(Float64(x * 0.5) - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = sqrt(z) * (sqrt(2.0) * ((x * 0.5) - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[z], $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 6: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+132} \lor \neg \left(x \leq 5.2 \cdot 10^{+40}\right):\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (or (<= x -9.5e+132) (not (<= x 5.2e+40)))
     (* (* x 0.5) t_1)
     (* y (- t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((x <= -9.5e+132) || !(x <= 5.2e+40)) {
		tmp = (x * 0.5) * t_1;
	} else {
		tmp = y * -t_1;
	}
	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 = sqrt((z * 2.0d0))
    if ((x <= (-9.5d+132)) .or. (.not. (x <= 5.2d+40))) then
        tmp = (x * 0.5d0) * t_1
    else
        tmp = y * -t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((x <= -9.5e+132) || !(x <= 5.2e+40)) {
		tmp = (x * 0.5) * t_1;
	} else {
		tmp = y * -t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (x <= -9.5e+132) or not (x <= 5.2e+40):
		tmp = (x * 0.5) * t_1
	else:
		tmp = y * -t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if ((x <= -9.5e+132) || !(x <= 5.2e+40))
		tmp = Float64(Float64(x * 0.5) * t_1);
	else
		tmp = Float64(y * Float64(-t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((x <= -9.5e+132) || ~((x <= 5.2e+40)))
		tmp = (x * 0.5) * t_1;
	else
		tmp = y * -t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[x, -9.5e+132], N[Not[LessEqual[x, 5.2e+40]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] * t$95$1), $MachinePrecision], N[(y * (-t$95$1)), $MachinePrecision]]]

Derivation

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

Alternative 7: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+132} \lor \neg \left(x \leq 9 \cdot 10^{+40}\right):\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\frac{-1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (or (<= x -9.5e+132) (not (<= x 9e+40)))
     (* (* x 0.5) t_1)
     (/ t_1 (/ -1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((x <= -9.5e+132) || !(x <= 9e+40)) {
		tmp = (x * 0.5) * t_1;
	} else {
		tmp = t_1 / (-1.0 / y);
	}
	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 = sqrt((z * 2.0d0))
    if ((x <= (-9.5d+132)) .or. (.not. (x <= 9d+40))) then
        tmp = (x * 0.5d0) * t_1
    else
        tmp = t_1 / ((-1.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((x <= -9.5e+132) || !(x <= 9e+40)) {
		tmp = (x * 0.5) * t_1;
	} else {
		tmp = t_1 / (-1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (x <= -9.5e+132) or not (x <= 9e+40):
		tmp = (x * 0.5) * t_1
	else:
		tmp = t_1 / (-1.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if ((x <= -9.5e+132) || !(x <= 9e+40))
		tmp = Float64(Float64(x * 0.5) * t_1);
	else
		tmp = Float64(t_1 / Float64(-1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((x <= -9.5e+132) || ~((x <= 9e+40)))
		tmp = (x * 0.5) * t_1;
	else
		tmp = t_1 / (-1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[x, -9.5e+132], N[Not[LessEqual[x, 9e+40]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] * t$95$1), $MachinePrecision], N[(t$95$1 / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 29.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(-\sqrt{z \cdot 2}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y (- (sqrt (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	return y * -sqrt((z * 2.0));
}

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 * -sqrt((z * 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * -Math.sqrt((z * 2.0));
}

Python

def code(x, y, z, t):
	return y * -math.sqrt((z * 2.0))

Julia

function code(x, y, z, t)
	return Float64(y * Float64(-sqrt(Float64(z * 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * -sqrt((z * 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(y * (-N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]

Derivation

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

Alternative 9: 2.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \sqrt{z \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y (sqrt (* z 2.0))))

C

double code(double x, double y, double z, double t) {
	return y * sqrt((z * 2.0));
}

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 * sqrt((z * 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return y * Math.sqrt((z * 2.0));
}

Python

def code(x, y, z, t):
	return y * math.sqrt((z * 2.0))

Julia

function code(x, y, z, t)
	return Float64(y * sqrt(Float64(z * 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = y * sqrt((z * 2.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(y * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 99.4% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * pow(exp(1.0), ((t * t) / 2.0));
}

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 * 0.5d0) - y) * sqrt((z * 2.0d0))) * (exp(1.0d0) ** ((t * t) / 2.0d0))
end function

Java

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

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.pow(math.exp(1.0), ((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * (exp(1.0) ^ Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * (exp(1.0) ^ ((t * t) / 2.0));
end

Wolfram

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))