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

Percentage Accurate: 99.4% → 99.8%

Time: 13.7s

Alternatives: 11

Speedup: 1.0×

• 44.5% 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: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot x - y\\ \mathbf{if}\;t \leq 1.22:\\ \;\;\;\;t_1 \cdot \sqrt{2 \cdot z}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+203} \lor \neg \left(t \leq 2.2 \cdot 10^{+244}\right):\\ \;\;\;\;\left(t \cdot \left(t_1 \cdot \sqrt{2}\right)\right) \cdot \sqrt{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\sqrt{z \cdot \left(2 + 2 \cdot {t}^{2}\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* 0.5 x) y)))
   (if (<= t 1.22)
     (* t_1 (sqrt (* 2.0 z)))
     (if (or (<= t 2.25e+203) (not (<= t 2.2e+244)))
       (* (* t (* t_1 (sqrt 2.0))) (sqrt z))
       (* y (- (sqrt (* z (+ 2.0 (* 2.0 (pow t 2.0)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.22) {
		tmp = t_1 * sqrt((2.0 * z));
	} else if ((t <= 2.25e+203) || !(t <= 2.2e+244)) {
		tmp = (t * (t_1 * sqrt(2.0))) * sqrt(z);
	} else {
		tmp = y * -sqrt((z * (2.0 + (2.0 * pow(t, 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 = (0.5d0 * x) - y
    if (t <= 1.22d0) then
        tmp = t_1 * sqrt((2.0d0 * z))
    else if ((t <= 2.25d+203) .or. (.not. (t <= 2.2d+244))) then
        tmp = (t * (t_1 * sqrt(2.0d0))) * sqrt(z)
    else
        tmp = y * -sqrt((z * (2.0d0 + (2.0d0 * (t ** 2.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.22) {
		tmp = t_1 * Math.sqrt((2.0 * z));
	} else if ((t <= 2.25e+203) || !(t <= 2.2e+244)) {
		tmp = (t * (t_1 * Math.sqrt(2.0))) * Math.sqrt(z);
	} else {
		tmp = y * -Math.sqrt((z * (2.0 + (2.0 * Math.pow(t, 2.0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (0.5 * x) - y
	tmp = 0
	if t <= 1.22:
		tmp = t_1 * math.sqrt((2.0 * z))
	elif (t <= 2.25e+203) or not (t <= 2.2e+244):
		tmp = (t * (t_1 * math.sqrt(2.0))) * math.sqrt(z)
	else:
		tmp = y * -math.sqrt((z * (2.0 + (2.0 * math.pow(t, 2.0)))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(0.5 * x) - y)
	tmp = 0.0
	if (t <= 1.22)
		tmp = Float64(t_1 * sqrt(Float64(2.0 * z)));
	elseif ((t <= 2.25e+203) || !(t <= 2.2e+244))
		tmp = Float64(Float64(t * Float64(t_1 * sqrt(2.0))) * sqrt(z));
	else
		tmp = Float64(y * Float64(-sqrt(Float64(z * Float64(2.0 + Float64(2.0 * (t ^ 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (0.5 * x) - y;
	tmp = 0.0;
	if (t <= 1.22)
		tmp = t_1 * sqrt((2.0 * z));
	elseif ((t <= 2.25e+203) || ~((t <= 2.2e+244)))
		tmp = (t * (t_1 * sqrt(2.0))) * sqrt(z);
	else
		tmp = y * -sqrt((z * (2.0 + (2.0 * (t ^ 2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t, 1.22], N[(t$95$1 * N[Sqrt[N[(2.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.25e+203], N[Not[LessEqual[t, 2.2e+244]], $MachinePrecision]], N[(N[(t * N[(t$95$1 * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision], N[(y * (-N[Sqrt[N[(z * N[(2.0 + N[(2.0 * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]]]

Derivation

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

Alternative 3: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot \left(2 + 2 \cdot {t}^{2}\right)}\\ t_2 := 0.5 \cdot x - y\\ \mathbf{if}\;t \leq 0.0116:\\ \;\;\;\;t_2 \cdot \sqrt{2 \cdot z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+179}:\\ \;\;\;\;0.5 \cdot \left(x \cdot t_1\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+243}:\\ \;\;\;\;y \cdot \left(-t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(t_2 \cdot \sqrt{2}\right)\right) \cdot \sqrt{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z (+ 2.0 (* 2.0 (pow t 2.0)))))) (t_2 (- (* 0.5 x) y)))
   (if (<= t 0.0116)
     (* t_2 (sqrt (* 2.0 z)))
     (if (<= t 8e+179)
       (* 0.5 (* x t_1))
       (if (<= t 5.3e+243)
         (* y (- t_1))
         (* (* t (* t_2 (sqrt 2.0))) (sqrt z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * (2.0 + (2.0 * pow(t, 2.0)))));
	double t_2 = (0.5 * x) - y;
	double tmp;
	if (t <= 0.0116) {
		tmp = t_2 * sqrt((2.0 * z));
	} else if (t <= 8e+179) {
		tmp = 0.5 * (x * t_1);
	} else if (t <= 5.3e+243) {
		tmp = y * -t_1;
	} else {
		tmp = (t * (t_2 * sqrt(2.0))) * sqrt(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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z * (2.0d0 + (2.0d0 * (t ** 2.0d0)))))
    t_2 = (0.5d0 * x) - y
    if (t <= 0.0116d0) then
        tmp = t_2 * sqrt((2.0d0 * z))
    else if (t <= 8d+179) then
        tmp = 0.5d0 * (x * t_1)
    else if (t <= 5.3d+243) then
        tmp = y * -t_1
    else
        tmp = (t * (t_2 * sqrt(2.0d0))) * sqrt(z)
    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 + (2.0 * Math.pow(t, 2.0)))));
	double t_2 = (0.5 * x) - y;
	double tmp;
	if (t <= 0.0116) {
		tmp = t_2 * Math.sqrt((2.0 * z));
	} else if (t <= 8e+179) {
		tmp = 0.5 * (x * t_1);
	} else if (t <= 5.3e+243) {
		tmp = y * -t_1;
	} else {
		tmp = (t * (t_2 * Math.sqrt(2.0))) * Math.sqrt(z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * (2.0 + (2.0 * math.pow(t, 2.0)))))
	t_2 = (0.5 * x) - y
	tmp = 0
	if t <= 0.0116:
		tmp = t_2 * math.sqrt((2.0 * z))
	elif t <= 8e+179:
		tmp = 0.5 * (x * t_1)
	elif t <= 5.3e+243:
		tmp = y * -t_1
	else:
		tmp = (t * (t_2 * math.sqrt(2.0))) * math.sqrt(z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * Float64(2.0 + Float64(2.0 * (t ^ 2.0)))))
	t_2 = Float64(Float64(0.5 * x) - y)
	tmp = 0.0
	if (t <= 0.0116)
		tmp = Float64(t_2 * sqrt(Float64(2.0 * z)));
	elseif (t <= 8e+179)
		tmp = Float64(0.5 * Float64(x * t_1));
	elseif (t <= 5.3e+243)
		tmp = Float64(y * Float64(-t_1));
	else
		tmp = Float64(Float64(t * Float64(t_2 * sqrt(2.0))) * sqrt(z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * (2.0 + (2.0 * (t ^ 2.0)))));
	t_2 = (0.5 * x) - y;
	tmp = 0.0;
	if (t <= 0.0116)
		tmp = t_2 * sqrt((2.0 * z));
	elseif (t <= 8e+179)
		tmp = 0.5 * (x * t_1);
	elseif (t <= 5.3e+243)
		tmp = y * -t_1;
	else
		tmp = (t * (t_2 * sqrt(2.0))) * sqrt(z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * N[(2.0 + N[(2.0 * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.5 * x), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t, 0.0116], N[(t$95$2 * N[Sqrt[N[(2.0 * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+179], N[(0.5 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+243], N[(y * (-t$95$1)), $MachinePrecision], N[(N[(t * N[(t$95$2 * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 5: 83.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((0.5 * x) - y) * sqrt((z * (2.0 + (2.0 * pow(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 = ((0.5d0 * x) - y) * sqrt((z * (2.0d0 + (2.0d0 * (t ** 2.0d0)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 6: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot x - y\\ \mathbf{if}\;t \leq 1:\\ \;\;\;\;t_1 \cdot \sqrt{2 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* 0.5 x) y)))
   (if (<= t 1.0)
     (* t_1 (sqrt (* 2.0 z)))
     (* t (* t_1 (* (sqrt 2.0) (sqrt z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.0) {
		tmp = t_1 * sqrt((2.0 * z));
	} else {
		tmp = t * (t_1 * (sqrt(2.0) * sqrt(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) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 * x) - y
    if (t <= 1.0d0) then
        tmp = t_1 * sqrt((2.0d0 * z))
    else
        tmp = t * (t_1 * (sqrt(2.0d0) * sqrt(z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.0) {
		tmp = t_1 * Math.sqrt((2.0 * z));
	} else {
		tmp = t * (t_1 * (Math.sqrt(2.0) * Math.sqrt(z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (0.5 * x) - y
	tmp = 0
	if t <= 1.0:
		tmp = t_1 * math.sqrt((2.0 * z))
	else:
		tmp = t * (t_1 * (math.sqrt(2.0) * math.sqrt(z)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(0.5 * x) - y)
	tmp = 0.0
	if (t <= 1.0)
		tmp = Float64(t_1 * sqrt(Float64(2.0 * z)));
	else
		tmp = Float64(t * Float64(t_1 * Float64(sqrt(2.0) * sqrt(z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (0.5 * x) - y;
	tmp = 0.0;
	if (t <= 1.0)
		tmp = t_1 * sqrt((2.0 * z));
	else
		tmp = t * (t_1 * (sqrt(2.0) * sqrt(z)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

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

Alternative 7: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot x - y\\ \mathbf{if}\;t \leq 1:\\ \;\;\;\;t_1 \cdot \sqrt{2 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(t_1 \cdot \sqrt{2}\right)\right) \cdot \sqrt{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* 0.5 x) y)))
   (if (<= t 1.0)
     (* t_1 (sqrt (* 2.0 z)))
     (* (* t (* t_1 (sqrt 2.0))) (sqrt z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.0) {
		tmp = t_1 * sqrt((2.0 * z));
	} else {
		tmp = (t * (t_1 * sqrt(2.0))) * sqrt(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) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 * x) - y
    if (t <= 1.0d0) then
        tmp = t_1 * sqrt((2.0d0 * z))
    else
        tmp = (t * (t_1 * sqrt(2.0d0))) * sqrt(z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (0.5 * x) - y;
	double tmp;
	if (t <= 1.0) {
		tmp = t_1 * Math.sqrt((2.0 * z));
	} else {
		tmp = (t * (t_1 * Math.sqrt(2.0))) * Math.sqrt(z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (0.5 * x) - y
	tmp = 0
	if t <= 1.0:
		tmp = t_1 * math.sqrt((2.0 * z))
	else:
		tmp = (t * (t_1 * math.sqrt(2.0))) * math.sqrt(z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(0.5 * x) - y)
	tmp = 0.0
	if (t <= 1.0)
		tmp = Float64(t_1 * sqrt(Float64(2.0 * z)));
	else
		tmp = Float64(Float64(t * Float64(t_1 * sqrt(2.0))) * sqrt(z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (0.5 * x) - y;
	tmp = 0.0;
	if (t <= 1.0)
		tmp = t_1 * sqrt((2.0 * z));
	else
		tmp = (t * (t_1 * sqrt(2.0))) * sqrt(z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

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

Alternative 8: 43.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{2 \cdot z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-31} \lor \neg \left(y \leq 1.95 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(-t_1\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* 2.0 z))))
   (if (or (<= y -1.65e-31) (not (<= y 1.95e-5)))
     (* y (- t_1))
     (* 0.5 (* x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((2.0 * z));
	double tmp;
	if ((y <= -1.65e-31) || !(y <= 1.95e-5)) {
		tmp = y * -t_1;
	} else {
		tmp = 0.5 * (x * 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((2.0d0 * z))
    if ((y <= (-1.65d-31)) .or. (.not. (y <= 1.95d-5))) then
        tmp = y * -t_1
    else
        tmp = 0.5d0 * (x * 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((2.0 * z));
	double tmp;
	if ((y <= -1.65e-31) || !(y <= 1.95e-5)) {
		tmp = y * -t_1;
	} else {
		tmp = 0.5 * (x * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((2.0 * z))
	tmp = 0
	if (y <= -1.65e-31) or not (y <= 1.95e-5):
		tmp = y * -t_1
	else:
		tmp = 0.5 * (x * t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(2.0 * z))
	tmp = 0.0
	if ((y <= -1.65e-31) || !(y <= 1.95e-5))
		tmp = Float64(y * Float64(-t_1));
	else
		tmp = Float64(0.5 * Float64(x * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((2.0 * z));
	tmp = 0.0;
	if ((y <= -1.65e-31) || ~((y <= 1.95e-5)))
		tmp = y * -t_1;
	else
		tmp = 0.5 * (x * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(2.0 * z), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[y, -1.65e-31], N[Not[LessEqual[y, 1.95e-5]], $MachinePrecision]], N[(y * (-t$95$1)), $MachinePrecision], N[(0.5 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 57.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 10: 29.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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((2.0d0 * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 11: 2.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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((2.0d0 * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(y * N[Sqrt[N[(2.0 * z), $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 2023343 
(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))))