Main:z from

Percentage Accurate: 91.4% → 99.5%

Time: 33.5s

Alternatives: 16

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(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 = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(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 = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{1 + y}\\ t_2 := \sqrt{z + 1}\\ t_3 := \sqrt{x + 1}\\ t_4 := \sqrt{1 + t}\\ \mathbf{if}\;z \leq 7.6 \cdot 10^{+40}:\\ \;\;\;\;\left(\left(t_3 - \sqrt{x}\right) + \left(\left(t_1 - \sqrt{y}\right) + \frac{1}{t_2 + \sqrt{z}}\right)\right) + \frac{1}{t_4 + \sqrt{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{x} + t_3} + \left(\frac{1}{t_1 + \sqrt{y}} + \left(t_4 + \left(\left(t_2 - \sqrt{z}\right) - \sqrt{t}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ 1.0 y)))
        (t_2 (sqrt (+ z 1.0)))
        (t_3 (sqrt (+ x 1.0)))
        (t_4 (sqrt (+ 1.0 t))))
   (if (<= z 7.6e+40)
     (+
      (+ (- t_3 (sqrt x)) (+ (- t_1 (sqrt y)) (/ 1.0 (+ t_2 (sqrt z)))))
      (/ 1.0 (+ t_4 (sqrt t))))
     (+
      (/ 1.0 (+ (sqrt x) t_3))
      (+ (/ 1.0 (+ t_1 (sqrt y))) (+ t_4 (- (- t_2 (sqrt z)) (sqrt t))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((1.0 + y));
	double t_2 = sqrt((z + 1.0));
	double t_3 = sqrt((x + 1.0));
	double t_4 = sqrt((1.0 + t));
	double tmp;
	if (z <= 7.6e+40) {
		tmp = ((t_3 - sqrt(x)) + ((t_1 - sqrt(y)) + (1.0 / (t_2 + sqrt(z))))) + (1.0 / (t_4 + sqrt(t)));
	} else {
		tmp = (1.0 / (sqrt(x) + t_3)) + ((1.0 / (t_1 + sqrt(y))) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = sqrt((1.0d0 + y))
    t_2 = sqrt((z + 1.0d0))
    t_3 = sqrt((x + 1.0d0))
    t_4 = sqrt((1.0d0 + t))
    if (z <= 7.6d+40) then
        tmp = ((t_3 - sqrt(x)) + ((t_1 - sqrt(y)) + (1.0d0 / (t_2 + sqrt(z))))) + (1.0d0 / (t_4 + sqrt(t)))
    else
        tmp = (1.0d0 / (sqrt(x) + t_3)) + ((1.0d0 / (t_1 + sqrt(y))) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((1.0 + y));
	double t_2 = Math.sqrt((z + 1.0));
	double t_3 = Math.sqrt((x + 1.0));
	double t_4 = Math.sqrt((1.0 + t));
	double tmp;
	if (z <= 7.6e+40) {
		tmp = ((t_3 - Math.sqrt(x)) + ((t_1 - Math.sqrt(y)) + (1.0 / (t_2 + Math.sqrt(z))))) + (1.0 / (t_4 + Math.sqrt(t)));
	} else {
		tmp = (1.0 / (Math.sqrt(x) + t_3)) + ((1.0 / (t_1 + Math.sqrt(y))) + (t_4 + ((t_2 - Math.sqrt(z)) - Math.sqrt(t))));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((1.0 + y))
	t_2 = math.sqrt((z + 1.0))
	t_3 = math.sqrt((x + 1.0))
	t_4 = math.sqrt((1.0 + t))
	tmp = 0
	if z <= 7.6e+40:
		tmp = ((t_3 - math.sqrt(x)) + ((t_1 - math.sqrt(y)) + (1.0 / (t_2 + math.sqrt(z))))) + (1.0 / (t_4 + math.sqrt(t)))
	else:
		tmp = (1.0 / (math.sqrt(x) + t_3)) + ((1.0 / (t_1 + math.sqrt(y))) + (t_4 + ((t_2 - math.sqrt(z)) - math.sqrt(t))))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(1.0 + y))
	t_2 = sqrt(Float64(z + 1.0))
	t_3 = sqrt(Float64(x + 1.0))
	t_4 = sqrt(Float64(1.0 + t))
	tmp = 0.0
	if (z <= 7.6e+40)
		tmp = Float64(Float64(Float64(t_3 - sqrt(x)) + Float64(Float64(t_1 - sqrt(y)) + Float64(1.0 / Float64(t_2 + sqrt(z))))) + Float64(1.0 / Float64(t_4 + sqrt(t))));
	else
		tmp = Float64(Float64(1.0 / Float64(sqrt(x) + t_3)) + Float64(Float64(1.0 / Float64(t_1 + sqrt(y))) + Float64(t_4 + Float64(Float64(t_2 - sqrt(z)) - sqrt(t)))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((1.0 + y));
	t_2 = sqrt((z + 1.0));
	t_3 = sqrt((x + 1.0));
	t_4 = sqrt((1.0 + t));
	tmp = 0.0;
	if (z <= 7.6e+40)
		tmp = ((t_3 - sqrt(x)) + ((t_1 - sqrt(y)) + (1.0 / (t_2 + sqrt(z))))) + (1.0 / (t_4 + sqrt(t)));
	else
		tmp = (1.0 / (sqrt(x) + t_3)) + ((1.0 / (t_1 + sqrt(y))) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 7.6e+40], N[(N[(N[(t$95$3 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[Sqrt[y], $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$2 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$4 + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / N[(t$95$1 + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(N[(t$95$2 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ t_2 := t_1 - \sqrt{x}\\ t_3 := \sqrt{1 + t}\\ t_4 := \sqrt{1 + y} - \sqrt{y}\\ t_5 := \sqrt{z + 1}\\ \mathbf{if}\;t_2 + t_4 \leq 0.4:\\ \;\;\;\;\frac{1}{\sqrt{x} + t_1} + \left(t_4 + \left(t_3 + \left(\left(t_5 - \sqrt{z}\right) - \sqrt{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 + \left(t_4 + \frac{1}{t_5 + \sqrt{z}}\right)\right) + \frac{1}{t_3 + \sqrt{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0)))
        (t_2 (- t_1 (sqrt x)))
        (t_3 (sqrt (+ 1.0 t)))
        (t_4 (- (sqrt (+ 1.0 y)) (sqrt y)))
        (t_5 (sqrt (+ z 1.0))))
   (if (<= (+ t_2 t_4) 0.4)
     (+ (/ 1.0 (+ (sqrt x) t_1)) (+ t_4 (+ t_3 (- (- t_5 (sqrt z)) (sqrt t)))))
     (+ (+ t_2 (+ t_4 (/ 1.0 (+ t_5 (sqrt z))))) (/ 1.0 (+ t_3 (sqrt t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double t_2 = t_1 - sqrt(x);
	double t_3 = sqrt((1.0 + t));
	double t_4 = sqrt((1.0 + y)) - sqrt(y);
	double t_5 = sqrt((z + 1.0));
	double tmp;
	if ((t_2 + t_4) <= 0.4) {
		tmp = (1.0 / (sqrt(x) + t_1)) + (t_4 + (t_3 + ((t_5 - sqrt(z)) - sqrt(t))));
	} else {
		tmp = (t_2 + (t_4 + (1.0 / (t_5 + sqrt(z))))) + (1.0 / (t_3 + sqrt(t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    t_2 = t_1 - sqrt(x)
    t_3 = sqrt((1.0d0 + t))
    t_4 = sqrt((1.0d0 + y)) - sqrt(y)
    t_5 = sqrt((z + 1.0d0))
    if ((t_2 + t_4) <= 0.4d0) then
        tmp = (1.0d0 / (sqrt(x) + t_1)) + (t_4 + (t_3 + ((t_5 - sqrt(z)) - sqrt(t))))
    else
        tmp = (t_2 + (t_4 + (1.0d0 / (t_5 + sqrt(z))))) + (1.0d0 / (t_3 + sqrt(t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double t_2 = t_1 - Math.sqrt(x);
	double t_3 = Math.sqrt((1.0 + t));
	double t_4 = Math.sqrt((1.0 + y)) - Math.sqrt(y);
	double t_5 = Math.sqrt((z + 1.0));
	double tmp;
	if ((t_2 + t_4) <= 0.4) {
		tmp = (1.0 / (Math.sqrt(x) + t_1)) + (t_4 + (t_3 + ((t_5 - Math.sqrt(z)) - Math.sqrt(t))));
	} else {
		tmp = (t_2 + (t_4 + (1.0 / (t_5 + Math.sqrt(z))))) + (1.0 / (t_3 + Math.sqrt(t)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	t_2 = t_1 - math.sqrt(x)
	t_3 = math.sqrt((1.0 + t))
	t_4 = math.sqrt((1.0 + y)) - math.sqrt(y)
	t_5 = math.sqrt((z + 1.0))
	tmp = 0
	if (t_2 + t_4) <= 0.4:
		tmp = (1.0 / (math.sqrt(x) + t_1)) + (t_4 + (t_3 + ((t_5 - math.sqrt(z)) - math.sqrt(t))))
	else:
		tmp = (t_2 + (t_4 + (1.0 / (t_5 + math.sqrt(z))))) + (1.0 / (t_3 + math.sqrt(t)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	t_2 = Float64(t_1 - sqrt(x))
	t_3 = sqrt(Float64(1.0 + t))
	t_4 = Float64(sqrt(Float64(1.0 + y)) - sqrt(y))
	t_5 = sqrt(Float64(z + 1.0))
	tmp = 0.0
	if (Float64(t_2 + t_4) <= 0.4)
		tmp = Float64(Float64(1.0 / Float64(sqrt(x) + t_1)) + Float64(t_4 + Float64(t_3 + Float64(Float64(t_5 - sqrt(z)) - sqrt(t)))));
	else
		tmp = Float64(Float64(t_2 + Float64(t_4 + Float64(1.0 / Float64(t_5 + sqrt(z))))) + Float64(1.0 / Float64(t_3 + sqrt(t))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	t_2 = t_1 - sqrt(x);
	t_3 = sqrt((1.0 + t));
	t_4 = sqrt((1.0 + y)) - sqrt(y);
	t_5 = sqrt((z + 1.0));
	tmp = 0.0;
	if ((t_2 + t_4) <= 0.4)
		tmp = (1.0 / (sqrt(x) + t_1)) + (t_4 + (t_3 + ((t_5 - sqrt(z)) - sqrt(t))));
	else
		tmp = (t_2 + (t_4 + (1.0 / (t_5 + sqrt(z))))) + (1.0 / (t_3 + sqrt(t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t$95$2 + t$95$4), $MachinePrecision], 0.4], N[(N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(t$95$3 + N[(N[(t$95$5 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 + N[(t$95$4 + N[(1.0 / N[(t$95$5 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$3 + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 3: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{1 + y} - \sqrt{y}\\ t_2 := \sqrt{z + 1}\\ t_3 := \sqrt{x + 1}\\ t_4 := t_3 - \sqrt{x}\\ t_5 := \sqrt{1 + t}\\ \mathbf{if}\;t_4 \leq 0.4:\\ \;\;\;\;\frac{1}{\sqrt{x} + t_3} + \left(t_1 + \left(t_5 + \left(\left(t_2 - \sqrt{z}\right) - \sqrt{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_4 + \left(t_1 + \frac{1}{t_2 + \sqrt{z}}\right)\right) + \left(t_5 - \sqrt{t}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (sqrt (+ 1.0 y)) (sqrt y)))
        (t_2 (sqrt (+ z 1.0)))
        (t_3 (sqrt (+ x 1.0)))
        (t_4 (- t_3 (sqrt x)))
        (t_5 (sqrt (+ 1.0 t))))
   (if (<= t_4 0.4)
     (+ (/ 1.0 (+ (sqrt x) t_3)) (+ t_1 (+ t_5 (- (- t_2 (sqrt z)) (sqrt t)))))
     (+ (+ t_4 (+ t_1 (/ 1.0 (+ t_2 (sqrt z))))) (- t_5 (sqrt t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((1.0 + y)) - sqrt(y);
	double t_2 = sqrt((z + 1.0));
	double t_3 = sqrt((x + 1.0));
	double t_4 = t_3 - sqrt(x);
	double t_5 = sqrt((1.0 + t));
	double tmp;
	if (t_4 <= 0.4) {
		tmp = (1.0 / (sqrt(x) + t_3)) + (t_1 + (t_5 + ((t_2 - sqrt(z)) - sqrt(t))));
	} else {
		tmp = (t_4 + (t_1 + (1.0 / (t_2 + sqrt(z))))) + (t_5 - sqrt(t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = sqrt((1.0d0 + y)) - sqrt(y)
    t_2 = sqrt((z + 1.0d0))
    t_3 = sqrt((x + 1.0d0))
    t_4 = t_3 - sqrt(x)
    t_5 = sqrt((1.0d0 + t))
    if (t_4 <= 0.4d0) then
        tmp = (1.0d0 / (sqrt(x) + t_3)) + (t_1 + (t_5 + ((t_2 - sqrt(z)) - sqrt(t))))
    else
        tmp = (t_4 + (t_1 + (1.0d0 / (t_2 + sqrt(z))))) + (t_5 - sqrt(t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((1.0 + y)) - Math.sqrt(y);
	double t_2 = Math.sqrt((z + 1.0));
	double t_3 = Math.sqrt((x + 1.0));
	double t_4 = t_3 - Math.sqrt(x);
	double t_5 = Math.sqrt((1.0 + t));
	double tmp;
	if (t_4 <= 0.4) {
		tmp = (1.0 / (Math.sqrt(x) + t_3)) + (t_1 + (t_5 + ((t_2 - Math.sqrt(z)) - Math.sqrt(t))));
	} else {
		tmp = (t_4 + (t_1 + (1.0 / (t_2 + Math.sqrt(z))))) + (t_5 - Math.sqrt(t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((1.0 + y)) - math.sqrt(y)
	t_2 = math.sqrt((z + 1.0))
	t_3 = math.sqrt((x + 1.0))
	t_4 = t_3 - math.sqrt(x)
	t_5 = math.sqrt((1.0 + t))
	tmp = 0
	if t_4 <= 0.4:
		tmp = (1.0 / (math.sqrt(x) + t_3)) + (t_1 + (t_5 + ((t_2 - math.sqrt(z)) - math.sqrt(t))))
	else:
		tmp = (t_4 + (t_1 + (1.0 / (t_2 + math.sqrt(z))))) + (t_5 - math.sqrt(t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(sqrt(Float64(1.0 + y)) - sqrt(y))
	t_2 = sqrt(Float64(z + 1.0))
	t_3 = sqrt(Float64(x + 1.0))
	t_4 = Float64(t_3 - sqrt(x))
	t_5 = sqrt(Float64(1.0 + t))
	tmp = 0.0
	if (t_4 <= 0.4)
		tmp = Float64(Float64(1.0 / Float64(sqrt(x) + t_3)) + Float64(t_1 + Float64(t_5 + Float64(Float64(t_2 - sqrt(z)) - sqrt(t)))));
	else
		tmp = Float64(Float64(t_4 + Float64(t_1 + Float64(1.0 / Float64(t_2 + sqrt(z))))) + Float64(t_5 - sqrt(t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((1.0 + y)) - sqrt(y);
	t_2 = sqrt((z + 1.0));
	t_3 = sqrt((x + 1.0));
	t_4 = t_3 - sqrt(x);
	t_5 = sqrt((1.0 + t));
	tmp = 0.0;
	if (t_4 <= 0.4)
		tmp = (1.0 / (sqrt(x) + t_3)) + (t_1 + (t_5 + ((t_2 - sqrt(z)) - sqrt(t))));
	else
		tmp = (t_4 + (t_1 + (1.0 / (t_2 + sqrt(z))))) + (t_5 - sqrt(t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$4, 0.4], N[(N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(t$95$5 + N[(N[(t$95$2 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$4 + N[(t$95$1 + N[(1.0 / N[(t$95$2 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 4: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ \mathbf{if}\;y \leq 2.8 \cdot 10^{+33}:\\ \;\;\;\;\left(\left(t_1 - \sqrt{x}\right) + \left(\left(\sqrt{1 + y} - \sqrt{y}\right) + \frac{1}{\sqrt{z + 1} + \sqrt{z}}\right)\right) + \left(\sqrt{1 + t} - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - x\right)}{\sqrt{x} + t_1}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))))
   (if (<= y 2.8e+33)
     (+
      (+
       (- t_1 (sqrt x))
       (+ (- (sqrt (+ 1.0 y)) (sqrt y)) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
      (- (sqrt (+ 1.0 t)) (sqrt t)))
     (/ (+ 1.0 (- x x)) (+ (sqrt x) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double tmp;
	if (y <= 2.8e+33) {
		tmp = ((t_1 - sqrt(x)) + ((sqrt((1.0 + y)) - sqrt(y)) + (1.0 / (sqrt((z + 1.0)) + sqrt(z))))) + (sqrt((1.0 + t)) - sqrt(t));
	} else {
		tmp = (1.0 + (x - x)) / (sqrt(x) + t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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((x + 1.0d0))
    if (y <= 2.8d+33) then
        tmp = ((t_1 - sqrt(x)) + ((sqrt((1.0d0 + y)) - sqrt(y)) + (1.0d0 / (sqrt((z + 1.0d0)) + sqrt(z))))) + (sqrt((1.0d0 + t)) - sqrt(t))
    else
        tmp = (1.0d0 + (x - x)) / (sqrt(x) + t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double tmp;
	if (y <= 2.8e+33) {
		tmp = ((t_1 - Math.sqrt(x)) + ((Math.sqrt((1.0 + y)) - Math.sqrt(y)) + (1.0 / (Math.sqrt((z + 1.0)) + Math.sqrt(z))))) + (Math.sqrt((1.0 + t)) - Math.sqrt(t));
	} else {
		tmp = (1.0 + (x - x)) / (Math.sqrt(x) + t_1);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	tmp = 0
	if y <= 2.8e+33:
		tmp = ((t_1 - math.sqrt(x)) + ((math.sqrt((1.0 + y)) - math.sqrt(y)) + (1.0 / (math.sqrt((z + 1.0)) + math.sqrt(z))))) + (math.sqrt((1.0 + t)) - math.sqrt(t))
	else:
		tmp = (1.0 + (x - x)) / (math.sqrt(x) + t_1)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	tmp = 0.0
	if (y <= 2.8e+33)
		tmp = Float64(Float64(Float64(t_1 - sqrt(x)) + Float64(Float64(sqrt(Float64(1.0 + y)) - sqrt(y)) + Float64(1.0 / Float64(sqrt(Float64(z + 1.0)) + sqrt(z))))) + Float64(sqrt(Float64(1.0 + t)) - sqrt(t)));
	else
		tmp = Float64(Float64(1.0 + Float64(x - x)) / Float64(sqrt(x) + t_1));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	tmp = 0.0;
	if (y <= 2.8e+33)
		tmp = ((t_1 - sqrt(x)) + ((sqrt((1.0 + y)) - sqrt(y)) + (1.0 / (sqrt((z + 1.0)) + sqrt(z))))) + (sqrt((1.0 + t)) - sqrt(t));
	else
		tmp = (1.0 + (x - x)) / (sqrt(x) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 2.8e+33], N[(N[(N[(t$95$1 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[x], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 98.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ t_2 := t_1 - \sqrt{x}\\ t_3 := \sqrt{z + 1}\\ \mathbf{if}\;y \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + \left(t_2 + \left(\frac{1}{t_3 + \sqrt{z}} + \left(\left(1 + y \cdot 0.5\right) - \sqrt{y}\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+33}:\\ \;\;\;\;t_2 + \left(\frac{1}{\sqrt{1 + y} + \sqrt{y}} + \left(t_3 - \sqrt{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - x\right)}{\sqrt{x} + t_1}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))) (t_2 (- t_1 (sqrt x))) (t_3 (sqrt (+ z 1.0))))
   (if (<= y 1.45e-7)
     (+
      (- (sqrt (+ 1.0 t)) (sqrt t))
      (+ t_2 (+ (/ 1.0 (+ t_3 (sqrt z))) (- (+ 1.0 (* y 0.5)) (sqrt y)))))
     (if (<= y 2.8e+33)
       (+ t_2 (+ (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y))) (- t_3 (sqrt z))))
       (/ (+ 1.0 (- x x)) (+ (sqrt x) t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double t_2 = t_1 - sqrt(x);
	double t_3 = sqrt((z + 1.0));
	double tmp;
	if (y <= 1.45e-7) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + (t_2 + ((1.0 / (t_3 + sqrt(z))) + ((1.0 + (y * 0.5)) - sqrt(y))));
	} else if (y <= 2.8e+33) {
		tmp = t_2 + ((1.0 / (sqrt((1.0 + y)) + sqrt(y))) + (t_3 - sqrt(z)));
	} else {
		tmp = (1.0 + (x - x)) / (sqrt(x) + t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    t_2 = t_1 - sqrt(x)
    t_3 = sqrt((z + 1.0d0))
    if (y <= 1.45d-7) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + (t_2 + ((1.0d0 / (t_3 + sqrt(z))) + ((1.0d0 + (y * 0.5d0)) - sqrt(y))))
    else if (y <= 2.8d+33) then
        tmp = t_2 + ((1.0d0 / (sqrt((1.0d0 + y)) + sqrt(y))) + (t_3 - sqrt(z)))
    else
        tmp = (1.0d0 + (x - x)) / (sqrt(x) + t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double t_2 = t_1 - Math.sqrt(x);
	double t_3 = Math.sqrt((z + 1.0));
	double tmp;
	if (y <= 1.45e-7) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + (t_2 + ((1.0 / (t_3 + Math.sqrt(z))) + ((1.0 + (y * 0.5)) - Math.sqrt(y))));
	} else if (y <= 2.8e+33) {
		tmp = t_2 + ((1.0 / (Math.sqrt((1.0 + y)) + Math.sqrt(y))) + (t_3 - Math.sqrt(z)));
	} else {
		tmp = (1.0 + (x - x)) / (Math.sqrt(x) + t_1);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	t_2 = t_1 - math.sqrt(x)
	t_3 = math.sqrt((z + 1.0))
	tmp = 0
	if y <= 1.45e-7:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + (t_2 + ((1.0 / (t_3 + math.sqrt(z))) + ((1.0 + (y * 0.5)) - math.sqrt(y))))
	elif y <= 2.8e+33:
		tmp = t_2 + ((1.0 / (math.sqrt((1.0 + y)) + math.sqrt(y))) + (t_3 - math.sqrt(z)))
	else:
		tmp = (1.0 + (x - x)) / (math.sqrt(x) + t_1)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	t_2 = Float64(t_1 - sqrt(x))
	t_3 = sqrt(Float64(z + 1.0))
	tmp = 0.0
	if (y <= 1.45e-7)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + Float64(t_2 + Float64(Float64(1.0 / Float64(t_3 + sqrt(z))) + Float64(Float64(1.0 + Float64(y * 0.5)) - sqrt(y)))));
	elseif (y <= 2.8e+33)
		tmp = Float64(t_2 + Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + y)) + sqrt(y))) + Float64(t_3 - sqrt(z))));
	else
		tmp = Float64(Float64(1.0 + Float64(x - x)) / Float64(sqrt(x) + t_1));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	t_2 = t_1 - sqrt(x);
	t_3 = sqrt((z + 1.0));
	tmp = 0.0;
	if (y <= 1.45e-7)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + (t_2 + ((1.0 / (t_3 + sqrt(z))) + ((1.0 + (y * 0.5)) - sqrt(y))));
	elseif (y <= 2.8e+33)
		tmp = t_2 + ((1.0 / (sqrt((1.0 + y)) + sqrt(y))) + (t_3 - sqrt(z)));
	else
		tmp = (1.0 + (x - x)) / (sqrt(x) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 1.45e-7], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + N[(t$95$2 + N[(N[(1.0 / N[(t$95$3 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+33], N[(t$95$2 + N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[x], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 96.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;\left(\left(1 + \left(\sqrt{1 + y} + \frac{1}{\sqrt{z + 1} + \sqrt{z}}\right)\right) - \sqrt{y}\right) + \frac{1}{\sqrt{t} + \left(1 + t \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - x\right)}{\sqrt{x} + \sqrt{x + 1}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 8.5e+31)
   (+
    (-
     (+ 1.0 (+ (sqrt (+ 1.0 y)) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))))
     (sqrt y))
    (/ 1.0 (+ (sqrt t) (+ 1.0 (* t 0.5)))))
   (/ (+ 1.0 (- x x)) (+ (sqrt x) (sqrt (+ x 1.0))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+31) {
		tmp = ((1.0 + (sqrt((1.0 + y)) + (1.0 / (sqrt((z + 1.0)) + sqrt(z))))) - sqrt(y)) + (1.0 / (sqrt(t) + (1.0 + (t * 0.5))));
	} else {
		tmp = (1.0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 8.5d+31) then
        tmp = ((1.0d0 + (sqrt((1.0d0 + y)) + (1.0d0 / (sqrt((z + 1.0d0)) + sqrt(z))))) - sqrt(y)) + (1.0d0 / (sqrt(t) + (1.0d0 + (t * 0.5d0))))
    else
        tmp = (1.0d0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+31) {
		tmp = ((1.0 + (Math.sqrt((1.0 + y)) + (1.0 / (Math.sqrt((z + 1.0)) + Math.sqrt(z))))) - Math.sqrt(y)) + (1.0 / (Math.sqrt(t) + (1.0 + (t * 0.5))));
	} else {
		tmp = (1.0 + (x - x)) / (Math.sqrt(x) + Math.sqrt((x + 1.0)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 8.5e+31:
		tmp = ((1.0 + (math.sqrt((1.0 + y)) + (1.0 / (math.sqrt((z + 1.0)) + math.sqrt(z))))) - math.sqrt(y)) + (1.0 / (math.sqrt(t) + (1.0 + (t * 0.5))))
	else:
		tmp = (1.0 + (x - x)) / (math.sqrt(x) + math.sqrt((x + 1.0)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 8.5e+31)
		tmp = Float64(Float64(Float64(1.0 + Float64(sqrt(Float64(1.0 + y)) + Float64(1.0 / Float64(sqrt(Float64(z + 1.0)) + sqrt(z))))) - sqrt(y)) + Float64(1.0 / Float64(sqrt(t) + Float64(1.0 + Float64(t * 0.5)))));
	else
		tmp = Float64(Float64(1.0 + Float64(x - x)) / Float64(sqrt(x) + sqrt(Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 8.5e+31)
		tmp = ((1.0 + (sqrt((1.0 + y)) + (1.0 / (sqrt((z + 1.0)) + sqrt(z))))) - sqrt(y)) + (1.0 / (sqrt(t) + (1.0 + (t * 0.5))));
	else
		tmp = (1.0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 8.5e+31], N[(N[(N[(1.0 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[t], $MachinePrecision] + N[(1.0 + N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[x], $MachinePrecision] + N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 90.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{1 + y}\\ \mathbf{if}\;z \leq 1.45 \cdot 10^{-15}:\\ \;\;\;\;\left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\right) - \sqrt{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+19}:\\ \;\;\;\;1 + \left(t_1 - \left(\left(\sqrt{y} + \sqrt{z}\right) - \sqrt{z + 1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} + \left(t_1 - \left(\sqrt{x} + \sqrt{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ 1.0 y))))
   (if (<= z 1.45e-15)
     (- (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0) (sqrt z))
     (if (<= z 7e+19)
       (+ 1.0 (- t_1 (- (+ (sqrt y) (sqrt z)) (sqrt (+ z 1.0)))))
       (+ (sqrt (+ x 1.0)) (- t_1 (+ (sqrt x) (sqrt y))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((1.0 + y));
	double tmp;
	if (z <= 1.45e-15) {
		tmp = ((sqrt((1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z);
	} else if (z <= 7e+19) {
		tmp = 1.0 + (t_1 - ((sqrt(y) + sqrt(z)) - sqrt((z + 1.0))));
	} else {
		tmp = sqrt((x + 1.0)) + (t_1 - (sqrt(x) + sqrt(y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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((1.0d0 + y))
    if (z <= 1.45d-15) then
        tmp = ((sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0) - sqrt(z)
    else if (z <= 7d+19) then
        tmp = 1.0d0 + (t_1 - ((sqrt(y) + sqrt(z)) - sqrt((z + 1.0d0))))
    else
        tmp = sqrt((x + 1.0d0)) + (t_1 - (sqrt(x) + sqrt(y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((1.0 + y));
	double tmp;
	if (z <= 1.45e-15) {
		tmp = ((Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0) - Math.sqrt(z);
	} else if (z <= 7e+19) {
		tmp = 1.0 + (t_1 - ((Math.sqrt(y) + Math.sqrt(z)) - Math.sqrt((z + 1.0))));
	} else {
		tmp = Math.sqrt((x + 1.0)) + (t_1 - (Math.sqrt(x) + Math.sqrt(y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((1.0 + y))
	tmp = 0
	if z <= 1.45e-15:
		tmp = ((math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0) - math.sqrt(z)
	elif z <= 7e+19:
		tmp = 1.0 + (t_1 - ((math.sqrt(y) + math.sqrt(z)) - math.sqrt((z + 1.0))))
	else:
		tmp = math.sqrt((x + 1.0)) + (t_1 - (math.sqrt(x) + math.sqrt(y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(1.0 + y))
	tmp = 0.0
	if (z <= 1.45e-15)
		tmp = Float64(Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z));
	elseif (z <= 7e+19)
		tmp = Float64(1.0 + Float64(t_1 - Float64(Float64(sqrt(y) + sqrt(z)) - sqrt(Float64(z + 1.0)))));
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) + Float64(t_1 - Float64(sqrt(x) + sqrt(y))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((1.0 + y));
	tmp = 0.0;
	if (z <= 1.45e-15)
		tmp = ((sqrt((1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z);
	elseif (z <= 7e+19)
		tmp = 1.0 + (t_1 - ((sqrt(y) + sqrt(z)) - sqrt((z + 1.0))));
	else
		tmp = sqrt((x + 1.0)) + (t_1 - (sqrt(x) + sqrt(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 1.45e-15], N[(N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+19], N[(1.0 + N[(t$95$1 - N[(N[(N[Sqrt[y], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision] - N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[(t$95$1 - N[(N[Sqrt[x], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 89.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.65 \cdot 10^{-15}:\\ \;\;\;\;\left(\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\right) - \sqrt{z}\\ \mathbf{elif}\;z \leq 125000000000:\\ \;\;\;\;\left(\sqrt{z + 1} - \sqrt{z}\right) + 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} + \left(\sqrt{1 + y} - \left(\sqrt{x} + \sqrt{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.65e-15)
   (- (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0) (sqrt z))
   (if (<= z 125000000000.0)
     (+ (- (sqrt (+ z 1.0)) (sqrt z)) 2.0)
     (+ (sqrt (+ x 1.0)) (- (sqrt (+ 1.0 y)) (+ (sqrt x) (sqrt y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.65e-15) {
		tmp = ((sqrt((1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z);
	} else if (z <= 125000000000.0) {
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	} else {
		tmp = sqrt((x + 1.0)) + (sqrt((1.0 + y)) - (sqrt(x) + sqrt(y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= 1.65d-15) then
        tmp = ((sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0) - sqrt(z)
    else if (z <= 125000000000.0d0) then
        tmp = (sqrt((z + 1.0d0)) - sqrt(z)) + 2.0d0
    else
        tmp = sqrt((x + 1.0d0)) + (sqrt((1.0d0 + y)) - (sqrt(x) + sqrt(y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.65e-15) {
		tmp = ((Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0) - Math.sqrt(z);
	} else if (z <= 125000000000.0) {
		tmp = (Math.sqrt((z + 1.0)) - Math.sqrt(z)) + 2.0;
	} else {
		tmp = Math.sqrt((x + 1.0)) + (Math.sqrt((1.0 + y)) - (Math.sqrt(x) + Math.sqrt(y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 1.65e-15:
		tmp = ((math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0) - math.sqrt(z)
	elif z <= 125000000000.0:
		tmp = (math.sqrt((z + 1.0)) - math.sqrt(z)) + 2.0
	else:
		tmp = math.sqrt((x + 1.0)) + (math.sqrt((1.0 + y)) - (math.sqrt(x) + math.sqrt(y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.65e-15)
		tmp = Float64(Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z));
	elseif (z <= 125000000000.0)
		tmp = Float64(Float64(sqrt(Float64(z + 1.0)) - sqrt(z)) + 2.0);
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) + Float64(sqrt(Float64(1.0 + y)) - Float64(sqrt(x) + sqrt(y))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.65e-15)
		tmp = ((sqrt((1.0 + t)) - sqrt(t)) + 3.0) - sqrt(z);
	elseif (z <= 125000000000.0)
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	else
		tmp = sqrt((x + 1.0)) + (sqrt((1.0 + y)) - (sqrt(x) + sqrt(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 1.65e-15], N[(N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 125000000000.0], N[(N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[x], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 9: 89.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;\left(\sqrt{z + 1} - \sqrt{z}\right) + 2\\ \mathbf{elif}\;y \leq 10^{+23}:\\ \;\;\;\;\left(1 + \sqrt{1 + y}\right) - \sqrt{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - x\right)}{\sqrt{x} + \sqrt{x + 1}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.2e-31)
   (+ (- (sqrt (+ z 1.0)) (sqrt z)) 2.0)
   (if (<= y 1e+23)
     (- (+ 1.0 (sqrt (+ 1.0 y))) (sqrt y))
     (/ (+ 1.0 (- x x)) (+ (sqrt x) (sqrt (+ x 1.0)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	} else if (y <= 1e+23) {
		tmp = (1.0 + sqrt((1.0 + y))) - sqrt(y);
	} else {
		tmp = (1.0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 2.2d-31) then
        tmp = (sqrt((z + 1.0d0)) - sqrt(z)) + 2.0d0
    else if (y <= 1d+23) then
        tmp = (1.0d0 + sqrt((1.0d0 + y))) - sqrt(y)
    else
        tmp = (1.0d0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (Math.sqrt((z + 1.0)) - Math.sqrt(z)) + 2.0;
	} else if (y <= 1e+23) {
		tmp = (1.0 + Math.sqrt((1.0 + y))) - Math.sqrt(y);
	} else {
		tmp = (1.0 + (x - x)) / (Math.sqrt(x) + Math.sqrt((x + 1.0)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e-31:
		tmp = (math.sqrt((z + 1.0)) - math.sqrt(z)) + 2.0
	elif y <= 1e+23:
		tmp = (1.0 + math.sqrt((1.0 + y))) - math.sqrt(y)
	else:
		tmp = (1.0 + (x - x)) / (math.sqrt(x) + math.sqrt((x + 1.0)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e-31)
		tmp = Float64(Float64(sqrt(Float64(z + 1.0)) - sqrt(z)) + 2.0);
	elseif (y <= 1e+23)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + y))) - sqrt(y));
	else
		tmp = Float64(Float64(1.0 + Float64(x - x)) / Float64(sqrt(x) + sqrt(Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e-31)
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	elseif (y <= 1e+23)
		tmp = (1.0 + sqrt((1.0 + y))) - sqrt(y);
	else
		tmp = (1.0 + (x - x)) / (sqrt(x) + sqrt((x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e-31], N[(N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], If[LessEqual[y, 1e+23], N[(N[(1.0 + N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[x], $MachinePrecision] + N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 84.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;\left(\sqrt{z + 1} - \sqrt{z}\right) + 2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+24}:\\ \;\;\;\;\sqrt{1 + y} - \left(\sqrt{y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} - \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.2e-31)
   (+ (- (sqrt (+ z 1.0)) (sqrt z)) 2.0)
   (if (<= y 3.2e+24)
     (- (sqrt (+ 1.0 y)) (+ (sqrt y) -1.0))
     (- (sqrt (+ x 1.0)) (sqrt x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	} else if (y <= 3.2e+24) {
		tmp = sqrt((1.0 + y)) - (sqrt(y) + -1.0);
	} else {
		tmp = sqrt((x + 1.0)) - sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 2.2d-31) then
        tmp = (sqrt((z + 1.0d0)) - sqrt(z)) + 2.0d0
    else if (y <= 3.2d+24) then
        tmp = sqrt((1.0d0 + y)) - (sqrt(y) + (-1.0d0))
    else
        tmp = sqrt((x + 1.0d0)) - sqrt(x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (Math.sqrt((z + 1.0)) - Math.sqrt(z)) + 2.0;
	} else if (y <= 3.2e+24) {
		tmp = Math.sqrt((1.0 + y)) - (Math.sqrt(y) + -1.0);
	} else {
		tmp = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e-31:
		tmp = (math.sqrt((z + 1.0)) - math.sqrt(z)) + 2.0
	elif y <= 3.2e+24:
		tmp = math.sqrt((1.0 + y)) - (math.sqrt(y) + -1.0)
	else:
		tmp = math.sqrt((x + 1.0)) - math.sqrt(x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e-31)
		tmp = Float64(Float64(sqrt(Float64(z + 1.0)) - sqrt(z)) + 2.0);
	elseif (y <= 3.2e+24)
		tmp = Float64(sqrt(Float64(1.0 + y)) - Float64(sqrt(y) + -1.0));
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) - sqrt(x));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e-31)
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	elseif (y <= 3.2e+24)
		tmp = sqrt((1.0 + y)) - (sqrt(y) + -1.0);
	else
		tmp = sqrt((x + 1.0)) - sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e-31], N[(N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], If[LessEqual[y, 3.2e+24], N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[y], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 84.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;\left(\sqrt{z + 1} - \sqrt{z}\right) + 2\\ \mathbf{elif}\;y \leq 10^{+23}:\\ \;\;\;\;\left(1 + \sqrt{1 + y}\right) - \sqrt{y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} - \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.2e-31)
   (+ (- (sqrt (+ z 1.0)) (sqrt z)) 2.0)
   (if (<= y 1e+23)
     (- (+ 1.0 (sqrt (+ 1.0 y))) (sqrt y))
     (- (sqrt (+ x 1.0)) (sqrt x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	} else if (y <= 1e+23) {
		tmp = (1.0 + sqrt((1.0 + y))) - sqrt(y);
	} else {
		tmp = sqrt((x + 1.0)) - sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 2.2d-31) then
        tmp = (sqrt((z + 1.0d0)) - sqrt(z)) + 2.0d0
    else if (y <= 1d+23) then
        tmp = (1.0d0 + sqrt((1.0d0 + y))) - sqrt(y)
    else
        tmp = sqrt((x + 1.0d0)) - sqrt(x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e-31) {
		tmp = (Math.sqrt((z + 1.0)) - Math.sqrt(z)) + 2.0;
	} else if (y <= 1e+23) {
		tmp = (1.0 + Math.sqrt((1.0 + y))) - Math.sqrt(y);
	} else {
		tmp = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e-31:
		tmp = (math.sqrt((z + 1.0)) - math.sqrt(z)) + 2.0
	elif y <= 1e+23:
		tmp = (1.0 + math.sqrt((1.0 + y))) - math.sqrt(y)
	else:
		tmp = math.sqrt((x + 1.0)) - math.sqrt(x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e-31)
		tmp = Float64(Float64(sqrt(Float64(z + 1.0)) - sqrt(z)) + 2.0);
	elseif (y <= 1e+23)
		tmp = Float64(Float64(1.0 + sqrt(Float64(1.0 + y))) - sqrt(y));
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) - sqrt(x));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e-31)
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	elseif (y <= 1e+23)
		tmp = (1.0 + sqrt((1.0 + y))) - sqrt(y);
	else
		tmp = sqrt((x + 1.0)) - sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e-31], N[(N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], If[LessEqual[y, 1e+23], N[(N[(1.0 + N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 12: 61.6% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} - \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 5.0)
   (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 2.0)
   (- (sqrt (+ x 1.0)) (sqrt x))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.0) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 2.0;
	} else {
		tmp = sqrt((x + 1.0)) - sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 5.0d0) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 2.0d0
    else
        tmp = sqrt((x + 1.0d0)) - sqrt(x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 5.0) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 2.0;
	} else {
		tmp = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 5.0:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 2.0
	else:
		tmp = math.sqrt((x + 1.0)) - math.sqrt(x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 5.0)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 2.0);
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) - sqrt(x));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 5.0)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 2.0;
	else
		tmp = sqrt((x + 1.0)) - sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 5.0], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 13: 81.3% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.85:\\ \;\;\;\;\left(\sqrt{z + 1} - \sqrt{z}\right) + 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1} - \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.85)
   (+ (- (sqrt (+ z 1.0)) (sqrt z)) 2.0)
   (- (sqrt (+ x 1.0)) (sqrt x))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.85) {
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	} else {
		tmp = sqrt((x + 1.0)) - sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 (y <= 3.85d0) then
        tmp = (sqrt((z + 1.0d0)) - sqrt(z)) + 2.0d0
    else
        tmp = sqrt((x + 1.0d0)) - sqrt(x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.85) {
		tmp = (Math.sqrt((z + 1.0)) - Math.sqrt(z)) + 2.0;
	} else {
		tmp = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 3.85:
		tmp = (math.sqrt((z + 1.0)) - math.sqrt(z)) + 2.0
	else:
		tmp = math.sqrt((x + 1.0)) - math.sqrt(x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.85)
		tmp = Float64(Float64(sqrt(Float64(z + 1.0)) - sqrt(z)) + 2.0);
	else
		tmp = Float64(sqrt(Float64(x + 1.0)) - sqrt(x));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.85)
		tmp = (sqrt((z + 1.0)) - sqrt(z)) + 2.0;
	else
		tmp = sqrt((x + 1.0)) - sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 3.85], N[(N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 14: 35.9% accurate, 4.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \sqrt{x + 1} - \sqrt{x} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return sqrt((x + 1.0)) - sqrt(x);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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((x + 1.0d0)) - sqrt(x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return Math.sqrt((x + 1.0)) - Math.sqrt(x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return math.sqrt((x + 1.0)) - math.sqrt(x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = sqrt((x + 1.0)) - sqrt(x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 15: 35.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \left(1 + x \cdot 0.5\right) - \sqrt{x} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- (+ 1.0 (* x 0.5)) (sqrt x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (1.0 + (x * 0.5)) - sqrt(x);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 = (1.0d0 + (x * 0.5d0)) - sqrt(x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (1.0 + (x * 0.5)) - Math.sqrt(x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (1.0 + (x * 0.5)) - math.sqrt(x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(1.0 + Float64(x * 0.5)) - sqrt(x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (1.0 + (x * 0.5)) - sqrt(x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 16: 34.9% accurate, 823.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 = 1.0d0
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

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1. Add Preprocessing

Developer target: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (+
  (+
   (+
    (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
    (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y))))
   (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z))))
  (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / (sqrt((x + 1.0)) + sqrt(x))) + (1.0 / (sqrt((y + 1.0)) + sqrt(y)))) + (1.0 / (sqrt((z + 1.0)) + sqrt(z)))) + (sqrt((t + 1.0)) - sqrt(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 = (((1.0d0 / (sqrt((x + 1.0d0)) + sqrt(x))) + (1.0d0 / (sqrt((y + 1.0d0)) + sqrt(y)))) + (1.0d0 / (sqrt((z + 1.0d0)) + sqrt(z)))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / Float64(sqrt(Float64(x + 1.0)) + sqrt(x))) + Float64(1.0 / Float64(sqrt(Float64(y + 1.0)) + sqrt(y)))) + Float64(1.0 / Float64(sqrt(Float64(z + 1.0)) + sqrt(z)))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023364 
(FPCore (x y z t)
  :name "Main:z from "
  :precision binary64

  :herbie-target
  (+ (+ (+ (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))) (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (- (sqrt (+ t 1.0)) (sqrt t)))

  (+ (+ (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y))) (- (sqrt (+ z 1.0)) (sqrt z))) (- (sqrt (+ t 1.0)) (sqrt t))))