expfmod (used to be hard to sample)

Percentage Accurate: 6.8% → 63.2%

Time: 18.9s

Alternatives: 9

Speedup: 5.0×

• could not determine a ground truth

  1. x = -1.463489897511801e+116

Specification

Math

\[\begin{array}{l} \\ \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right) \cdot e^{-x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (fmod (exp x) (sqrt (cos x))) (exp (- x))))

C

double code(double x) {
	return fmod(exp(x), sqrt(cos(x))) * exp(-x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = mod(exp(x), sqrt(cos(x))) * exp(-x)
end function

Python

def code(x):
	return math.fmod(math.exp(x), math.sqrt(math.cos(x))) * math.exp(-x)

Julia

function code(x)
	return Float64(rem(exp(x), sqrt(cos(x))) * exp(Float64(-x)))
end

Wolfram

code[x_] := N[(N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision] * N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]

Initial Program: 6.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right) \cdot e^{-x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (fmod (exp x) (sqrt (cos x))) (exp (- x))))

C

double code(double x) {
	return fmod(exp(x), sqrt(cos(x))) * exp(-x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = mod(exp(x), sqrt(cos(x))) * exp(-x)
end function

Python

def code(x):
	return math.fmod(math.exp(x), math.sqrt(math.cos(x))) * math.exp(-x)

Julia

function code(x)
	return Float64(rem(exp(x), sqrt(cos(x))) * exp(Float64(-x)))
end

Wolfram

code[x_] := N[(N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision] * N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]

Alternative 1: 63.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := 1 + \frac{t_0}{e^{x}}\\ t_2 := e^{-x}\\ t_3 := t_0 \cdot t_2\\ \mathbf{if}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 2\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{{t_1}^{2} + -1}{t_1 - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (+ 1.0 (/ t_0 (exp x))))
        (t_2 (exp (- x)))
        (t_3 (* t_0 t_2)))
   (if (or (<= t_3 0.0) (not (<= t_3 2.0)))
     t_2
     (/ (+ (pow t_1 2.0) -1.0) (- t_1 -1.0)))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = 1.0 + (t_0 / exp(x));
	double t_2 = exp(-x);
	double t_3 = t_0 * t_2;
	double tmp;
	if ((t_3 <= 0.0) || !(t_3 <= 2.0)) {
		tmp = t_2;
	} else {
		tmp = (pow(t_1, 2.0) + -1.0) / (t_1 - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = 1.0d0 + (t_0 / exp(x))
    t_2 = exp(-x)
    t_3 = t_0 * t_2
    if ((t_3 <= 0.0d0) .or. (.not. (t_3 <= 2.0d0))) then
        tmp = t_2
    else
        tmp = ((t_1 ** 2.0d0) + (-1.0d0)) / (t_1 - (-1.0d0))
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = 1.0 + (t_0 / math.exp(x))
	t_2 = math.exp(-x)
	t_3 = t_0 * t_2
	tmp = 0
	if (t_3 <= 0.0) or not (t_3 <= 2.0):
		tmp = t_2
	else:
		tmp = (math.pow(t_1, 2.0) + -1.0) / (t_1 - -1.0)
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = Float64(1.0 + Float64(t_0 / exp(x)))
	t_2 = exp(Float64(-x))
	t_3 = Float64(t_0 * t_2)
	tmp = 0.0
	if ((t_3 <= 0.0) || !(t_3 <= 2.0))
		tmp = t_2;
	else
		tmp = Float64(Float64((t_1 ^ 2.0) + -1.0) / Float64(t_1 - -1.0));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(t$95$0 / N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$0 * t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 2.0]], $MachinePrecision]], t$95$2, N[(N[(N[Power[t$95$1, 2.0], $MachinePrecision] + -1.0), $MachinePrecision] / N[(t$95$1 - -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 63.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-x}\\ t_1 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_2 := t_1 \cdot t_0\\ t_3 := \frac{t_1}{e^{x}}\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - {\left(1 + t_3\right)}^{2}}{-2 - t_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (exp (- x)))
        (t_1 (fmod (exp x) (sqrt (cos x))))
        (t_2 (* t_1 t_0))
        (t_3 (/ t_1 (exp x))))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0)))
     t_0
     (/ (- 1.0 (pow (+ 1.0 t_3) 2.0)) (- -2.0 t_3)))))

C

double code(double x) {
	double t_0 = exp(-x);
	double t_1 = fmod(exp(x), sqrt(cos(x)));
	double t_2 = t_1 * t_0;
	double t_3 = t_1 / exp(x);
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_0;
	} else {
		tmp = (1.0 - pow((1.0 + t_3), 2.0)) / (-2.0 - t_3);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = exp(-x)
    t_1 = mod(exp(x), sqrt(cos(x)))
    t_2 = t_1 * t_0
    t_3 = t_1 / exp(x)
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_0
    else
        tmp = (1.0d0 - ((1.0d0 + t_3) ** 2.0d0)) / ((-2.0d0) - t_3)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.exp(-x)
	t_1 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_2 = t_1 * t_0
	t_3 = t_1 / math.exp(x)
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_0
	else:
		tmp = (1.0 - math.pow((1.0 + t_3), 2.0)) / (-2.0 - t_3)
	return tmp

Julia

function code(x)
	t_0 = exp(Float64(-x))
	t_1 = rem(exp(x), sqrt(cos(x)))
	t_2 = Float64(t_1 * t_0)
	t_3 = Float64(t_1 / exp(x))
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 - (Float64(1.0 + t_3) ^ 2.0)) / Float64(-2.0 - t_3));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$1 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[Exp[x], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$0, N[(N[(1.0 - N[Power[N[(1.0 + t$95$3), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(-2.0 - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := e^{-x}\\ t_2 := t_0 \cdot t_1\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;{\left(e^{0.3333333333333333}\right)}^{\left(\left(\log \log \left(e^{t_0}\right) - x\right) \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (exp (- x)))
        (t_2 (* t_0 t_1)))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0)))
     t_1
     (pow (exp 0.3333333333333333) (* (- (log (log (exp t_0))) x) 3.0)))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = exp(-x);
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_1;
	} else {
		tmp = pow(exp(0.3333333333333333), ((log(log(exp(t_0))) - x) * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = exp(-x)
    t_2 = t_0 * t_1
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_1
    else
        tmp = exp(0.3333333333333333d0) ** ((log(log(exp(t_0))) - x) * 3.0d0)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = math.exp(-x)
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_1
	else:
		tmp = math.pow(math.exp(0.3333333333333333), ((math.log(math.log(math.exp(t_0))) - x) * 3.0))
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_1;
	else
		tmp = exp(0.3333333333333333) ^ Float64(Float64(log(log(exp(t_0))) - x) * 3.0);
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$1, N[Power[N[Exp[0.3333333333333333], $MachinePrecision], N[(N[(N[Log[N[Log[N[Exp[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - x), $MachinePrecision] * 3.0), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

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

Alternative 4: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := e^{-x}\\ t_2 := t_0 \cdot t_1\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\log \left(e^{t_0}\right)}{e^{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (exp (- x)))
        (t_2 (* t_0 t_1)))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0))) t_1 (/ (log (exp t_0)) (exp x)))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = exp(-x);
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_1;
	} else {
		tmp = log(exp(t_0)) / exp(x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = exp(-x)
    t_2 = t_0 * t_1
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_1
    else
        tmp = log(exp(t_0)) / exp(x)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = math.exp(-x)
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_1
	else:
		tmp = math.log(math.exp(t_0)) / math.exp(x)
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_1;
	else
		tmp = Float64(log(exp(t_0)) / exp(x));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$1, N[(N[Log[N[Exp[t$95$0], $MachinePrecision]], $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 63.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := e^{-x}\\ t_2 := t_0 \cdot t_1\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{t_0}{e^{x}}\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (exp (- x)))
        (t_2 (* t_0 t_1)))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0)))
     t_1
     (+ (+ 1.0 (/ t_0 (exp x))) -1.0))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = exp(-x);
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_1;
	} else {
		tmp = (1.0 + (t_0 / exp(x))) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = exp(-x)
    t_2 = t_0 * t_1
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_1
    else
        tmp = (1.0d0 + (t_0 / exp(x))) + (-1.0d0)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = math.exp(-x)
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_1
	else:
		tmp = (1.0 + (t_0 / math.exp(x))) + -1.0
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(1.0 + Float64(t_0 / exp(x))) + -1.0);
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$1, N[(N[(1.0 + N[(t$95$0 / N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 63.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := e^{-x}\\ t_2 := t_0 \cdot t_1\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{e^{x}}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (exp (- x)))
        (t_2 (* t_0 t_1)))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0))) t_1 (/ 1.0 (/ (exp x) t_0)))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = exp(-x);
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (exp(x) / t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = exp(-x)
    t_2 = t_0 * t_1
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_1
    else
        tmp = 1.0d0 / (exp(x) / t_0)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = math.exp(-x)
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_1
	else:
		tmp = 1.0 / (math.exp(x) / t_0)
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(exp(x) / t_0));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$1, N[(1.0 / N[(N[Exp[x], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 7: 63.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(e^{x}\right) \bmod \left(\sqrt{\cos x}\right)\right)\\ t_1 := e^{-x}\\ t_2 := t_0 \cdot t_1\\ \mathbf{if}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{e^{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fmod (exp x) (sqrt (cos x))))
        (t_1 (exp (- x)))
        (t_2 (* t_0 t_1)))
   (if (or (<= t_2 0.0) (not (<= t_2 2.0))) t_1 (/ t_0 (exp x)))))

C

double code(double x) {
	double t_0 = fmod(exp(x), sqrt(cos(x)));
	double t_1 = exp(-x);
	double t_2 = t_0 * t_1;
	double tmp;
	if ((t_2 <= 0.0) || !(t_2 <= 2.0)) {
		tmp = t_1;
	} else {
		tmp = t_0 / exp(x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = mod(exp(x), sqrt(cos(x)))
    t_1 = exp(-x)
    t_2 = t_0 * t_1
    if ((t_2 <= 0.0d0) .or. (.not. (t_2 <= 2.0d0))) then
        tmp = t_1
    else
        tmp = t_0 / exp(x)
    end if
    code = tmp
end function

Python

def code(x):
	t_0 = math.fmod(math.exp(x), math.sqrt(math.cos(x)))
	t_1 = math.exp(-x)
	t_2 = t_0 * t_1
	tmp = 0
	if (t_2 <= 0.0) or not (t_2 <= 2.0):
		tmp = t_1
	else:
		tmp = t_0 / math.exp(x)
	return tmp

Julia

function code(x)
	t_0 = rem(exp(x), sqrt(cos(x)))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_0 * t_1)
	tmp = 0.0
	if ((t_2 <= 0.0) || !(t_2 <= 2.0))
		tmp = t_1;
	else
		tmp = Float64(t_0 / exp(x));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[With[{TMP1 = N[Exp[x], $MachinePrecision], TMP2 = N[Sqrt[N[Cos[x], $MachinePrecision]], $MachinePrecision]}, Mod[Abs[TMP1], Abs[TMP2]] * Sign[TMP1]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2.0]], $MachinePrecision]], t$95$1, N[(t$95$0 / N[Exp[x], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 61.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ e^{3 \cdot \log \left(1 + \mathsf{expm1}\left(x \cdot -0.3333333333333333\right)\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (exp (* 3.0 (log (+ 1.0 (expm1 (* x -0.3333333333333333)))))))

C

double code(double x) {
	return exp((3.0 * log((1.0 + expm1((x * -0.3333333333333333))))));
}

Java

public static double code(double x) {
	return Math.exp((3.0 * Math.log((1.0 + Math.expm1((x * -0.3333333333333333))))));
}

Python

def code(x):
	return math.exp((3.0 * math.log((1.0 + math.expm1((x * -0.3333333333333333))))))

Julia

function code(x)
	return exp(Float64(3.0 * log(Float64(1.0 + expm1(Float64(x * -0.3333333333333333))))))
end

Wolfram

code[x_] := N[Exp[N[(3.0 * N[Log[N[(1.0 + N[(Exp[N[(x * -0.3333333333333333), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 9: 61.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ e^{-x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (exp (- x)))

C

double code(double x) {
	return exp(-x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = exp(-x)
end function

Java

public static double code(double x) {
	return Math.exp(-x);
}

Python

def code(x):
	return math.exp(-x)

Julia

function code(x)
	return exp(Float64(-x))
end

MATLAB

function tmp = code(x)
	tmp = exp(-x);
end

Wolfram

code[x_] := N[Exp[(-x)], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x)
  :name "expfmod (used to be hard to sample)"
  :precision binary64
  (* (fmod (exp x) (sqrt (cos x))) (exp (- x))))