exp-w (used to crash)

Percentage Accurate: 99.4% → 99.4%

Time: 13.4s

Alternatives: 9

Speedup: N/A×

• could not determine a ground truth

  1. w = 2.00000000000000007e154
  2. l = -2

Specification

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w) * (l ** exp(w))
end function

Java

public static double code(double w, double l) {
	return Math.exp(-w) * Math.pow(l, Math.exp(w));
}

Python

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))

Julia

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end

MATLAB

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end

Wolfram

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))

C

double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = exp(-w) * (l ** exp(w))
end function

Java

public static double code(double w, double l) {
	return Math.exp(-w) * Math.pow(l, Math.exp(w));
}

Python

def code(w, l):
	return math.exp(-w) * math.pow(l, math.exp(w))

Julia

function code(w, l)
	return Float64(exp(Float64(-w)) * (l ^ exp(w)))
end

MATLAB

function tmp = code(w, l)
	tmp = exp(-w) * (l ^ exp(w));
end

Wolfram

code[w_, l_] := N[(N[Exp[(-w)], $MachinePrecision] * N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{{\ell}^{\left(e^{w}\right)}}{e^{w}} \end{array} \]

FPCore

(FPCore (w l) :precision binary64 (/ (pow l (exp w)) (exp w)))

C

double code(double w, double l) {
	return pow(l, exp(w)) / exp(w);
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = (l ** exp(w)) / exp(w)
end function

Java

public static double code(double w, double l) {
	return Math.pow(l, Math.exp(w)) / Math.exp(w);
}

Python

def code(w, l):
	return math.pow(l, math.exp(w)) / math.exp(w)

Julia

function code(w, l)
	return Float64((l ^ exp(w)) / exp(w))
end

MATLAB

function tmp = code(w, l)
	tmp = (l ^ exp(w)) / exp(w);
end

Wolfram

code[w_, l_] := N[(N[Power[l, N[Exp[w], $MachinePrecision]], $MachinePrecision] / N[Exp[w], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 98.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -1:\\ \;\;\;\;e^{-w}\\ \mathbf{elif}\;w \leq 22:\\ \;\;\;\;e^{w} \cdot {\ell}^{\left(w + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;e^{w \cdot \log \ell - w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -1.0)
   (exp (- w))
   (if (<= w 22.0) (* (exp w) (pow l (+ w 1.0))) (exp (- (* w (log l)) w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -1.0) {
		tmp = exp(-w);
	} else if (w <= 22.0) {
		tmp = exp(w) * pow(l, (w + 1.0));
	} else {
		tmp = exp(((w * log(l)) - w));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-1.0d0)) then
        tmp = exp(-w)
    else if (w <= 22.0d0) then
        tmp = exp(w) * (l ** (w + 1.0d0))
    else
        tmp = exp(((w * log(l)) - w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -1.0) {
		tmp = Math.exp(-w);
	} else if (w <= 22.0) {
		tmp = Math.exp(w) * Math.pow(l, (w + 1.0));
	} else {
		tmp = Math.exp(((w * Math.log(l)) - w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -1.0:
		tmp = math.exp(-w)
	elif w <= 22.0:
		tmp = math.exp(w) * math.pow(l, (w + 1.0))
	else:
		tmp = math.exp(((w * math.log(l)) - w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -1.0)
		tmp = exp(Float64(-w));
	elseif (w <= 22.0)
		tmp = Float64(exp(w) * (l ^ Float64(w + 1.0)));
	else
		tmp = exp(Float64(Float64(w * log(l)) - w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -1.0)
		tmp = exp(-w);
	elseif (w <= 22.0)
		tmp = exp(w) * (l ^ (w + 1.0));
	else
		tmp = exp(((w * log(l)) - w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -1.0], N[Exp[(-w)], $MachinePrecision], If[LessEqual[w, 22.0], N[(N[Exp[w], $MachinePrecision] * N[Power[l, N[(w + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(N[(w * N[Log[l], $MachinePrecision]), $MachinePrecision] - w), $MachinePrecision]], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 98.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.0075:\\ \;\;\;\;e^{-w}\\ \mathbf{elif}\;w \leq 0.92:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(1 + \log \ell\right)\right)\\ \mathbf{else}:\\ \;\;\;\;e^{w \cdot \log \ell - w}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -0.0075)
   (exp (- w))
   (if (<= w 0.92)
     (* l (+ 1.0 (* w (+ 1.0 (log l)))))
     (exp (- (* w (log l)) w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.0075) {
		tmp = exp(-w);
	} else if (w <= 0.92) {
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	} else {
		tmp = exp(((w * log(l)) - w));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-0.0075d0)) then
        tmp = exp(-w)
    else if (w <= 0.92d0) then
        tmp = l * (1.0d0 + (w * (1.0d0 + log(l))))
    else
        tmp = exp(((w * log(l)) - w))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.0075) {
		tmp = Math.exp(-w);
	} else if (w <= 0.92) {
		tmp = l * (1.0 + (w * (1.0 + Math.log(l))));
	} else {
		tmp = Math.exp(((w * Math.log(l)) - w));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.0075:
		tmp = math.exp(-w)
	elif w <= 0.92:
		tmp = l * (1.0 + (w * (1.0 + math.log(l))))
	else:
		tmp = math.exp(((w * math.log(l)) - w))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.0075)
		tmp = exp(Float64(-w));
	elseif (w <= 0.92)
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(1.0 + log(l)))));
	else
		tmp = exp(Float64(Float64(w * log(l)) - w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.0075)
		tmp = exp(-w);
	elseif (w <= 0.92)
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	else
		tmp = exp(((w * log(l)) - w));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.0075], N[Exp[(-w)], $MachinePrecision], If[LessEqual[w, 0.92], N[(l * N[(1.0 + N[(w * N[(1.0 + N[Log[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[N[(N[(w * N[Log[l], $MachinePrecision]), $MachinePrecision] - w), $MachinePrecision]], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 98.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.0075:\\ \;\;\;\;e^{-w}\\ \mathbf{elif}\;w \leq 0.76:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(1 + \log \ell\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{\ell}^{w}}{e^{w}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -0.0075)
   (exp (- w))
   (if (<= w 0.76) (* l (+ 1.0 (* w (+ 1.0 (log l))))) (/ (pow l w) (exp w)))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -0.0075) {
		tmp = exp(-w);
	} else if (w <= 0.76) {
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	} else {
		tmp = pow(l, w) / exp(w);
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-0.0075d0)) then
        tmp = exp(-w)
    else if (w <= 0.76d0) then
        tmp = l * (1.0d0 + (w * (1.0d0 + log(l))))
    else
        tmp = (l ** w) / exp(w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -0.0075) {
		tmp = Math.exp(-w);
	} else if (w <= 0.76) {
		tmp = l * (1.0 + (w * (1.0 + Math.log(l))));
	} else {
		tmp = Math.pow(l, w) / Math.exp(w);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -0.0075:
		tmp = math.exp(-w)
	elif w <= 0.76:
		tmp = l * (1.0 + (w * (1.0 + math.log(l))))
	else:
		tmp = math.pow(l, w) / math.exp(w)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -0.0075)
		tmp = exp(Float64(-w));
	elseif (w <= 0.76)
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(1.0 + log(l)))));
	else
		tmp = Float64((l ^ w) / exp(w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -0.0075)
		tmp = exp(-w);
	elseif (w <= 0.76)
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	else
		tmp = (l ^ w) / exp(w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -0.0075], N[Exp[(-w)], $MachinePrecision], If[LessEqual[w, 0.76], N[(l * N[(1.0 + N[(w * N[(1.0 + N[Log[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[l, w], $MachinePrecision] / N[Exp[w], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 98.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -1:\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\ell}^{\left(w + 1\right)}}{e^{w}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (<= w -1.0) (exp (- w)) (/ (pow l (+ w 1.0)) (exp w))))

C

double code(double w, double l) {
	double tmp;
	if (w <= -1.0) {
		tmp = exp(-w);
	} else {
		tmp = pow(l, (w + 1.0)) / exp(w);
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if (w <= (-1.0d0)) then
        tmp = exp(-w)
    else
        tmp = (l ** (w + 1.0d0)) / exp(w)
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if (w <= -1.0) {
		tmp = Math.exp(-w);
	} else {
		tmp = Math.pow(l, (w + 1.0)) / Math.exp(w);
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if w <= -1.0:
		tmp = math.exp(-w)
	else:
		tmp = math.pow(l, (w + 1.0)) / math.exp(w)
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if (w <= -1.0)
		tmp = exp(Float64(-w));
	else
		tmp = Float64((l ^ Float64(w + 1.0)) / exp(w));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if (w <= -1.0)
		tmp = exp(-w);
	else
		tmp = (l ^ (w + 1.0)) / exp(w);
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[LessEqual[w, -1.0], N[Exp[(-w)], $MachinePrecision], N[(N[Power[l, N[(w + 1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[w], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 98.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.0075 \lor \neg \left(w \leq 5500000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(1 + w \cdot \left(1 + \log \ell\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.0075) (not (<= w 5500000.0)))
   (exp (- w))
   (* l (+ 1.0 (* w (+ 1.0 (log l)))))))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.0075) || !(w <= 5500000.0)) {
		tmp = exp(-w);
	} else {
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((w <= (-0.0075d0)) .or. (.not. (w <= 5500000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l * (1.0d0 + (w * (1.0d0 + log(l))))
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.0075) || !(w <= 5500000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l * (1.0 + (w * (1.0 + Math.log(l))));
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.0075) or not (w <= 5500000.0):
		tmp = math.exp(-w)
	else:
		tmp = l * (1.0 + (w * (1.0 + math.log(l))))
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.0075) || !(w <= 5500000.0))
		tmp = exp(Float64(-w));
	else
		tmp = Float64(l * Float64(1.0 + Float64(w * Float64(1.0 + log(l)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.0075) || ~((w <= 5500000.0)))
		tmp = exp(-w);
	else
		tmp = l * (1.0 + (w * (1.0 + log(l))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.0075], N[Not[LessEqual[w, 5500000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], N[(l * N[(1.0 + N[(w * N[(1.0 + N[Log[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 97.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;w \leq -0.68 \lor \neg \left(w \leq 5500000\right):\\ \;\;\;\;e^{-w}\\ \mathbf{else}:\\ \;\;\;\;\ell\\ \end{array} \end{array} \]

FPCore

(FPCore (w l)
 :precision binary64
 (if (or (<= w -0.68) (not (<= w 5500000.0))) (exp (- w)) l))

C

double code(double w, double l) {
	double tmp;
	if ((w <= -0.68) || !(w <= 5500000.0)) {
		tmp = exp(-w);
	} else {
		tmp = l;
	}
	return tmp;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((w <= (-0.68d0)) .or. (.not. (w <= 5500000.0d0))) then
        tmp = exp(-w)
    else
        tmp = l
    end if
    code = tmp
end function

Java

public static double code(double w, double l) {
	double tmp;
	if ((w <= -0.68) || !(w <= 5500000.0)) {
		tmp = Math.exp(-w);
	} else {
		tmp = l;
	}
	return tmp;
}

Python

def code(w, l):
	tmp = 0
	if (w <= -0.68) or not (w <= 5500000.0):
		tmp = math.exp(-w)
	else:
		tmp = l
	return tmp

Julia

function code(w, l)
	tmp = 0.0
	if ((w <= -0.68) || !(w <= 5500000.0))
		tmp = exp(Float64(-w));
	else
		tmp = l;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, l)
	tmp = 0.0;
	if ((w <= -0.68) || ~((w <= 5500000.0)))
		tmp = exp(-w);
	else
		tmp = l;
	end
	tmp_2 = tmp;
end

Wolfram

code[w_, l_] := If[Or[LessEqual[w, -0.68], N[Not[LessEqual[w, 5500000.0]], $MachinePrecision]], N[Exp[(-w)], $MachinePrecision], l]

Derivation

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1. Add Preprocessing

Alternative 8: 4.4% accurate, 305.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (w l) :precision binary64 1.0)

C

double code(double w, double l) {
	return 1.0;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = 1.0d0
end function

Java

public static double code(double w, double l) {
	return 1.0;
}

Python

def code(w, l):
	return 1.0

Julia

function code(w, l)
	return 1.0
end

MATLAB

function tmp = code(w, l)
	tmp = 1.0;
end

Wolfram

code[w_, l_] := 1.0

Derivation

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

Alternative 9: 56.9% accurate, 305.0× speedup

Math

\[\begin{array}{l} \\ \ell \end{array} \]

FPCore

(FPCore (w l) :precision binary64 l)

C

double code(double w, double l) {
	return l;
}

Fortran

real(8) function code(w, l)
    real(8), intent (in) :: w
    real(8), intent (in) :: l
    code = l
end function

Java

public static double code(double w, double l) {
	return l;
}

Python

def code(w, l):
	return l

Julia

function code(w, l)
	return l
end

MATLAB

function tmp = code(w, l)
	tmp = l;
end

Wolfram

code[w_, l_] := l

Derivation

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

Reproduce

herbie shell --seed 2024003 
(FPCore (w l)
  :name "exp-w (used to crash)"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))