Henrywood and Agarwal, Equation (9a)

Percentage Accurate: 80.7% → 88.1%

Time: 14.7s

Alternatives: 3

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * sqrt((1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    code = w0 * sqrt((1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))))
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * Math.sqrt((1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Python

def code(w0, M, D, h, l, d):
	return w0 * math.sqrt((1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))))

Julia

function code(w0, M, D, h, l, d)
	return Float64(w0 * sqrt(Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))))
end

MATLAB

function tmp = code(w0, M, D, h, l, d)
	tmp = w0 * sqrt((1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l))));
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := N[(w0 * N[Sqrt[N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * sqrt((1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    code = w0 * sqrt((1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))))
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * Math.sqrt((1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Python

def code(w0, M, D, h, l, d):
	return w0 * math.sqrt((1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))))

Julia

function code(w0, M, D, h, l, d)
	return Float64(w0 * sqrt(Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))))
end

MATLAB

function tmp = code(w0, M, D, h, l, d)
	tmp = w0 * sqrt((1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l))));
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := N[(w0 * N[Sqrt[N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} D_m = \left|D\right| \\ [w0, M, D_m, h, l, d] = \mathsf{sort}([w0, M, D_m, h, l, d])\\ \\ \begin{array}{l} t_0 := D\_m \cdot \frac{M}{d \cdot 2}\\ w0 \cdot \sqrt{1 - \left(t\_0 \cdot \frac{t\_0}{\ell}\right) \cdot h} \end{array} \end{array} \]

FPCore

D_m = (fabs.f64 D)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
(FPCore (w0 M D_m h l d)
 :precision binary64
 (let* ((t_0 (* D_m (/ M (* d 2.0)))))
   (* w0 (sqrt (- 1.0 (* (* t_0 (/ t_0 l)) h))))))

C

D_m = fabs(D);
assert(w0 < M && M < D_m && D_m < h && h < l && l < d);
double code(double w0, double M, double D_m, double h, double l, double d) {
	double t_0 = D_m * (M / (d * 2.0));
	return w0 * sqrt((1.0 - ((t_0 * (t_0 / l)) * h)));
}

Fortran

D_m = abs(d)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
real(8) function code(w0, m, d_m, h, l, d)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d_m
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d
    real(8) :: t_0
    t_0 = d_m * (m / (d * 2.0d0))
    code = w0 * sqrt((1.0d0 - ((t_0 * (t_0 / l)) * h)))
end function

Java

D_m = Math.abs(D);
assert w0 < M && M < D_m && D_m < h && h < l && l < d;
public static double code(double w0, double M, double D_m, double h, double l, double d) {
	double t_0 = D_m * (M / (d * 2.0));
	return w0 * Math.sqrt((1.0 - ((t_0 * (t_0 / l)) * h)));
}

Python

D_m = math.fabs(D)
[w0, M, D_m, h, l, d] = sort([w0, M, D_m, h, l, d])
def code(w0, M, D_m, h, l, d):
	t_0 = D_m * (M / (d * 2.0))
	return w0 * math.sqrt((1.0 - ((t_0 * (t_0 / l)) * h)))

Julia

D_m = abs(D)
w0, M, D_m, h, l, d = sort([w0, M, D_m, h, l, d])
function code(w0, M, D_m, h, l, d)
	t_0 = Float64(D_m * Float64(M / Float64(d * 2.0)))
	return Float64(w0 * sqrt(Float64(1.0 - Float64(Float64(t_0 * Float64(t_0 / l)) * h))))
end

MATLAB

D_m = abs(D);
w0, M, D_m, h, l, d = num2cell(sort([w0, M, D_m, h, l, d])){:}
function tmp = code(w0, M, D_m, h, l, d)
	t_0 = D_m * (M / (d * 2.0));
	tmp = w0 * sqrt((1.0 - ((t_0 * (t_0 / l)) * h)));
end

Wolfram

D_m = N[Abs[D], $MachinePrecision]
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
code[w0_, M_, D$95$m_, h_, l_, d_] := Block[{t$95$0 = N[(D$95$m * N[(M / N[(d * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(w0 * N[Sqrt[N[(1.0 - N[(N[(t$95$0 * N[(t$95$0 / l), $MachinePrecision]), $MachinePrecision] * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 82.5%

   \[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \]

3. Simplified 83.6%

   \[\leadsto \color{blue}{w0 \cdot \sqrt{1 - {\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2} \cdot \frac{h}{\ell}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 83.2%

      \[\leadsto w0 \cdot \sqrt{1 - {\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2} \cdot \color{blue}{\frac{1}{\frac{\ell}{h}}}} \]

   2. un-div-inv 83.6%

      \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\frac{{\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2}}{\frac{\ell}{h}}}} \]

   3. associate-/r* 83.6%

      \[\leadsto w0 \cdot \sqrt{1 - \frac{{\left(D \cdot \color{blue}{\frac{M}{2 \cdot d}}\right)}^{2}}{\frac{\ell}{h}}} \]

6. Applied egg-rr 83.6%

   \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\frac{{\left(D \cdot \frac{M}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}}} \]
7. Step-by-step derivation

   1. associate-/r/ 87.2%

      \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\frac{{\left(D \cdot \frac{M}{2 \cdot d}\right)}^{2}}{\ell} \cdot h}} \]

   2. associate-/r* 87.2%

      \[\leadsto w0 \cdot \sqrt{1 - \frac{{\left(D \cdot \color{blue}{\frac{\frac{M}{2}}{d}}\right)}^{2}}{\ell} \cdot h} \]

8. Simplified 87.2%

   \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\frac{{\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2}}{\ell} \cdot h}} \]
9. Step-by-step derivation

   1. unpow2 87.2%

      \[\leadsto w0 \cdot \sqrt{1 - \frac{\color{blue}{\left(D \cdot \frac{\frac{M}{2}}{d}\right) \cdot \left(D \cdot \frac{\frac{M}{2}}{d}\right)}}{\ell} \cdot h} \]

   2. associate-/l/ 87.2%

      \[\leadsto w0 \cdot \sqrt{1 - \frac{\left(D \cdot \color{blue}{\frac{M}{d \cdot 2}}\right) \cdot \left(D \cdot \frac{\frac{M}{2}}{d}\right)}{\ell} \cdot h} \]

   3. associate-/l/ 87.2%

      \[\leadsto w0 \cdot \sqrt{1 - \frac{\left(D \cdot \frac{M}{d \cdot 2}\right) \cdot \left(D \cdot \color{blue}{\frac{M}{d \cdot 2}}\right)}{\ell} \cdot h} \]

10. Applied egg-rr 87.2%

    \[\leadsto w0 \cdot \sqrt{1 - \frac{\color{blue}{\left(D \cdot \frac{M}{d \cdot 2}\right) \cdot \left(D \cdot \frac{M}{d \cdot 2}\right)}}{\ell} \cdot h} \]
11. Step-by-step derivation

    1. associate-/l* 89.9%

       \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\left(\left(D \cdot \frac{M}{d \cdot 2}\right) \cdot \frac{D \cdot \frac{M}{d \cdot 2}}{\ell}\right)} \cdot h} \]

12. Applied egg-rr 89.9%

    \[\leadsto w0 \cdot \sqrt{1 - \color{blue}{\left(\left(D \cdot \frac{M}{d \cdot 2}\right) \cdot \frac{D \cdot \frac{M}{d \cdot 2}}{\ell}\right)} \cdot h} \]
13. Add Preprocessing

Alternative 2: 70.3% accurate, 21.6× speedup

Math

\[\begin{array}{l} D_m = \left|D\right| \\ [w0, M, D_m, h, l, d] = \mathsf{sort}([w0, M, D_m, h, l, d])\\ \\ \begin{array}{l} \mathbf{if}\;M \leq 7.2 \cdot 10^{-70}:\\ \;\;\;\;w0\\ \mathbf{else}:\\ \;\;\;\;\frac{w0 \cdot D\_m}{D\_m}\\ \end{array} \end{array} \]

FPCore

D_m = (fabs.f64 D)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
(FPCore (w0 M D_m h l d)
 :precision binary64
 (if (<= M 7.2e-70) w0 (/ (* w0 D_m) D_m)))

C

D_m = fabs(D);
assert(w0 < M && M < D_m && D_m < h && h < l && l < d);
double code(double w0, double M, double D_m, double h, double l, double d) {
	double tmp;
	if (M <= 7.2e-70) {
		tmp = w0;
	} else {
		tmp = (w0 * D_m) / D_m;
	}
	return tmp;
}

Fortran

D_m = abs(d)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
real(8) function code(w0, m, d_m, h, l, d)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d_m
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d
    real(8) :: tmp
    if (m <= 7.2d-70) then
        tmp = w0
    else
        tmp = (w0 * d_m) / d_m
    end if
    code = tmp
end function

Java

D_m = Math.abs(D);
assert w0 < M && M < D_m && D_m < h && h < l && l < d;
public static double code(double w0, double M, double D_m, double h, double l, double d) {
	double tmp;
	if (M <= 7.2e-70) {
		tmp = w0;
	} else {
		tmp = (w0 * D_m) / D_m;
	}
	return tmp;
}

Python

D_m = math.fabs(D)
[w0, M, D_m, h, l, d] = sort([w0, M, D_m, h, l, d])
def code(w0, M, D_m, h, l, d):
	tmp = 0
	if M <= 7.2e-70:
		tmp = w0
	else:
		tmp = (w0 * D_m) / D_m
	return tmp

Julia

D_m = abs(D)
w0, M, D_m, h, l, d = sort([w0, M, D_m, h, l, d])
function code(w0, M, D_m, h, l, d)
	tmp = 0.0
	if (M <= 7.2e-70)
		tmp = w0;
	else
		tmp = Float64(Float64(w0 * D_m) / D_m);
	end
	return tmp
end

MATLAB

D_m = abs(D);
w0, M, D_m, h, l, d = num2cell(sort([w0, M, D_m, h, l, d])){:}
function tmp_2 = code(w0, M, D_m, h, l, d)
	tmp = 0.0;
	if (M <= 7.2e-70)
		tmp = w0;
	else
		tmp = (w0 * D_m) / D_m;
	end
	tmp_2 = tmp;
end

Wolfram

D_m = N[Abs[D], $MachinePrecision]
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
code[w0_, M_, D$95$m_, h_, l_, d_] := If[LessEqual[M, 7.2e-70], w0, N[(N[(w0 * D$95$m), $MachinePrecision] / D$95$m), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if M < 7.2000000000000004e-70

   1. Initial program 84.2%

      \[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{w0 \cdot \sqrt{1 - {\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2} \cdot \frac{h}{\ell}}} \]
   4. Add Preprocessing

   5. Taylor expanded in D around 0 78.6%

      \[\leadsto \color{blue}{w0} \]

   if 7.2000000000000004e-70 < M

   1. Initial program 77.2%

      \[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{w0 \cdot \sqrt{1 - {\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2} \cdot \frac{h}{\ell}}} \]
   4. Add Preprocessing

   5. Taylor expanded in D around inf 34.0%

      \[\leadsto w0 \cdot \sqrt{\color{blue}{{D}^{2} \cdot \left(\frac{1}{{D}^{2}} - 0.25 \cdot \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell}\right)}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 34.0%

         \[\leadsto w0 \cdot \sqrt{{D}^{2} \cdot \color{blue}{\left(\frac{1}{{D}^{2}} + \left(-0.25\right) \cdot \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell}\right)}} \]

      2. metadata-eval 34.0%

         \[\leadsto w0 \cdot \sqrt{{D}^{2} \cdot \left(\frac{1}{{D}^{2}} + \color{blue}{-0.25} \cdot \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell}\right)} \]

      3. associate-/l* 40.4%

         \[\leadsto w0 \cdot \sqrt{{D}^{2} \cdot \left(\frac{1}{{D}^{2}} + -0.25 \cdot \color{blue}{\left({M}^{2} \cdot \frac{h}{{d}^{2} \cdot \ell}\right)}\right)} \]

   7. Simplified 40.4%

      \[\leadsto w0 \cdot \sqrt{\color{blue}{{D}^{2} \cdot \left(\frac{1}{{D}^{2}} + -0.25 \cdot \left({M}^{2} \cdot \frac{h}{{d}^{2} \cdot \ell}\right)\right)}} \]

   8. Taylor expanded in w0 around 0 20.1%

      \[\leadsto \color{blue}{\left(D \cdot w0\right) \cdot \sqrt{-0.25 \cdot \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell} + \frac{1}{{D}^{2}}}} \]
   9. Step-by-step derivation

      1. associate-*l* 15.9%

         \[\leadsto \color{blue}{D \cdot \left(w0 \cdot \sqrt{-0.25 \cdot \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell} + \frac{1}{{D}^{2}}}\right)} \]

      2. fma-define 15.9%

         \[\leadsto D \cdot \left(w0 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(-0.25, \frac{{M}^{2} \cdot h}{{d}^{2} \cdot \ell}, \frac{1}{{D}^{2}}\right)}}\right) \]

      3. associate-/l* 17.6%

         \[\leadsto D \cdot \left(w0 \cdot \sqrt{\mathsf{fma}\left(-0.25, \color{blue}{{M}^{2} \cdot \frac{h}{{d}^{2} \cdot \ell}}, \frac{1}{{D}^{2}}\right)}\right) \]

      4. *-commutative 17.6%

         \[\leadsto D \cdot \left(w0 \cdot \sqrt{\mathsf{fma}\left(-0.25, {M}^{2} \cdot \frac{h}{\color{blue}{\ell \cdot {d}^{2}}}, \frac{1}{{D}^{2}}\right)}\right) \]

      5. associate-/r* 17.6%

         \[\leadsto D \cdot \left(w0 \cdot \sqrt{\mathsf{fma}\left(-0.25, {M}^{2} \cdot \color{blue}{\frac{\frac{h}{\ell}}{{d}^{2}}}, \frac{1}{{D}^{2}}\right)}\right) \]

   10. Simplified 17.6%

       \[\leadsto \color{blue}{D \cdot \left(w0 \cdot \sqrt{\mathsf{fma}\left(-0.25, {M}^{2} \cdot \frac{\frac{h}{\ell}}{{d}^{2}}, \frac{1}{{D}^{2}}\right)}\right)} \]

   11. Taylor expanded in M around 0 42.3%

       \[\leadsto D \cdot \color{blue}{\frac{w0}{D}} \]
   12. Step-by-step derivation

       1. associate-*r/ 49.3%

          \[\leadsto \color{blue}{\frac{D \cdot w0}{D}} \]

   13. Applied egg-rr 49.3%

       \[\leadsto \color{blue}{\frac{D \cdot w0}{D}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq 7.2 \cdot 10^{-70}:\\ \;\;\;\;w0\\ \mathbf{else}:\\ \;\;\;\;\frac{w0 \cdot D}{D}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.5% accurate, 216.0× speedup

Math

\[\begin{array}{l} D_m = \left|D\right| \\ [w0, M, D_m, h, l, d] = \mathsf{sort}([w0, M, D_m, h, l, d])\\ \\ w0 \end{array} \]

FPCore

D_m = (fabs.f64 D)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
(FPCore (w0 M D_m h l d) :precision binary64 w0)

C

D_m = fabs(D);
assert(w0 < M && M < D_m && D_m < h && h < l && l < d);
double code(double w0, double M, double D_m, double h, double l, double d) {
	return w0;
}

Fortran

D_m = abs(d)
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
real(8) function code(w0, m, d_m, h, l, d)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d_m
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d
    code = w0
end function

Java

D_m = Math.abs(D);
assert w0 < M && M < D_m && D_m < h && h < l && l < d;
public static double code(double w0, double M, double D_m, double h, double l, double d) {
	return w0;
}

Python

D_m = math.fabs(D)
[w0, M, D_m, h, l, d] = sort([w0, M, D_m, h, l, d])
def code(w0, M, D_m, h, l, d):
	return w0

Julia

D_m = abs(D)
w0, M, D_m, h, l, d = sort([w0, M, D_m, h, l, d])
function code(w0, M, D_m, h, l, d)
	return w0
end

MATLAB

D_m = abs(D);
w0, M, D_m, h, l, d = num2cell(sort([w0, M, D_m, h, l, d])){:}
function tmp = code(w0, M, D_m, h, l, d)
	tmp = w0;
end

Wolfram

D_m = N[Abs[D], $MachinePrecision]
NOTE: w0, M, D_m, h, l, and d should be sorted in increasing order before calling this function.
code[w0_, M_, D$95$m_, h_, l_, d_] := w0

Derivation

1. Initial program 82.5%

   \[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \]

3. Simplified 83.6%

   \[\leadsto \color{blue}{w0 \cdot \sqrt{1 - {\left(D \cdot \frac{\frac{M}{2}}{d}\right)}^{2} \cdot \frac{h}{\ell}}} \]
4. Add Preprocessing

5. Taylor expanded in D around 0 73.4%

   \[\leadsto \color{blue}{w0} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024148 
(FPCore (w0 M D h l d)
  :name "Henrywood and Agarwal, Equation (9a)"
  :precision binary64
  (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))