Average Error: 16.6 → 12.6
Time: 6.4s
Precision: binary64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
↓
\[\pi \cdot \ell + \frac{-1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}} \]
(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))
↓
(FPCore (F l)
 :precision binary64
 (+ (* PI l) (/ -1.0 (/ F (/ (tan (* PI l)) F)))))
double code(double F, double l) {
	return (((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l)));
}
↓
double code(double F, double l) {
	return (((double) M_PI) * l) + (-1.0 / (F / (tan((((double) M_PI) * l)) / F)));
}

public static double code(double F, double l) {
	return (Math.PI * l) - ((1.0 / (F * F)) * Math.tan((Math.PI * l)));
}
↓
public static double code(double F, double l) {
	return (Math.PI * l) + (-1.0 / (F / (Math.tan((Math.PI * l)) / F)));
}

def code(F, l):
	return (math.pi * l) - ((1.0 / (F * F)) * math.tan((math.pi * l)))
↓
def code(F, l):
	return (math.pi * l) + (-1.0 / (F / (math.tan((math.pi * l)) / F)))

function code(F, l)
	return Float64(Float64(pi * l) - Float64(Float64(1.0 / Float64(F * F)) * tan(Float64(pi * l))))
end
↓
function code(F, l)
	return Float64(Float64(pi * l) + Float64(-1.0 / Float64(F / Float64(tan(Float64(pi * l)) / F))))
end

function tmp = code(F, l)
	tmp = (pi * l) - ((1.0 / (F * F)) * tan((pi * l)));
end
↓
function tmp = code(F, l)
	tmp = (pi * l) + (-1.0 / (F / (tan((pi * l)) / F)));
end

code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] - N[(N[(1.0 / N[(F * F), $MachinePrecision]), $MachinePrecision] * N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] + N[(-1.0 / N[(F / N[(N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell + \frac{-1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}

Error

Bits error versus F

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.6

    \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]

  2. Simplified16.3

    \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

  3. Applied egg-rr12.6

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \frac{1}{F}} \]

  4. Applied egg-rr12.6

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}} \]

  5. Final simplification12.6

    \[\leadsto \pi \cdot \ell + \frac{-1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}} \]

Reproduce

herbie shell --seed 2022166 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))