?

Average Error: 0.4 → 0.3
Time: 1.8min
Precision: binary64
Cost: 26368

?

\[\left(0 \leq u1 \land u1 \leq 1\right) \land \left(0 \leq u2 \land u2 \leq 1\right)\]
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5 \]
↓
\[\frac{\sqrt{-2 \cdot \log u1}}{6} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5 \]
(FPCore (u1 u2)
 :precision binary64
 (+
  (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))
  0.5))
↓
(FPCore (u1 u2)
 :precision binary64
 (+ (* (/ (sqrt (* -2.0 (log u1))) 6.0) (cos (* (* 2.0 PI) u2))) 0.5))
double code(double u1, double u2) {
	return (((1.0 / 6.0) * pow((-2.0 * log(u1)), 0.5)) * cos(((2.0 * ((double) M_PI)) * u2))) + 0.5;
}
↓
double code(double u1, double u2) {
	return ((sqrt((-2.0 * log(u1))) / 6.0) * cos(((2.0 * ((double) M_PI)) * u2))) + 0.5;
}

public static double code(double u1, double u2) {
	return (((1.0 / 6.0) * Math.pow((-2.0 * Math.log(u1)), 0.5)) * Math.cos(((2.0 * Math.PI) * u2))) + 0.5;
}
↓
public static double code(double u1, double u2) {
	return ((Math.sqrt((-2.0 * Math.log(u1))) / 6.0) * Math.cos(((2.0 * Math.PI) * u2))) + 0.5;
}

def code(u1, u2):
	return (((1.0 / 6.0) * math.pow((-2.0 * math.log(u1)), 0.5)) * math.cos(((2.0 * math.pi) * u2))) + 0.5
↓
def code(u1, u2):
	return ((math.sqrt((-2.0 * math.log(u1))) / 6.0) * math.cos(((2.0 * math.pi) * u2))) + 0.5

function code(u1, u2)
	return Float64(Float64(Float64(Float64(1.0 / 6.0) * (Float64(-2.0 * log(u1)) ^ 0.5)) * cos(Float64(Float64(2.0 * pi) * u2))) + 0.5)
end
↓
function code(u1, u2)
	return Float64(Float64(Float64(sqrt(Float64(-2.0 * log(u1))) / 6.0) * cos(Float64(Float64(2.0 * pi) * u2))) + 0.5)
end

function tmp = code(u1, u2)
	tmp = (((1.0 / 6.0) * ((-2.0 * log(u1)) ^ 0.5)) * cos(((2.0 * pi) * u2))) + 0.5;
end
↓
function tmp = code(u1, u2)
	tmp = ((sqrt((-2.0 * log(u1))) / 6.0) * cos(((2.0 * pi) * u2))) + 0.5;
end

code[u1_, u2_] := N[(N[(N[(N[(1.0 / 6.0), $MachinePrecision] * N[Power[N[(-2.0 * N[Log[u1], $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(2.0 * Pi), $MachinePrecision] * u2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 0.5), $MachinePrecision]
↓
code[u1_, u2_] := N[(N[(N[(N[Sqrt[N[(-2.0 * N[Log[u1], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 6.0), $MachinePrecision] * N[Cos[N[(N[(2.0 * Pi), $MachinePrecision] * u2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + 0.5), $MachinePrecision]

\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5
↓
\frac{\sqrt{-2 \cdot \log u1}}{6} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.4

    \[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5 \]

  2. Applied egg-rr0.3

    \[\leadsto \color{blue}{\frac{\sqrt{-2 \cdot \log u1}}{6}} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5 \]

Alternatives

Alternative 1
Error0.4
Cost26368
\[\left(\sqrt{-2 \cdot \log u1} \cdot 0.16666666666666666\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5 \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (u1 u2)
  :name "normal distribution"
  :precision binary64
  :pre (and (and (<= 0.0 u1) (<= u1 1.0)) (and (<= 0.0 u2) (<= u2 1.0)))
  (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))