Average Error: 1.0 → 0.0
Time: 2.2s
Precision: binary64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]
↓
\[\frac{1.3333333333333333}{\sqrt{2 - \left(v \cdot v\right) \cdot 6} \cdot \left(\pi \cdot \left(1 - v \cdot v\right)\right)} \]
(FPCore (v)
 :precision binary64
 (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))
↓
(FPCore (v)
 :precision binary64
 (/
  1.3333333333333333
  (* (sqrt (- 2.0 (* (* v v) 6.0))) (* PI (- 1.0 (* v v))))))
double code(double v) {
	return 4.0 / (((3.0 * ((double) M_PI)) * (1.0 - (v * v))) * sqrt((2.0 - (6.0 * (v * v)))));
}
↓
double code(double v) {
	return 1.3333333333333333 / (sqrt((2.0 - ((v * v) * 6.0))) * (((double) M_PI) * (1.0 - (v * v))));
}

public static double code(double v) {
	return 4.0 / (((3.0 * Math.PI) * (1.0 - (v * v))) * Math.sqrt((2.0 - (6.0 * (v * v)))));
}
↓
public static double code(double v) {
	return 1.3333333333333333 / (Math.sqrt((2.0 - ((v * v) * 6.0))) * (Math.PI * (1.0 - (v * v))));
}

def code(v):
	return 4.0 / (((3.0 * math.pi) * (1.0 - (v * v))) * math.sqrt((2.0 - (6.0 * (v * v)))))
↓
def code(v):
	return 1.3333333333333333 / (math.sqrt((2.0 - ((v * v) * 6.0))) * (math.pi * (1.0 - (v * v))))

function code(v)
	return Float64(4.0 / Float64(Float64(Float64(3.0 * pi) * Float64(1.0 - Float64(v * v))) * sqrt(Float64(2.0 - Float64(6.0 * Float64(v * v))))))
end
↓
function code(v)
	return Float64(1.3333333333333333 / Float64(sqrt(Float64(2.0 - Float64(Float64(v * v) * 6.0))) * Float64(pi * Float64(1.0 - Float64(v * v)))))
end

function tmp = code(v)
	tmp = 4.0 / (((3.0 * pi) * (1.0 - (v * v))) * sqrt((2.0 - (6.0 * (v * v)))));
end
↓
function tmp = code(v)
	tmp = 1.3333333333333333 / (sqrt((2.0 - ((v * v) * 6.0))) * (pi * (1.0 - (v * v))));
end

code[v_] := N[(4.0 / N[(N[(N[(3.0 * Pi), $MachinePrecision] * N[(1.0 - N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(2.0 - N[(6.0 * N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[v_] := N[(1.3333333333333333 / N[(N[Sqrt[N[(2.0 - N[(N[(v * v), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(Pi * N[(1.0 - N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{1.3333333333333333}{\sqrt{2 - \left(v \cdot v\right) \cdot 6} \cdot \left(\pi \cdot \left(1 - v \cdot v\right)\right)}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{1.3333333333333333}{\sqrt{2 - \left(v \cdot v\right) \cdot 6} \cdot \left(\pi \cdot \left(1 - v \cdot v\right)\right)}} \]

  3. Final simplification0.0

    \[\leadsto \frac{1.3333333333333333}{\sqrt{2 - \left(v \cdot v\right) \cdot 6} \cdot \left(\pi \cdot \left(1 - v \cdot v\right)\right)} \]

Reproduce

herbie shell --seed 2022131 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))