Falkner and Boettcher, Equation (22+)

Percentage Accurate: 98.5% → 100.0%

Time: 2.1s

Alternatives: 3

Speedup: N/A×

Specification

Math

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

FPCore

(FPCore (v)
 :precision binary64
 (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

C

double code(double v) {
	return 4.0 / (((3.0 * ((double) M_PI)) * (1.0 - (v * v))) * sqrt((2.0 - (6.0 * (v * v)))));
}

Java

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)))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (v)
 :precision binary64
 (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

C

double code(double v) {
	return 4.0 / (((3.0 * ((double) M_PI)) * (1.0 - (v * v))) * sqrt((2.0 - (6.0 * (v * v)))));
}

Java

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)))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 100.0% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{4}{\left(1 - v \cdot v\right) \cdot \left(\pi \cdot 3\right)}}{\sqrt{\mathsf{fma}\left(-6, v \cdot v, 2\right)}} \end{array} \]

FPCore

(FPCore (v)
 :precision binary64
 (/ (/ 4.0 (* (- 1.0 (* v v)) (* PI 3.0))) (sqrt (fma -6.0 (* v v) 2.0))))

C

double code(double v) {
	return (4.0 / ((1.0 - (v * v)) * (((double) M_PI) * 3.0))) / sqrt(fma(-6.0, (v * v), 2.0));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 98.5%

   \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-PI.f64 N/A

      \[\leadsto \frac{4}{\left(\left(3 \cdot \color{blue}{\mathsf{PI}\left(\right)}\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{4}{\left(\color{blue}{\left(3 \cdot \mathsf{PI}\left(\right)\right)} \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]

   6. lift--.f64 N/A

      \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \color{blue}{\left(1 - v \cdot v\right)}\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - \color{blue}{v \cdot v}\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]

   8. lift-sqrt.f64 N/A

      \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \color{blue}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}} \]

   9. lift--.f64 N/A

      \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{\color{blue}{2 - 6 \cdot \left(v \cdot v\right)}}} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - \color{blue}{6 \cdot \left(v \cdot v\right)}}} \]

   11. lift-*.f64 N/A

       \[\leadsto \frac{4}{\left(\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \color{blue}{\left(v \cdot v\right)}}} \]

   12. associate-/r* N/A

       \[\leadsto \color{blue}{\frac{\frac{4}{\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}} \]

   13. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{\frac{4}{\left(3 \cdot \mathsf{PI}\left(\right)\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}} \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{\frac{4}{\left(1 - v \cdot v\right) \cdot \left(\pi \cdot 3\right)}}{\sqrt{\mathsf{fma}\left(-6, v \cdot v, 2\right)}}} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot v\right) \cdot v\\ \frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{\frac{4 - t\_0 \cdot t\_0}{2 + t\_0}}} \end{array} \end{array} \]

FPCore

(FPCore (v)
 :precision binary64
 (let* ((t_0 (* (* 6.0 v) v)))
   (/
    4.0
    (*
     (* (* 3.0 PI) (- 1.0 (* v v)))
     (sqrt (/ (- 4.0 (* t_0 t_0)) (+ 2.0 t_0)))))))

C

double code(double v) {
	double t_0 = (6.0 * v) * v;
	return 4.0 / (((3.0 * ((double) M_PI)) * (1.0 - (v * v))) * sqrt(((4.0 - (t_0 * t_0)) / (2.0 + t_0))));
}

Java

public static double code(double v) {
	double t_0 = (6.0 * v) * v;
	return 4.0 / (((3.0 * Math.PI) * (1.0 - (v * v))) * Math.sqrt(((4.0 - (t_0 * t_0)) / (2.0 + t_0))));
}

Python

def code(v):
	t_0 = (6.0 * v) * v
	return 4.0 / (((3.0 * math.pi) * (1.0 - (v * v))) * math.sqrt(((4.0 - (t_0 * t_0)) / (2.0 + t_0))))

Julia

function code(v)
	t_0 = Float64(Float64(6.0 * v) * v)
	return Float64(4.0 / Float64(Float64(Float64(3.0 * pi) * Float64(1.0 - Float64(v * v))) * sqrt(Float64(Float64(4.0 - Float64(t_0 * t_0)) / Float64(2.0 + t_0)))))
end

MATLAB

function tmp = code(v)
	t_0 = (6.0 * v) * v;
	tmp = 4.0 / (((3.0 * pi) * (1.0 - (v * v))) * sqrt(((4.0 - (t_0 * t_0)) / (2.0 + t_0))));
end

Wolfram

code[v_] := Block[{t$95$0 = N[(N[(6.0 * v), $MachinePrecision] * v), $MachinePrecision]}, N[(4.0 / N[(N[(N[(3.0 * Pi), $MachinePrecision] * N[(1.0 - N[(v * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(N[(4.0 - N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(2.0 + t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 98.5%

   \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. flip-- N/A

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

   3. lower-/.f64 N/A

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

   4. metadata-eval N/A

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

   5. lower--.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. associate-*r* N/A

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

   10. lower-*.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. associate-*r* N/A

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

   15. lower-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. lower-+.f64 98.5

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

   18. lift-*.f64 N/A

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

   19. lift-*.f64 N/A

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

   20. associate-*r* N/A

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

   21. lower-*.f64 N/A

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

   22. lower-*.f64 98.5

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

4. Applied rewrites 98.5%

   \[\leadsto \frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{\color{blue}{\frac{4 - \left(\left(6 \cdot v\right) \cdot v\right) \cdot \left(\left(6 \cdot v\right) \cdot v\right)}{2 + \left(6 \cdot v\right) \cdot v}}}} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, N/A× speedup

Math

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

FPCore

(FPCore (v)
 :precision binary64
 (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

C

double code(double v) {
	return 4.0 / (((3.0 * ((double) M_PI)) * (1.0 - (v * v))) * sqrt((2.0 - (6.0 * (v * v)))));
}

Java

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)))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Derivation

1. Initial program 98.5%

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

Reproduce

herbie shell --seed 2025057 
(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)))))))