Average Error: 1.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{3 \cdot \pi} \cdot \frac{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}\]
\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}{3 \cdot \pi} \cdot \frac{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{1 - v \cdot v}
double code(double v) {
	return ((double) (4.0 / ((double) (((double) (((double) (3.0 * ((double) M_PI))) * ((double) (1.0 - ((double) (v * v)))))) * ((double) sqrt(((double) (2.0 - ((double) (6.0 * ((double) (v * v))))))))))));
}
↓
double code(double v) {
	return ((double) (((double) (1.0 / ((double) (3.0 * ((double) M_PI))))) * ((double) (((double) (4.0 / ((double) sqrt(((double) (2.0 - ((double) (6.0 * ((double) (v * v)))))))))) / ((double) (1.0 - ((double) (v * v))))))));
}

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. Using strategy rm

  3. Applied *-un-lft-identity1.0

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

  4. Applied times-frac0.0

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

  6. Applied *-un-lft-identity0.0

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

  7. Applied times-frac0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020122 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))