Average Error: 1.0 → 0.0
Time: 3.3s
Precision: binary64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{3 \cdot \left(\pi \cdot \left(1 - v \cdot v\right)\right)} \cdot e^{\log \left(\frac{4}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}\right)}\]
\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 \left(\pi \cdot \left(1 - v \cdot v\right)\right)} \cdot e^{\log \left(\frac{4}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}\right)}
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) (((double) M_PI) * ((double) (1.0 - ((double) (v * v)))))))))) * ((double) exp(((double) log(((double) (4.0 / ((double) sqrt(((double) (2.0 - ((double) (v * ((double) (v * 6.0))))))))))))))));
}

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. Simplified0.0

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

  6. Simplified0.0

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

  8. Applied add-exp-log0.0

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

  9. Applied add-exp-log0.0

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

  10. Applied div-exp0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020184 
(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)))))))