Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)
double code(double v) {
	return ((double) (((double) (((double) (((double) sqrt(2.0)) / 4.0)) * ((double) sqrt(((double) (1.0 - ((double) (3.0 * ((double) (v * v)))))))))) * ((double) (1.0 - ((double) (v * v))))));
}
↓
double code(double v) {
	return ((double) (((double) (((double) (((double) sqrt(2.0)) / 4.0)) * ((double) log(((double) exp(((double) sqrt(((double) (1.0 - ((double) (3.0 * ((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 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020128 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))