Average Error: 0.5 → 0.5
Time: 5.4s
Precision: binary64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1}{\frac{v \cdot v - 1}{1 - \left(v \cdot v\right) \cdot 5}}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1}{\frac{v \cdot v - 1}{1 - \left(v \cdot v\right) \cdot 5}}\right)
double code(double v) {
	return ((double) acos((((double) (1.0 - ((double) (5.0 * ((double) (v * v)))))) / ((double) (((double) (v * v)) - 1.0)))));
}
↓
double code(double v) {
	return ((double) acos((1.0 / (((double) (((double) (v * v)) - 1.0)) / ((double) (1.0 - ((double) (((double) (v * v)) * 5.0))))))));
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied clear-num0.5

    \[\leadsto \cos^{-1} \color{blue}{\left(\frac{1}{\frac{v \cdot v - 1}{1 - 5 \cdot \left(v \cdot v\right)}}\right)}\]

  4. Final simplification0.5

    \[\leadsto \cos^{-1} \left(\frac{1}{\frac{v \cdot v - 1}{1 - \left(v \cdot v\right) \cdot 5}}\right)\]

Reproduce

herbie shell --seed 2020199 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))