(cos (/ (acos (/ r (sqrt (* (* (- q) q) q)))) 3))

Average Error: 3.4 → 3.4

Time: 3.2s

Precision: binary64

Math

\[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(\left(-q\right) \cdot q\right) \cdot q}}\right)}{3}\right)\]

↓

\[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(\left(-q\right) \cdot q\right) \cdot q}}\right)}{3}\right)\]

Error

Bits error versus r

Bits error versus q

Derivation

1. Initial program 3.4

   \[\cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(\left(-q\right) \cdot q\right) \cdot q}}\right)}{3}\right)\]

2. Final simplification 3.4

   \[\leadsto \cos \left(\frac{\cos^{-1} \left(\frac{r}{\sqrt{\left(\left(-q\right) \cdot q\right) \cdot q}}\right)}{3}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (r q)
  :name "(cos (/ (acos (/ r (sqrt (* (* (- q) q) q)))) 3))"
  :precision binary64
  (cos (/ (acos (/ r (sqrt (* (* (neg q) q) q)))) 3.0)))