Details

Time bar (total: 16.6s)

sample155.0ms

Algorithm
intervals
Results
69.0ms257×body160nan
39.0ms491×body80nan
23.0ms256×body80valid

simplify6.3s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize13.0ms

Local error

Found 2 expressions with local error:

30.5b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity sqrt-prod
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip-- distribute-lft-out
Counts
2 → 32
Calls
2 calls:
Slowest
18.0ms
(+ x (sqrt (- (* x x) 1)))
8.0ms
(sqrt (- (* x x) 1))

series107.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
55.0ms
(+ x (sqrt (- (* x x) 1)))
52.0ms
(sqrt (- (* x x) 1))

simplify1.3s

Counts
38 → 38

prune268.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ -1/8 (* x (* x x)))
0.1b
(* x (* x x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-cbrt-cube add-exp-log
6×add-sqr-sqrt prod-exp cbrt-unprod
5×*-un-lft-identity pow-prod-up add-cube-cbrt
3×cbrt-undiv times-frac div-exp associate-*l* pow-prod-down associate-/l*
2×insert-posit16 add-log-exp
1×pow2 clear-num associate-/r* frac-2neg pow-plus cube-unmult associate-*r* pow-sqr *-commutative div-inv unswap-sqr
Counts
2 → 49
Calls
2 calls:
Slowest
16.0ms
(* x (* x x))
13.0ms
(/ -1/8 (* x (* x x)))

series142.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(/ -1/8 (* x (* x x)))
67.0ms
(* x (* x x))

simplify3.1s

Counts
55 → 55

prune528.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s7724×body160nan
1.3s16384×body80nan
927.0ms8000×body80valid