Details

Time bar (total: 4.7s)

sample34.0ms

Algorithm
intervals
Results
9.0ms273×body80nan
8.0ms256×body80valid

simplify20.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp difference-of-squares
Counts
1 → 16
Calls
1 calls:
11.0ms
(sqrt (- 1.0 (* x x)))

series81.0ms

Counts
1 → 3
Calls
1 calls:
81.0ms
(sqrt (- 1.0 (* x x)))

simplify838.0ms

Counts
19 → 19

prune106.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0b
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
54×add-sqr-sqrt
52×associate-*r*
32×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
20×unpow-prod-down
12×add-exp-log
9×unswap-sqr
8×unpow2 sqr-pow
7×add-cbrt-cube
4×pow1 prod-exp add-log-exp
3×associate-*r/ div-exp associate-*l*
2×cbrt-unprod
1×cbrt-undiv +-commutative pow-to-exp flip3-+ pow-prod-down frac-add pow-exp sum-log *-commutative flip-+ div-inv
Counts
2 → 92
Calls
2 calls:
31.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
22.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

series532.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
440.0ms
(+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

simplify753.0ms

Counts
98 → 98

prune296.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify621.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
666.0ms8000×body80valid
263.0ms7966×body80nan