Details

Time bar (total: 9.9s)

sample139.0ms

Algorithm
intervals
Results
61.0ms100×body2560valid
25.0ms89×body1280valid
15.0ms262×body80nan
8.0ms34×body640valid
3.0ms20×body320valid
1.0msbody160valid
0.0msbody80valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11411
22511
33111
43611
done3611

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize34.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (- 1.0 (* ti ti)))
2.4b
(- 1.0 (sqrt (- 1.0 (* ti ti))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
*-un-lft-identity sqrt-prod
add-log-exp
pow1 add-cube-cbrt difference-of-squares
flip3-- add-cbrt-cube sqrt-div add-exp-log flip--
rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
2 → 31
Calls
2 calls:
10.0ms
(sqrt (- 1.0 (* ti ti)))
24.0ms
(- 1.0 (sqrt (- 1.0 (* ti ti))))

series257.0ms

Counts
2 → 6
Calls
2 calls:
128.0ms
(sqrt (- 1.0 (* ti ti)))
129.0ms
(- 1.0 (sqrt (- 1.0 (* ti ti))))

simplify834.0ms

Counts
37 → 37
Iterations

Useful iterations: done (832.0ms)

IterNodesCost
093525
1222478
2919448
done5001442

prune221.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 59.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt 1.0) ti))
0.0b
(* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti)))
0.0b
(sqrt (- (sqrt 1.0) ti))
5.6b
(- 1.0 (* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×sqrt-prod
18×*-un-lft-identity
16×sqrt-div
10×pow1 add-cube-cbrt
associate-*r*
associate-*l*
add-cbrt-cube add-exp-log add-log-exp
flip3-- flip--
frac-times sqrt-pow1 flip3-+ pow1/2 flip-+ difference-of-squares unswap-sqr
pow-prod-down
rem-sqrt-square associate-*l/ associate-*r/ distribute-lft-out distribute-lft-out--
sub-neg sqrt-unprod diff-log prod-exp *-commutative cbrt-unprod
Counts
4 → 88
Calls
4 calls:
20.0ms
(sqrt (+ (sqrt 1.0) ti))
115.0ms
(* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti)))
22.0ms
(sqrt (- (sqrt 1.0) ti))
10.0ms
(- 1.0 (* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti))))

series786.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (+ (sqrt 1.0) ti))
277.0ms
(* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti)))
125.0ms
(sqrt (- (sqrt 1.0) ti))
252.0ms
(- 1.0 (* (sqrt (+ (sqrt 1.0) ti)) (sqrt (- (sqrt 1.0) ti))))

simplify1.3s

Counts
100 → 100
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01711668
14001445
215521372
done50001370

prune632.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.1b

regimes161.0ms

Accuracy

0% (0.1b remaining)

Error of 59.4b against oracle of 59.2b and baseline of 59.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01519
11819
done1819

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.5s3194×body2560valid
863.0ms2509×body1280valid
849.0ms8104×body80nan
407.0ms1244×body640valid
109.0ms632×body320valid
37.0ms306×body160valid
12.0ms111×body80valid
2.0msbody5120valid