Details

Time bar (total: 14.9s)

sample104.0ms

Algorithm
intervals
Results
32.0ms268×body160nan
25.0ms574×body80nan
14.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done12
212
111
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
26.9b
(sqrt (- (* x x) 1.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×add-cube-cbrt sqrt-prod add-log-exp
3×pow1 fma-def
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 flip-+ flip-- distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
29.0ms
(+ x (sqrt (- (* x x) 1.0)))
18.0ms
(sqrt (- (* x x) 1.0))

series153.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(+ x (sqrt (- (* x x) 1.0)))
60.0ms
(sqrt (- (* x x) 1.0))

simplify1.6s

Counts
41 → 41
Iterations
IterNodes
done5000
32088
2660
1231
094

prune173.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
9×associate-*r*
7×associate-*l* add-cube-cbrt
6×pow1
4×frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp unswap-sqr
3×fma-def flip3-- pow-prod-down flip--
2×expm1-log1p-u sqrt-pow1 pow1/2 associate-*l/ associate-*r/ log1p-expm1-u difference-of-squares
1×+-commutative sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 60
Calls
2 calls:
6.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
57.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series465.0ms

Counts
2 → 6
Calls
2 calls:
194.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
271.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.3s

Counts
66 → 66
Iterations
IterNodes
done5000
33839
21125
1386
0156

prune323.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (- x (sqrt 1.0))))
0.5b
(cbrt (sqrt (- x (sqrt 1.0))))
0.5b
(cbrt (sqrt (- x (sqrt 1.0))))
0.6b
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
87×cbrt-prod
80×add-sqr-sqrt
67×sqrt-prod
42×*-un-lft-identity
22×add-cube-cbrt
18×cbrt-div sqrt-div swap-sqr difference-of-squares
12×associate-*r* associate-*l*
11×pow1
9×flip3-- pow1/3 flip-- distribute-lft-out-- unswap-sqr
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 142
Calls
4 calls:
5.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
5.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
6.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
52.0ms
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
283.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
239.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
249.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
418.0ms
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))

simplify3.8s

Counts
154 → 154
Iterations
IterNodes
done5000
34959
21367
1511
0210

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.2s16309×body80nan
909.0ms7780×body160nan
632.0ms8000×body80valid