Details

Time bar (total: 27.9s)

sample97.0ms

Algorithm
intervals
Results
29.0ms321×body80valid
22.0ms356×body80nan

simplify14.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22110
33610
46210
513310
619110
737310
8154110
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.4b
(- (* y y) (* z z))
22.8b
(sqrt (- (* y y) (* z z)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div
3×flip3-- associate-*l* flip-- difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 54
Calls
3 calls:
40.0ms
(* x (sqrt (- (* y y) (* z z))))
24.0ms
(- (* y y) (* z z))
11.0ms
(sqrt (- (* y y) (* z z)))

series217.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(* x (sqrt (- (* y y) (* z z))))
42.0ms
(- (* y y) (* z z))
74.0ms
(sqrt (- (* y y) (* z z)))

simplify970.0ms

Counts
63 → 63
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
085765
1185697
2443613
31486613
done5001613

prune198.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* y y) (* z z))
2.4b
(- (* y y) (* z z))
22.8b
(sqrt (- (* y y) (* z z)))
22.8b
(sqrt (- (* y y) (* z z)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 58
Calls
4 calls:
13.0ms
(- (* y y) (* z z))
10.0ms
(- (* y y) (* z z))
16.0ms
(sqrt (- (* y y) (* z z)))
16.0ms
(sqrt (- (* y y) (* z z)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* y y) (* z z))
34.0ms
(- (* y y) (* z z))
64.0ms
(sqrt (- (* y y) (* z z)))
52.0ms
(sqrt (- (* y y) (* z z)))

simplify3.5s

Counts
70 → 70
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
055808
1120744
2301640
3975640
44860640
done5000640

prune317.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* y y) (* z z))
2.4b
(- (* y y) (* z z))
23.7b
(cbrt (- (* y y) (* z z)))
23.7b
(cbrt (- (* y y) (* z z)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-log-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div flip3-- add-cbrt-cube flip-- difference-of-squares
2×sub-neg pow1/3 diff-log
Counts
4 → 54
Calls
4 calls:
9.0ms
(- (* y y) (* z z))
9.0ms
(- (* y y) (* z z))
12.0ms
(cbrt (- (* y y) (* z z)))
7.0ms
(cbrt (- (* y y) (* z z)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* y y) (* z z))
37.0ms
(- (* y y) (* z z))
119.0ms
(cbrt (- (* y y) (* z z)))
119.0ms
(cbrt (- (* y y) (* z z)))

simplify3.8s

Counts
66 → 66
Iterations

Useful iterations: done (3.8s)

IterNodesCost
070860
1158840
2391716
31104702
44673694
done5001690

prune294.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes451.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 25.3b

bsearch218.0ms

Steps
ItersRangePoint
11
-8.501644981951623e-221
-2.751809256330958e-243
-2.794570820839951e-243

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21411
done1411

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.2s10075×body80valid
590.0ms10255×body80nan