Details

Time bar (total: 37.7s)

sample732.0ms

Algorithm
intervals
Results
345.0ms80×body10240exit
182.0ms68×body1280valid
51.0ms48×body640valid
18.0ms95×body80valid
17.0ms30×body320valid
5.0ms15×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done8
08

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.2b
(sin (expm1 a))
36.7b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
2×expm1-udef
1×expm1-log1p sin-diff
Counts
4 → 39
Calls
4 calls:
0.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
6.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series247.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
113.0ms
(expm1 (sin (expm1 a)))
84.0ms
(sin (expm1 a))
47.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.9s

Counts
51 → 51
Iterations
IterNodes
done5001
31239
2311
1114
070

prune867.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (sin (expm1 a)))
0.4b
(cbrt (sin (expm1 a)))
0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
36.7b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×pow1
8×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
1.0ms
(cbrt (sin (expm1 a)))
1.0ms
(cbrt (sin (expm1 a)))
12.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
0.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series608.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(cbrt (sin (expm1 a)))
200.0ms
(cbrt (sin (expm1 a)))
217.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify1.2s

Counts
89 → 89
Iterations
IterNodes
done5001
2738
1203
097

prune764.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 30.6b

localize91.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
Counts
4 → 48
Calls
4 calls:
7.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series504.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
158.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
152.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
4.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify3.4s

Counts
60 → 60
Iterations
IterNodes
done5001
54488
4862
3257
299
146
034

prune661.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 30.5b

localize116.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.8b
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

series566.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
195.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
208.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
15.0ms
(fmod (* (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (expm1 (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)

simplify4.0s

Counts
60 → 60
Iterations
IterNodes
done5000
42947
3516
2163
164
042

prune432.0ms

Pruning

28 alts after pruning (25 fresh and 3 done)

Merged error: 30.5b

regimes739.0ms

Accuracy

0% (2.0b remaining)

Error of 33.4b against oracle of 31.4b and baseline of 33.4b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done14
114
013

end0.0ms

sample20.8s

Algorithm
intervals
Results
10.4s2619×body10240exit
6.3s2315×body1280valid
1.7s1623×body640valid
1.3s2825×body80valid
527.0ms810×body320valid
174.0ms423×body160valid
19.0ms3×body5120valid
2.0ms1×body2560valid