Details

Time bar (total: 34.7s)

sample874.0ms

Algorithm
intervals
Results
482.0ms80×body10240exit
203.0ms68×body1280valid
54.0ms48×body640valid
34.0ms15×body160valid
20.0ms95×body80valid
17.0ms30×body320valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done8
08

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize148.0ms

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)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
Counts
4 → 28
Calls
4 calls:
1.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms
(expm1 (sin (expm1 a)))
6.0ms
(sin (expm1 a))
31.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series163.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms
(expm1 (sin (expm1 a)))
145.0ms
(sin (expm1 a))
13.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify1.7s

Counts
40 → 40
Iterations
IterNodes
done5000
84003
71217
6519
5217
484
355
244
139
035

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.1b

localize55.0ms

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)

rewrite18.0ms

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×add-cbrt-cube 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 → 69
Calls
4 calls:
1.0ms
(cbrt (sin (expm1 a)))
1.0ms
(cbrt (sin (expm1 a)))
14.0ms
(* (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)

series724.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (sin (expm1 a)))
243.0ms
(cbrt (sin (expm1 a)))
231.0ms
(* (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)

simplify2.3s

Counts
81 → 81
Iterations
IterNodes
done5000
2499
1120
063

prune695.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 30.6b

localize61.0ms

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)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log add-log-exp
3×pow1/3
Counts
4 → 40
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)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

series486.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
178.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
141.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms
(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)

simplify898.0ms

Counts
52 → 52
Iterations
IterNodes
done5001
4884
3234
292
142
030

prune607.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 30.6b

localize92.0ms

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 (* (* (log (exp (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)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log add-log-exp
3×pow1/3
Counts
4 → 40
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 (* (* (log (exp (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)

series483.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
147.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
149.0ms
(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
8.0ms
(fmod (* (* (log (exp (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)

simplify2.1s

Counts
52 → 52
Iterations
IterNodes
done5000
41458
3336
2122
149
033

prune344.0ms

Pruning

30 alts after pruning (27 fresh and 3 done)

Merged error: 30.6b

regimes636.0ms

Accuracy

0% (1.9b remaining)

Error of 33.4b against oracle of 31.5b and baseline of 33.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done15
115
013

end0.0ms

sample21.9s

Algorithm
intervals
Results
10.9s2619×body10240exit
7.0s2315×body1280valid
2.0s1623×body640valid
586.0ms2825×body80valid
503.0ms810×body320valid
432.0ms3×body5120valid
151.0ms423×body160valid
4.0ms1×body2560valid