Details

Time bar (total: 42.5s)

sample798.0ms

Algorithm
intervals
Results
314.0ms66×body10240exit
257.0ms70×body1280valid
72.0ms48×body640valid
23.0ms26×body320valid
22.0ms90×body80valid
11.0ms22×body160valid

simplify34.0ms

Counts
1 → 1
Iterations
IterNodes
done8
08

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b
(expm1 (sin (expm1 a)))
0.4b
(sin (expm1 a))
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite11.0ms

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 insert-posit16 add-log-exp
2×expm1-udef
1×expm1-log1p sin-diff
Counts
4 → 43
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)

series245.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
135.0ms
(expm1 (sin (expm1 a)))
94.0ms
(sin (expm1 a))
14.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts
55 → 55
Iterations
IterNodes
done5000
52343
4983
3411
2204
1118
074

prune440.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(sin (expm1 a))
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×sin-diff expm1-udef
Counts
4 → 41
Calls
4 calls:
2.0ms
(sin (expm1 a))
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series101.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sin (expm1 a))
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.1s

Counts
53 → 53
Iterations
IterNodes
done5000
73494
62077
51016
4465
3217
2108
173
046

prune553.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.6b

localize132.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
37.3b
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×*-un-lft-identity add-cube-cbrt
11×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 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 → 73
Calls
4 calls:
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)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series228.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (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)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.6s

Counts
85 → 85
Iterations
IterNodes
done5001
42186
3806
2378
1174
093

prune1.1s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 31.4b

localize113.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
37.3b
(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.4b
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod pow1/3
Counts
4 → 42
Calls
4 calls:
6.0ms
(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
0.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series228.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
3.0ms
(fmod (atan2 (expm1 (* (* (* (cbrt (sin (expm1 a))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.5s

Counts
54 → 54
Iterations
IterNodes
done5002
52653
4947
3448
2217
1113
068

prune655.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 31.3b

regimes811.0ms

Accuracy

0% (2.0b remaining)

Error of 33.3b against oracle of 31.3b and baseline of 33.3b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample25.4s

Algorithm
intervals
Results
13.1s2530×body10240exit
7.5s2264×body1280valid
2.9s1619×body640valid
768.0ms2827×body80valid
694.0ms858×body320valid
214.0ms427×body160valid
26.0ms3×body5120valid
7.0ms2×body2560valid