Details

Time bar (total: 40.1s)

sample937.0ms

Algorithm
intervals
Results
313.0ms66×body10240exit
230.0ms70×body1280valid
126.0ms48×body640valid
21.0ms26×body320valid
20.0ms90×body80valid
11.0ms22×body160valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done8
08

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize44.0ms

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)

rewrite13.0ms

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)

series307.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 (expm1 (sin (expm1 a))) (atan a))
147.0ms
(expm1 (sin (expm1 a)))
143.0ms
(sin (expm1 a))
14.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.8s

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

prune546.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.8b

localize78.0ms

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)

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×sin-diff expm1-udef
Counts
4 → 41
Calls
4 calls:
5.0ms
(sin (expm1 a))
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series125.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(sin (expm1 a))
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify4.2s

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

prune584.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.6b

localize135.0ms

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)

rewrite27.0ms

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:
24.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series216.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
5.0ms
(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
4.0ms
(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify2.4s

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

prune929.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 31.4b

localize104.0ms

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)

series240.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(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)

simplify2.6s

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

prune498.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 31.3b

regimes825.0ms

Accuracy

0% (2.0b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample22.4s

Algorithm
intervals
Results
11.7s2530×body10240exit
7.1s2264×body1280valid
2.0s1619×body640valid
637.0ms858×body320valid
538.0ms2827×body80valid
201.0ms427×body160valid
24.0ms3×body5120valid
4.0ms2×body2560valid