Details

Time bar (total: 1.9s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1

sample30.0ms

Algorithm
intervals
Results
12.0ms59×body2048valid
5.0ms38×body1024valid
5.0ms136×body128valid
2.0ms18×body512valid
0.0ms5×body256valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
07111
17111

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.7b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.6b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×*-un-lft-identity_binary64 add-log-exp_binary64 add-sqr-sqrt_binary64
1×sub-neg_binary64 pow1_binary64 flip3--_binary64 diff-log_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 flip--_binary64 diff-atan_binary64
Counts
1 → 14
Calls
1 calls:
4.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series24.0ms

Counts
1 → 3
Calls
1 calls:
24.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify105.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
04851291
14851291

prune16.0ms

Filtered
12 candidates to 17 candidates (-41.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New16117
Fresh000
Picked011
Done000
Total16218

Merged error: 0.5b

Counts
18 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(*.f64 N (+.f64 N 1))
0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
4×pow1_binary64 associate-*r*_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-*l*_binary64
2×add-log-exp_binary64 associate-*r/_binary64
1×pow-prod-down_binary64 flip3-+_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 flip-+_binary64 *-commutative_binary64
Counts
2 → 30
Calls
2 calls:
7.0ms
(*.f64 N (+.f64 N 1))
1.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series68.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(*.f64 N (+.f64 N 1))
13.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify69.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
05424383

prune34.0ms

Filtered
26 candidates to 36 candidates (-38.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New32436
Fresh000
Picked011
Done101
Total33538

Merged error: 0.5b

Counts
38 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
12.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
12.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
21×pow1_binary64
14×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×pow1/2_binary64 sqrt-pow1_binary64
8×swap-sqr_binary64
6×associate-*r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64
5×pow-prod-up_binary64
4×add-log-exp_binary64 unswap-sqr_binary64
3×pow-prod-down_binary64 pow-sqr_binary64
2×rem-sqrt-square_binary64
1×cbrt-unprod_binary64 rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 82
Calls
4 calls:
1.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
7.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series116.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
17.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
40.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
46.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051561485

prune72.0ms

Filtered
46 candidates to 94 candidates (-104.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh123
Picked011
Done011
Total91899

Merged error: 0.4b

Counts
99 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
12.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
12.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
12.7b
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-pow1_binary64
45×pow1_binary64
30×pow1/2_binary64 pow-prod-up_binary64
16×add-sqr-sqrt_binary64
14×sqrt-prod_binary64
9×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
7×pow-prod-down_binary64
6×associate-*l*_binary64 pow-sqr_binary64
4×add-log-exp_binary64
3×cbrt-unprod_binary64 rem-sqrt-square_binary64 prod-exp_binary64
2×swap-sqr_binary64 sqrt-unprod_binary64 unswap-sqr_binary64
1×associate-*r*_binary64 *-commutative_binary64
Counts
4 → 85
Calls
4 calls:
18.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
2.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series156.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
51.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
39.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
42.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
048931397
148931397

prune81.0ms

Filtered
47 candidates to 97 candidates (-106.4%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh055
Picked011
Done022
Total978105

Merged error: 0.4b

Counts
105 → 8

regimes22.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11013

end0.0ms

sample895.0ms

Algorithm
intervals
Results
411.0ms2114×body2048valid
166.0ms4152×body128valid
136.0ms981×body1024valid
56.0ms504×body512valid
19.0ms249×body256valid

Profiling

Loading profile data...