Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample46.0ms (1.7%)

Algorithm

1×

intervals

Results

18.0ms	78×	body	1024	valid
8.0ms	120×	body	128	valid
7.0ms	13×	body	256	valid
5.0ms	37×	body	512	valid
3.0ms	8×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify97.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.5b	(log.f64 (+.f64 N 1))
2.5b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_78`
11×	`log-prod_binary64_164`
8×	`add-sqr-sqrt_binary64_100` `pow1_binary64_139`
6×	`add-cube-cbrt_binary64_113` `log-pow_binary64_167`
4×	`distribute-lft-out--_binary64_30` `associate--l+_binary64_15` `log-div_binary64_165` `cancel-sign-sub-inv_binary64_44`
3×	`associate--r+_binary64_14` `add-exp-log_binary64_116`
2×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `distribute-lft-out_binary64_29` `associate--l-_binary64_16` `flip3-+_binary64_81`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `rem-log-exp_binary64_119` `difference-of-squares_binary64_47` `sub-neg_binary64_71`

Counts

2 → 44

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series42.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
13.0ms	(log.f64 (+.f64 N 1))

simplify92.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4943	668
1	4943	668

prune52.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Merged error: 0.0b

Counts

51 → 3

Compiler

Compiled 652 to 425 computations (34.8% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1/3 (pow.f64 N 3))
0.5b	(/.f64 1/2 (*.f64 N N))
11.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite58.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`times-frac_binary64_84`
39×	`*-un-lft-identity_binary64_78`
36×	`add-sqr-sqrt_binary64_100`
32×	`add-cube-cbrt_binary64_113`
13×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
12×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
10×	`add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`associate-/l*_binary64_23`
5×	`div-exp_binary64_129`
4×	`cube-mult_binary64_108` `sqr-pow_binary64_50` `div-inv_binary64_75` `unpow3_binary64_144`
3×	`cbrt-undiv_binary64_112` `frac-sub_binary64_87` `distribute-lft-out--_binary64_30` `pow1_binary64_139`
2×	`diff-log_binary64_170` `frac-2neg_binary64_89` `difference-of-squares_binary64_47` `clear-num_binary64_77` `distribute-lft-out_binary64_29`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `flip3--_binary64_82` `associate--l+_binary64_15` `flip--_binary64_53` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

3 → 114

Calls

3 calls:

36.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
4.0ms	(/.f64 1/2 (*.f64 N N))

series56.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

24.0ms	(/.f64 1/3 (pow.f64 N 3))
17.0ms	(/.f64 1/2 (*.f64 N N))
15.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4955	1941
1	4955	1941

prune134.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Merged error: 0.0b

Counts

126 → 3

Compiler

Compiled 2554 to 1762 computations (31% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.7b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_78`
24×	`times-frac_binary64_84`
19×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
16×	`log-prod_binary64_164`
7×	`add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
4×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22` `pow1_binary64_139`
2×	`add-log-exp_binary64_117` `div-exp_binary64_129` `div-inv_binary64_75` `rem-log-exp_binary64_119` `associate-/l/_binary64_25`
1×	`cbrt-undiv_binary64_112` `flip-+_binary64_52` `frac-2neg_binary64_89` `log-div_binary64_165` `clear-num_binary64_77` `log-pow_binary64_167` `flip3-+_binary64_81`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series51.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(/.f64 (+.f64 N 1) N)
22.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5161	940

prune50.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

Compiler

Compiled 809 to 547 computations (32.4% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N)))
0.3b	(*.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))) (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
2.7b	(log.f64 (/.f64 (+.f64 N 1) N))
2.7b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_100`
43×	`*-un-lft-identity_binary64_78`
32×	`log-prod_binary64_164`
30×	`sqrt-prod_binary64_94`
29×	`add-cube-cbrt_binary64_113` `pow1_binary64_139`
24×	`times-frac_binary64_84`
12×	`add-exp-log_binary64_116`
11×	`swap-sqr_binary64_45`
9×	`sqrt-pow1_binary64_96` `log-pow_binary64_167` `pow1/2_binary64_158`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-cbrt-cube_binary64_114` `distribute-lft-out_binary64_29`
5×	`pow-prod-up_binary64_148`
4×	`add-log-exp_binary64_117` `rem-log-exp_binary64_119` `unswap-sqr_binary64_46`
3×	`pow-sqr_binary64_51` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149`
2×	`div-exp_binary64_129` `div-inv_binary64_75` `log-div_binary64_165`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `sqr-abs_binary64_93` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `sqrt-unprod_binary64_98` `rem-square-sqrt_binary64_90` `pow-plus_binary64_141`

Counts

4 → 123

Calls

4 calls:

8.0ms	(*.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))) (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
2.0ms	(sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N)))

series111.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N)))
27.0ms	(*.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))) (sqrt.f64 (log.f64 (/.f64 (+.f64 N 1) N))))
22.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
20.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify73.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4950	2042
1	4950	2042

prune134.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	135	4	139

Merged error: 0.0b

Counts

139 → 4

Compiler

Compiled 2433 to 1771 computations (27.2% saved)

regimes72.0ms (2.6%)

Compiler: Compiled 540 to 446 computations (17.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	47
1	50	47

end0.0ms (0%)

sample1.4s (52.9%)

Algorithm

1×

intervals

Results

450.0ms	1961×	body	1024	valid
250.0ms	4364×	body	128	valid
143.0ms	966×	body	512	valid
93.0ms	245×	body	2048	valid
45.0ms	464×	body	256	valid

Compiler

Compiled 301 to 248 computations (17.6% saved)

Details

analyze2.0ms (0.1%)

sample46.0ms (1.7%)

simplify97.0ms (3.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.5%)

series42.0ms (1.6%)

simplify92.0ms (3.4%)

prune52.0ms (1.9%)

localize10.0ms (0.4%)

rewrite58.0ms (2.1%)

series56.0ms (2.1%)

simplify65.0ms (2.4%)

prune134.0ms (4.9%)

localize5.0ms (0.2%)

rewrite16.0ms (0.6%)

series51.0ms (1.9%)

simplify57.0ms (2.1%)

prune50.0ms (1.8%)

localize7.0ms (0.3%)

rewrite30.0ms (1.1%)

series111.0ms (4.1%)

simplify73.0ms (2.7%)

prune134.0ms (4.9%)

regimes72.0ms (2.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample1.4s (52.9%)

Profiling