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)

sample38.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	57×	body	1024	valid
8.0ms	139×	body	128	valid
6.0ms	38×	body	512	valid
3.0ms	8×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify166.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 28.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.6b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.7b	(log.f64 (+.f64 N 1))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_77`
11×	`log-prod_binary64_160`
7×	`pow1_binary64_135` `add-sqr-sqrt_binary64_98`
5×	`add-cube-cbrt_binary64_109` `log-pow_binary64_163`
4×	`associate--l+_binary64_16` `distribute-lft-out--_binary64_31` `log-div_binary64_161`
3×	`add-exp-log_binary64_112` `associate--r+_binary64_15`
2×	`add-cbrt-cube_binary64_110` `associate--l-_binary64_17` `add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_115` `sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166`

Counts

2 → 40

Calls

2 calls:

7.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series81.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
26.0ms	(log.f64 (+.f64 N 1))

simplify104.0ms (3%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4866	648
1	4866	648

prune58.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.1b

Counts

47 → 4

Compiler

Compiled 653 to 433 computations (33.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
2.7b	(log.f64 (+.f64 N 1))
2.7b	(log.f64 (+.f64 N 1))
2.7b	(log.f64 (+.f64 N 1))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`log-prod_binary64_160`
21×	`*-un-lft-identity_binary64_77`
11×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
8×	`associate--l+_binary64_16`
7×	`add-exp-log_binary64_112` `pow1_binary64_135` `distribute-lft-in_binary64_28` `distribute-rgt-in_binary64_29`
6×	`add-log-exp_binary64_113` `log-div_binary64_161` `associate--r+_binary64_15`
5×	`distribute-lft-out_binary64_30`
4×	`add-cbrt-cube_binary64_110`
3×	`rem-log-exp_binary64_115` `flip-+_binary64_51` `flip3-+_binary64_80` `log-pow_binary64_163`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166`

Counts

4 → 71

Calls

4 calls:

8.0ms	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
4.0ms	(log.f64 (+.f64 N 1))
4.0ms	(log.f64 (+.f64 N 1))
3.0ms	(log.f64 (+.f64 N 1))

series186.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
24.0ms	(log.f64 (+.f64 N 1))
22.0ms	(log.f64 (+.f64 N 1))
22.0ms	(log.f64 (+.f64 N 1))

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5389	1362

prune119.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.1b

Counts

87 → 5

Compiler

Compiled 2481 to 1553 computations (37.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
2.7b	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
2.7b	(log.f64 (cbrt.f64 (+.f64 N 1)))
21.0b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))

rewrite65.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64_135`
41×	`*-un-lft-identity_binary64_77`
37×	`log-pow_binary64_163`
28×	`cbrt-div_binary64_106`
26×	`log-prod_binary64_160`
20×	`log-div_binary64_161`
18×	`distribute-lft-out_binary64_30`
16×	`distribute-lft-out--_binary64_31`
15×	`flip-+_binary64_51` `flip3-+_binary64_80`
14×	`associate--l+_binary64_16`
13×	`add-sqr-sqrt_binary64_98`
12×	`cbrt-prod_binary64_105`
11×	`add-cube-cbrt_binary64_109`
8×	`add-exp-log_binary64_112` `frac-times_binary64_87` `associate-+l-_binary64_14` `associate-+r+_binary64_11`
7×	`pow-prod-down_binary64_145` `pow1/3_binary64_156`
5×	`add-log-exp_binary64_113`
4×	`add-cbrt-cube_binary64_110` `associate-l/_binary64_22` `associate-r/_binary64_21`
3×	`rem-log-exp_binary64_115` `associate--r+_binary64_15`
2×	`associate--l-_binary64_17` `pow-sqr_binary64_50` `sub-neg_binary64_70` `pow-prod-up_binary64_144` `diff-log_binary64_166` `sum-log_binary64_165`
1×	`pow2_binary64_155` `associate-+l+_binary64_12` `pow-plus_binary64_137` `flip--_binary64_52` `+-commutative_binary64_9` `associate-+r-_binary64_13` `difference-of-squares_binary64_46` `prod-exp_binary64_123` `flip3--_binary64_81`

Counts

4 → 119

Calls

4 calls:

24.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))
10.0ms	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
9.0ms	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
4.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))

series313.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1)))) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N)))
71.0ms	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 N))
63.0ms	(log.f64 (*.f64 (cbrt.f64 (+.f64 N 1)) (cbrt.f64 (+.f64 N 1))))
54.0ms	(log.f64 (cbrt.f64 (+.f64 N 1)))

simplify78.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4840	2258
1	4840	2258

prune171.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Merged error: 0.1b

Counts

136 → 5

Compiler

Compiled 2951 to 2168 computations (26.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_77`
24×	`times-frac_binary64_83`
19×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
16×	`log-prod_binary64_160`
7×	`add-exp-log_binary64_112` `distribute-lft-out_binary64_30`
4×	`add-cbrt-cube_binary64_110` `associate-/l*_binary64_24`
3×	`associate-/r*_binary64_23` `pow1_binary64_135`
2×	`rem-log-exp_binary64_115` `add-log-exp_binary64_113` `div-exp_binary64_125` `associate-/l/_binary64_26` `div-inv_binary64_74`
1×	`flip-+_binary64_51` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `log-div_binary64_161` `clear-num_binary64_76` `log-pow_binary64_163` `frac-2neg_binary64_88`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series106.0ms (3%)

Counts

2 → 6

Calls

2 calls:

60.0ms	(/.f64 (+.f64 N 1) N)
46.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5305	940

prune51.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	66	5	71

Merged error: 0.1b

Counts

71 → 5

Compiler

Compiled 785 to 527 computations (32.9% saved)

regimes104.0ms (3%)

Compiler: Compiled 714 to 571 computations (20% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	56
1	61	56

end0.0ms (0%)

sample1.6s (46.2%)

Algorithm

1×

intervals

Results

515.0ms	2112×	body	1024	valid
256.0ms	4176×	body	128	valid
153.0ms	952×	body	512	valid
106.0ms	264×	body	2048	valid
47.0ms	496×	body	256	valid

Compiler

Compiled 373 to 296 computations (20.6% saved)

Details

analyze2.0ms (0.1%)

sample38.0ms (1.1%)

simplify166.0ms (4.7%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite13.0ms (0.4%)

series81.0ms (2.3%)

simplify104.0ms (3%)

prune58.0ms (1.7%)

localize14.0ms (0.4%)

rewrite26.0ms (0.7%)

series186.0ms (5.3%)

simplify67.0ms (1.9%)

prune119.0ms (3.4%)

localize12.0ms (0.3%)

rewrite65.0ms (1.8%)

series313.0ms (8.9%)

simplify78.0ms (2.2%)

prune171.0ms (4.9%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series106.0ms (3%)

simplify76.0ms (2.2%)

prune51.0ms (1.5%)

regimes104.0ms (3%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (46.2%)

Profiling