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)

sample40.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	62×	body	1024	valid
7.0ms	130×	body	128	valid
6.0ms	44×	body	512	valid
3.0ms	9×	body	2048	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (2.7%)

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

Error

30.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.1b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.4b	(log.f64 (+.f64 N 1))

rewrite60.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

30.3b

Rules

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

Counts

2 → 44

Calls

2 calls:

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

Compiler

Compiled 607 to 404 computations (33.4% saved)

series101.0ms (2.8%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

57.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
25.0ms	(log.f64 (+.f64 N 1))

Compiler

Compiled 502 to 409 computations (18.5% saved)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4920	794
1	4920	794

prune53.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Error

0.0b

Counts

63 → 3

Compiler

Compiled 750 to 475 computations (36.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
0.3b	(/.f64 1/2 (*.f64 N N))
0.4b	(/.f64 1/3 (pow.f64 N 3))
11.4b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))))

rewrite257.0ms (7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`times-frac_binary64_84`
49×	`add-sqr-sqrt_binary64_100`
47×	`*-un-lft-identity_binary64_78`
35×	`add-cube-cbrt_binary64_113`
14×	`add-exp-log_binary64_116` `cancel-sign-sub-inv_binary64_44`
13×	`associate-/r*_binary64_22`
12×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
11×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
8×	`associate-+r+_binary64_10`
6×	`div-inv_binary64_75` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`div-exp_binary64_129`
4×	`pow1_binary64_139` `distribute-lft-out--_binary64_30` `unpow3_binary64_144` `cube-mult_binary64_108` `sqr-pow_binary64_50`
3×	`frac-add_binary64_86` `distribute-lft-out_binary64_29` `cbrt-undiv_binary64_112`
2×	`diff-log_binary64_170` `sum-log_binary64_169` `frac-sub_binary64_87` `flip3--_binary64_82` `flip--_binary64_53` `sub-neg_binary64_71` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`flip3-+_binary64_81` `flip-+_binary64_52` `associate-+r-_binary64_12` `+-commutative_binary64_8` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`

Counts

4 → 140

Calls

4 calls:

41.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))))
12.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
5.0ms	(/.f64 1/3 (pow.f64 N 3))
4.0ms	(/.f64 1/2 (*.f64 N N))

Compiler

Compiled 3338 to 2324 computations (30.4% saved)

series169.0ms (4.6%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

54.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))))
47.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
29.0ms	(/.f64 1/3 (pow.f64 N 3))
25.0ms	(/.f64 1/2 (*.f64 N N))

Compiler

Compiled 676 to 570 computations (15.7% saved)

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4963	2387
1	4963	2387

prune177.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Error

0.0b

Counts

162 → 4

Compiler

Compiled 3177 to 2229 computations (29.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.3b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite60.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

2 → 60

Calls

2 calls:

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

Compiler

Compiled 810 to 553 computations (31.7% saved)

series96.0ms (2.6%)

Error

0.0b

Counts

2 → 17

Calls

2 calls:

49.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
36.0ms	(/.f64 (+.f64 N 1) N)

Compiler

Compiled 362 to 315 computations (13% saved)

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5148	1053

prune56.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	77	4	81

Error

0.0b

Counts

81 → 4

Compiler

Compiled 905 to 644 computations (28.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 1 (/.f64 1 N)))
0.1b	(sqrt.f64 (+.f64 1 (/.f64 1 N)))
2.3b	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))
2.3b	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))

rewrite130.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`*-un-lft-identity_binary64_78`
20×	`sqrt-prod_binary64_94`
16×	`log-prod_binary64_164`
12×	`add-sqr-sqrt_binary64_100`
10×	`pow1_binary64_139` `add-cube-cbrt_binary64_113`
8×	`sqrt-div_binary64_95` `distribute-lft-out_binary64_29`
6×	`log-pow_binary64_167` `add-exp-log_binary64_116`
4×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `log-div_binary64_165` `flip-+_binary64_52` `div-inv_binary64_75` `add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
2×	`rem-log-exp_binary64_119` `rem-sqrt-square_binary64_91`

Counts

4 → 76

Calls

4 calls:

7.0ms	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))
7.0ms	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))
7.0ms	(sqrt.f64 (+.f64 1 (/.f64 1 N)))
6.0ms	(sqrt.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 1724 to 1515 computations (12.1% saved)

series158.0ms (4.3%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

39.0ms	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))
35.0ms	(log.f64 (sqrt.f64 (+.f64 1 (/.f64 1 N))))
22.0ms	(sqrt.f64 (+.f64 1 (/.f64 1 N)))
22.0ms	(sqrt.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 1596 to 1413 computations (11.5% saved)

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5046	1582

prune123.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Error

0.0b

Counts

116 → 4

Compiler

Compiled 2172 to 1832 computations (15.7% saved)

regimes106.0ms (2.9%)

Accuracy

Total 0.1b remaining (70.8%)

Threshold costs 0.1b (70.8%)

Compiler

Compiled 800 to 638 computations (20.3% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	87	68
1	87	68

end0.0ms (0%)

sample1.6s (44.7%)

Algorithm

1×

intervals

Results

442.0ms	1934×	body	1024	valid
246.0ms	4274×	body	128	valid
146.0ms	1012×	body	512	valid
91.0ms	244×	body	2048	valid
47.0ms	536×	body	256	valid

Compiler

Compiled 444 to 356 computations (19.8% saved)

Details

analyze2.0ms (0.1%)

sample40.0ms (1.1%)

simplify100.0ms (2.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite60.0ms (1.6%)

series101.0ms (2.8%)

simplify75.0ms (2.1%)

prune53.0ms (1.4%)

localize10.0ms (0.3%)

rewrite257.0ms (7%)

series169.0ms (4.6%)

simplify96.0ms (2.6%)

prune177.0ms (4.8%)

localize5.0ms (0.1%)

rewrite60.0ms (1.6%)

series96.0ms (2.6%)

simplify61.0ms (1.7%)

prune56.0ms (1.5%)

localize7.0ms (0.2%)

rewrite130.0ms (3.5%)

series158.0ms (4.3%)

simplify74.0ms (2%)

prune123.0ms (3.4%)

regimes106.0ms (2.9%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (44.7%)

Profiling