Details

analyze1.1s (7.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample193.0ms (1.3%)

Algorithm

1×

intervals

Results

49.0ms	84×	body	1024	valid
35.0ms	43×	body	1024	nan
27.0ms	47×	body	2048	valid
17.0ms	43×	body	512	valid
14.0ms	78×	body	128	overflowed
11.0ms	24×	body	512	nan
7.0ms	73×	body	128	valid
5.0ms	10×	body	512	invalid
3.0ms	3×	body	1024	invalid
3.0ms	11×	body	256	nan
2.0ms	9×	body	256	invalid
2.0ms	37×	body	128	nan
2.0ms	9×	body	256	valid
1.0ms	1×	body	2048	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify139.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

prune2.0ms (0%)

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: 31.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
30×	`*-un-lft-identity_binary64_78`
26×	`pow-unpow_binary64_155`
21×	`add-cube-cbrt_binary64_113`
20×	`unpow-prod-down_binary64_157`
18×	`times-frac_binary64_84`
9×	`sqr-pow_binary64_50` `difference-of-squares_binary64_47`
7×	`cancel-sign-sub-inv_binary64_44`
5×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `div-inv_binary64_75` `pow-pow_binary64_150` `distribute-lft-out_binary64_29`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `sub-neg_binary64_71`

Counts

3 → 85

Calls

3 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
3.0ms	(pow.f64 x (/.f64 1 n))

series247.0ms (1.7%)

Counts

3 → 18

Calls

3 calls:

109.0ms	(pow.f64 x (/.f64 1 n))
106.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
32.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5485	1848

prune140.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	5	104

Merged error: 1.3b

Counts

104 → 5

Compiler

Compiled 2149 to 1484 computations (30.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(log.f64 (+.f64 x 1))
1.8b	(log.f64 (+.f64 x 1))
2.0b	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
10.5b	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_116`
17×	`*-un-lft-identity_binary64_78`
16×	`add-log-exp_binary64_117`
13×	`add-sqr-sqrt_binary64_100`
11×	`add-cube-cbrt_binary64_113`
9×	`add-cbrt-cube_binary64_114` `flip-+_binary64_52` `frac-sub_binary64_87` `times-frac_binary64_84` `associate-/l*_binary64_23` `flip3-+_binary64_81`
8×	`frac-add_binary64_86` `unpow-prod-down_binary64_157` `log-prod_binary64_164` `associate-*r/_binary64_20` `pow1_binary64_139`
6×	`div-exp_binary64_129` `log-div_binary64_165`
4×	`diff-log_binary64_170` `log-pow_binary64_167` `sum-log_binary64_169`
3×	`prod-exp_binary64_127` `cancel-sign-sub-inv_binary64_44`
2×	`associate-+l-_binary64_13` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `unpow2_binary64_143` `sqr-pow_binary64_50` `rem-log-exp_binary64_119` `distribute-lft-out_binary64_29` `div-sub_binary64_83` `associate--l-_binary64_16`
1×	`cbrt-unprod_binary64_111` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `frac-2neg_binary64_89` `associate--l+_binary64_15` `div-inv_binary64_75` `associate--r+_binary64_14` `flip--_binary64_53` `associate-/r*_binary64_22` `difference-of-squares_binary64_47` `clear-num_binary64_77` `sub-div_binary64_85` `sub-neg_binary64_71`

Counts

4 → 100

Calls

4 calls:

19.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
7.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
3.0ms	(log.f64 (+.f64 x 1))
3.0ms	(log.f64 (+.f64 x 1))

series301.0ms (2.1%)

Counts

4 → 18

Calls

4 calls:

185.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
99.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
9.0ms	(log.f64 (+.f64 x 1))
8.0ms	(log.f64 (+.f64 x 1))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4959	4634
1	4959	4634

prune291.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 1.2b

Counts

123 → 11

Compiler

Compiled 6139 to 3738 computations (39.1% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(cbrt.f64 (-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))))))
10.5b	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
10.5b	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
10.5b	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))

rewrite127.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-log-exp_binary64_117`
36×	`frac-sub_binary64_87`
32×	`frac-add_binary64_86` `associate-*r/_binary64_20`
27×	`flip-+_binary64_52` `flip3-+_binary64_81`
16×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
12×	`cbrt-div_binary64_110` `diff-log_binary64_170` `sum-log_binary64_169`
9×	`cancel-sign-sub-inv_binary64_44`
8×	`add-cube-cbrt_binary64_113`
6×	`associate-+l-_binary64_13` `log-div_binary64_165` `div-sub_binary64_83` `associate--l-_binary64_16`
5×	`cbrt-prod_binary64_109`
4×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116` `difference-of-squares_binary64_47` `sub-div_binary64_85` `pow1_binary64_139`
3×	`associate--l+_binary64_15` `associate--r+_binary64_14` `sub-neg_binary64_71`
1×	`pow1/3_binary64_160`

Counts

4 → 124

Calls

4 calls:

25.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
20.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
20.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
17.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))))))

series874.0ms (6.1%)

Counts

4 → 24

Calls

4 calls:

349.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))))))
182.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
172.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))
171.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))))

simplify148.0ms (1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5270	14604

prune1.4s (9.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	146	13	159

Merged error: 1.2b

Counts

159 → 13

Compiler

Compiled 22205 to 13294 computations (40.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.9b	(log.f64 (cbrt.f64 (+.f64 x 1)))
1.9b	(log.f64 (cbrt.f64 (+.f64 x 1)))
2.0b	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
14.0b	(-.f64 (+.f64 (/.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x 1)))) (log.f64 (cbrt.f64 (+.f64 x 1)))) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)))))

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
16×	`add-log-exp_binary64_117`
15×	`add-sqr-sqrt_binary64_100`
14×	`log-prod_binary64_164`
13×	`add-cube-cbrt_binary64_113`
9×	`add-cbrt-cube_binary64_114` `flip-+_binary64_52` `frac-sub_binary64_87` `times-frac_binary64_84` `associate-/l*_binary64_23` `flip3-+_binary64_81`
8×	`frac-add_binary64_86` `unpow-prod-down_binary64_157` `cbrt-prod_binary64_109` `associate-*r/_binary64_20` `pow1_binary64_139`
6×	`cbrt-div_binary64_110` `div-exp_binary64_129` `log-div_binary64_165` `log-pow_binary64_167`
4×	`diff-log_binary64_170` `sum-log_binary64_169`
3×	`prod-exp_binary64_127` `cancel-sign-sub-inv_binary64_44`
2×	`associate-+l-_binary64_13` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `associate-+r-_binary64_12` `cbrt-undiv_binary64_112` `unpow2_binary64_143` `pow1/3_binary64_160` `sqr-pow_binary64_50` `rem-log-exp_binary64_119` `distribute-lft-out_binary64_29` `div-sub_binary64_83` `associate--l-_binary64_16`
1×	`cbrt-unprod_binary64_111` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `frac-2neg_binary64_89` `associate--l+_binary64_15` `div-inv_binary64_75` `associate--r+_binary64_14` `flip--_binary64_53` `associate-/r*_binary64_22` `difference-of-squares_binary64_47` `clear-num_binary64_77` `sub-div_binary64_85` `sub-neg_binary64_71`

Counts

4 → 108

Calls

4 calls:

25.0ms	(-.f64 (+.f64 (/.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x 1)))) (log.f64 (cbrt.f64 (+.f64 x 1)))) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)))))
7.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
4.0ms	(log.f64 (cbrt.f64 (+.f64 x 1)))
4.0ms	(log.f64 (cbrt.f64 (+.f64 x 1)))

series326.0ms (2.3%)

Counts

4 → 18

Calls

4 calls:

186.0ms	(-.f64 (+.f64 (/.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 x 1)))) (log.f64 (cbrt.f64 (+.f64 x 1)))) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n)))) (+.f64 (/.f64 (log.f64 x) n) (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)))))
103.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
19.0ms	(log.f64 (cbrt.f64 (+.f64 x 1)))
18.0ms	(log.f64 (cbrt.f64 (+.f64 x 1)))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4950	5202
1	4950	5202

prune365.0ms (2.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	126	13	139

Merged error: 1.2b

Counts

139 → 13

Compiler

Compiled 7039 to 4556 computations (35.3% saved)

regimes760.0ms (5.3%)

Compiler: Compiled 8517 to 5866 computations (31.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	137	216
1	137	216

end0.0ms (0%)

sample7.6s (52.4%)

Algorithm

1×

intervals

Results

1.5s	2755×	body	1024	valid
1.1s	1447×	body	1024	nan
988.0ms	1704×	body	2048	valid
499.0ms	2589×	body	128	overflowed
466.0ms	1246×	body	512	valid
326.0ms	714×	body	512	nan
175.0ms	192×	body	1024	invalid
165.0ms	1760×	body	128	valid
120.0ms	535×	body	256	valid
110.0ms	217×	body	512	invalid
72.0ms	318×	body	256	nan
52.0ms	780×	body	128	nan
43.0ms	156×	body	256	invalid
34.0ms	269×	body	128	invalid
6.0ms	6×	body	2048	nan
2.0ms	2×	body	2048	invalid

Compiler

Compiled 2170 to 1478 computations (31.9% saved)

Details

analyze1.1s (7.3%)

sample193.0ms (1.3%)

simplify139.0ms (1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite27.0ms (0.2%)

series247.0ms (1.7%)

simplify64.0ms (0.4%)

prune140.0ms (1%)

localize23.0ms (0.2%)

rewrite47.0ms (0.3%)

series301.0ms (2.1%)

simplify90.0ms (0.6%)

prune291.0ms (2%)

localize31.0ms (0.2%)

rewrite127.0ms (0.9%)

series874.0ms (6.1%)

simplify148.0ms (1%)

prune1.4s (9.8%)

localize25.0ms (0.2%)

rewrite62.0ms (0.4%)

series326.0ms (2.3%)

simplify96.0ms (0.7%)

prune365.0ms (2.5%)

regimes760.0ms (5.3%)

bsearch4.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample7.6s (52.4%)

Profiling