Details

analyze426.0ms (4.3%)

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
0%	99.9%	0.1%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

27.0ms

256×

body

128

valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify477.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (309.0ms)

Iter	Nodes	Cost
0	4948	18
1	4948	18

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_10649`
12×	`log-prod_binary64_10735`
11×	`add-sqr-sqrt_binary64_10671`
10×	`add-log-exp_binary64_10688`
9×	`add-cube-cbrt_binary64_10684`
6×	`pow1_binary64_10710` `associate--r+_binary64_10585` `distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598`
5×	`add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687`
4×	`associate-r_binary64_10589` `associate-l_binary64_10590`
2×	`associate-*l/_binary64_10592` `sum-log_binary64_10740` `sub-neg_binary64_10642` `cancel-sign-sub-inv_binary64_10615` `associate-+l+_binary64_10582` `flip-+_binary64_10623` `flip3-+_binary64_10652` `distribute-lft-out_binary64_10600` `diff-log_binary64_10741`
1×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `associate-+l-_binary64_10584` `log-pow_binary64_10738` `pow-prod-down_binary64_10720` `unswap-sqr_binary64_10617` `+-commutative_binary64_10579` `*-commutative_binary64_10580` `flip3--_binary64_10653` `flip--_binary64_10624`

Counts

3 → 62

Calls

3 calls:

13.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
11.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
8.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series285.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

163.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
67.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
54.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify132.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5016	1135

prune142.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 0.0b

Counts

72 → 6

Compiler

Compiled 1356 to 776 computations (42.8% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.7b	(cbrt.f64 y)
0.7b	(cbrt.f64 y)

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`log-prod_binary64_10735`
18×	`cbrt-prod_binary64_10680` `*-un-lft-identity_binary64_10649` `add-sqr-sqrt_binary64_10671`
16×	`add-cube-cbrt_binary64_10684`
12×	`distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598` `associate-+r+_binary64_10581`
10×	`associate-*l/_binary64_10592`
7×	`pow1_binary64_10710`
6×	`add-log-exp_binary64_10688` `add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687` `flip-+_binary64_10623` `flip3-+_binary64_10652`
5×	`associate-r_binary64_10589`
4×	`frac-add_binary64_10657` `associate-l_binary64_10590`
3×	`pow1/3_binary64_10731`
2×	`log-pow_binary64_10738` `distribute-lft-out_binary64_10600`
1×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `sum-log_binary64_10740` `pow-prod-down_binary64_10720` `unswap-sqr_binary64_10617` `+-commutative_binary64_10579` `*-commutative_binary64_10580`

Counts

4 → 85

Calls

4 calls:

24.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
21.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
2.0ms	(cbrt.f64 y)
2.0ms	(cbrt.f64 y)

series1.5s (15.1%)

Counts

4 → 12

Calls

4 calls:

756.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (cbrt.f64 y)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
420.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
166.0ms	(cbrt.f64 y)
157.0ms	(cbrt.f64 y)

simplify184.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4892	1464
1	4892	1464

prune243.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 0b

Counts

103 → 7

Compiler

Compiled 2738 to 1582 computations (42.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
0.1b	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
0.7b	(cbrt.f64 (neg.f64 y))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64_10710`
11×	`*-un-lft-identity_binary64_10649` `add-sqr-sqrt_binary64_10671`
10×	`cbrt-prod_binary64_10680`
9×	`add-log-exp_binary64_10688` `add-exp-log_binary64_10687` `add-cube-cbrt_binary64_10684`
6×	`log-pow_binary64_10738` `add-cbrt-cube_binary64_10685` `associate-l_binary64_10590`
5×	`pow-prod-down_binary64_10720` `pow1/3_binary64_10731`
3×	`distribute-lft-neg-in_binary64_10606` `distribute-rgt-neg-in_binary64_10607` `associate-r_binary64_10589`
2×	`prod-exp_binary64_10698` `sum-log_binary64_10740` `associate-+l+_binary64_10582` `flip-+_binary64_10623` `rem-log-exp_binary64_10690` `flip3-+_binary64_10652` `associate-*r/_binary64_10591`
1×	`cbrt-unprod_binary64_10682` `associate-+l-_binary64_10584` `sub-neg_binary64_10642` `unswap-sqr_binary64_10617` `cancel-sign-sub-inv_binary64_10615` `+-commutative_binary64_10579` `*-commutative_binary64_10580` `distribute-rgt-in_binary64_10599` `neg-mul-1_binary64_10645` `distribute-lft-in_binary64_10598` `distribute-lft-out_binary64_10600` `log-prod_binary64_10735` `diff-log_binary64_10741`

Counts

4 → 72

Calls

4 calls:

21.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
12.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
8.0ms	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
4.0ms	(cbrt.f64 (neg.f64 y))

series1.3s (13.1%)

Counts

4 → 12

Calls

4 calls:

584.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))
312.0ms	(log.f64 (*.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1)))
248.0ms	(+.f64 (-.f64 x (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 y)) (cbrt.f64 -1))) (+.f64 3/2 (*.f64 y 3)))) y)
157.0ms	(cbrt.f64 (neg.f64 y))

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5040	1686

prune200.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	84	7	91

Merged error: 0b

Counts

91 → 7

Compiler

Compiled 2137 to 1435 computations (32.8% saved)

localize42.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.7b	(cbrt.f64 y)
5.0b	(pow.f64 y 1/3)

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_10649`
12×	`add-sqr-sqrt_binary64_10671` `add-cube-cbrt_binary64_10684` `log-prod_binary64_10735` `associate-+r+_binary64_10581`
10×	`associate-*l/_binary64_10592` `pow1_binary64_10710` `add-exp-log_binary64_10687`
9×	`cbrt-prod_binary64_10680` `add-cbrt-cube_binary64_10685`
6×	`add-log-exp_binary64_10688` `distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598` `flip-+_binary64_10623` `flip3-+_binary64_10652`
4×	`frac-add_binary64_10657` `associate-l_binary64_10590`
3×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `pow-prod-down_binary64_10720` `pow-unpow_binary64_10726` `unpow-prod-down_binary64_10728`
2×	`distribute-lft-out_binary64_10600`
1×	`sum-log_binary64_10740` `+-commutative_binary64_10579` `sqr-pow_binary64_10621` `pow-pow_binary64_10721` `-commutative_binary64_10580` `unpow1/3_binary64_10716` `pow-exp_binary64_10717` `pow1/3_binary64_10731` `pow-to-exp_binary64_10718` `associate-r*_binary64_10589`

Counts

4 → 78

Calls

4 calls:

23.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
16.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2))
5.0ms	(pow.f64 y 1/3)
2.0ms	(cbrt.f64 y)

series1.8s (18.4%)

Counts

4 → 12

Calls

4 calls:

1.1s	(+.f64 (.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2)) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
452.0ms	(.f64 (+.f64 y 1/2) (.f64 (log.f64 (pow.f64 y 1/3)) 2))
162.0ms	(cbrt.f64 y)
160.0ms	(pow.f64 y 1/3)

simplify152.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4913	1215
1	4913	1215

prune207.0ms (2.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	90	7	97

Merged error: 0b

Counts

97 → 7

Compiler

Compiled 2371 to 1423 computations (40% saved)

regimes412.0ms (4.1%)

Compiler: Compiled 2310 to 1841 computations (20.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	22
1	65	22

end0.0ms (0%)

sample1.9s (19.6%)

Algorithm

1×

intervals

Results

687.0ms	7999×	body	128	valid
4.0ms	53×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 491 to 392 computations (20.2% saved)

Details

analyze426.0ms (4.3%)

sample42.0ms (0.4%)

simplify477.0ms (4.8%)

prune4.0ms (0%)

localize17.0ms (0.2%)

rewrite40.0ms (0.4%)

series285.0ms (2.9%)

simplify132.0ms (1.3%)

prune142.0ms (1.4%)

localize31.0ms (0.3%)

rewrite68.0ms (0.7%)

series1.5s (15.1%)

simplify184.0ms (1.8%)

prune243.0ms (2.4%)

localize30.0ms (0.3%)

rewrite56.0ms (0.6%)

series1.3s (13.1%)

simplify109.0ms (1.1%)

prune200.0ms (2%)

localize42.0ms (0.4%)

rewrite63.0ms (0.6%)

series1.8s (18.4%)

simplify152.0ms (1.5%)

prune207.0ms (2.1%)

regimes412.0ms (4.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (19.6%)

Profiling