Details

analyze48.0ms (1.1%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 29 to 29 computations (0% saved)

simplify238.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

prune4.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_12013`
22×	`add-exp-log_binary64_12051`
20×	`add-sqr-sqrt_binary64_12035`
16×	`add-cbrt-cube_binary64_12049`
15×	`associate-r_binary64_11953`
14×	`pow1_binary64_12074`
12×	`add-cube-cbrt_binary64_12048`
7×	`prod-exp_binary64_12062`
6×	`cancel-sign-sub-inv_binary64_11979` `add-log-exp_binary64_12052`
5×	`distribute-lft-in_binary64_11962` `pow-prod-down_binary64_12084` `cbrt-unprod_binary64_12046` `distribute-rgt-in_binary64_11963`
4×	`distribute-lft-out_binary64_11964` `div-exp_binary64_12064` `associate-l_binary64_11954` `sqrt-prod_binary64_12029`
3×	`times-frac_binary64_12019` `div-inv_binary64_12010` `distribute-lft-out--_binary64_11965` `associate-/l*_binary64_11958`
2×	`rec-exp_binary64_12063` `-commutative_binary64_11944` `pow-flip_binary64_12087` `unswap-sqr_binary64_11981` `associate--l+_binary64_11950` `difference-of-squares_binary64_11982` `cbrt-undiv_binary64_12047` `associate-r/_binary64_11955` `1-exp_binary64_12057` `sub-neg_binary64_12006`
1×	`+-commutative_binary64_11943` `sum-log_binary64_12104` `flip3-+_binary64_12016` `associate-/r*_binary64_11957` `clear-num_binary64_12012` `flip3--_binary64_12017` `flip-+_binary64_11987` `difference-of-sqr-1_binary64_11983` `inv-pow_binary64_12098` `flip--_binary64_11988` `frac-2neg_binary64_12024`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series93.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
21.0ms	(*.f64 3 (sqrt.f64 x))
18.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
12.0ms	(/.f64 1 (*.f64 x 9))

simplify47.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5251	1423

prune142.0ms (3.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	96	15	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	15	113

Error

0.0b

Counts

113 → 15

Compiler

Compiled 2277 to 1660 computations (27.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.3b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.4b	(/.f64 1/9 x)

rewrite50.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_12013`
20×	`add-sqr-sqrt_binary64_12035`
16×	`add-cube-cbrt_binary64_12048`
13×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
11×	`pow1_binary64_12074`
9×	`times-frac_binary64_12019` `associate-l_binary64_11954`
6×	`add-log-exp_binary64_12052` `associate-r_binary64_11953` `associate-*r/_binary64_11955`
5×	`distribute-lft-in_binary64_11962` `distribute-rgt-in_binary64_11963`
4×	`distribute-lft-out_binary64_11964` `pow-prod-down_binary64_12084` `sqrt-prod_binary64_12029` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
3×	`flip3-+_binary64_12016` `associate-/r_binary64_11957` `flip-+_binary64_11987` `associate-/l_binary64_11958`
2×	`*-commutative_binary64_11944` `unswap-sqr_binary64_11981`
1×	`+-commutative_binary64_11943` `sum-log_binary64_12104` `clear-num_binary64_12012` `div-exp_binary64_12064` `div-inv_binary64_12010` `cbrt-undiv_binary64_12047` `frac-2neg_binary64_12024`

Counts

4 → 91

Calls

4 calls:

15.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
14.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
7.0ms	(+.f64 (/.f64 1/9 x) y)
3.0ms	(/.f64 1/9 x)

series102.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
32.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
16.0ms	(+.f64 (/.f64 1/9 x) y)
13.0ms	(/.f64 1/9 x)

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4877	1561
1	4877	1561

prune121.0ms (2.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	103	15	118

Error

0.0b

Counts

118 → 15

Compiler

Compiled 2120 to 1492 computations (29.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))))
0.4b	(/.f64 1/9 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))

rewrite168.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64_12019`
165×	`*-un-lft-identity_binary64_12013`
164×	`add-sqr-sqrt_binary64_12035`
160×	`add-cube-cbrt_binary64_12048`
148×	`sqrt-prod_binary64_12029`
25×	`associate-/l*_binary64_11958`
18×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
12×	`associate-/r*_binary64_11957`
11×	`pow1_binary64_12074`
9×	`associate-l_binary64_11954` `div-inv_binary64_12010`
6×	`associate-r_binary64_11953` `associate-*r/_binary64_11955`
5×	`distribute-lft-in_binary64_11962` `distribute-rgt-in_binary64_11963`
4×	`add-log-exp_binary64_12052` `div-exp_binary64_12064` `pow-prod-down_binary64_12084` `cbrt-undiv_binary64_12047` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
3×	`distribute-lft-out_binary64_11964`
2×	`flip3-+_binary64_12016` `*-commutative_binary64_11944` `clear-num_binary64_12012` `unswap-sqr_binary64_11981` `flip-+_binary64_11987` `frac-2neg_binary64_12024`
1×	`associate-/l/_binary64_11960`

Counts

4 → 266

Calls

4 calls:

60.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))))
53.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
12.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))
4.0ms	(/.f64 1/9 (sqrt.f64 x))

series148.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))))
50.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
27.0ms	(/.f64 1/9 (sqrt.f64 x))
16.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))

simplify130.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4952	5404
1	4952	5404

prune367.0ms (8.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	281	12	293

Error

Counts

293 → 12

Compiler

Compiled 6559 to 3908 computations (40.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
0.4b	(/.f64 (sqrt.f64 x) 1/3)
0.4b	(/.f64 1/9 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))

rewrite121.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

314×	`times-frac_binary64_12019`
193×	`add-sqr-sqrt_binary64_12035`
190×	`*-un-lft-identity_binary64_12013`
185×	`add-cube-cbrt_binary64_12048`
166×	`sqrt-prod_binary64_12029`
31×	`associate-/l*_binary64_11958`
22×	`associate-l_binary64_11954`
18×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
15×	`associate-/r*_binary64_11957`
11×	`div-inv_binary64_12010`
6×	`div-exp_binary64_12064` `pow1_binary64_12074` `cbrt-undiv_binary64_12047`
5×	`associate-r_binary64_11953`
4×	`add-log-exp_binary64_12052`
3×	`distribute-lft-out_binary64_11964` `clear-num_binary64_12012` `unswap-sqr_binary64_11981` `frac-2neg_binary64_12024`
2×	`flip3-+_binary64_12016` `flip-+_binary64_11987` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `associate-*r/_binary64_11955` `frac-times_binary64_12023`
1×	`distribute-lft-in_binary64_11962` `-commutative_binary64_11944` `pow-prod-down_binary64_12084` `associate-l/_binary64_11956` `distribute-rgt-in_binary64_11963` `associate-/l/_binary64_11960`

Counts

4 → 303

Calls

4 calls:

62.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
12.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))
4.0ms	(/.f64 1/9 (sqrt.f64 x))
4.0ms	(/.f64 (sqrt.f64 x) 1/3)

series122.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
31.0ms	(/.f64 1/9 (sqrt.f64 x))
21.0ms	(/.f64 (sqrt.f64 x) 1/3)
15.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))

simplify118.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4938	6026
1	4938	6026

prune421.0ms (9.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	312	3	315
Fresh	9	1	10
Picked	0	1	1
Done	0	1	1
Total	321	6	327

Error

Counts

327 → 6

Compiler

Compiled 7239 to 4255 computations (41.2% saved)

regimes310.0ms (6.9%)

Accuracy

Total 0.4b remaining (99.8%)

Threshold costs 0.4b (99.8%)

Compiler

Compiled 3293 to 2806 computations (14.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms (0%)

sample1.6s (35.1%)

Algorithm

1×

intervals

Results

355.0ms	8000×	body	128	valid
6.0ms	137×	body	128	nan
3.0ms	76×	body	128	invalid

Compiler

Compiled 1131 to 965 computations (14.7% saved)

Details

analyze48.0ms (1.1%)

sample18.0ms (0.4%)

simplify238.0ms (5.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite40.0ms (0.9%)

series93.0ms (2.1%)

simplify47.0ms (1%)

prune142.0ms (3.2%)

localize8.0ms (0.2%)

rewrite50.0ms (1.1%)

series102.0ms (2.3%)

simplify79.0ms (1.7%)

prune121.0ms (2.7%)

localize10.0ms (0.2%)

rewrite168.0ms (3.7%)

series148.0ms (3.3%)

simplify130.0ms (2.9%)

prune367.0ms (8.1%)

localize9.0ms (0.2%)

rewrite121.0ms (2.7%)

series122.0ms (2.7%)

simplify118.0ms (2.6%)

prune421.0ms (9.3%)

regimes310.0ms (6.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (35.1%)

Profiling