Details

analyze58.0ms (1.4%)

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)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	7×	body	128	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify303.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	1572	18
1	1572	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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1/9 x)

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_12546`
19×	`add-sqr-sqrt_binary64_12567`
15×	`add-cube-cbrt_binary64_12578`
12×	`add-cbrt-cube_binary64_12579` `add-exp-log_binary64_12581`
11×	`associate-r_binary64_12488`
10×	`pow1_binary64_12604`
9×	`times-frac_binary64_12552`
4×	`prod-exp_binary64_12592` `sqrt-prod_binary64_12561` `pow-prod-down_binary64_12614` `associate-r/_binary64_12490` `associate-l*_binary64_12489` `cbrt-unprod_binary64_12576`
3×	`distribute-lft-out_binary64_12499` `associate-/l_binary64_12493` `add-log-exp_binary64_12582` `associate-/r_binary64_12492`
2×	`flip-+_binary64_12520` `unswap-sqr_binary64_12514` `flip3-+_binary64_12549` `*-commutative_binary64_12479` `frac-add_binary64_12554`
1×	`cbrt-undiv_binary64_12577` `distribute-rgt-in_binary64_12498` `distribute-lft-in_binary64_12497` `div-inv_binary64_12543` `div-exp_binary64_12594` `clear-num_binary64_12545` `frac-2neg_binary64_12557`

Counts

3 → 75

Calls

3 calls:

17.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
5.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1/9 x)

series133.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

77.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
35.0ms	(*.f64 3 (sqrt.f64 x))
22.0ms	(/.f64 1/9 x)

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5146	1145

prune130.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	14	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	72	14	86

Merged error: 0.0b

Counts

86 → 14

Compiler

Compiled 1736 to 1227 computations (29.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
0.3b	(/.f64 1/3 x)
0.3b	(*.f64 (sqrt.f64 x) 3)
0.3b	(*.f64 (sqrt.f64 x) (/.f64 1/3 x))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_12567`
27×	`*-un-lft-identity_binary64_12546`
25×	`add-cube-cbrt_binary64_12578`
21×	`associate-r_binary64_12488`
20×	`times-frac_binary64_12552`
18×	`add-cbrt-cube_binary64_12579` `add-exp-log_binary64_12581`
13×	`pow1_binary64_12604` `associate-l_binary64_12489`
9×	`sqrt-prod_binary64_12561`
6×	`prod-exp_binary64_12592` `unswap-sqr_binary64_12514` `cbrt-unprod_binary64_12576`
5×	`pow-prod-down_binary64_12614`
4×	`add-log-exp_binary64_12582`
3×	`associate-/l_binary64_12493` `associate-r/_binary64_12490` `-commutative_binary64_12479` `associate-/r_binary64_12492`
2×	`cbrt-undiv_binary64_12577` `div-inv_binary64_12543` `div-exp_binary64_12594`
1×	`flip-+_binary64_12520` `distribute-lft-out_binary64_12499` `distribute-rgt-in_binary64_12498` `distribute-lft-in_binary64_12497` `flip3-+_binary64_12549` `clear-num_binary64_12545` `difference-of-sqr--1_binary64_12517` `frac-2neg_binary64_12557`

Counts

4 → 110

Calls

4 calls:

9.0ms	(*.f64 (sqrt.f64 x) (/.f64 1/3 x))
9.0ms	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
6.0ms	(*.f64 (sqrt.f64 x) 3)
3.0ms	(/.f64 1/3 x)

series150.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
40.0ms	(*.f64 (sqrt.f64 x) (/.f64 1/3 x))
28.0ms	(*.f64 (sqrt.f64 x) 3)
25.0ms	(/.f64 1/3 x)

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4919	1476
1	4919	1476

prune147.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

Compiler

Compiled 2650 to 1697 computations (36% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (*.f64 (sqrt.f64 x) 3) (+.f64 y -1)))
0.1b	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
0.3b	(*.f64 (sqrt.f64 x) 3)
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_12567`
25×	`*-un-lft-identity_binary64_12546`
23×	`add-cube-cbrt_binary64_12578`
18×	`times-frac_binary64_12552`
16×	`sqrt-prod_binary64_12561`
13×	`add-cbrt-cube_binary64_12579` `add-exp-log_binary64_12581`
11×	`pow1_binary64_12604`
8×	`associate-r_binary64_12488`
7×	`associate-l_binary64_12489`
6×	`associate-r/_binary64_12490` `add-log-exp_binary64_12582` `associate-/r_binary64_12492`
4×	`prod-exp_binary64_12592` `pow-prod-down_binary64_12614` `cbrt-unprod_binary64_12576`
3×	`flip-+_binary64_12520` `associate-/l*_binary64_12493` `flip3-+_binary64_12549`
2×	`associate-+r+_binary64_12480` `distribute-rgt-in_binary64_12498` `unswap-sqr_binary64_12514` `distribute-lft-in_binary64_12497` `*-commutative_binary64_12479` `frac-add_binary64_12554`
1×	`cbrt-undiv_binary64_12577` `distribute-lft-out_binary64_12499` `+-commutative_binary64_12478` `sum-log_binary64_12634` `div-inv_binary64_12543` `div-exp_binary64_12594` `clear-num_binary64_12545` `difference-of-sqr--1_binary64_12517` `frac-2neg_binary64_12557`

Counts

4 → 100

Calls

4 calls:

11.0ms	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (*.f64 (sqrt.f64 x) 3) (+.f64 y -1)))
9.0ms	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
5.0ms	(*.f64 (sqrt.f64 x) 3)
5.0ms	(/.f64 1/3 (sqrt.f64 x))

series237.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (*.f64 (sqrt.f64 x) 3) (+.f64 y -1)))
60.0ms	(.f64 (.f64 (sqrt.f64 x) 3) (+.f64 y -1))
52.0ms	(/.f64 1/3 (sqrt.f64 x))
27.0ms	(*.f64 (sqrt.f64 x) 3)

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4918	1758
1	4918	1758

prune134.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 0.0b

Counts

123 → 9

Compiler

Compiled 2486 to 1689 computations (32.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
0.1b	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1))
0.4b	(/.f64 1/3 (sqrt.f64 x))
0.4b	(/.f64 (sqrt.f64 x) 1/3)

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_12567`
56×	`times-frac_binary64_12552`
50×	`*-un-lft-identity_binary64_12546`
48×	`add-cube-cbrt_binary64_12578`
34×	`sqrt-prod_binary64_12561`
22×	`associate-l_binary64_12489`
13×	`add-cbrt-cube_binary64_12579` `add-exp-log_binary64_12581`
9×	`associate-/l_binary64_12493` `associate-r/_binary64_12490` `associate-/r*_binary64_12492`
6×	`pow1_binary64_12604` `add-log-exp_binary64_12582`
5×	`flip-+_binary64_12520` `flip3-+_binary64_12549` `associate-r_binary64_12488` `frac-add_binary64_12554`
4×	`frac-times_binary64_12556`
3×	`cbrt-undiv_binary64_12577` `unswap-sqr_binary64_12514` `div-inv_binary64_12543` `div-exp_binary64_12594`
2×	`prod-exp_binary64_12592` `associate-+r+_binary64_12480` `distribute-rgt-in_binary64_12498` `associate-*l/_binary64_12491` `distribute-lft-in_binary64_12497` `clear-num_binary64_12545` `frac-2neg_binary64_12557` `cbrt-unprod_binary64_12576`
1×	`distribute-lft-out_binary64_12499` `pow-prod-down_binary64_12614` `+-commutative_binary64_12478` `sum-log_binary64_12634` `*-commutative_binary64_12479` `difference-of-sqr--1_binary64_12517`

Counts

4 → 146

Calls

4 calls:

12.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1))
10.0ms	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
5.0ms	(/.f64 (sqrt.f64 x) 1/3)
4.0ms	(/.f64 1/3 (sqrt.f64 x))

series257.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(+.f64 (.f64 1 (/.f64 1/3 (sqrt.f64 x))) (.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
64.0ms	(/.f64 1/3 (sqrt.f64 x))
60.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1))
30.0ms	(/.f64 (sqrt.f64 x) 1/3)

simplify79.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4933	2600
1	4933	2600

prune193.0ms (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	158	9	167

Merged error: 0b

Counts

167 → 9

Compiler

Compiled 3430 to 2271 computations (33.8% saved)

regimes310.0ms (7.5%)

Compiler: Compiled 2981 to 2509 computations (15.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	20
1	20	20

end0.0ms (0%)

sample1.6s (38.8%)

Algorithm

1×

intervals

Results

359.0ms	8000×	body	128	valid
6.0ms	129×	body	128	nan
3.0ms	75×	body	128	invalid

Compiler

Compiled 1028 to 866 computations (15.8% saved)

Details

analyze58.0ms (1.4%)

sample19.0ms (0.5%)

simplify303.0ms (7.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite32.0ms (0.8%)

series133.0ms (3.2%)

simplify40.0ms (1%)

prune130.0ms (3.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.9%)

series150.0ms (3.6%)

simplify77.0ms (1.9%)

prune147.0ms (3.5%)

localize10.0ms (0.2%)

rewrite38.0ms (0.9%)

series237.0ms (5.7%)

simplify80.0ms (1.9%)

prune134.0ms (3.2%)

localize10.0ms (0.2%)

rewrite45.0ms (1.1%)

series257.0ms (6.2%)

simplify79.0ms (1.9%)

prune193.0ms (4.7%)

regimes310.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (38.8%)

Profiling