Details

analyze355.0ms (8.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4830	36
1	4830	36
0	2	2
1	2	2

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)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	4×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify169.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

prune5.0ms (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)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_14059`
25×	`add-sqr-sqrt_binary64_14081`
22×	`add-exp-log_binary64_14097`
16×	`add-cbrt-cube_binary64_14095`
15×	`associate-r_binary64_13999`
14×	`pow1_binary64_14120`
13×	`add-cube-cbrt_binary64_14094`
9×	`add-log-exp_binary64_14098` `cancel-sign-sub-inv_binary64_14025`
7×	`prod-exp_binary64_14108`
6×	`distribute-lft-out--_binary64_14011`
5×	`distribute-rgt-in_binary64_14009` `distribute-lft-in_binary64_14008` `cbrt-unprod_binary64_14092` `pow-prod-down_binary64_14130`
4×	`div-exp_binary64_14110` `sqrt-prod_binary64_14075` `distribute-lft-out_binary64_14010` `difference-of-squares_binary64_14028` `associate-l_binary64_14000`
3×	`times-frac_binary64_14065` `div-inv_binary64_14056` `sub-neg_binary64_14052` `associate--l+_binary64_13996` `associate-/l*_binary64_14004`
2×	`flip--_binary64_14034` `pow-flip_binary64_14133` `-commutative_binary64_13990` `cbrt-undiv_binary64_14093` `unswap-sqr_binary64_14027` `associate-r/_binary64_14001` `diff-log_binary64_14151` `rec-exp_binary64_14109` `1-exp_binary64_14103` `difference-of-sqr-1_binary64_14029` `flip3--_binary64_14063`
1×	`frac-2neg_binary64_14070` `sum-log_binary64_14150` `associate-/r*_binary64_14003` `clear-num_binary64_14058` `inv-pow_binary64_14144`

Counts

4 → 108

Calls

4 calls:

15.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
9.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series85.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
16.0ms	(*.f64 3 (sqrt.f64 x))
14.0ms	(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
12.0ms	(/.f64 1 (*.f64 x 9))

simplify58.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5040	1579

prune153.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 0.0b

Counts

122 → 12

Compiler

Compiled 2348 to 1705 computations (27.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_14059`
20×	`add-sqr-sqrt_binary64_14081`
16×	`add-cube-cbrt_binary64_14094`
13×	`add-cbrt-cube_binary64_14095` `add-exp-log_binary64_14097`
11×	`pow1_binary64_14120`
9×	`add-log-exp_binary64_14098` `times-frac_binary64_14065` `associate-l_binary64_14000`
6×	`associate-r_binary64_13999` `distribute-lft-out_binary64_14010` `associate-*r/_binary64_14001`
5×	`distribute-rgt-in_binary64_14009` `distribute-lft-in_binary64_14008`
4×	`prod-exp_binary64_14108` `cbrt-unprod_binary64_14092` `sqrt-prod_binary64_14075` `pow-prod-down_binary64_14130`
3×	`sum-log_binary64_14150` `flip-+_binary64_14033` `associate-/r_binary64_14003` `flip3-+_binary64_14062` `associate-/l_binary64_14004`
2×	`*-commutative_binary64_13990` `unswap-sqr_binary64_14027`
1×	`frac-2neg_binary64_14070` `div-exp_binary64_14110` `div-inv_binary64_14056` `clear-num_binary64_14058` `cbrt-undiv_binary64_14093` `+-commutative_binary64_13989` `associate-+r+_binary64_13991`

Counts

4 → 94

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)))
10.0ms	(+.f64 -1 (+.f64 (/.f64 1/9 x) y))
3.0ms	(/.f64 1/9 x)

series109.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
41.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
13.0ms	(/.f64 1/9 x)
13.0ms	(+.f64 -1 (+.f64 (/.f64 1/9 x) y))

simplify101.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4921	1641
1	4921	1641

prune130.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 2110 to 1488 computations (29.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite166.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64_14065`
165×	`*-un-lft-identity_binary64_14059`
164×	`add-sqr-sqrt_binary64_14081`
160×	`add-cube-cbrt_binary64_14094`
148×	`sqrt-prod_binary64_14075`
25×	`associate-/l*_binary64_14004`
18×	`add-cbrt-cube_binary64_14095` `add-exp-log_binary64_14097`
12×	`associate-/r*_binary64_14003`
11×	`pow1_binary64_14120`
9×	`div-inv_binary64_14056` `associate-l_binary64_14000`
6×	`associate-r_binary64_13999` `associate-*r/_binary64_14001`
5×	`distribute-rgt-in_binary64_14009` `distribute-lft-in_binary64_14008`
4×	`add-log-exp_binary64_14098` `prod-exp_binary64_14108` `div-exp_binary64_14110` `cbrt-unprod_binary64_14092` `cbrt-undiv_binary64_14093` `pow-prod-down_binary64_14130`
3×	`distribute-lft-out_binary64_14010`
2×	`frac-2neg_binary64_14070` `flip-+_binary64_14033` `*-commutative_binary64_13990` `clear-num_binary64_14058` `unswap-sqr_binary64_14027` `flip3-+_binary64_14062`
1×	`associate-/l/_binary64_14006`

Counts

4 → 266

Calls

4 calls:

57.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
53.0ms	(.f64 3 (.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))
7.0ms	(/.f64 1/9 (sqrt.f64 x))

series144.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y))))
45.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x)) y)))
30.0ms	(/.f64 1/9 (sqrt.f64 x))
16.0ms	(/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))

simplify147.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4952	5404
1	4952	5404

prune394.0ms (9.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	279	12	291

Merged error: 0b

Counts

291 → 12

Compiler

Compiled 6527 to 3891 computations (40.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_14081`
26×	`*-un-lft-identity_binary64_14059`
20×	`add-exp-log_binary64_14097`
19×	`add-cube-cbrt_binary64_14094`
17×	`associate-l_binary64_14000`
16×	`add-cbrt-cube_binary64_14095` `associate-r_binary64_13999`
13×	`pow1_binary64_14120`
11×	`times-frac_binary64_14065`
9×	`add-log-exp_binary64_14098` `cancel-sign-sub-inv_binary64_14025`
8×	`prod-exp_binary64_14108`
6×	`cbrt-unprod_binary64_14092`
5×	`distribute-rgt-in_binary64_14009` `distribute-lft-in_binary64_14008` `unswap-sqr_binary64_14027` `pow-prod-down_binary64_14130`
4×	`sqrt-prod_binary64_14075` `difference-of-squares_binary64_14028`
3×	`*-commutative_binary64_13990` `sub-neg_binary64_14052` `associate--l+_binary64_13996`
2×	`flip--_binary64_14034` `div-exp_binary64_14110` `associate-*r/_binary64_14001` `diff-log_binary64_14151` `distribute-lft-out--_binary64_14011` `difference-of-sqr-1_binary64_14029` `flip3--_binary64_14063`
1×	`sum-log_binary64_14150` `associate-*l/_binary64_14002` `div-inv_binary64_14056` `cbrt-undiv_binary64_14093` `rec-exp_binary64_14109` `1-exp_binary64_14103`

Counts

4 → 111

Calls

4 calls:

17.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1))
8.0ms	(*.f64 (/.f64 1 x) 1/9)
7.0ms	(-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1)
5.0ms	(*.f64 3 (sqrt.f64 x))

series84.0ms (2%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1))
16.0ms	(*.f64 3 (sqrt.f64 x))
14.0ms	(-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1)
11.0ms	(*.f64 (/.f64 1 x) 1/9)

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4933	1627
1	4933	1627

prune124.0ms (3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	123	12	135

Merged error: 0b

Counts

135 → 12

Compiler

Compiled 2222 to 1570 computations (29.3% saved)

regimes264.0ms (6.4%)

Compiler: Compiled 2573 to 2212 computations (14% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	20
1	24	20

end0.0ms (0%)

sample1.4s (33.7%)

Algorithm

1×

intervals

Results

368.0ms	8000×	body	128	valid
6.0ms	132×	body	128	nan
3.0ms	71×	body	128	invalid

Compiler

Compiled 892 to 766 computations (14.1% saved)

Details

analyze355.0ms (8.6%)

sample20.0ms (0.5%)

simplify169.0ms (4.1%)

prune5.0ms (0.1%)

localize14.0ms (0.3%)

rewrite44.0ms (1.1%)

series85.0ms (2.1%)

simplify58.0ms (1.4%)

prune153.0ms (3.7%)

localize9.0ms (0.2%)

rewrite49.0ms (1.2%)

series109.0ms (2.6%)

simplify101.0ms (2.4%)

prune130.0ms (3.1%)

localize10.0ms (0.2%)

rewrite166.0ms (4%)

series144.0ms (3.5%)

simplify147.0ms (3.5%)

prune394.0ms (9.5%)

localize10.0ms (0.2%)

rewrite46.0ms (1.1%)

series84.0ms (2%)

simplify54.0ms (1.3%)

prune124.0ms (3%)

regimes264.0ms (6.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (33.7%)

Profiling