Details

analyze229.0ms (4.6%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample17.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify163.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	105	16
1	105	16

prune3.0ms (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: 5.4b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.7b	(.f64 y (+.f64 1 (.f64 z z)))
3.9b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_12552`
26×	`add-exp-log_binary64_12581`
20×	`add-sqr-sqrt_binary64_12567`
18×	`*-un-lft-identity_binary64_12546` `add-cube-cbrt_binary64_12578`
16×	`add-cbrt-cube_binary64_12579`
13×	`associate-/l*_binary64_12493`
12×	`div-exp_binary64_12594`
6×	`cbrt-undiv_binary64_12577`
5×	`prod-exp_binary64_12592`
4×	`associate-*r/_binary64_12490` `pow1_binary64_12604`
3×	`associate-r_binary64_12488` `div-inv_binary64_12543` `associate-l_binary64_12489` `cbrt-unprod_binary64_12576`
2×	`flip-+_binary64_12520` `1-exp_binary64_12587` `associate-/r/_binary64_12494` `rec-exp_binary64_12593` `flip3-+_binary64_12549` `add-log-exp_binary64_12582`
1×	`associate-/l/_binary64_12495` `distribute-rgt-in_binary64_12498` `unswap-sqr_binary64_12514` `distribute-lft-in_binary64_12497` `pow-prod-down_binary64_12614` `-commutative_binary64_12479` `clear-num_binary64_12545` `associate-/r_binary64_12492` `frac-2neg_binary64_12557`

Counts

2 → 74

Calls

2 calls:

14.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series169.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

94.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
75.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4945	1317
1	4945	1317

prune90.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	70	10	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Merged error: 3.3b

Counts

81 → 10

Compiler

Compiled 1416 to 872 computations (38.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (/.f64 1 x) y)
4.6b	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

468×	`times-frac_binary64_12552`
228×	`*-un-lft-identity_binary64_12546` `add-cube-cbrt_binary64_12578` `add-sqr-sqrt_binary64_12567`
56×	`associate-/l*_binary64_12493`
26×	`add-exp-log_binary64_12581`
22×	`div-inv_binary64_12543`
17×	`div-exp_binary64_12594`
16×	`add-cbrt-cube_binary64_12579`
9×	`cbrt-undiv_binary64_12577`
6×	`associate-/r*_binary64_12492`
2×	`associate-/l/_binary64_12495` `1-exp_binary64_12587` `associate-/r/_binary64_12494` `rec-exp_binary64_12593` `pow1_binary64_12604` `clear-num_binary64_12545` `add-log-exp_binary64_12582` `frac-2neg_binary64_12557`
1×	`flip-+_binary64_12520` `flip3-+_binary64_12549`

Counts

2 → 268

Calls

2 calls:

19.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))
7.0ms	(/.f64 (/.f64 1 x) y)

series120.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))
20.0ms	(/.f64 (/.f64 1 x) y)

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5134	7926

prune356.0ms (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	275	9	284

Merged error: 3.3b

Counts

284 → 9

Compiler

Compiled 6559 to 3600 computations (45.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.6b	(/.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (cbrt.f64 (+.f64 1 (.f64 z z))) (cbrt.f64 (+.f64 1 (*.f64 z z)))))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 z z)))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 z z)))
14.0b	(cbrt.f64 (+.f64 1 (*.f64 z z)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_12581`
19×	`add-cbrt-cube_binary64_12579`
18×	`cbrt-undiv_binary64_12577` `cbrt-div_binary64_12575` `div-exp_binary64_12594`
13×	`prod-exp_binary64_12592` `cbrt-unprod_binary64_12576`
9×	`flip-+_binary64_12520` `*-un-lft-identity_binary64_12546` `cbrt-prod_binary64_12574` `flip3-+_binary64_12549` `add-cube-cbrt_binary64_12578` `add-sqr-sqrt_binary64_12567`
8×	`associate-/r/_binary64_12494`
7×	`times-frac_binary64_12552`
5×	`associate-/l*_binary64_12493`
4×	`pow1_binary64_12604` `frac-times_binary64_12556` `add-log-exp_binary64_12582`
3×	`div-inv_binary64_12543` `pow1/3_binary64_12625`
2×	`associate-l/_binary64_12491` `associate-r/_binary64_12490`
1×	`associate-/l/_binary64_12495` `clear-num_binary64_12545` `associate-/r*_binary64_12492` `frac-2neg_binary64_12557`

Counts

4 → 89

Calls

4 calls:

26.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (cbrt.f64 (+.f64 1 (.f64 z z))) (cbrt.f64 (+.f64 1 (*.f64 z z)))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))

series613.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (cbrt.f64 (+.f64 1 (.f64 z z))) (cbrt.f64 (+.f64 1 (*.f64 z z)))))
94.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))
85.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))
84.0ms	(cbrt.f64 (+.f64 1 (*.f64 z z)))

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4922	2740
1	4922	2740

prune229.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	9	110

Merged error: 3.3b

Counts

110 → 9

Compiler

Compiled 4962 to 3034 computations (38.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
1.7b	(.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y))
13.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
13.6b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite220.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

525×	`times-frac_binary64_12552`
399×	`add-sqr-sqrt_binary64_12567`
242×	`*-un-lft-identity_binary64_12546`
216×	`add-cube-cbrt_binary64_12578`
140×	`sqrt-prod_binary64_12561`
113×	`add-exp-log_binary64_12581`
84×	`associate-l_binary64_12489`
76×	`associate-r_binary64_12488`
66×	`div-exp_binary64_12594`
45×	`add-cbrt-cube_binary64_12579`
42×	`unswap-sqr_binary64_12514`
25×	`prod-exp_binary64_12592`
24×	`associate-/l*_binary64_12493`
21×	`cbrt-undiv_binary64_12577`
20×	`sqrt-div_binary64_12562`
16×	`associate-/r/_binary64_12494` `div-inv_binary64_12543`
11×	`1-exp_binary64_12587` `rec-exp_binary64_12593`
10×	`flip-+_binary64_12520` `flip3-+_binary64_12549`
9×	`cbrt-unprod_binary64_12576`
8×	`pow1_binary64_12604`
4×	`add-log-exp_binary64_12582`
3×	`associate-/r*_binary64_12492`
2×	`sqrt-pow1_binary64_12563` `rem-sqrt-square_binary64_12559` `pow1/2_binary64_12623`
1×	`associate-/l/_binary64_12495` `associate-l/_binary64_12491` `pow-prod-down_binary64_12614` `associate-r/_binary64_12490` `*-commutative_binary64_12479` `clear-num_binary64_12545` `frac-times_binary64_12556` `frac-2neg_binary64_12557`

Counts

4 → 394

Calls

4 calls:

128.0ms	(.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y))
13.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series256.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
94.0ms	(.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 z z)))) y))
34.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
32.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify171.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4948	12629
1	4948	12629

prune927.0ms (18.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	406	0	406
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	406	9	415

Merged error: 3.3b

Counts

415 → 9

Compiler

Compiled 12820 to 7941 computations (38.1% saved)

regimes169.0ms (3.4%)

Compiler: Compiled 1541 to 1288 computations (16.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	70
1	22	70

end0.0ms (0%)

sample768.0ms (15.4%)

Algorithm

1×

intervals

Results

297.0ms	8000×	body	128	valid
17.0ms	481×	body	128	invalid

Compiler

Compiled 287 to 224 computations (22% saved)

Details

analyze229.0ms (4.6%)

sample17.0ms (0.3%)

simplify163.0ms (3.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite26.0ms (0.5%)

series169.0ms (3.4%)

simplify87.0ms (1.7%)

prune90.0ms (1.8%)

localize10.0ms (0.2%)

rewrite62.0ms (1.2%)

series120.0ms (2.4%)

simplify138.0ms (2.8%)

prune356.0ms (7.1%)

localize19.0ms (0.4%)

rewrite50.0ms (1%)

series613.0ms (12.3%)

simplify88.0ms (1.8%)

prune229.0ms (4.6%)

localize11.0ms (0.2%)

rewrite220.0ms (4.4%)

series256.0ms (5.1%)

simplify171.0ms (3.4%)

prune927.0ms (18.5%)

regimes169.0ms (3.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample768.0ms (15.4%)

Profiling