Details

analyze484.0ms (9.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 9 to 9 computations (0% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	89×	body	128	nan
1.0ms	19×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

prune2.0ms (0%)

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: 20.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.1b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.5b	(/.f64 A (*.f64 V l))
17.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`pow1_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series195.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

106.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
55.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
35.0ms	(/.f64 A (*.f64 V l))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4940	857
1	4940	857

prune80.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	58	17	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	17	76

Merged error: 7.4b

Counts

76 → 17

Compiler

Compiled 1125 to 398 computations (64.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.1b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
3.8b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
17.3b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
27×	`add-exp-log_binary64`
26×	`associate-r_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
14×	`cbrt-prod_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
6×	`associate-*r/_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `frac-times_binary64` `associate-*l/_binary64`
2×	`sqrt-pow1_binary64` `div-inv_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `pow1/3_binary64`

Counts

4 → 106

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
13.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
12.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

series483.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt.f64 A)
144.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
91.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
75.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4942	1503
1	4942	1503

prune112.0ms (2.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	115	20	135

Merged error: 4.0b

Counts

135 → 20

Compiler

Compiled 2100 to 772 computations (63.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 1 (/.f64 V (/.f64 A l)))
1.1b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
3.9b	(/.f64 V (/.f64 A l))
17.3b	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))

rewrite186.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1155×	`times-frac_binary64`
574×	`add-sqr-sqrt_binary64`
539×	`*-un-lft-identity_binary64`
533×	`add-cube-cbrt_binary64`
281×	`sqrt-prod_binary64`
140×	`associate-r_binary64`
57×	`associate-/r*_binary64`
48×	`div-inv_binary64`
26×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
12×	`div-exp_binary64`
9×	`pow1_binary64` `cbrt-undiv_binary64`
8×	`unswap-sqr_binary64`
7×	`rem-sqrt-square_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `sqrt-pow1_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `-commutative_binary64`

Counts

4 → 590

Calls

4 calls:

50.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
21.0ms	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
14.0ms	(/.f64 1 (/.f64 V (/.f64 A l)))
6.0ms	(/.f64 V (/.f64 A l))

series303.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
95.0ms	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
49.0ms	(/.f64 V (/.f64 A l))
38.0ms	(/.f64 1 (/.f64 V (/.f64 A l)))

simplify182.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

602 → 602

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4929	12550
1	4929	12550

prune608.0ms (11.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	590	12	602
Fresh	9	9	18
Picked	1	0	1
Done	1	0	1
Total	601	21	622

Merged error: 0.0b

Counts

622 → 21

Compiler

Compiled 12044 to 4038 computations (66.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 l)
0.6b	(cbrt.f64 l)
0.6b	(cbrt.f64 A)
0.6b	(cbrt.f64 A)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 A)
1.0ms	(cbrt.f64 A)
1.0ms	(cbrt.f64 l)
1.0ms	(cbrt.f64 l)

series620.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt.f64 A)
153.0ms	(cbrt.f64 A)
152.0ms	(cbrt.f64 l)
140.0ms	(cbrt.f64 l)

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5028	340

prune60.0ms (1.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	56	21	77

Merged error: 0.0b

Counts

77 → 21

Compiler

Compiled 1464 to 478 computations (67.3% saved)

regimes281.0ms (5.5%)

Compiler: Compiled 2671 to 2103 computations (21.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	19	38

end0.0ms (0%)

sample1.2s (22.6%)

Algorithm

1×

intervals

Results

314.0ms	8000×	body	128	valid
102.0ms	2861×	body	128	nan
35.0ms	871×	body	128	invalid

Compiler

Compiled 403 to 314 computations (22.1% saved)

Details

analyze484.0ms (9.5%)

sample25.0ms (0.5%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series195.0ms (3.8%)

simplify83.0ms (1.6%)

prune80.0ms (1.6%)

localize11.0ms (0.2%)

rewrite52.0ms (1%)

series483.0ms (9.4%)

simplify72.0ms (1.4%)

prune112.0ms (2.2%)

localize8.0ms (0.2%)

rewrite186.0ms (3.6%)

series303.0ms (5.9%)

simplify182.0ms (3.6%)

prune608.0ms (11.9%)

localize16.0ms (0.3%)

rewrite9.0ms (0.2%)

series620.0ms (12.1%)

simplify47.0ms (0.9%)

prune60.0ms (1.2%)

regimes281.0ms (5.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (22.6%)

Profiling