Details

analyze461.0ms (9.2%)

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)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
4.0ms	121×	body	128	nan
1.0ms	28×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify8.0ms (0.2%)

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: 21.3b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.6b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
7.4b	(/.f64 A (*.f64 V l))
15.3b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite21.0ms (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:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series206.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
68.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
36.0ms	(/.f64 A (*.f64 V l))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4940	857
1	4940	857

prune84.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	60	15	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	15	76

Merged error: 4.8b

Counts

76 → 15

Compiler

Compiled 1096 to 375 computations (65.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
0.6b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.6b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
15.3b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite53.0ms (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 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
9.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

series459.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt.f64 A)
143.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
87.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
72.0ms	(.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	4941	1503
1	4941	1503

prune104.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	116	17	133

Merged error: 2.4b

Counts

133 → 17

Compiler

Compiled 2079 to 749 computations (64% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 V (/.f64 A l)))
0.6b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
5.3b	(/.f64 V (/.f64 A l))
15.3b	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))

rewrite197.0ms (3.9%)

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`
32×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`div-exp_binary64`
14×	`associate-/r/_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×	`1-exp_binary64` `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 → 593

Calls

4 calls:

52.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
23.0ms	(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))

series290.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))
92.0ms	(sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l))))
48.0ms	(/.f64 V (/.f64 A l))
36.0ms	(/.f64 1 (/.f64 V (/.f64 A l)))

simplify188.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4931	12577
1	4931	12577

prune604.0ms (12%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	594	11	605
Fresh	9	7	16
Picked	0	1	1
Done	0	0	0
Total	603	19	622

Merged error: 0.0b

Counts

622 → 19

Compiler

Compiled 12055 to 4029 computations (66.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

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

series635.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt.f64 l)
159.0ms	(cbrt.f64 l)
155.0ms	(cbrt.f64 A)
154.0ms	(cbrt.f64 A)

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5028	340

prune77.0ms (1.5%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	3	14	17
Picked	0	1	1
Done	0	1	1
Total	57	18	75

Merged error: 0.0b

Counts

75 → 18

Compiler

Compiled 1688 to 753 computations (55.4% saved)

regimes256.0ms (5.1%)

Compiler: Compiled 2390 to 1911 computations (20% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	45
1	20	45

end0.0ms (0%)

sample1.1s (21.9%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
113.0ms	3004×	body	128	nan
32.0ms	885×	body	128	invalid

Compiler

Compiled 363 to 288 computations (20.7% saved)

Details

analyze461.0ms (9.2%)

sample27.0ms (0.5%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite21.0ms (0.4%)

series206.0ms (4.1%)

simplify85.0ms (1.7%)

prune84.0ms (1.7%)

localize10.0ms (0.2%)

rewrite53.0ms (1%)

series459.0ms (9.1%)

simplify72.0ms (1.4%)

prune104.0ms (2.1%)

localize8.0ms (0.2%)

rewrite197.0ms (3.9%)

series290.0ms (5.8%)

simplify188.0ms (3.7%)

prune604.0ms (12%)

localize16.0ms (0.3%)

rewrite9.0ms (0.2%)

series635.0ms (12.6%)

simplify48.0ms (1%)

prune77.0ms (1.5%)

regimes256.0ms (5.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (21.9%)

Profiling