Details

analyze2.3s (24.7%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample48.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	254×	body	128	valid
1.0ms	2×	body	1024	valid
1.0ms	10×	body	128	invalid
1.0ms	2×	body	512	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify206.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5353	43

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.8b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_760`
19×	`add-sqr-sqrt_binary64_782`
12×	`add-log-exp_binary64_799`
10×	`cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795`
6×	`exp-prod_binary64_812` `unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `exp-sum_binary64_806` `pow1_binary64_821`
4×	`cos-sum_binary64_894` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
3×	`diff-log_binary64_852` `rem-exp-log_binary64_800` `sub-neg_binary64_753` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `sum-log_binary64_851` `sqr-pow_binary64_732` `cos-diff_binary64_897` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 71

Calls

4 calls:

20.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series601.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
153.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
98.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
88.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5185	1713

prune122.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Merged error: 0.4b

Counts

84 → 2

Compiler

Compiled 2911 to 1413 computations (51.5% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

0.0b

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

0.0b

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_760`
17×	`add-sqr-sqrt_binary64_782`
14×	`add-log-exp_binary64_799`
8×	`cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795`
6×	`exp-prod_binary64_812` `unpow-prod-down_binary64_839`
5×	`distribute-lft-out--_binary64_712` `exp-sum_binary64_806`
4×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `add-exp-log_binary64_798` `difference-of-squares_binary64_729` `pow1_binary64_821`
3×	`rem-exp-log_binary64_800` `add-cbrt-cube_binary64_796` `pow-unpow_binary64_837`
2×	`sum-log_binary64_851` `sub-neg_binary64_753`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r+_binary64_696` `sqr-pow_binary64_732` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

3 → 63

Calls

3 calls:

20.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

19.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

12.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series825.0ms (9%)

Counts

3 → 9

Calls

3 calls:

473.0ms

(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))

251.0ms

(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

101.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5417	1705

prune84.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	72	2	74

Merged error: 0.4b

Counts

74 → 2

Compiler

Compiled 1863 to 1005 computations (46.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
2.2b	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
7.3b	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
23.7b	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
10×	`log-prod_binary64_846`
9×	`add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821`
6×	`add-exp-log_binary64_798` `unpow-prod-down_binary64_839`
5×	`exp-sum_binary64_806`
4×	`log-div_binary64_847` `exp-prod_binary64_812` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
3×	`distribute-lft-out--_binary64_712` `pow-unpow_binary64_837`
2×	`exp-diff_binary64_808` `log-pow_binary64_849` `flip--_binary64_735` `flip3--_binary64_764`
1×	`unpow2_binary64_825` `pow-exp_binary64_828` `rem-exp-log_binary64_800` `pow-to-exp_binary64_829` `rem-log-exp_binary64_801` `sqr-pow_binary64_732` `times-frac_binary64_766` `pow-pow_binary64_832`

Counts

4 → 63

Calls

4 calls:

12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
9.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.6s (16.9%)

Counts

4 → 12

Calls

4 calls:

1.0s	(cos.f64 (exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
292.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
149.0ms	(log.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
97.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5565	1393

prune107.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	73	4	77

Merged error: 0.4b

Counts

77 → 4

Compiler

Compiled 2701 to 1406 computations (47.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
27.2b	(cos.f64 (.f64 K (.f64 m 1/2)))

rewrite62.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64_760`
18×	`add-sqr-sqrt_binary64_782`
15×	`add-log-exp_binary64_799`
9×	`add-cube-cbrt_binary64_795`
8×	`cancel-sign-sub-inv_binary64_726`
6×	`exp-prod_binary64_812` `unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `distribute-lft-out--_binary64_712` `exp-sum_binary64_806` `pow1_binary64_821`
4×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
3×	`rem-exp-log_binary64_800` `pow-unpow_binary64_837`
2×	`sum-log_binary64_851` `sub-neg_binary64_753`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r+_binary64_696` `sqr-pow_binary64_732` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 70

Calls

4 calls:

20.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
19.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
4.0ms	(cos.f64 (.f64 K (.f64 m 1/2)))

series647.0ms (7%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
252.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
109.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
19.0ms	(cos.f64 (.f64 K (.f64 m 1/2)))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5440	1815

prune111.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	82	4	86

Merged error: 0.4b

Counts

86 → 4

Compiler

Compiled 2465 to 1355 computations (45% saved)

regimes259.0ms (2.8%)

Compiler: Compiled 3104 to 2502 computations (19.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	31
1	62	31

end0.0ms (0%)

sample1.8s (20%)

Algorithm

1×

intervals

Results

846.0ms	7835×	body	128	valid
40.0ms	87×	body	1024	invalid
33.0ms	292×	body	128	invalid
32.0ms	65×	body	1024	valid
24.0ms	72×	body	512	valid
21.0ms	66×	body	512	invalid
11.0ms	52×	body	256	invalid
10.0ms	15×	body	2048	invalid
6.0ms	28×	body	256	valid

Compiler

Compiled 556 to 448 computations (19.4% saved)

Details

analyze2.3s (24.7%)

sample48.0ms (0.5%)

simplify206.0ms (2.2%)

prune5.0ms (0.1%)

localize24.0ms (0.3%)

rewrite60.0ms (0.7%)

series601.0ms (6.5%)

simplify53.0ms (0.6%)

prune122.0ms (1.3%)

localize16.0ms (0.2%)

rewrite57.0ms (0.6%)

series825.0ms (9%)

simplify57.0ms (0.6%)

prune84.0ms (0.9%)

localize22.0ms (0.2%)

rewrite50.0ms (0.5%)

series1.6s (16.9%)

simplify44.0ms (0.5%)

prune107.0ms (1.2%)

localize19.0ms (0.2%)

rewrite62.0ms (0.7%)

series647.0ms (7%)

simplify58.0ms (0.6%)

prune111.0ms (1.2%)

regimes259.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (20%)

Profiling