Details

analyze2.2s (19.9%)

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)

sample53.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	253×	body	128	valid
5.0ms	4×	body	256	invalid
2.0ms	4×	body	1024	invalid
1.0ms	3×	body	512	invalid
1.0ms	7×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify132.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5097	43

prune8.0ms (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

Error

16.5b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize25.0ms (0.2%)

Local error

Found 8 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	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
32.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
7×	`add-exp-log_binary64_798` `pow1_binary64_821`
6×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`cancel-sign-sub-inv_binary64_726` `associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `difference-of-squares_binary64_729` `flip-+_binary64_734` `associate-*r/_binary64_702`
1×	`unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `distribute-rgt-in_binary64_710` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `times-frac_binary64_766` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 68

Calls

8 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms	(*.f64 K (+.f64 m n))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.1s (9.8%)

Counts

4 → 82

Calls

4 calls:

607.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
295.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
132.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
54.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 4552 to 3601 computations (20.9% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5072	2692

prune258.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	4	151

Error

0.6b

Counts

151 → 4

Compiler

Compiled 5023 to 2333 computations (53.6% saved)

localize15.0ms (0.1%)

Local error

Found 8 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	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795`
8×	`add-log-exp_binary64_799` `associate-r_binary64_700`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
5×	`exp-sum_binary64_806`
4×	`difference-of-squares_binary64_729`
3×	`associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711` `distribute-lft-out--_binary64_712` `sub-neg_binary64_753` `times-frac_binary64_766`
1×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `flip3-+_binary64_763` `exp-diff_binary64_808` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `-commutative_binary64_691` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 74

Calls

8 calls:

22.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.4s (13%)

Counts

4 → 90

Calls

4 calls:

612.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
414.0ms	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
276.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
134.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

Compiler

Compiled 4165 to 3432 computations (17.6% saved)

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4984	3619
1	4984	3619

prune202.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	164	4	168

Error

0.6b

Counts

168 → 4

Compiler

Compiled 4340 to 1984 computations (54.3% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (cos.f64 (-.f64 (.f64 (*.f64 K n) 1/2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (.f64 (.f64 K n) 1/2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
24.0b	(cos.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`cancel-sign-sub-inv_binary64_726` `unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `pow1_binary64_821`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796`
3×	`pow-unpow_binary64_837`
2×	`difference-of-squares_binary64_729` `sub-neg_binary64_753`
1×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `unpow2_binary64_825` `flip3-+_binary64_763` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `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 → 59

Calls

8 calls:

14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(cos.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))
5.0ms	(-.f64 (.f64 (.f64 K n) 1/2) M)
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series1.0s (9.4%)

Counts

4 → 82

Calls

4 calls:

609.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
277.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
87.0ms	(-.f64 (.f64 (.f64 K n) 1/2) M)
66.0ms	(cos.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))

Compiler

Compiled 4039 to 3297 computations (18.4% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4979	2561
1	4979	2561

prune204.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	141	4	145

Error

0.6b

Counts

145 → 4

Compiler

Compiled 4375 to 2137 computations (51.2% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 K n) 1/2) M)
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
2.2b	(exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M)))
4.9b	(log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))
19.0b	(cos.f64 (exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_782`
11×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821`
6×	`add-exp-log_binary64_798` `unpow-prod-down_binary64_839` `log-prod_binary64_846`
4×	`log-div_binary64_847` `exp-prod_binary64_812` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`exp-sum_binary64_806` `pow-unpow_binary64_837`
2×	`exp-diff_binary64_808` `difference-of-squares_binary64_729` `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` `distribute-lft-out--_binary64_712` `rem-log-exp_binary64_801` `sqr-pow_binary64_732` `times-frac_binary64_766` `pow-pow_binary64_832`

Counts

4 → 59

Calls

8 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(cos.f64 (exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))))
7.0ms	(exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M)))
6.0ms	(log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)

series655.0ms (5.9%)

Counts

4 → 54

Calls

4 calls:

299.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
180.0ms	(cos.f64 (exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))))
103.0ms	(exp.f64 (log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M)))
72.0ms	(log.f64 (-.f64 (.f64 (.f64 K n) 1/2) M))

Compiler

Compiled 3326 to 2777 computations (16.5% saved)

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5132	1734

prune155.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	113	4	117

Error

0.6b

Counts

117 → 4

Compiler

Compiled 3527 to 1827 computations (48.2% saved)

simplify29.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	763	1327
1	763	1327

regimes392.0ms (3.5%)

Compiler: Compiled 4310 to 3695 computations (14.3% saved)

bsearch0.0ms (0%)

regimes263.0ms (2.4%)

Compiler: Compiled 1880 to 1790 computations (4.8% saved)

bsearch67.0ms (0.6%)

Steps

Iters	Range		Point
10	5.169128363677321e-178	5.860158168811536e-160	3.8610656095079626e-162
6	-7.563022201179984e-172	-1.461637696612751e-172	-3.0224362588245987e-172

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes46.0ms (0.4%)

Accuracy

Total 0.2b remaining (17.7%)

Threshold costs 0.2b (17.7%)

Compiler

Compiled 25 to 140 computations (-460% saved)

bsearch4.0ms (0%)

Compiler: Compiled 61 to 60 computations (1.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	219	91
1	219	91

end0.0ms (0%)

sample2.2s (19.6%)

Algorithm

1×

intervals

Results

807.0ms	7834×	body	128	valid
35.0ms	68×	body	1024	valid
31.0ms	76×	body	1024	invalid
30.0ms	288×	body	128	invalid
23.0ms	76×	body	512	invalid
22.0ms	61×	body	512	valid
11.0ms	55×	body	256	invalid
10.0ms	18×	body	2048	invalid
8.0ms	37×	body	256	valid

Compiler

Compiled 951 to 818 computations (14% saved)

Pareto

0.21976649065711304

Details

analyze2.2s (19.9%)

sample53.0ms (0.5%)

simplify132.0ms (1.2%)

prune8.0ms (0.1%)

localize25.0ms (0.2%)

rewrite49.0ms (0.4%)

series1.1s (9.8%)

simplify75.0ms (0.7%)

prune258.0ms (2.3%)

localize15.0ms (0.1%)

rewrite68.0ms (0.6%)

series1.4s (13%)

simplify80.0ms (0.7%)

prune202.0ms (1.8%)

localize24.0ms (0.2%)

rewrite44.0ms (0.4%)

series1.0s (9.4%)

simplify88.0ms (0.8%)

prune204.0ms (1.8%)

localize22.0ms (0.2%)

rewrite39.0ms (0.4%)

series655.0ms (5.9%)

simplify122.0ms (1.1%)

prune155.0ms (1.4%)

simplify29.0ms (0.3%)

regimes392.0ms (3.5%)

bsearch0.0ms (0%)

regimes263.0ms (2.4%)

bsearch67.0ms (0.6%)

regimes46.0ms (0.4%)

bsearch4.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (19.6%)

Profiling