Details

analyze2.4s (28.8%)

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 (0.6%)

Algorithm

1×

intervals

Results

29.0ms	253×	body	128	valid
2.0ms	3×	body	1024	invalid
2.0ms	14×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify207.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5053	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: 13.0b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
33.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1109`
12×	`*-un-lft-identity_binary64_1088`
8×	`add-log-exp_binary64_1124`
6×	`unpow-prod-down_binary64_1164` `add-cube-cbrt_binary64_1120`
5×	`add-exp-log_binary64_1123` `pow1_binary64_1146`
4×	`add-cbrt-cube_binary64_1121`
3×	`pow-unpow_binary64_1162` `difference-of-squares_binary64_1057`
2×	`sub-neg_binary64_1081` `distribute-lft-out--_binary64_1042`
1×	`cos-sum_binary64_1219` `sqr-pow_binary64_1060` `flip3--_binary64_1092` `sum-log_binary64_1176` `times-frac_binary64_1094` `flip--_binary64_1063` `pow-exp_binary64_1153` `pow-pow_binary64_1157` `+-commutative_binary64_1020` `diff-log_binary64_1177` `flip-+_binary64_1062` `pow-to-exp_binary64_1154` `unpow2_binary64_1150` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041` `cos-diff_binary64_1222`

Counts

4 → 55

Calls

4 calls:

16.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
12.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series593.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
152.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
107.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
101.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4977	1262
1	4977	1262

prune102.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	4	68

Merged error: 0.6b

Counts

68 → 4

Compiler

Compiled 2382 to 1200 computations (49.6% saved)

localize13.0ms (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	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_1088`
12×	`add-sqr-sqrt_binary64_1109`
10×	`add-log-exp_binary64_1124`
6×	`unpow-prod-down_binary64_1164`
5×	`add-cube-cbrt_binary64_1120`
4×	`add-exp-log_binary64_1123` `pow1_binary64_1146`
3×	`add-cbrt-cube_binary64_1121` `pow-unpow_binary64_1162` `distribute-lft-out--_binary64_1042` `difference-of-squares_binary64_1057`
2×	`sum-log_binary64_1176` `diff-log_binary64_1177` `distribute-lft-out_binary64_1041`
1×	`associate--r+_binary64_1026` `sqr-pow_binary64_1060` `flip3--_binary64_1092` `sub-neg_binary64_1081` `times-frac_binary64_1094` `flip--_binary64_1063` `pow-exp_binary64_1153` `pow-pow_binary64_1157` `+-commutative_binary64_1020` `flip-+_binary64_1062` `pow-to-exp_binary64_1154` `unpow2_binary64_1150` `flip3-+_binary64_1091`

Counts

3 → 49

Calls

3 calls:

17.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series630.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

270.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
241.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
119.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5055	1313

prune73.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Merged error: 0.6b

Counts

62 → 4

Compiler

Compiled 1565 to 872 computations (44.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.6b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))
0.6b	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
33.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1109`
14×	`*-un-lft-identity_binary64_1088`
12×	`unpow-prod-down_binary64_1164` `cbrt-prod_binary64_1116` `add-cube-cbrt_binary64_1120`
6×	`cube-prod_binary64_1113` `add-exp-log_binary64_1123` `pow1_binary64_1146` `pow-unpow_binary64_1162`
5×	`add-cbrt-cube_binary64_1121`
4×	`add-log-exp_binary64_1124`
3×	`sqr-pow_binary64_1060`
2×	`unpow3_binary64_1151` `cube-mult_binary64_1115` `pow-exp_binary64_1153` `pow-pow_binary64_1157` `pow-to-exp_binary64_1154` `difference-of-squares_binary64_1057`
1×	`cos-sum_binary64_1219` `rem-cube-cbrt_binary64_1110` `sub-neg_binary64_1081` `rem-cbrt-cube_binary64_1111` `times-frac_binary64_1094` `pow1/3_binary64_1167` `unpow2_binary64_1150` `distribute-lft-out--_binary64_1042` `cos-diff_binary64_1222`

Counts

4 → 74

Calls

4 calls:

12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
3.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))

series880.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

491.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3)
145.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
143.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) 3))
101.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5162	1685

prune133.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0.6b

Counts

90 → 4

Compiler

Compiled 3173 to 1686 computations (46.9% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.2b	(.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
33.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
33.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1109`
21×	`sqrt-prod_binary64_1103`
20×	`pow1_binary64_1146`
13×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
9×	`sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
8×	`swap-sqr_binary64_1055`
6×	`associate-r_binary64_1030` `add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `associate-l_binary64_1031`
5×	`pow-prod-up_binary64_1155`
4×	`unswap-sqr_binary64_1056` `add-log-exp_binary64_1124`
3×	`pow-prod-down_binary64_1156` `pow-sqr_binary64_1061`
2×	`cos-sum_binary64_1219` `sub-neg_binary64_1081` `cos-diff_binary64_1222`
1×	`*-commutative_binary64_1021` `pow-plus_binary64_1148` `rem-sqrt-square_binary64_1101` `cbrt-unprod_binary64_1118` `pow2_binary64_1166` `rem-square-sqrt_binary64_1100` `sqrt-unprod_binary64_1107` `prod-exp_binary64_1134`

Counts

4 → 80

Calls

4 calls:

12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
2.0ms	(sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

series823.0ms (10%)

Counts

4 → 12

Calls

4 calls:

386.0ms	(sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
152.0ms	(.f64 (sqrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (sqrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
148.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
136.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5014	1643

prune151.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	92	4	96

Merged error: 0.6b

Counts

96 → 4

Compiler

Compiled 3742 to 1902 computations (49.2% saved)

regimes80.0ms (1%)

Compiler: Compiled 630 to 545 computations (13.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.6s (19.3%)

Algorithm

1×

intervals

Results

898.0ms	7828×	body	128	valid
39.0ms	80×	body	1024	invalid
37.0ms	300×	body	128	invalid
37.0ms	72×	body	1024	valid
28.0ms	86×	body	512	invalid
21.0ms	61×	body	512	valid
16.0ms	22×	body	2048	invalid
11.0ms	48×	body	256	invalid
9.0ms	37×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 171 to 144 computations (15.8% saved)

Details

analyze2.4s (28.8%)

sample48.0ms (0.6%)

simplify207.0ms (2.5%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite55.0ms (0.7%)

series593.0ms (7.2%)

simplify82.0ms (1%)

prune102.0ms (1.2%)

localize13.0ms (0.2%)

rewrite53.0ms (0.6%)

series630.0ms (7.7%)

simplify61.0ms (0.7%)

prune73.0ms (0.9%)

localize24.0ms (0.3%)

rewrite39.0ms (0.5%)

series880.0ms (10.7%)

simplify54.0ms (0.7%)

prune133.0ms (1.6%)

localize26.0ms (0.3%)

rewrite44.0ms (0.5%)

series823.0ms (10%)

simplify71.0ms (0.9%)

prune151.0ms (1.8%)

regimes80.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (19.3%)

Profiling