Details

analyze2.4s (29.4%)

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)

sample54.0ms (0.7%)

Algorithm

1×

intervals

Results

33.0ms	246×	body	128	valid
3.0ms	6×	body	1024	valid
1.0ms	4×	body	512	invalid
1.0ms	3×	body	256	valid
1.0ms	2×	body	256	invalid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify211.0ms (2.5%)

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: 16.1b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(*.f64 K (+.f64 m n))
35.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1127`
15×	`*-un-lft-identity_binary64_1105`
12×	`add-exp-log_binary64_1143`
11×	`add-cbrt-cube_binary64_1141` `add-cube-cbrt_binary64_1140`
7×	`pow1_binary64_1166`
6×	`unpow-prod-down_binary64_1184`
4×	`add-log-exp_binary64_1144` `cos-sum_binary64_1239` `times-frac_binary64_1111` `associate-r_binary64_1045` `associate-*r/_binary64_1047`
3×	`associate-/r_binary64_1049` `associate-l*_binary64_1046` `cancel-sign-sub-inv_binary64_1071` `pow-unpow_binary64_1182`
2×	`difference-of-squares_binary64_1074` `prod-exp_binary64_1154` `div-exp_binary64_1156` `cbrt-undiv_binary64_1139` `cbrt-unprod_binary64_1138` `flip-+_binary64_1079` `flip3-+_binary64_1108` `associate-/l/_binary64_1052`
1×	`-commutative_binary64_1036` `pow-pow_binary64_1177` `div-inv_binary64_1102` `distribute-lft-out_binary64_1056` `frac-2neg_binary64_1116` `sub-neg_binary64_1098` `clear-num_binary64_1104` `sqr-pow_binary64_1077` `pow-exp_binary64_1173` `unswap-sqr_binary64_1073` `pow-prod-down_binary64_1176` `distribute-lft-in_binary64_1054` `unpow2_binary64_1170` `pow-to-exp_binary64_1174` `distribute-rgt-in_binary64_1055` `distribute-lft-out--_binary64_1057` `associate-/l_binary64_1050` `cos-diff_binary64_1242`

Counts

4 → 79

Calls

4 calls:

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))
7.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms	(*.f64 K (+.f64 m n))

series378.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
109.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
65.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
49.0ms	(*.f64 K (+.f64 m n))

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5163	1297

prune148.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	6	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 2.2b

Counts

92 → 6

Compiler

Compiled 3189 to 1605 computations (49.7% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1127`
6×	`unpow-prod-down_binary64_1184`
5×	`*-un-lft-identity_binary64_1105`
3×	`pow-unpow_binary64_1182` `add-cube-cbrt_binary64_1140`
2×	`difference-of-squares_binary64_1074` `pow1_binary64_1166` `add-exp-log_binary64_1143`
1×	`pow-pow_binary64_1177` `add-log-exp_binary64_1144` `sqr-pow_binary64_1077` `times-frac_binary64_1111` `pow-exp_binary64_1173` `add-cbrt-cube_binary64_1141` `unpow2_binary64_1170` `pow-to-exp_binary64_1174` `distribute-lft-out--_binary64_1057`

Counts

1 → 21

Calls

1 calls:

12.0ms

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

series100.0ms (1.2%)

Counts

1 → 3

Calls

1 calls:

100.0ms

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

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5286	402

prune36.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	24	6	30

Merged error: 2.2b

Counts

30 → 6

Compiler

Compiled 764 to 456 computations (40.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
35.7b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_1105`
32×	`cbrt-prod_binary64_1136`
23×	`add-sqr-sqrt_binary64_1127`
16×	`cbrt-div_binary64_1137`
15×	`add-cube-cbrt_binary64_1140`
11×	`pow1_binary64_1166`
9×	`swap-sqr_binary64_1072`
8×	`distribute-lft-out_binary64_1056` `pow1/3_binary64_1187` `flip-+_binary64_1079` `flip3-+_binary64_1108`
7×	`associate-r_binary64_1045` `associate-l_binary64_1046`
6×	`add-exp-log_binary64_1143`
4×	`add-log-exp_binary64_1144` `frac-times_binary64_1115` `cos-sum_binary64_1239` `add-cbrt-cube_binary64_1141` `unswap-sqr_binary64_1073`
3×	`cancel-sign-sub-inv_binary64_1071`
2×	`pow-sqr_binary64_1078` `pow-prod-up_binary64_1175` `associate-l/_binary64_1048` `pow-prod-down_binary64_1176` `associate-r/_binary64_1047`
1×	`*-commutative_binary64_1036` `pow-plus_binary64_1168` `prod-exp_binary64_1154` `sub-neg_binary64_1098` `cbrt-unprod_binary64_1138` `pow2_binary64_1186` `cos-diff_binary64_1242`

Counts

4 → 93

Calls

4 calls:

23.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
12.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))

series912.0ms (11%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
226.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
217.0ms	(cbrt.f64 (+.f64 m n))
205.0ms	(cbrt.f64 (+.f64 m n))

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4804	1641
1	4804	1641

prune192.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	101	10	111

Merged error: 2.1b

Counts

111 → 10

Compiler

Compiled 4860 to 2179 computations (55.2% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2)
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 m n)))
0.6b	(cbrt.f64 (cbrt.f64 (+.f64 m n)))
36.1b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`cbrt-prod_binary64_1136`
19×	`*-un-lft-identity_binary64_1105`
13×	`add-sqr-sqrt_binary64_1127` `add-cube-cbrt_binary64_1140`
10×	`unpow-prod-down_binary64_1184`
8×	`cbrt-div_binary64_1137`
5×	`pow1_binary64_1166` `add-exp-log_binary64_1143`
4×	`add-log-exp_binary64_1144` `cos-sum_binary64_1239` `add-cbrt-cube_binary64_1141`
3×	`distribute-lft-out_binary64_1056` `pow1/3_binary64_1187` `cancel-sign-sub-inv_binary64_1071` `pow-unpow_binary64_1182`
2×	`pow-pow_binary64_1177` `flip-+_binary64_1079` `flip3-+_binary64_1108`
1×	`sub-neg_binary64_1098` `sqr-pow_binary64_1077` `pow-exp_binary64_1173` `unpow2_binary64_1170` `pow-to-exp_binary64_1174` `cos-diff_binary64_1242`

Counts

4 → 72

Calls

4 calls:

28.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))
7.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2)
4.0ms	(cbrt.f64 (cbrt.f64 (+.f64 m n)))
4.0ms	(cbrt.f64 (cbrt.f64 (+.f64 m n)))

series1.1s (13.6%)

Counts

4 → 12

Calls

4 calls:

369.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2)
262.0ms	(cbrt.f64 (cbrt.f64 (+.f64 m n)))
261.0ms	(cbrt.f64 (cbrt.f64 (+.f64 m n)))
235.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) 2) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4883	1410
1	4883	1410

prune147.0ms (1.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	83	11	94

Merged error: 2.1b

Counts

94 → 11

Compiler

Compiled 4279 to 1694 computations (60.4% saved)

regimes180.0ms (2.2%)

Compiler: Compiled 2360 to 1630 computations (30.9% 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%)

sample1.8s (22.1%)

Algorithm

1×

intervals

Results

922.0ms	7847×	body	128	valid
48.0ms	97×	body	1024	invalid
32.0ms	61×	body	1024	valid
30.0ms	273×	body	128	invalid
29.0ms	84×	body	512	invalid
21.0ms	58×	body	512	valid
15.0ms	20×	body	2048	invalid
13.0ms	55×	body	256	invalid
8.0ms	34×	body	256	valid

Compiler

Compiled 517 to 361 computations (30.2% saved)

Details

analyze2.4s (29.4%)

sample54.0ms (0.7%)

simplify211.0ms (2.5%)

prune5.0ms (0.1%)

localize26.0ms (0.3%)

rewrite45.0ms (0.5%)

series378.0ms (4.6%)

simplify51.0ms (0.6%)

prune148.0ms (1.8%)

localize14.0ms (0.2%)

rewrite14.0ms (0.2%)

series100.0ms (1.2%)

simplify62.0ms (0.8%)

prune36.0ms (0.4%)

localize27.0ms (0.3%)

rewrite56.0ms (0.7%)

series912.0ms (11%)

simplify103.0ms (1.2%)

prune192.0ms (2.3%)

localize33.0ms (0.4%)

rewrite55.0ms (0.7%)

series1.1s (13.6%)

simplify50.0ms (0.6%)

prune147.0ms (1.8%)

regimes180.0ms (2.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (22.1%)

Profiling