Details

analyze2.1s (18.9%)

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)

sample44.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	245×	body	128	valid
2.0ms	5×	body	1024	valid
1.0ms	3×	body	1024	invalid
1.0ms	3×	body	512	valid
1.0ms	3×	body	512	invalid
1.0ms	1×	body	2048	valid
1.0ms	7×	body	128	invalid
0.0ms	1×	body	256	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify136.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 18.7b

Counts

2 → 1

Compiler

Compiled 57 to 45 computations (21.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b	(/.f64 (*.f64 K (+.f64 m n)) 2)
36.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760`
12×	`add-cube-cbrt_binary64_795`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`associate-r_binary64_700`
8×	`cancel-sign-sub-inv_binary64_726`
7×	`exp-sum_binary64_806` `pow1_binary64_821`
6×	`unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `times-frac_binary64_766`
3×	`associate-/r_binary64_704` `difference-of-squares_binary64_729` `associate-l_binary64_701` `associate-r/_binary64_702` `pow-unpow_binary64_837`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l/_binary64_707` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `unpow2_binary64_825` `flip3-+_binary64_763` `exp-diff_binary64_808` `pow-exp_binary64_828` `div-inv_binary64_757` `flip-+_binary64_734` `associate-/l_binary64_705` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `sqr-pow_binary64_732` `cos-diff_binary64_897` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 82

Calls

4 calls:

32.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

series2.0s (17.6%)

Counts

4 → 80

Calls

4 calls:

1.3s	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
283.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
208.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
124.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

Compiler

Compiled 9054 to 6262 computations (30.8% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5120	6458

prune319.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Merged error: 2.3b

Counts

163 → 8

Compiler

Compiled 7320 to 3311 computations (54.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(-.f64 l (fabs.f64 (-.f64 m n)))
0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_760`
26×	`add-sqr-sqrt_binary64_782`
19×	`add-log-exp_binary64_799`
11×	`cancel-sign-sub-inv_binary64_726`
10×	`add-cube-cbrt_binary64_795` `distribute-lft-out--_binary64_712`
8×	`diff-log_binary64_852` `exp-prod_binary64_812`
7×	`difference-of-squares_binary64_729` `exp-sum_binary64_806`
6×	`unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `rem-exp-log_binary64_800` `pow1_binary64_821`
4×	`add-cbrt-cube_binary64_796`
3×	`sub-neg_binary64_753` `pow-unpow_binary64_837`
2×	`neg-log_binary64_853` `distribute-rgt-neg-in_binary64_718` `times-frac_binary64_766` `flip--_binary64_735` `flip3--_binary64_764`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 82

Calls

4 calls:

24.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
4.0ms	(-.f64 l (fabs.f64 (-.f64 m n)))

series741.0ms (6.7%)

Counts

4 → 67

Calls

4 calls:

314.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
230.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
143.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
54.0ms	(-.f64 l (fabs.f64 (-.f64 m n)))

Compiler

Compiled 3335 to 2816 computations (15.6% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	2967
1	4979	2967

prune177.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	149	8	157

Merged error: 2.3b

Counts

157 → 8

Compiler

Compiled 4235 to 1946 computations (54% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 1/2 (.f64 K m)) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
25.4b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
11×	`cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
7×	`exp-sum_binary64_806` `pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894`
3×	`difference-of-squares_binary64_729` `associate-l_binary64_701` `sub-neg_binary64_753` `pow-unpow_binary64_837`
2×	`distribute-lft-out--_binary64_712`
1×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `times-frac_binary64_766` `-commutative_binary64_691` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 73

Calls

4 calls:

33.0ms	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
5.0ms	(-.f64 (.f64 1/2 (.f64 K m)) M)

series1.4s (12.8%)

Counts

4 → 72

Calls

4 calls:

962.0ms	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
273.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
101.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
85.0ms	(-.f64 (.f64 1/2 (.f64 K m)) M)

Compiler

Compiled 5945 to 4367 computations (26.5% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5437	4708

prune236.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	145	8	153

Merged error: 2.3b

Counts

153 → 8

Compiler

Compiled 5659 to 2645 computations (53.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 l (fabs.f64 (-.f64 m n)))
0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
29.2b	(cos.f64 (/.f64 -1 M))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64_760`
20×	`add-sqr-sqrt_binary64_782`
17×	`add-log-exp_binary64_799`
9×	`add-cube-cbrt_binary64_795` `distribute-lft-out--_binary64_712`
8×	`exp-prod_binary64_812` `cancel-sign-sub-inv_binary64_726`
7×	`diff-log_binary64_852` `exp-sum_binary64_806`
6×	`unpow-prod-down_binary64_839`
5×	`add-exp-log_binary64_798` `rem-exp-log_binary64_800` `difference-of-squares_binary64_729` `pow1_binary64_821`
4×	`add-cbrt-cube_binary64_796`
3×	`pow-unpow_binary64_837`
2×	`neg-log_binary64_853` `distribute-rgt-neg-in_binary64_718` `sub-neg_binary64_753`
1×	`unpow2_binary64_825` `exp-diff_binary64_808` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `sqr-pow_binary64_732` `times-frac_binary64_766` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 72

Calls

4 calls:

24.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
4.0ms	(-.f64 l (fabs.f64 (-.f64 m n)))
2.0ms	(cos.f64 (/.f64 -1 M))

series569.0ms (5.1%)

Counts

4 → 52

Calls

4 calls:

276.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
221.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
59.0ms	(-.f64 l (fabs.f64 (-.f64 m n)))
12.0ms	(cos.f64 (/.f64 -1 M))

Compiler

Compiled 3032 to 2542 computations (16.2% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5148	2628

prune149.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Merged error: 2.3b

Counts

132 → 9

Compiler

Compiled 3654 to 1863 computations (49% saved)

regimes475.0ms (4.3%)

Compiler: Compiled 6428 to 5286 computations (17.8% 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%)

sample2.2s (19.6%)

Algorithm

1×

intervals

Results

800.0ms	7837×	body	128	valid
33.0ms	73×	body	1024	invalid
30.0ms	69×	body	1024	valid
30.0ms	303×	body	128	invalid
26.0ms	85×	body	512	invalid
18.0ms	59×	body	512	valid
11.0ms	57×	body	256	invalid
8.0ms	14×	body	2048	invalid
7.0ms	33×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 1110 to 912 computations (17.8% saved)

Details

analyze2.1s (18.9%)

sample44.0ms (0.4%)

simplify136.0ms (1.2%)

prune5.0ms (0%)

localize20.0ms (0.2%)

rewrite68.0ms (0.6%)

series2.0s (17.6%)

simplify75.0ms (0.7%)

prune319.0ms (2.9%)

localize17.0ms (0.2%)

rewrite56.0ms (0.5%)

series741.0ms (6.7%)

simplify75.0ms (0.7%)

prune177.0ms (1.6%)

localize20.0ms (0.2%)

rewrite63.0ms (0.6%)

series1.4s (12.8%)

simplify79.0ms (0.7%)

prune236.0ms (2.1%)

localize20.0ms (0.2%)

rewrite47.0ms (0.4%)

series569.0ms (5.1%)

simplify53.0ms (0.5%)

prune149.0ms (1.3%)

regimes475.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (19.6%)

Profiling