Details

analyze2.4s (20%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5136	473
0	5	5
1	5	5

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

Symmetry

Compiler

Compiled 30 to 24 computations (20% saved)

sample46.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	250×	body	128	valid
1.0ms	4×	body	512	valid
1.0ms	9×	body	128	invalid
1.0ms	3×	body	512	invalid
1.0ms	2×	body	1024	invalid
0.0ms	2×	body	256	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5097	43

prune10.0ms (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

14.3b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize18.0ms (0.1%)

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	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
31.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite173.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

14.1b

Rules

21×	`*-un-lft-identity_binary64_760`
19×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
9×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821` `add-exp-log_binary64_798`
6×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `associate-l_binary64_701` `distribute-lft-out_binary64_711`
2×	`sub-neg_binary64_753` `associate-*r/_binary64_702` `diff-log_binary64_852`
1×	`cos-diff_binary64_897` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `flip3-+_binary64_763` `flip-+_binary64_734` `*-commutative_binary64_691` `sum-log_binary64_851` `flip3--_binary64_764` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

4 → 76

Calls

4 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.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))
7.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 2874 to 1432 computations (50.2% saved)

series1.3s (10.7%)

Error

1.4b

Counts

4 → 90

Calls

4 calls:

648.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
285.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
151.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
92.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 7819 to 5299 computations (32.2% saved)

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4981	3381
1	4981	3381

prune239.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Error

1.3b

Counts

167 → 6

Compiler

Compiled 5641 to 2684 computations (52.4% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite115.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

17×	`*-un-lft-identity_binary64_760`
13×	`add-sqr-sqrt_binary64_782`
10×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`pow1_binary64_821` `add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `add-cbrt-cube_binary64_796` `distribute-lft-out_binary64_711`
2×	`sum-log_binary64_851` `diff-log_binary64_852`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `associate--r+_binary64_696` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690`

Counts

3 → 53

Calls

3 calls:

20.0ms	(-.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)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 1647 to 852 computations (48.3% saved)

series1.6s (13.1%)

Error

1.3b

Counts

3 → 93

Calls

3 calls:

613.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
595.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
285.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 6452 to 4486 computations (30.5% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4966	3491
1	4966	3491

prune161.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	146	6	152

Error

1.3b

Counts

152 → 6

Compiler

Compiled 3882 to 1755 computations (54.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(cbrt.f64 (+.f64 m n))
0.6b	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
31.3b	(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))

rewrite206.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

33×	`*-un-lft-identity_binary64_760`
32×	`cbrt-prod_binary64_791`
23×	`add-sqr-sqrt_binary64_782`
16×	`cbrt-div_binary64_792`
15×	`add-cube-cbrt_binary64_795`
11×	`pow1_binary64_821`
9×	`swap-sqr_binary64_727`
8×	`pow1/3_binary64_842` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711`
7×	`associate-l_binary64_701` `associate-r_binary64_700`
6×	`add-exp-log_binary64_798`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `frac-times_binary64_770` `unswap-sqr_binary64_728`
3×	`cancel-sign-sub-inv_binary64_726`
2×	`pow-prod-down_binary64_831` `pow-prod-up_binary64_830` `pow-sqr_binary64_733` `associate-l/_binary64_703` `associate-r/_binary64_702`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753` `pow2_binary64_841` `pow-plus_binary64_823` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 93

Calls

4 calls:

20.0ms	(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))

Compiler

Compiled 4557 to 1701 computations (62.7% saved)

series426.0ms (3.5%)

Error

1.3b

Counts

4 → 36

Calls

4 calls:

162.0ms	(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))
90.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
64.0ms	(cbrt.f64 (+.f64 m n))
61.0ms	(cbrt.f64 (+.f64 m n))

Compiler

Compiled 4101 to 2841 computations (30.7% saved)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4988	1868
1	4988	1868

prune213.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	128	7	135

Error

1.2b

Counts

135 → 7

Compiler

Compiled 5470 to 2378 computations (56.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 m n))
0.6b	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
0.6b	(cbrt.f64 n)
28.7b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 n)) 2) M))

rewrite186.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

31×	`*-un-lft-identity_binary64_760` `cbrt-prod_binary64_791`
23×	`add-sqr-sqrt_binary64_782`
15×	`add-cube-cbrt_binary64_795`
14×	`cbrt-div_binary64_792`
11×	`pow1_binary64_821`
9×	`swap-sqr_binary64_727`
8×	`pow1/3_binary64_842`
7×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-l_binary64_701` `associate-r_binary64_700`
6×	`add-exp-log_binary64_798`
4×	`cos-sum_binary64_894` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `frac-times_binary64_770` `unswap-sqr_binary64_728`
3×	`cancel-sign-sub-inv_binary64_726`
2×	`pow-prod-down_binary64_831` `pow-prod-up_binary64_830` `pow-sqr_binary64_733` `associate-l/_binary64_703` `associate-r/_binary64_702`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753` `pow2_binary64_841` `pow-plus_binary64_823` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 90

Calls

4 calls:

21.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 n)) 2) M))
12.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
3.0ms	(cbrt.f64 (+.f64 m n))
1.0ms	(cbrt.f64 n)

Compiler

Compiled 4195 to 1667 computations (60.3% saved)

series795.0ms (6.5%)

Error

1.2b

Counts

4 → 36

Calls

4 calls:

503.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 n)) 2) M))
94.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
80.0ms	(cbrt.f64 n)
60.0ms	(cbrt.f64 (+.f64 m n))

Compiler

Compiled 4563 to 3307 computations (27.5% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4943	2452
1	4943	2452

prune210.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	126	7	133

Error

1.2b

Counts

133 → 7

Compiler

Compiled 5294 to 2439 computations (53.9% saved)

regimes811.0ms (6.6%)

Accuracy

Total 0.2b remaining (17.3%)

Threshold costs 0.2b (17.3%)

Compiler

Compiled 10976 to 8586 computations (21.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	33
1	62	33

Removed

()

end0.0ms (0%)

sample2.9s (23.3%)

Algorithm

1×

intervals

Results

797.0ms	7832×	body	128	valid
36.0ms	314×	body	128	invalid
34.0ms	86×	body	1024	invalid
27.0ms	62×	body	1024	valid
26.0ms	90×	body	512	invalid
18.0ms	57×	body	512	valid
15.0ms	49×	body	256	valid
10.0ms	52×	body	256	invalid
10.0ms	18×	body	2048	invalid

Compiler

Compiled 1869 to 1463 computations (21.7% saved)

Details

analyze2.4s (20%)

sample46.0ms (0.4%)

simplify50.0ms (0.4%)

prune10.0ms (0.1%)

localize18.0ms (0.1%)

rewrite173.0ms (1.4%)

series1.3s (10.7%)

simplify78.0ms (0.6%)

prune239.0ms (2%)

localize14.0ms (0.1%)

rewrite115.0ms (0.9%)

series1.6s (13.1%)

simplify77.0ms (0.6%)

prune161.0ms (1.3%)

localize22.0ms (0.2%)

rewrite206.0ms (1.7%)

series426.0ms (3.5%)

simplify74.0ms (0.6%)

prune213.0ms (1.7%)

localize23.0ms (0.2%)

rewrite186.0ms (1.5%)

series795.0ms (6.5%)

simplify87.0ms (0.7%)

prune210.0ms (1.7%)

regimes811.0ms (6.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (23.3%)

Profiling