Details

analyze2.4s

Algorithm

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

sample48.0ms

Algorithm

intervals

Results

27.0ms	251×	body	80	valid
2.0ms	5×	body	320	invalid
1.0ms	3×	body	640	invalid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5362	28

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 16.4b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(*.f64 K (+.f64 m n))
32.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `prod-exp_binary64` `cos-sum_binary64` `times-frac_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

10.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(*.f64 K (+.f64 m n))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series61.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(*.f64 K (+.f64 m n))
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify36.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4936	801
1	4936	801

prune83.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 1.0b

Counts

79 → 5

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
3×	`pow-unpow_binary64` `add-cube-cbrt_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `pow-exp_binary64`

Counts

1 → 21

Calls

1 calls:

12.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify61.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4875	270
1	4875	270

prune30.0ms

Filtered

15 candidates to 24 candidates (-60.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Merged error: 1.0b

Counts

29 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
15.0b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
15.0b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
41.3b	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `pow1/3_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
62.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
65.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
24.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify46.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	975
1	4994	975

prune94.0ms

Filtered

55 candidates to 64 candidates (-16.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	63	6	69

Merged error: 1.0b

Counts

69 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
32.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
5×	`add-log-exp_binary64`
4×	`associate-r_binary64` `log-prod_binary64` `log-pow_binary64`
3×	`sub-neg_binary64` `associate-l_binary64` `cos-diff_binary64` `cos-sum_binary64`
2×	`associate-*r/_binary64` `exp-diff_binary64` `exp-sum_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `log-div_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

7.0ms	(*.f64 K (+.f64 m n))
10.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
10.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series92.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 K (+.f64 m n))
36.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
26.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify76.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4935	788
1	4935	788

prune58.0ms

Filtered

53 candidates to 74 candidates (-39.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	74	6	80

Merged error: 1.0b

Counts

80 → 6

regimes305.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

856.0ms	7825×	body	80	valid
52.0ms	87×	body	1280	invalid
32.0ms	74×	body	640	invalid
29.0ms	46×	body	1280	valid
27.0ms	261×	body	80	invalid
27.0ms	59×	body	640	valid
22.0ms	69×	body	320	invalid
16.0ms	49×	body	320	valid
9.0ms	42×	body	160	invalid
5.0ms	21×	body	160	valid
2.0ms	2×	body	2560	invalid

Details

analyze2.4s

sample48.0ms

simplify40.0ms

prune9.0ms

localize27.0ms

rewrite39.0ms

series61.0ms

simplify36.0ms

prune83.0ms

localize16.0ms

rewrite12.0ms

series14.0ms

simplify61.0ms

prune30.0ms

localize29.0ms

rewrite35.0ms

series211.0ms

simplify46.0ms

prune94.0ms

localize28.0ms

rewrite39.0ms

series92.0ms

simplify76.0ms

prune58.0ms

regimes305.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling