Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample26.0ms

Algorithm

intervals

Results

13.0ms	86×	body	1280	valid
5.0ms	142×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 14.0b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-atan_binary64`

Counts

1 → 14

Calls

1 calls:

4.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify114.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5627	291

prune12.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Merged error: 0.2b

Counts

18 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`add-log-exp_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series37.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(*.f64 N (+.f64 N 1))
8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify96.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5425	383

prune28.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	33	5	38

Merged error: 0.1b

Counts

38 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
8×	`swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
6.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
8.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
27.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
30.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5159	1485

prune74.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	91	8	99

Merged error: 0.1b

Counts

99 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64`
45×	`pow1_binary64`
30×	`pow1/2_binary64` `pow-prod-up_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-l_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64`
2×	`swap-sqr_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64`
1×	`associate-r_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
24.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
26.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
28.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify105.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4895	1397
1	4895	1397

prune87.0ms

Filtered

49 candidates to 97 candidates (-98.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	97	8	105

Merged error: 0.1b

Counts

105 → 8

regimes42.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample804.0ms

Algorithm

intervals

Results

440.0ms	2815×	body	1280	valid
145.0ms	4102×	body	80	valid
77.0ms	614×	body	640	valid
30.0ms	317×	body	320	valid
11.0ms	152×	body	160	valid

Details

analyze1.0ms

sample26.0ms

simplify15.0ms

prune5.0ms

localize6.0ms

rewrite4.0ms

series12.0ms

simplify114.0ms

prune12.0ms

localize5.0ms

rewrite8.0ms

series37.0ms

simplify96.0ms

prune28.0ms

localize8.0ms

rewrite12.0ms

series73.0ms

simplify79.0ms

prune74.0ms

localize11.0ms

rewrite23.0ms

series90.0ms

simplify105.0ms

prune87.0ms

regimes42.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample804.0ms

Profiling