Details

analyze1.0ms

Algorithm

Search

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

sample27.0ms

Algorithm

intervals

Results

14.0ms	91×	body	1280	valid
5.0ms	140×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 11.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1.0))
1.0b	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1.0))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

series6.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1.0))
5.0ms	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

simplify79.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5349	236

prune29.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Merged error: 0.1b

Counts

28 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1.0))
0.1b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

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

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1.0))
3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune43.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Merged error: 0.1b

Counts

38 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 N (+.f64 1.0 N))) (cbrt.f64 (*.f64 N (+.f64 1.0 N))))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
16.2b	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1.0 N))) (cbrt.f64 (*.f64 N (+.f64 1.0 N))))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
5.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (cbrt.f64 (.f64 N (+.f64 1.0 N))) (cbrt.f64 (*.f64 N (+.f64 1.0 N))))
11.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
12.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))
15.0ms	(cbrt.f64 (*.f64 N (+.f64 1.0 N)))

simplify38.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4929	1087
1	4929	1087

prune121.0ms

Filtered

71 candidates to 84 candidates (-18.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Merged error: 0.1b

Counts

89 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
15.7b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
15.7b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 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 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
6.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
3.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
8.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
8.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5253	989

prune68.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Merged error: 0.1b

Counts

99 → 8

regimes41.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample814.0ms

Algorithm

intervals

Results

446.0ms	2851×	body	1280	valid
142.0ms	4039×	body	80	valid
85.0ms	654×	body	640	valid
30.0ms	312×	body	320	valid
11.0ms	144×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify8.0ms

prune2.0ms

localize5.0ms

rewrite5.0ms

series6.0ms

simplify79.0ms

prune29.0ms

localize5.0ms

rewrite8.0ms

series9.0ms

simplify70.0ms

prune43.0ms

localize9.0ms

rewrite22.0ms

series52.0ms

simplify38.0ms

prune121.0ms

localize8.0ms

rewrite12.0ms

series21.0ms

simplify46.0ms

prune68.0ms

regimes41.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample814.0ms

Profiling