Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	89×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 19.8b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
18.4b	(sqrt (+ (* x x) y))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`fma-def`
8×	`add-cube-cbrt`
5×	`associate-l` `sqrt-prod` `hypot-def`
4×	`swap-sqr` `distribute-lft-out` `add-log-exp`
3×	`pow1` `associate-r`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `*-commutative` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 54

Calls

2 calls:

9.0ms	(+ (* x x) y)
9.0ms	(sqrt (+ (* x x) y))

series67.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(+ (* x x) y)
43.0ms	(sqrt (+ (* x x) y))

simplify63.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	149	170
1	495	157
2	1652	147
3	5001	142

prune98.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	4	61

Merged error: 0b

Counts

61 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

18.4b

(sqrt (* 1 (fma x x y)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

13×	`sqrt-prod`
11×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `unswap-sqr`
3×	`rem-sqrt-square` `associate-r` `associate-l`
2×	`sqrt-pow1`
1×	`add-exp-log` `expm1-log1p-u` `pow1/2` `pow-prod-down` `*-commutative` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

5.0ms

(sqrt (* 1 (fma x x y)))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(sqrt (* 1 (fma x x y)))

simplify192.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	107	113
1	297	103
2	1155	98
3	4924	97
4	5001	97

prune37.0ms

Filtered

31 candidates to 17 candidates (54.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Merged error: 0b

Counts

35 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

18.4b	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
28.5b	(cbrt (* x x))
28.5b	(cbrt (* x x))
28.5b	(cbrt (* x x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
9×	`swap-sqr` `associate-r` `associate-l`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 90

Calls

4 calls:

1.0ms	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
4.0ms	(cbrt (* x x))
4.0ms	(cbrt (* x x))
8.0ms	(cbrt (* x x))

series703.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
183.0ms	(cbrt (* x x))
189.0ms	(cbrt (* x x))
182.0ms	(cbrt (* x x))

simplify113.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	176	542
1	567	507
2	2959	459
3	5001	452

prune198.0ms

Filtered

102 candidates to 78 candidates (76.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/2 (/ y x) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/2 (/ y x) x)

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(fma 1/2 (/ y x) x)

simplify108.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	21	44
1	48	39
2	156	39
3	585	39
4	2784	39
5	5001	39

prune21.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	13	4	17

Merged error: 0b

Counts

17 → 4

regimes98.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 20.5b

bsearch55.0ms

Steps

Iters	Range		Point
7	2.897814718770587e+103	1.4843112306718033e+105	7.942052068260315e+104
7	-5.278913287823028e+154	-1.5250798497753893e+153	-1.3645593651226006e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	35	9
2	37	9
3	37	9

end0.0ms

sample461.0ms

Algorithm

intervals

Results

197.0ms	8000×	body	80	valid
55.0ms	2668×	body	80	nan