Details

sample277.0ms

Algorithm

intervals

Results

90.0ms	123×	body	320	valid
89.0ms	223×	body	80	nan
64.0ms	128×	body	160	valid
1.0ms	5×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	2529
5	1599
4	844
3	368
2	117
1	45
0	19

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.5b

localize58.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
8.1b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow1/3` `associate-l/` `associate-r/` `flip-+` `flip--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

32.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
46.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series969.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
435.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
67.0ms	(sqrt (- (* g g) (* h h)))
81.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
3	3613
2	1081
1	413
0	181

prune796.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.0b

localize47.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `cbrt-div` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
15.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
9.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
378.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
50.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

81 → 81

Iterations

Iter	Nodes
3	2952
2	788
1	301
0	143

prune812.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.7b

localize60.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 74

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
14.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* g g) (* h h))
55.0ms	(- (* g g) (* h h))
63.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify4.3s

Counts

86 → 86

Iterations

Iter	Nodes
4	8974
3	1671
2	397
1	136
0	64

prune755.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.7b

localize83.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
7.7b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) a))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
11×	`sqrt-prod`
9×	`difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `div-inv`

Counts

4 → 90

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
13.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) a))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
279.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) a))
82.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	2919
2	870
1	371
0	190

prune860.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 30.6b

regimes1.5s

Accuracy

0% (1.6b remaining)

Error of 31.4b against oracle of 29.8b and baseline of 31.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.1s	3663×	body	320	valid
2.0s	4193×	body	160	valid
1.7s	7671×	body	80	nan
26.0ms	144×	body	80	valid