Details

sample222.0ms

Algorithm

intervals

Results

76.0ms	251×	body	80	nan
71.0ms	128×	body	320	valid
45.0ms	122×	body	160	valid
1.0ms	6×	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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize55.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
7.5b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite64.0ms

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:

27.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
17.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
10.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series949.0ms

Counts

4 → 12

Calls

4 calls:

446.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
377.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
68.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
3	3607
2	1083
1	413
0	181

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.5b

localize51.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.5b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
58.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
384.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
72.0ms	(sqrt (- (* g g) (* h h)))
94.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	3570
2	915
1	317
0	143

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.0b

localize53.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

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:

12.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
11.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
39.0ms	(- (* g g) (* h h))
75.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify5.3s

Counts

86 → 86

Iterations

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

prune1.8s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 30.0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

15.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify2.1s

Counts

88 → 88

Iterations

Iter	Nodes
5	3997
4	1337
3	566
2	234
1	106
0	47

prune1.8s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 30.0b

regimes1.6s

Accuracy

33.9% (1.1b remaining)

Error of 31.0b against oracle of 30.0b and baseline of 31.6b

bsearch5.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	60
1	60
0	45

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.8s	3714×	body	320	valid
2.4s	4111×	body	160	valid
1.7s	7829×	body	80	nan
31.0ms	175×	body	80	valid