Details

sample219.0ms

Algorithm

intervals

Results

88.0ms	104×	body	320	valid
56.0ms	285×	body	80	nan
49.0ms	146×	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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.3b

localize53.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
9.1b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite84.0ms

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:

43.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
16.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
12.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

411.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
367.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
82.0ms	(sqrt (- (* g g) (* h h)))
66.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
3	3607
2	1083
1	413
0	181

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 33.2b

localize56.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite62.0ms

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:

10.0ms	(- (* g g) (* h h))
16.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
18.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* g g) (* h h))
351.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
86.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

81 → 81

Iterations

Iter	Nodes
3	2952
2	788
1	301
0	143

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize84.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite41.0ms

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
39.0ms	(- (* g g) (* h h))
59.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify4.7s

Counts

86 → 86

Iterations

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

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 32.6b

localize69.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite67.0ms

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:

15.0ms	(- (* g g) (* h h))
25.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
17.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* g g) (* h h))
366.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
59.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
3	2952
2	788
1	301
0	143

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.6b

regimes799.0ms

Accuracy

59.6% (1.3b remaining)

Error of 31.5b against oracle of 30.1b and baseline of 33.4b

bsearch776.0ms

Steps

Iters	Range		Point
11	-4.5596823755857694e-157	-7.384045806005983e-186	-1.6297615549700884e-171

simplify13.0ms

Iterations

Iter	Nodes
2	41
1	41
0	33

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.6s	3746×	body	320	valid
2.4s	4124×	body	160	valid
2.2s	8203×	body	80	nan
25.0ms	130×	body	80	valid