Details

sample192.0ms

Algorithm

intervals

Results

73.0ms	143×	body	320	valid
52.0ms	227×	body	80	nan
36.0ms	109×	body	160	valid
0.0ms	4×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3432
4	1243
3	370
2	119
1	47
0	19

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.3b

localize52.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

236×	`add-sqr-sqrt`
124×	`associate-l`
114×	`*-un-lft-identity`
112×	`cbrt-prod` `cbrt-div`
80×	`times-frac`
78×	`add-cube-cbrt`
72×	`frac-times` `associate-/r*`
67×	`sqrt-prod`
52×	`difference-of-squares`
48×	`associate-r`
46×	`unswap-sqr`
36×	`associate-*l/`
34×	`*-commutative`
24×	`swap-sqr`
21×	`flip3--` `flip--`
19×	`flip3-+` `flip-+`
18×	`associate-/l*`
12×	`distribute-lft-out--`
6×	`pow1` `clear-num` `frac-2neg`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv` `distribute-lft-out`

Counts

4 → 342

Calls

4 calls:

570.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
626.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
130.0ms	(sqrt (- (* g g) (* h h)))
131.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

493.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
387.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
80.0ms	(sqrt (- (* g g) (* h h)))
82.0ms	(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts

354 → 354

Iterations

Iter	Nodes
done	5000
1	2105
0	734

prune2.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 25.8b

localize69.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

441×	`add-sqr-sqrt`
239×	`*-un-lft-identity`
225×	`prod-diff`
197×	`add-cube-cbrt`
163×	`associate-l`
129×	`swap-sqr`
118×	`associate-r`
77×	`difference-of-squares`
74×	`unswap-sqr`
68×	`*-commutative`
67×	`sqrt-prod`
57×	`cbrt-prod`
56×	`cbrt-div`
40×	`times-frac`
36×	`frac-times` `associate-/r*`
22×	`flip3--` `flip--`
18×	`associate-*l/`
17×	`distribute-lft-out--`
15×	`fma-neg`
9×	`associate-/l*`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`sub-neg` `distribute-rgt-neg-in` `pow1/3` `diff-log` `div-inv`

Counts

4 → 505

Calls

4 calls:

64.0ms	(- (* g g) (* h h))
701.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
126.0ms	(sqrt (- (* g g) (* h h)))
110.0ms	(sqrt (- (* g g) (* h h)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
387.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
78.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify3.2s

Counts

517 → 517

Iterations

Iter	Nodes
done	5000
2	4970
1	1744
0	729

prune2.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 25.0b

localize78.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
2.0b	(- (* g g) (* h h))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite457.0ms

Algorithm

rewrite-expression-head

Rules

642×	`add-sqr-sqrt`
450×	`prod-diff`
364×	`*-un-lft-identity`
316×	`add-cube-cbrt`
234×	`swap-sqr`
202×	`associate-l`
186×	`associate-r`
102×	`*-commutative` `unswap-sqr`
100×	`difference-of-squares`
66×	`sqrt-prod`
30×	`fma-neg`
20×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 666

Calls

4 calls:

67.0ms	(- (* g g) (* h h))
103.0ms	(- (* g g) (* h h))
125.0ms	(sqrt (- (* g g) (* h h)))
111.0ms	(sqrt (- (* g g) (* h h)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
52.0ms	(- (* g g) (* h h))
74.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

678 → 678

Iterations

Iter	Nodes
done	5000
3	3601
2	1403
1	706
0	308

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 25.0b

localize83.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
2.0b	(- (* g g) (* h h))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

642×	`add-sqr-sqrt`
450×	`prod-diff`
364×	`*-un-lft-identity`
316×	`add-cube-cbrt`
234×	`swap-sqr`
202×	`associate-l`
186×	`associate-r`
102×	`*-commutative` `unswap-sqr`
100×	`difference-of-squares`
66×	`sqrt-prod`
30×	`fma-neg`
20×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 666

Calls

4 calls:

88.0ms	(- (* g g) (* h h))
77.0ms	(- (* g g) (* h h))
150.0ms	(sqrt (- (* g g) (* h h)))
113.0ms	(sqrt (- (* g g) (* h h)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
55.0ms	(- (* g g) (* h h))
88.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify2.8s

Counts

678 → 678

Iterations

Iter	Nodes
done	5000
3	3601
2	1403
1	706
0	308

prune1.6s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 25.0b

regimes1.5s

Accuracy

26.7% (1.3b remaining)

Error of 30.4b against oracle of 29.1b and baseline of 30.9b

bsearch322.0ms

Steps

Iters	Range		Point
10	1.7822550191445485e-157	2.855344257932453e-141	1.820567991238995e-157

simplify21.0ms

Iterations

Iter	Nodes
done	46
2	46
1	44
0	33

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.8s	3746×	body	320	valid
1.9s	4110×	body	160	valid
1.7s	7860×	body	80	nan
27.0ms	144×	body	80	valid