Details

sample65.0ms

Algorithm

intervals

Results

19.0ms	117×	body	320	valid
14.0ms	246×	body	80	nan
14.0ms	136×	body	160	valid
0.0ms	3×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	122	36
3	301	36
4	574	36
5	885	36
6	1154	36
7	1428	36
8	2979	36
done	5000	36

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize16.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
297.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
45.0ms	(sqrt (- (* g g) (* h h)))
43.0ms	(sqrt (- (* g g) (* h h)))

simplify485.0ms

Counts

80 → 80

Iterations

Useful iterations: done (482.0ms)

Iter	Nodes	Cost
0	183	1500
1	412	1315
2	1436	1211
done	5001	1198

prune414.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 32.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
300.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
46.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: 3 (382.0ms)

Iter	Nodes	Cost
0	144	1192
1	310	1048
2	1053	954
3	4257	944
done	5000	944

prune444.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.9b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (* g g) (* h h))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify995.0ms

Counts

82 → 82

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	62	912
1	136	824
2	471	722
3	1868	722
done	5001	720

prune427.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.9b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (* g g) (* h h))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify991.0ms

Counts

82 → 82

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	62	912
1	136	824
2	471	722
3	1868	722
done	5001	720

prune376.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.9b

regimes569.0ms

Accuracy

65.6% (1.2b remaining)

Error of 31.6b against oracle of 30.3b and baseline of 33.9b

bsearch138.0ms

Steps

Iters	Range		Point
9	-1.4950050582891928e-169	-1.4248292396361266e-175	-1.2934885954313043e-169

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	66
1	39	66
done	39	66

end0.0ms

sample1.8s

Algorithm

intervals

Results

589.0ms	3698×	body	320	valid
441.0ms	4149×	body	160	valid
392.0ms	7929×	body	80	nan
8.0ms	153×	body	80	valid