Details

sample114.0ms

Algorithm

intervals

Results

42.0ms	116×	body	320	valid
21.0ms	133×	body	160	valid
20.0ms	255×	body	80	nan
1.0ms	7×	body	80	valid

simplify13.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	314	36
4	633	36
5	1023	36
6	1325	36
7	1628	36
8	2988	36
done	5001	36

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize37.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (- (* g g) (* h h)))

rewrite157.0ms

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:

48.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
69.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
20.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

430.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
445.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
62.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1363	1211
done	5000	1166

prune737.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.7b

localize47.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (- (* g g) (* h h)))

rewrite142.0ms

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:

10.0ms	(- (* g g) (* h h))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
25.0ms	(sqrt (- (* g g) (* h h)))
33.0ms	(sqrt (- (* g g) (* h h)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* g g) (* h h))
479.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
75.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	144	1192
1	303	1048
2	913	954
3	3379	944
done	5000	934

prune782.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.3b

localize44.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (- (* g g) (* h h)))

rewrite146.0ms

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:

15.0ms	(- (* g g) (* h h))
84.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
23.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* g g) (* h h))
472.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
80.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	144	1192
1	303	1048
2	913	954
3	3379	944
done	5000	934

prune669.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.3b

localize50.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (- (* g g) (* h h)))

rewrite110.0ms

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:

10.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
22.0ms	(sqrt (- (* g g) (* h h)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* g g) (* h h))
440.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
58.0ms	(sqrt (- (* g g) (* h h)))
76.0ms	(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune597.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.3b

regimes886.0ms

Accuracy

69.6% (1.1b remaining)

Error of 31.6b against oracle of 30.6b and baseline of 34.1b

bsearch235.0ms

Steps

Iters	Range		Point
9	-3.461821245196587e-165	-7.460550453002327e-171	-3.4219843915306896e-165

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	34	77
1	42	75
done	42	75

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.7s	8143×	body	80	nan
1.6s	3733×	body	320	valid
1.0s	4114×	body	160	valid
17.0ms	153×	body	80	valid