Details

sample105.0ms

Algorithm

intervals

Results

41.0ms	109×	body	320	valid
23.0ms	144×	body	160	valid
18.0ms	243×	body	80	nan
0.0ms	3×	body	80	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4583
7	1834
6	1286
5	947
4	584
3	298
2	122
1	43
0	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize51.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

27.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series945.0ms

Counts

4 → 12

Calls

4 calls:

421.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
416.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1399
1	395
0	166

prune754.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.5b

localize61.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite51.0ms

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×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
29.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
397.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1596
1	343
0	137

prune792.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.2b

localize49.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite52.0ms

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×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
30.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
353.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
72.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1596
1	343
0	137

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.2b

localize125.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

7.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
4	1718
3	582
2	238
1	98
0	44

prune709.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.2b

regimes1.5s

Accuracy

69.3% (1.1b remaining)

Error of 31.3b against oracle of 30.3b and baseline of 33.8b

bsearch254.0ms

Steps

Iters	Range		Point
10	-1.663081557722865e-151	-2.1148202087381245e-165	-5.401023155583568e-158

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	4098×	body	160	valid
1.2s	3746×	body	320	valid
993.0ms	7901×	body	80	nan
14.0ms	156×	body	80	valid