Details

sample150.0ms

Algorithm

intervals

Results

45.0ms	123×	body	320	valid
33.0ms	270×	body	80	nan
32.0ms	129×	body	160	valid
1.0ms	4×	body	80	valid

simplify4.9s

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.9b

localize54.0ms

Local error

Found 4 expressions with local error:

9.4b	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
10.8b	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
32.1b	(sqrt (* (+ g h) (- g h)))
32.1b	(sqrt (* (+ g h) (- g h)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

550×	`times-frac`
312×	`add-sqr-sqrt` `*-un-lft-identity`
226×	`cbrt-prod`
224×	`add-cube-cbrt`
44×	`distribute-lft-out--` `difference-of-squares`
21×	`div-inv`
16×	`sqrt-div`
10×	`frac-times` `pow1`
8×	`flip3--` `flip--`
6×	`cbrt-div` `flip3-+` `associate-*r/` `associate-/r/` `flip-+`
5×	`associate-*l/`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1/2` `pow1/3` `pow-prod-down` `sqrt-prod`

Counts

4 → 286

Calls

4 calls:

35.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
38.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
9.0ms	(sqrt (* (+ g h) (- g h)))
9.0ms	(sqrt (* (+ g h) (- g h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

358.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
467.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
90.0ms	(sqrt (* (+ g h) (- g h)))
92.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.1s

Counts

298 → 298

Iterations

Iter	Nodes
done	5000
1	2242
0	976

prune3.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.0b

localize68.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (* (+ g h) (- g h))) g)
9.4b	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
32.1b	(sqrt (* (+ h g) (- g h)))
32.1b	(sqrt (* (+ g h) (- g h)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

550×	`times-frac`
314×	`add-sqr-sqrt` `*-un-lft-identity`
225×	`cbrt-prod`
224×	`add-cube-cbrt`
45×	`distribute-lft-out--` `difference-of-squares`
21×	`div-inv`
16×	`sqrt-div`
10×	`pow1`
8×	`frac-times`
7×	`flip3--` `flip--`
6×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log`

Counts

4 → 286

Calls

4 calls:

18.0ms	(- (sqrt (* (+ g h) (- g h))) g)
34.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
15.0ms	(sqrt (* (+ h g) (- g h)))
26.0ms	(sqrt (* (+ g h) (- g h)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (sqrt (* (+ g h) (- g h))) g)
450.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
102.0ms	(sqrt (* (+ h g) (- g h)))
80.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.0s

Counts

298 → 298

Iterations

Iter	Nodes
done	5000
1	2230
0	980

prune3.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 33.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ g (sqrt (* (+ h g) (- g h))))
1.2b	(- (sqrt (* (- g h) (+ h g))) g)
32.1b	(sqrt (* (- g h) (+ h g)))
32.1b	(sqrt (* (+ h g) (- g h)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1`
8×	`frac-times` `*-un-lft-identity` `add-log-exp`
7×	`flip3-+` `flip3--` `flip-+` `flip--`
6×	`add-sqr-sqrt`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `add-cube-cbrt`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

16.0ms	(+ g (sqrt (* (+ h g) (- g h))))
30.0ms	(- (sqrt (* (- g h) (+ h g))) g)
9.0ms	(sqrt (* (- g h) (+ h g)))
9.0ms	(sqrt (* (+ h g) (- g h)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ g (sqrt (* (+ h g) (- g h))))
94.0ms	(- (sqrt (* (- g h) (+ h g))) g)
77.0ms	(sqrt (* (- g h) (+ h g)))
105.0ms	(sqrt (* (+ h g) (- g h)))

simplify616.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1150
1	321
0	144

prune982.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.4b

localize108.0ms

Local error

Found 4 expressions with local error:

32.1b	(sqrt (* (- g h) (+ h g)))
32.1b	(sqrt (* (+ g h) (- g h)))
32.1b	(sqrt (* (+ g h) (- g h)))
32.1b	(sqrt (* (+ g h) (- g h)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div`
16×	`frac-times` `pow1`
12×	`flip3-+` `flip3--` `flip-+` `flip--`
8×	`sqrt-pow1` `associate-l/` `associate-r/`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `pow-prod-down` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt (* (- g h) (+ h g)))
14.0ms	(sqrt (* (+ g h) (- g h)))
12.0ms	(sqrt (* (+ g h) (- g h)))
18.0ms	(sqrt (* (+ g h) (- g h)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (* (- g h) (+ h g)))
78.0ms	(sqrt (* (+ g h) (- g h)))
95.0ms	(sqrt (* (+ g h) (- g h)))
96.0ms	(sqrt (* (+ g h) (- g h)))

simplify752.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1092
1	238
0	104

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.4b

regimes649.0ms

Accuracy

73.6% (0.6b remaining)

Error of 31.6b against oracle of 31.0b and baseline of 33.3b

bsearch322.0ms

Steps

Iters	Range		Point
8	-1.622693661133134e-179	-2.2020829157506872e-182	-1.593804505093949e-179

simplify24.0ms

Iterations

Iter	Nodes
done	78
3	78
2	74
1	60
0	44

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	3804×	body	320	valid
1.6s	4042×	body	160	valid
1.1s	8006×	body	80	nan
18.0ms	154×	body	80	valid