Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify360.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	35	19
3	67	19
4	111	19
5	158	19
6	173	19
7	174	19
done	174	19

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize16.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (* x x) (* (* y 4.0) y))
30.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

15.0ms	(- (* x x) (* (* y 4.0) y))
50.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series162.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (* x x) (* (* y 4.0) y))
91.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.9s

Counts

50 → 50

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	82	1196
1	220	1174
2	738	1060
3	2712	1056
done	5000	1042

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
21.7b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
22.5b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-/r/`
7×	`add-cube-cbrt` `times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv`
3×	`pow1` `distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

3 → 68

Calls

3 calls:

113.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
42.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
31.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
75.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
78.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.6s

Counts

77 → 77

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	130	1924
1	351	1812
2	1311	1590
done	5000	1590

prune289.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
0.0b	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
2.6b	(- (* x x) (* (* y 4.0) y))
30.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 140

Calls

4 calls:

42.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
40.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
8.0ms	(- (* x x) (* (* y 4.0) y))
52.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3))
106.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 3)
77.0ms	(- (* x x) (* (* y 4.0) y))
101.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.3s

Counts

152 → 152

Iterations

Useful iterations: 2 (344.0ms)

Iter	Nodes	Cost
0	166	5027
1	477	4526
2	1656	4066
done	5001	4066

prune445.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune1.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes310.0ms

Accuracy

60.2% (12.6b remaining)

Error of 12.9b against oracle of 0.3b and baseline of 31.9b

bsearch233.0ms

Steps

Iters	Range		Point
10	1.2073698495971617e+61	3.217811591970086e+74	3.168622066814081e+74
8	1.6702892525439038e-56	5.683846200959625e-53	1.6377527584540488e-55
10	-3.4395002952206196e-47	-1.5066383282189058e-62	-1.5308621854628612e-62
5	-1.7457635943519997e+137	-5.665103565004941e+136	-1.2876568362185878e+137

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	31	73
1	36	71
done	36	71

end0.0ms

sample1.3s

Algorithm

intervals

Results

990.0ms

8000×

body

valid