Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify243.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize9.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite42.0ms

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:

12.0ms	(- (* x x) (* (* y 4.0) y))
28.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (* x x) (* (* y 4.0) y))
81.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.0s

Counts

50 → 50

Iterations

Useful iterations: done (3.0s)

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

prune187.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune10.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize22.0ms

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))))
22.8b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
25.0b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite158.0ms

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:

97.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
28.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
31.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
84.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
68.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.6s

Counts

77 → 77

Iterations

Useful iterations: 2 (293.0ms)

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

prune303.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3)
8.7b	(cbrt (pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3))
22.8b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
25.0b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
24×	`cbrt-prod`
18×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `times-frac` `cube-prod`
12×	`associate-/r/`
8×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
5×	`pow1`
4×	`pow-exp` `add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/l*` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 124

Calls

4 calls:

54.0ms	(pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3)
24.0ms	(cbrt (pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3))
31.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
42.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3)
89.0ms	(cbrt (pow (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))) 3))
83.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
92.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.2s

Counts

136 → 136

Iterations

Useful iterations: 2 (388.0ms)

Iter	Nodes	Cost
0	170	3242
1	469	2789
2	1915	2507
done	5000	2507

prune421.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes180.0ms

Accuracy

60.4% (12.4b remaining)

Error of 12.8b against oracle of 0.4b and baseline of 31.7b

bsearch106.0ms

Steps

Iters	Range		Point
8	1.9328563387545914e+264	1.958651676891247e+268	1.0276101681725595e+266
8	2.3613467040659447e-173	6.170963443896032e-170	2.757556978790064e-173

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	47
1	27	47
done	27	47

end0.0ms

sample818.0ms

Algorithm

intervals

Results

544.0ms

8000×

body

valid