Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	100×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.4b	(sqrt (+ (* x x) y))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

2 → 26

Calls

2 calls:

6.0ms	(+ (* x x) y)
11.0ms	(sqrt (+ (* x x) y))

series96.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* x x) y)
64.0ms	(sqrt (+ (* x x) y))

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
done	5005
3	1369
2	399
1	146
0	59

prune164.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) y)
0.1b	(* (sqrt (+ (* x x) y)) (+ (* x x) y))
19.4b	(sqrt (+ (* x x) y))
30.7b	(cbrt (* (sqrt (+ (* x x) y)) (+ (* x x) y)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`flip3-+` `sqrt-div` `flip-+`
11×	`pow1`
8×	`frac-times` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`associate-l/` `associate-r/`
3×	`sqrt-pow1` `pow1/2` `associate-r`
2×	`pow-plus` `cube-unmult` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

7.0ms	(+ (* x x) y)
49.0ms	(* (sqrt (+ (* x x) y)) (+ (* x x) y))
8.0ms	(sqrt (+ (* x x) y))
25.0ms	(cbrt (* (sqrt (+ (* x x) y)) (+ (* x x) y)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* x x) y)
103.0ms	(* (sqrt (+ (* x x) y)) (+ (* x x) y))
52.0ms	(sqrt (+ (* x x) y))
49.0ms	(cbrt (* (sqrt (+ (* x x) y)) (+ (* x x) y)))

simplify3.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5014
3	4885
2	1118
1	369
0	133

prune390.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`add-sqr-sqrt` `pow1` `+-commutative` `sum-log` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`

Counts

1 → 11

Calls

1 calls:

4.0ms

(+ x (* 1/2 (/ y x)))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(+ x (* 1/2 (/ y x)))

simplify2.4s

Counts

14 → 14

Iterations

Iter	Nodes
done	5000
4	2829
3	938
2	286
1	86
0	27

prune62.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (* -1/2 (/ y x)) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`add-sqr-sqrt` `pow1` `sub-neg` `*-un-lft-identity` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--`

Counts

1 → 12

Calls

1 calls:

8.0ms

(- (* -1/2 (/ y x)) x)

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(- (* -1/2 (/ y x)) x)

simplify2.7s

Counts

15 → 15

Iterations

Iter	Nodes
done	5005
4	3380
3	943
2	220
1	82
0	32

prune57.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes407.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.5b

bsearch72.0ms

Steps

Iters	Range		Point
7	1.9512761569531488e+87	3.570329597462732e+89	3.200301816232116e+89
10	-1.0872942423520943e+158	-1.101416214509623e+146	-1.3357280532097962e+154

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

710.0ms	8000×	body	80	valid
121.0ms	2706×	body	80	nan