Details

sample21.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	81×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
done	6	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.7b	(sqrt (+ (* x x) y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

8.0ms	(+ (* x x) y)
10.0ms	(sqrt (+ (* x x) y))

series68.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) y)
41.0ms	(sqrt (+ (* x x) y))

simplify474.0ms

Counts

32 → 32

Iterations

Useful iterations: done (473.0ms)

Iter	Nodes	Cost
0	59	319
1	154	294
2	700	258
done	5000	255

prune95.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x x) y)))
0.5b	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
19.7b	(sqrt (+ (* x x) y))
19.7b	(sqrt (+ (* x x) y))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ (* x x) y)))
64.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
9.0ms	(sqrt (+ (* x x) y))
10.0ms	(sqrt (+ (* x x) y))

series262.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt (sqrt (+ (* x x) y)))
57.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
47.0ms	(sqrt (+ (* x x) y))
42.0ms	(sqrt (+ (* x x) y))

simplify882.0ms

Counts

146 → 146

Iterations

Useful iterations: done (877.0ms)

Iter	Nodes	Cost
0	138	2475
1	308	1579
2	1334	1419
done	5000	1396

prune294.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-l`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

23.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify584.0ms

Counts

35 → 35

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	67	261
1	160	244
2	663	224
done	5000	224

prune63.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

15.0ms

(* 1/2 (/ y x))

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(* 1/2 (/ y x))

simplify1.6s

Counts

35 → 35

Iterations

Useful iterations: 3 (535.0ms)

Iter	Nodes	Cost
0	68	277
1	178	250
2	570	230
3	2465	229
done	5000	229

prune94.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes236.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.2b

bsearch45.0ms

Steps

Iters	Range		Point
7	5.97211645844156e+100	7.949077325264555e+102	6.791589890324519e+101
8	-6.888726652681395e+154	-1.350243324689865e+150	-1.3369273759662153e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	22	28
done	22	28

end0.0ms

sample970.0ms

Algorithm

intervals

Results

244.0ms	8000×	body	80	valid
98.0ms	2721×	body	80	nan