Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	98×	body	80	nan

simplify2.0ms

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: 21.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
20.4b	(sqrt (+ (* x x) y))

rewrite17.0ms

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)
9.0ms	(sqrt (+ (* x x) y))

series69.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* x x) y)
47.0ms	(sqrt (+ (* x x) y))

simplify3.1s

Counts

32 → 32

Iterations

Useful iterations: 4 (568.0ms)

Iter	Nodes	Cost
0	59	319
1	140	294
2	347	258
3	826	255
4	2004	254
5	4212	254
done	5000	254

prune74.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

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))))
20.4b	(sqrt (+ (* x x) y))
20.4b	(sqrt (+ (* x x) y))

rewrite93.0ms

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:

10.0ms	(sqrt (sqrt (+ (* x x) y)))
60.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
9.0ms	(sqrt (+ (* x x) y))
9.0ms	(sqrt (+ (* x x) y))

series197.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (sqrt (+ (* x x) y)))
42.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
40.0ms	(sqrt (+ (* x x) y))
44.0ms	(sqrt (+ (* x x) y))

simplify3.0s

Counts

146 → 146

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	138	2475
1	262	1570
2	631	1419
3	1554	1383
4	4280	1351
done	5001	1337

prune261.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 44

Calls

2 calls:

14.0ms	(* (/ y x) -1/2)
10.0ms	(- (* (/ y x) -1/2) x)

series57.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(* (/ y x) -1/2)
40.0ms	(- (* (/ y x) -1/2) x)

simplify1.7s

Counts

50 → 50

Iterations

Useful iterations: 3 (487.0ms)

Iter	Nodes	Cost
0	91	434
1	209	400
2	570	373
3	1747	371
done	5000	371

prune73.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

13.0ms	(* 1/2 (/ y x))
6.0ms	(+ x (* 1/2 (/ y x)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 1/2 (/ y x))
26.0ms	(+ x (* 1/2 (/ y x)))

simplify1.6s

Counts

49 → 49

Iterations

Useful iterations: 3 (358.0ms)

Iter	Nodes	Cost
0	87	443
1	222	397
2	640	373
3	1862	372
done	5001	372

prune70.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes148.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.6b

bsearch34.0ms

Steps

Iters	Range		Point
4	3.0943207782900225e+107	4.8205448993048816e+107	3.903488335015738e+107
9	-2.3499377934639055e+159	-2.508529027316973e+152	-1.3474120016627302e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample415.0ms

Algorithm

intervals

Results

142.0ms	8000×	body	80	valid
46.0ms	2733×	body	80	nan