Details

sample40.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
6.0ms	96×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize17.0ms

Local error

Found 1 expressions with local error:

16.2b

(sqrt (+ (* x x) y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

1 → 16

Calls

1 calls:

15.0ms

(sqrt (+ (* x x) y))

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(sqrt (+ (* x x) y))

simplify1.9s

Counts

19 → 19

Iterations

Iter	Nodes
done	5000
4	2302
3	793
2	279
1	115
0	52

prune91.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--`

Counts

2 → 46

Calls

2 calls:

8.0ms	(- (* -1/2 (/ y x)) x)
12.0ms	(* -1/2 (/ y x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(- (* -1/2 (/ y x)) x)
33.0ms	(* -1/2 (/ y x))

simplify1.4s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1752
2	641
1	229
0	94

prune168.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `div-inv`

Counts

2 → 45

Calls

2 calls:

8.0ms	(+ x (* 1/2 (/ y x)))
14.0ms	(* 1/2 (/ y x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ x (* 1/2 (/ y x)))
31.0ms	(* 1/2 (/ y x))

simplify1.7s

Counts

51 → 51

Iterations

Iter	Nodes
done	5003
3	2154
2	712
1	234
0	89

prune158.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (* (* x x) (* x x)) (* y y))
12.8b	(sqrt (- (* (* x x) (* x x)) (* y y)))
16.2b	(sqrt (- (* x x) y))
16.2b	(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
49×	`add-sqr-sqrt` `times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
19×	`difference-of-squares`
8×	`sqrt-div`
7×	`associate-/r` `associate-/l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`flip3--` `flip--`
4×	`insert-posit16`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 129

Calls

4 calls:

39.0ms	(- (* (* x x) (* x x)) (* y y))
68.0ms	(sqrt (- (* (* x x) (* x x)) (* y y)))
16.0ms	(sqrt (- (* x x) y))
119.0ms	(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* (* x x) (* x x)) (* y y))
67.0ms	(sqrt (- (* (* x x) (* x x)) (* y y)))
70.0ms	(sqrt (- (* x x) y))
130.0ms	(/ (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)))

simplify2.9s

Counts

141 → 141

Iterations

Iter	Nodes
done	5023
3	4225
2	941
1	375
0	187

prune510.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes217.0ms

Accuracy

97.9% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 19.7b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.514115744383235e+64	1.0077232000722927e+68	9.943288082924311e+67
9	-3.59454624536844e+155	-4.448318838164251e+147	-1.3262598264970426e+154

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample872.0ms

Algorithm

intervals

Results

453.0ms	8000×	body	80	valid
148.0ms	2731×	body	80	nan