Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	95×	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: 20.8b

localize5.0ms

Local error

Found 2 expressions with local error:

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

series72.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* x x) y)
50.0ms	(sqrt (+ (* x x) y))

simplify509.0ms

Counts

32 → 32

Iterations

Useful iterations: done (508.0ms)

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

prune76.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

6.0ms	(+ x (* 1/2 (/ y x)))
18.0ms	(* 1/2 (/ y x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ x (* 1/2 (/ y x)))
21.0ms	(* 1/2 (/ y x))

simplify2.1s

Counts

49 → 49

Iterations

Useful iterations: 3 (812.0ms)

Iter	Nodes	Cost
0	87	443
1	238	397
2	805	373
3	3487	372
done	5000	372

prune113.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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:

18.0ms	(- (* (/ y x) -1/2) x)
25.0ms	(* (/ y x) -1/2)

series86.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (* (/ y x) -1/2) x)
26.0ms	(* (/ y x) -1/2)

simplify650.0ms

Counts

50 → 50

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	91	434
1	216	400
2	879	373
done	5000	371

prune82.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

7.2b	(- (pow x 4) (* y y))
12.7b	(sqrt (- (pow x 4) (* y y)))
19.4b	(sqrt (- (* x x) y))
19.5b	(/ (sqrt (- (pow x 4) (* y y))) (sqrt (- (* x x) y)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

98×	`sqrt-prod`
75×	`add-sqr-sqrt`
63×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
41×	`difference-of-squares`
10×	`unpow-prod-down` `sqr-pow`
9×	`associate-/l*`
8×	`sqrt-div`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `sqrt-undiv` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 145

Calls

4 calls:

17.0ms	(- (pow x 4) (* y y))
15.0ms	(sqrt (- (pow x 4) (* y y)))
16.0ms	(sqrt (- (* x x) y))
63.0ms	(/ (sqrt (- (pow x 4) (* y y))) (sqrt (- (* x x) y)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (pow x 4) (* y y))
64.0ms	(sqrt (- (pow x 4) (* y y)))
62.0ms	(sqrt (- (* x x) y))
122.0ms	(/ (sqrt (- (pow x 4) (* y y))) (sqrt (- (* x x) y)))

simplify1.0s

Counts

157 → 157

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	227	3392
1	423	3054
2	1824	2970
done	5000	2949

prune548.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes164.0ms

Accuracy

99.8% (0.0b remaining)

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

bsearch48.0ms

Steps

Iters	Range		Point
8	6.056441033543998e+122	1.53950547797117e+126	8.970759006124064e+123
6	-2.34437933648138e+154	-5.198860796817705e+153	-1.3545742274115277e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample742.0ms

Algorithm

intervals

Results

257.0ms	8000×	body	80	valid
69.0ms	2612×	body	80	nan