Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	95×	body	80	nan

simplify4.0ms

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: 21.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.6b	(sqrt (+ (* x x) y))

rewrite28.0ms

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:

12.0ms	(+ (* x x) y)
15.0ms	(sqrt (+ (* x x) y))

series110.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* x x) y)
88.0ms	(sqrt (+ (* x x) y))

simplify502.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	697
1	154
0	59

prune170.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.9b	(/ -1/2 (/ x y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
43×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`div-inv`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
1×	`pow1` `clear-num` `frac-2neg` `associate-/r/` `add-log-exp`

Counts

1 → 70

Calls

1 calls:

10.0ms

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

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

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

simplify790.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1531
1	378
0	150

prune759.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

7.2b	(- (pow x 4) (* y y))
19.6b	(sqrt (/ (- (pow x 4) (* y y)) (- (pow x 2) y)))
36.5b	(/ (- (pow x 4) (* y y)) (- (pow x 2) y))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-sqr-sqrt`
106×	`difference-of-squares`
97×	`times-frac`
60×	`*-un-lft-identity`
54×	`sqrt-prod`
34×	`add-cube-cbrt`
31×	`unpow-prod-down` `sqr-pow`
13×	`distribute-lft-out--` `unpow2`
8×	`associate-/r*`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3--` `associate-/r/` `flip--`
2×	`rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-sub` `div-exp`

Counts

3 → 160

Calls

3 calls:

11.0ms	(- (pow x 4) (* y y))
52.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (pow x 2) y)))
56.0ms	(/ (- (pow x 4) (* y y)) (- (pow x 2) y))

series255.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(- (pow x 4) (* y y))
131.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (pow x 2) y)))
80.0ms	(/ (- (pow x 4) (* y y)) (- (pow x 2) y))

simplify1.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	2378
1	612
0	298

prune603.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

11.6b	(/ (/ (+ (fabs (* x x)) y) (cbrt (- (* x x) y))) (cbrt (- (* x x) y)))
20.5b	(cbrt (- (* x x) y))
20.5b	(cbrt (- (* x x) y))
20.5b	(cbrt (- (* x x) y))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

462×	`times-frac`
317×	`*-un-lft-identity`
280×	`cbrt-prod`
275×	`add-sqr-sqrt`
205×	`add-cube-cbrt`
70×	`difference-of-squares`
56×	`distribute-lft-out`
34×	`associate-/l*`
24×	`cbrt-div`
18×	`associate-/r/`
12×	`flip3--` `flip--`
9×	`add-exp-log` `div-inv`
7×	`associate-/r*`
6×	`add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 338

Calls

4 calls:

105.0ms	(/ (/ (+ (fabs (* x x)) y) (cbrt (- (* x x) y))) (cbrt (- (* x x) y)))
6.0ms	(cbrt (- (* x x) y))
6.0ms	(cbrt (- (* x x) y))
5.0ms	(cbrt (- (* x x) y))

series489.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (+ (fabs (* x x)) y) (cbrt (- (* x x) y))) (cbrt (- (* x x) y)))
141.0ms	(cbrt (- (* x x) y))
114.0ms	(cbrt (- (* x x) y))
130.0ms	(cbrt (- (* x x) y))

simplify729.0ms

Counts

350 → 350

Iterations

Iter	Nodes
done	5000
1	1120
0	459

prune2.1s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes323.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.4b

bsearch68.0ms

Steps

Iters	Range		Point
9	3.5533055332411143e+130	1.742174409442309e+138	1.5742125019904702e+131
10	-6.974394801174976e+154	-5.6292565617441764e+144	-1.1176150369578986e+154

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample806.0ms

Algorithm

intervals

Results

277.0ms	8000×	body	80	valid
79.0ms	2598×	body	80	nan