Details

sample49.0ms

Algorithm

intervals

Results

12.0ms	330×	body	80	valid
11.0ms	319×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	21	10
3	36	10
4	62	10
5	133	10
6	286	10
7	727	10
8	3329	10
done	5000	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize13.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (* y y) (* z z))
22.6b	(sqrt (- (* y y) (* z z)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
2×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

2 → 29

Calls

2 calls:

13.0ms	(- (* y y) (* z z))
16.0ms	(sqrt (- (* y y) (* z z)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* y y) (* z z))
50.0ms	(sqrt (- (* y y) (* z z)))

simplify394.0ms

Counts

35 → 35

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	55	404
1	141	372
2	653	320
done	5001	320

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune3.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ y z))
0.3b	(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`sqrt-prod`
14×	`sqrt-div`
13×	`*-un-lft-identity`
8×	`associate-r`
7×	`pow1` `add-cube-cbrt` `associate-l`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`associate-r/` `associate-l/` `distribute-lft-out` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 57

Calls

2 calls:

7.0ms	(sqrt (+ y z))
47.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

series108.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ y z))
72.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

simplify2.2s

Counts

63 → 63

Iterations

Useful iterations: 3 (884.0ms)

Iter	Nodes	Cost
0	112	794
1	238	719
2	897	697
3	4878	689
done	5001	689

prune183.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ y z))
0.3b	(* (sqrt (+ y z)) (sqrt (- y z)))
0.3b	(* (sqrt (+ y z)) (sqrt (- y z)))
0.3b	(* (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))) (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

386×	`sqrt-div`
144×	`frac-times`
78×	`pow1`
65×	`sqrt-pow1`
61×	`flip3-+` `flip-+`
60×	`flip3--` `flip--`
48×	`associate-r/` `associate-l/`
44×	`pow-prod-down`
40×	`add-sqr-sqrt`
34×	`sqrt-prod`
31×	`pow1/2`
27×	`*-un-lft-identity`
20×	`associate-r`
18×	`associate-l`
17×	`add-cube-cbrt`
14×	`pow-prod-up`
10×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`pow-sqr`
4×	`swap-sqr` `add-log-exp`
3×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-sqrt-square` `pow-plus` `rem-square-sqrt`

Counts

4 → 235

Calls

4 calls:

7.0ms	(sqrt (+ y z))
41.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
57.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
183.0ms	(* (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))) (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ y z))
95.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
89.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
118.0ms	(* (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))) (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))))

simplify1.4s

Counts

247 → 247

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	312	6752
1	532	5646
2	2117	5434
done	5000	5410

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes192.0ms

Accuracy

97.2% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 30.1b

bsearch120.0ms

Steps

Iters	Range		Point
6	-1.258338271859563e-209	-2.3111078813045203e-210	-2.3409862775359916e-210

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	9844×	body	80	nan
612.0ms	10169×	body	80	valid