Details

sample48.0ms

Algorithm

intervals

Results

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

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	22	10
3	39	10
4	71	10
5	164	10
6	369	10
7	908	10
8	3753	10
done	5000	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

2 → 35

Calls

2 calls:

13.0ms	(- (* y y) (* z z))
17.0ms	(sqrt (- (* y y) (* z z)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- (* y y) (* z z))
69.0ms	(sqrt (- (* y y) (* z z)))

simplify509.0ms

Counts

41 → 41

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	62	456
1	151	416
2	699	361
done	5001	361

prune115.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize4.0ms

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

prune5.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

20×	`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×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 62

Calls

2 calls:

17.0ms	(sqrt (+ y z))
55.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(sqrt (+ y z))
74.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

simplify809.0ms

Counts

68 → 68

Iterations

Useful iterations: done (807.0ms)

Iter	Nodes	Cost
0	116	824
1	253	744
2	939	718
done	5000	710

prune235.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize20.0ms

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)))))

rewrite286.0ms

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`
42×	`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×	`expm1-log1p-u` `swap-sqr` `log1p-expm1-u` `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` `hypot-def`

Counts

4 → 244

Calls

4 calls:

12.0ms	(sqrt (+ y z))
57.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
39.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
143.0ms	(* (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))) (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ y z))
82.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
73.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))
73.0ms	(* (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))) (sqrt (* (sqrt (+ y z)) (sqrt (- y z)))))

simplify1.3s

Counts

256 → 256

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	318	6846
1	550	5617
2	2151	5347
done	5001	5317

prune968.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes181.0ms

Accuracy

97.2% (0.8b remaining)

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

bsearch92.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

721.0ms	10169×	body	80	valid
555.0ms	9844×	body	80	nan