Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
6.0ms	221×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (+ x y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `sqrt-div`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `hypot-def` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 19

Calls

1 calls:

13.0ms

(sqrt (+ x y))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

(sqrt (+ x y))

simplify1.9s

Counts

22 → 22

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	55	184
1	124	160
2	390	155
3	1761	145
done	5000	142

prune47.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x y))
0.1b	(sqrt (sqrt (+ x y)))
0.1b	(sqrt (sqrt (+ x y)))
0.5b	(* (sqrt (sqrt (+ x y))) (sqrt (sqrt (+ x y))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

110×	`sqrt-prod`
58×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `sqrt-pow1`
34×	`sqrt-div`
32×	`pow1`
21×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow-prod-up` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 157

Calls

4 calls:

8.0ms	(sqrt (+ x y))
9.0ms	(sqrt (sqrt (+ x y)))
9.0ms	(sqrt (sqrt (+ x y)))
55.0ms	(* (sqrt (sqrt (+ x y))) (sqrt (sqrt (+ x y))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt (+ x y))
243.0ms	(sqrt (sqrt (+ x y)))
273.0ms	(sqrt (sqrt (+ x y)))
39.0ms	(* (sqrt (sqrt (+ x y))) (sqrt (sqrt (+ x y))))

simplify1.6s

Counts

169 → 169

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	168	2244
1	382	1414
2	1691	1335
done	5003	1318

prune410.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot (sqrt x) (sqrt y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `hypot-udef` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(hypot (sqrt x) (sqrt y))

series236.0ms

Counts

1 → 3

Calls

1 calls:

236.0ms

(hypot (sqrt x) (sqrt y))

simplify1.3s

Counts

13 → 13

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	49	138
1	121	125
2	438	107
3	2388	104
done	5001	102

prune55.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y))))
0.2b	(/ (* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y)))) (sqrt (sqrt (- x y))))
2.7b	(- (* x x) (* y y))
17.0b	(sqrt (- (* x x) (* y y)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-prod`
54×	`sqrt-div`
40×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
17×	`add-cube-cbrt`
11×	`pow1` `add-exp-log` `times-frac` `associate-/r*` `add-cbrt-cube`
10×	`associate-r` `associate-l`
9×	`flip3--` `sqrt-pow1` `flip--` `unswap-sqr`
8×	`frac-times` `associate-/l/`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1/2` `pow-prod-down` `difference-of-squares`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u`
2×	`cbrt-undiv` `sqrt-unprod` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 140

Calls

4 calls:

87.0ms	(* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y))))
67.0ms	(/ (* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y)))) (sqrt (sqrt (- x y))))
12.0ms	(- (* x x) (* y y))
17.0ms	(sqrt (- (* x x) (* y y)))

series792.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y))))
373.0ms	(/ (* (sqrt (sqrt (- (* x x) (* y y)))) (sqrt (sqrt (+ x y)))) (sqrt (sqrt (- x y))))
49.0ms	(- (* x x) (* y y))
66.0ms	(sqrt (- (* x x) (* y y)))

simplify1.7s

Counts

152 → 152

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	285	3220
1	657	2947
2	2920	2690
done	5002	2680

prune769.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4

end0.0ms

sample1.0s

Algorithm

intervals

Results

242.0ms	8000×	body	80	valid
212.0ms	7788×	body	80	nan