Details

sample89.0ms

Algorithm

intervals

Results

22.0ms	293×	body	160	nan
19.0ms	539×	body	80	nan
18.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.1b	(sqrt (- (* x x) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`add-log-exp`
6×	`add-cube-cbrt`
4×	`pow1` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `prod-diff` `add-exp-log` `log1p-expm1-u`
2×	`flip3--` `sqrt-div` `flip--` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `flip-+` `distribute-lft-out`

Counts

3 → 54

Calls

3 calls:

10.0ms	(- (* x x) 1.0)
26.0ms	(+ x (sqrt (- (* x x) 1.0)))
16.0ms	(sqrt (- (* x x) 1.0))

series271.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(- (* x x) 1.0)
117.0ms	(+ x (sqrt (- (* x x) 1.0)))
81.0ms	(sqrt (- (* x x) 1.0))

simplify1.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
2	1294
1	299
0	120

prune344.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`sqrt-prod`
15×	`*-un-lft-identity`
14×	`sqrt-div`
9×	`associate-r` `add-cube-cbrt`
8×	`pow1`
7×	`associate-l`
5×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `log1p-expm1-u` `flip--`
2×	`associate-l/` `associate-r/` `hypot-def` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 80

Calls

3 calls:

14.0ms	(sqrt (+ x (sqrt 1.0)))
5.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
57.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series561.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(sqrt (+ x (sqrt 1.0)))
213.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
263.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1770
1	446
0	181

prune472.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	16548×	body	80	nan
820.0ms	7742×	body	160	nan
482.0ms	8000×	body	80	valid