Details

sample36.0ms

Algorithm

intervals

Results

15.0ms

351×

body

valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	14	7
2	20	7
3	22	7
done	22	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 1 expressions with local error:

6.0b	(* x (+ 1.0 (* y y)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

31.0ms

(* x (+ 1.0 (* y y)))

series119.0ms

Counts

1 → 3

Calls

1 calls:

118.0ms

(* x (+ 1.0 (* y y)))

simplify881.0ms

Counts

25 → 25

Iterations

Useful iterations: done (880.0ms)

Iter	Nodes	Cost
0	50	247
1	161	244
2	756	208
done	5000	206

prune155.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (sqrt (+ 1.0 (* y y))))
0.1b	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
5.9b	(sqrt (+ 1.0 (* y y)))
5.9b	(sqrt (+ 1.0 (* y y)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-div`
17×	`add-sqr-sqrt`
13×	`pow1` `sqrt-prod`
12×	`associate-r`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3-+` `flip-+`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

36.0ms	(* x (sqrt (+ 1.0 (* y y))))
91.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
10.0ms	(sqrt (+ 1.0 (* y y)))
10.0ms	(sqrt (+ 1.0 (* y y)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* x (sqrt (+ 1.0 (* y y))))
115.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
83.0ms	(sqrt (+ 1.0 (* y y)))
82.0ms	(sqrt (+ 1.0 (* y y)))

simplify1.5s

Counts

95 → 95

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	122	1468
1	320	1152
2	1654	1040
done	5001	1016

prune593.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.9b	(sqrt (+ 1.0 (* y y)))
5.9b	(sqrt (+ 1.0 (* y y)))
5.9b	(sqrt (+ 1.0 (* y y)))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`associate-*r/`
18×	`sqrt-prod`
16×	`pow1`
14×	`associate-*l/`
13×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-l` `*-commutative`

Counts

4 → 98

Calls

4 calls:

307.0ms	(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
11.0ms	(sqrt (+ 1.0 (* y y)))
10.0ms	(sqrt (+ 1.0 (* y y)))
11.0ms	(sqrt (+ 1.0 (* y y)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
72.0ms	(sqrt (+ 1.0 (* y y)))
87.0ms	(sqrt (+ 1.0 (* y y)))
77.0ms	(sqrt (+ 1.0 (* y y)))

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	165	2960
1	462	2353
2	2398	2003
done	5000	1703

prune869.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.1b

localize55.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (+ 1.0 (* y y)))
5.9b	(sqrt (+ 1.0 (* y y)))
6.2b	(cbrt (+ 1.0 (* y y)))
6.2b	(cbrt (+ 1.0 (* y y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

22.0ms	(sqrt (+ 1.0 (* y y)))
11.0ms	(sqrt (+ 1.0 (* y y)))
6.0ms	(cbrt (+ 1.0 (* y y)))
7.0ms	(cbrt (+ 1.0 (* y y)))

series778.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (+ 1.0 (* y y)))
74.0ms	(sqrt (+ 1.0 (* y y)))
302.0ms	(cbrt (+ 1.0 (* y y)))
321.0ms	(cbrt (+ 1.0 (* y y)))

simplify847.0ms

Counts

68 → 68

Iterations

Useful iterations: done (844.0ms)

Iter	Nodes	Cost
0	105	920
1	245	834
2	981	776
done	5001	754

prune737.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 6.1b

regimes341.0ms

Accuracy

0% (0.2b remaining)

Error of 5.3b against oracle of 5.1b and baseline of 5.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	11	15
done	11	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

539.0ms

10768×

body

valid