Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
5.0ms	275×	body	80	nan
4.0ms	140×	body	80	valid
3.0ms	27×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
48.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
80.0ms	(/ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ 1.0 (sqrt x))
146.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.4s

Counts

145 → 145

Iterations

Useful iterations: 3 (611.0ms)

Iter	Nodes	Cost
0	215	1942
1	444	1778
2	1080	1696
3	2986	1673
done	5000	1673

prune314.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
29.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
25.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series425.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
260.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify648.0ms

Counts

105 → 105

Iterations

Useful iterations: done (646.0ms)

Iter	Nodes	Cost
0	189	1624
1	511	1459
2	2084	1222
done	5000	1213

prune244.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b	(* (sqrt x) (sqrt x))
2.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`sqrt-prod`
36×	`*-un-lft-identity`
34×	`pow1`
22×	`add-cube-cbrt`
19×	`swap-sqr`
16×	`sqrt-pow1` `pow1/2` `sqrt-div`
13×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
11×	`flip3-+` `flip-+`
10×	`pow-prod-up`
8×	`associate-*r/` `unswap-sqr`
6×	`pow-prod-down` `associate-*l/` `associate-/r/` `pow-sqr` `distribute-lft-out` `add-log-exp`
4×	`frac-times` `frac-add`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow2` `flip3--` `pow-plus` `sqrt-unprod` `div-exp` `rem-square-sqrt` `*-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 153

Calls

4 calls:

30.0ms	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
21.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms	(* (sqrt x) (sqrt x))
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
15.0ms	(* (sqrt x) (sqrt x))
17.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

simplify966.0ms

Counts

165 → 165

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	263	3042
1	675	1840
2	2645	1647
done	5000	1644

prune322.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x))
0.1b	(* (sqrt (+ x 1.0)) x)
0.1b	(* (sqrt x) (+ x 1.0))
0.4b	(/ (* 1.0 1.0) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
12×	`add-cube-cbrt` `flip3-+` `flip-+`
10×	`sqrt-div` `associate-r/` `associate-l/`
9×	`sqrt-prod`
8×	`pow1` `frac-add`
7×	`associate-r`
6×	`associate-/r/` `add-log-exp`
4×	`unswap-sqr`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log` `div-inv` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

6.0ms	(+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x))
12.0ms	(* (sqrt (+ x 1.0)) x)
11.0ms	(* (sqrt x) (+ x 1.0))
12.0ms	(/ (* 1.0 1.0) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x))
74.0ms	(* (sqrt (+ x 1.0)) x)
51.0ms	(* (sqrt x) (+ x 1.0))
267.0ms	(/ (* 1.0 1.0) (+ (* (sqrt x) (+ x 1.0)) (* (sqrt (+ x 1.0)) x)))

simplify795.0ms

Counts

108 → 108

Iterations

Useful iterations: done (792.0ms)

Iter	Nodes	Cost
0	235	2038
1	639	1902
2	2203	1728
done	5000	1719

prune258.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes37.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	17	24
done	17	24

end0.0ms

sample835.0ms

Algorithm

intervals

Results

172.0ms	1782×	body	640	valid
169.0ms	7968×	body	80	nan
147.0ms	1174×	body	1280	valid
105.0ms	4128×	body	80	valid
43.0ms	607×	body	320	valid
15.0ms	309×	body	160	valid