Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	58×	body	640	valid
6.0ms	269×	body	80	nan
5.0ms	34×	body	1280	valid
4.0ms	143×	body	80	valid
1.0ms	12×	body	320	valid
0.0ms	9×	body	160	valid

simplify5.0ms

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: 16.8b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
69.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
50.0ms	(/ 1.0 (sqrt x))
148.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

770 → 770

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	701	40764
1	1536	36194
2	4134	26234
done	5000	26138

prune997.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
9×	`pow1`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `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` `hypot-def` `div-inv` `associate-/l*`

Counts

4 → 151

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
55.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
32.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series445.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ x 1.0))
281.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
56.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.0s

Counts

163 → 163

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	241	3181
1	655	2542
2	2848	1975
done	5000	1965

prune320.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
1.0b	(- (+ x 1.0) x)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
41×	`distribute-lft-out`
39×	`sqrt-prod`
37×	`times-frac`
30×	`add-cube-cbrt`
29×	`add-exp-log` `add-cbrt-cube`
16×	`distribute-lft-out--`
12×	`prod-diff`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `difference-of-squares`
7×	`associate-r` `associate-/r` `associate-/l`
6×	`associate-l`
5×	`associate-*r/`
4×	`expm1-log1p-u` `fma-neg` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l/`
2×	`flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `sqrt-unprod` `div-sub` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 167

Calls

4 calls:

63.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
22.0ms	(- (+ x 1.0) x)

series687.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
490.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(- (+ x 1.0) x)

simplify1.5s

Counts

179 → 179

Iterations

Useful iterations: 2 (303.0ms)

Iter	Nodes	Cost
0	297	3589
1	839	3257
2	4215	2739
done	5000	2739

prune360.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`sqrt-prod`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
22×	`distribute-lft-out`
21×	`add-cube-cbrt`
19×	`times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`fma-def` `associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
22.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
62.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
502.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts

143 → 143

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	258	2403
1	731	2191
2	3385	1810
done	5001	1800

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	14	18
done	14	18

end0.0ms

sample841.0ms

Algorithm

intervals

Results

181.0ms	1842×	body	640	valid
171.0ms	8101×	body	80	nan
140.0ms	1127×	body	1280	valid
107.0ms	4061×	body	80	valid
44.0ms	616×	body	320	valid
18.0ms	354×	body	160	valid