Details

sample67.0ms

Algorithm

intervals

Results

14.0ms	17×	body	320	valid
11.0ms	69×	body	640	valid
9.0ms	252×	body	80	nan
8.0ms	32×	body	1280	valid
6.0ms	125×	body	80	valid
1.0ms	13×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 21.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 117

Calls

3 calls:

25.0ms	(/ 1.0 (sqrt (+ x 1.0)))
13.0ms	(/ 1.0 (sqrt x))
71.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series367.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(/ 1.0 (sqrt (+ x 1.0)))
48.0ms	(/ 1.0 (sqrt x))
213.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.8s

Counts

126 → 126

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	201	1764
1	411	1621
2	957	1551
3	2367	1528
done	5001	1517

prune420.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
0.2b	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.3b	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
105×	`times-frac`
65×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
52×	`sqrt-prod`
35×	`distribute-lft-out`
27×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
8×	`distribute-lft-out--`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `div-exp` `difference-of-squares`
3×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`
2×	`flip3--` `flip3-+` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`sub-neg` `diff-log` `frac-add` `prod-exp` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

16.0ms	(/ 1.0 (sqrt (+ x 1.0)))
13.0ms	(/ 1.0 (sqrt x))
247.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
49.0ms	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1.0 (sqrt (+ x 1.0)))
54.0ms	(/ 1.0 (sqrt x))
549.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
78.0ms	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

simplify1.9s

Counts

170 → 170

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	339	3045
1	822	2803
2	2557	2592
done	5002	2590

prune652.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
0.2b	(/ 1.0 (sqrt x))
2.4b	(- (* 1.0 (+ x 1.0)) (* x 1.0))
4.8b	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-exp-log` `add-cbrt-cube`
26×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`sqrt-prod`
22×	`associate-*r/`
14×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out`
12×	`frac-times` `prod-exp` `cbrt-unprod`
11×	`associate-/r/`
9×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-*l/` `frac-add` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`div-inv` `associate-/l*`
3×	`pow-prod-down`
2×	`flip3--` `frac-2neg` `associate--l+` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative`

Counts

4 → 135

Calls

4 calls:

143.0ms	(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
7.0ms	(/ 1.0 (sqrt x))
14.0ms	(- (* 1.0 (+ x 1.0)) (* x 1.0))
295.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

606.0ms	(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
64.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (* 1.0 (+ x 1.0)) (* x 1.0))
367.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify2.3s

Counts

147 → 147

Iterations

Useful iterations: 2 (988.0ms)

Iter	Nodes	Cost
0	333	3744
1	1007	3614
2	4625	2955
done	5000	2955

prune537.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
0.6b	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
4.8b	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
58×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`sqrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
20×	`associate-*r/`
18×	`distribute-lft-out`
15×	`flip3-+` `flip-+`
14×	`associate-l` `associate-/r*`
13×	`associate-/r/`
12×	`frac-times` `prod-exp` `cbrt-unprod`
9×	`pow1`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`associate-*l/` `frac-add`
5×	`div-inv`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`sqrt-div`
1×	`associate-r` `*-commutative`

Counts

4 → 164

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
129.0ms	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
288.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
506.0ms	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
584.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify1.6s

Counts

176 → 176

Iterations

Useful iterations: 2 (746.0ms)

Iter	Nodes	Cost
0	359	3687
1	988	3475
2	4112	3014
done	5000	3014

prune455.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

regimes44.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	16	21
done	16	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

675.0ms	1918×	body	640	valid
373.0ms	8150×	body	80	nan
210.0ms	1050×	body	1280	valid
190.0ms	4128×	body	80	valid
94.0ms	601×	body	320	valid
21.0ms	303×	body	160	valid