Details

sample54.0ms

Algorithm

intervals

Results

15.0ms	53×	body	1280	valid
13.0ms	138×	body	80	valid
6.0ms	33×	body	320	valid
5.0ms	25×	body	640	valid
1.0ms	7×	body	160	valid

simplify608.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

16.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series293.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ x (+ x 1.0))
67.0ms	(/ (+ x 1.0) (- x 1.0))
170.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1022	1427
3	2388	1414
done	5000	1412

prune406.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.8b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite610.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 135

Calls

4 calls:

52.0ms	(/ (+ x 1.0) (- x 1.0))
22.0ms	(/ x (+ x 1.0))
387.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
141.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ x 1.0) (- x 1.0))
37.0ms	(/ x (+ x 1.0))
167.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
180.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

147 → 147

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	211	2126
1	438	1956
2	1086	1832
3	2480	1817
done	5001	1813

prune487.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

31.0ms	(/ (+ x 1.0) (- x 1.0))
11.0ms	(/ x (+ x 1.0))
122.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (+ x 1.0) (- x 1.0))
45.0ms	(/ x (+ x 1.0))
202.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1019	1427
3	2385	1414
done	5000	1412

prune297.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.8b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
2.8b	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (/ (* x x) (* (+ x 1.0) (+ x 1.0))) (/ (+ (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))) x) (- x 1.0))))))
13.6b	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

1228×	`*-un-lft-identity`
789×	`times-frac`
544×	`add-sqr-sqrt`
326×	`unpow-prod-down` `cube-prod`
316×	`log-pow`
315×	`exp-prod`
273×	`distribute-lft-out--`
247×	`distribute-lft-out`
188×	`difference-of-squares`
108×	`add-cube-cbrt`
61×	`sqr-pow`
19×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow1` `add-log-exp`
5×	`difference-cubes` `cbrt-undiv` `div-exp`
4×	`frac-times` `prod-exp` `cbrt-unprod` `div-inv`
3×	`cube-div` `pow-unpow` `log-prod` `flip3--` `flip--`
2×	`associate-r/` `associate-l/` `pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `sub-neg` `log-div` `pow-pow` `frac-2neg` `exp-diff` `diff-log` `unpow3` `div-sub` `rem-log-exp` `frac-add` `clear-num` `associate-/r` `frac-sub` `associate-/l`

Counts

4 → 516

Calls

4 calls:

22.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
315.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
1.7s	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (/ (* x x) (* (+ x 1.0) (+ x 1.0))) (/ (+ (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))) x) (- x 1.0))))))
41.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

81.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
423.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
810.0ms	(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (/ (* x x) (* (+ x 1.0) (+ x 1.0))) (/ (+ (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))) x) (- x 1.0))))))
55.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

simplify2.3s

Counts

528 → 528

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	533	17840
1	1208	15845
2	3855	15461
done	5002	15454

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.7b

bsearch2.0ms

simplify13.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	47
1	31	45
2	38	45
3	41	45
done	41	45

end0.0ms

sample1.8s

Algorithm

intervals

Results

610.0ms	4051×	body	80	valid
603.0ms	1745×	body	1280	valid
219.0ms	1246×	body	640	valid
124.0ms	632×	body	320	valid
29.0ms	326×	body	160	valid