Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	45×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	137×	body	80	valid
1.0ms	12×	body	320	valid
1.0ms	14×	body	160	valid

simplify157.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite173.0ms

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))
26.0ms	(/ (+ x 1.0) (- x 1.0))
122.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ x (+ x 1.0))
69.0ms	(/ (+ x 1.0) (- x 1.0))
198.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

113 → 113

Iterations

Useful iterations: done (2.0s)

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

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(exp (/ x (+ x 1.0)))
3.7b	(log (exp (/ x (+ x 1.0))))
3.9b	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
45×	`times-frac`
36×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
12×	`distribute-lft-out`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-prod` `associate-/r/` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`associate-/l*`
3×	`flip3-+` `associate--l+` `flip-+` `div-inv`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 120

Calls

4 calls:

50.0ms	(/ (+ x 1.0) (- x 1.0))
32.0ms	(exp (/ x (+ x 1.0)))
25.0ms	(log (exp (/ x (+ x 1.0))))
325.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (+ x 1.0) (- x 1.0))
84.0ms	(exp (/ x (+ x 1.0)))
48.0ms	(log (exp (/ x (+ x 1.0))))
206.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts

132 → 132

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	210	1736
1	433	1535
2	1053	1450
3	2409	1427
done	5000	1425

prune453.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) (+ 1.0 x))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (- x 1.0) (+ 1.0 x)))
16.8b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

46×	`associate-*r/`
36×	`flip3-+` `flip-+`
32×	`frac-sub`
30×	`*-un-lft-identity`
28×	`frac-times`
24×	`flip3--` `flip--`
18×	`add-sqr-sqrt` `associate-/l/`
14×	`associate-*l/`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
9×	`associate-l`
8×	`associate-r` `associate-/r/`
7×	`distribute-lft-out`
6×	`swap-sqr` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate--l+`
3×	`sub-neg` `times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `associate--r+` `unswap-sqr`
1×	`pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 153

Calls

4 calls:

48.0ms	(* (- x 1.0) (+ 1.0 x))
45.0ms	(* (+ x 1.0) (+ x 1.0))
112.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (- x 1.0) (+ 1.0 x)))
40.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (- x 1.0) (+ 1.0 x))
29.0ms	(* (+ x 1.0) (+ x 1.0))
112.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (- x 1.0) (+ 1.0 x)))
56.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify4.1s

Counts

165 → 165

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	268	3700
1	866	3448
2	4705	3180
done	5001	3175

prune537.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
0.0b	(* (- x 1.0) (+ 1.0 x))
12.3b	(/ (- (+ (* 3.0 x) 1.0)) (* (- x 1.0) (+ 1.0 x)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`add-exp-log` `times-frac` `add-cbrt-cube` `associate-/l*`
8×	`frac-times` `flip3-+` `associate-/r/` `flip-+`
6×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
2×	`cbrt-undiv` `neg-mul-1` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-neg-frac`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `distribute-frac-neg` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 89

Calls

3 calls:

8.0ms	(+ (* 3.0 x) 1.0)
39.0ms	(* (- x 1.0) (+ 1.0 x))
78.0ms	(/ (- (+ (* 3.0 x) 1.0)) (* (- x 1.0) (+ 1.0 x)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* 3.0 x) 1.0)
148.0ms	(* (- x 1.0) (+ 1.0 x))
89.0ms	(/ (- (+ (* 3.0 x) 1.0)) (* (- x 1.0) (+ 1.0 x)))

simplify1.7s

Counts

98 → 98

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	170	1488
1	487	1448
2	2150	1322
done	5000	1321

prune352.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	29
1	22	29
2	26	29
3	29	29
4	30	29
done	30	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

418.0ms	1673×	body	1280	valid
303.0ms	4143×	body	80	valid
236.0ms	1251×	body	640	valid
113.0ms	612×	body	320	valid
25.0ms	321×	body	160	valid