Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	138×	body	80	valid
3.0ms	33×	body	320	valid
3.0ms	25×	body	640	valid
0.0ms	7×	body	160	valid

simplify525.0ms

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

localize15.0ms

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)))

rewrite169.0ms

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:

19.0ms	(/ x (+ x 1.0))
25.0ms	(/ (+ x 1.0) (- x 1.0))
121.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series261.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ x (+ x 1.0))
45.0ms	(/ (+ x 1.0) (- x 1.0))
168.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: done (2.1s)

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

prune316.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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)))

rewrite585.0ms

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:

45.0ms	(/ (+ x 1.0) (- x 1.0))
22.0ms	(/ x (+ x 1.0))
385.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
123.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
55.0ms	(/ x (+ x 1.0))
208.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
161.0ms	(- (/ 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

prune428.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
4.2b	(/ x (+ (pow x 3) (pow 1.0 3)))
10.1b	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
13.7b	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
55×	`times-frac`
37×	`add-sqr-sqrt`
35×	`distribute-lft-out`
33×	`associate-l`
32×	`add-cube-cbrt`
28×	`unpow-prod-down` `cube-prod`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
9×	`associate-/r*`
7×	`flip3-+` `sum-cubes` `flip-+`
6×	`pow1`
5×	`frac-sub`
4×	`frac-times` `associate-*r/` `associate-/r/`
3×	`associate-r` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `diff-log` `div-exp` `associate-*l/` `prod-exp` `associate--l+` `sum-log` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3--` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `flip--`

Counts

4 → 145

Calls

4 calls:

20.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
56.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
103.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
212.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
134.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
233.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
104.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify1.6s

Counts

157 → 157

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	238	3784
1	771	3250
2	2964	3040
done	5001	3028

prune580.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0))
0.1b	(* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0))
6.2b	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
22.1b	(- (* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0)) (* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0)))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

82×	`flip3-+` `flip-+`
72×	`frac-times`
64×	`frac-sub`
36×	`associate-r/` `associate-l/`
28×	`flip3--` `flip--`
22×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`associate-l`
9×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out`
5×	`sub-neg`
4×	`unpow-prod-down` `cube-prod` `associate--l+`
2×	`distribute-rgt-out` `unpow3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`+-commutative` `diff-log` `sum-log` `sum-cubes` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

133.0ms	(* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0))
140.0ms	(* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0))
46.0ms	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
55.0ms	(- (* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0)) (* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0))
68.0ms	(* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0))
47.0ms	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
46.0ms	(- (* (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (- x 1.0)) (* (+ (pow x 3) (pow 1.0 3)) (+ x 1.0)))

simplify849.0ms

Counts

174 → 174

Iterations

Useful iterations: done (837.0ms)

Iter	Nodes	Cost
0	443	10629
1	1638	9007
done	5002	8879

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes83.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch152.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	9628.580561968385
10	-6045414056204.408	-123.41774798665298	-11622.720294157465

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	35	135
1	50	120
done	50	120

end0.0ms

sample1.2s

Algorithm

intervals

Results

366.0ms	1745×	body	1280	valid
285.0ms	4051×	body	80	valid
235.0ms	1246×	body	640	valid
86.0ms	632×	body	320	valid
63.0ms	326×	body	160	valid