Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	76	13
9	97	13
10	127	13
11	143	13
12	151	13
done	151	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
55.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series170.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
132.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.9s

Counts

77 → 77

Iterations

Useful iterations: 3 (757.0ms)

Iter	Nodes	Cost
0	135	1218
1	317	1168
2	862	1110
3	3623	1097
done	5000	1097

prune131.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

342×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
73×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
18×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sub-neg` `diff-log` `frac-add` `sum-log`

Counts

4 → 259

Calls

4 calls:

47.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
31.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
51.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
59.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
210.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify2.1s

Counts

271 → 271

Iterations

Useful iterations: 2 (865.0ms)

Iter	Nodes	Cost
0	360	6049
1	1124	5295
2	4713	4757
done	5000	4757

prune412.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 1.0 (* x x)))
0.5b	(/ 1.0 (* x x))
0.9b	(/ 3.0 (pow x 3))
9.0b	(+ (+ (/ 3.0 x) (/ 1.0 (* x x))) (/ 3.0 (pow x 3)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
38×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add`
4×	`pow1` `cube-mult` `unpow3` `sum-log` `distribute-lft-out` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+`
2×	`+-commutative` `frac-2neg` `clear-num` `div-inv`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

14.0ms	(+ (/ 3.0 x) (/ 1.0 (* x x)))
3.0ms	(/ 1.0 (* x x))
4.0ms	(/ 3.0 (pow x 3))
85.0ms	(+ (+ (/ 3.0 x) (/ 1.0 (* x x))) (/ 3.0 (pow x 3)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (/ 3.0 x) (/ 1.0 (* x x)))
25.0ms	(/ 1.0 (* x x))
41.0ms	(/ 3.0 (pow x 3))
30.0ms	(+ (+ (/ 3.0 x) (/ 1.0 (* x x))) (/ 3.0 (pow x 3)))

simplify989.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (228.0ms)

Iter	Nodes	Cost
0	195	1727
1	452	1482
2	2041	1402
done	5000	1402

prune220.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* x (+ (* 3.0 x) 1.0)) (pow x 3))
0.1b	(* x (+ (* 3.0 x) 1.0))
0.1b	(* (pow x 3) 3.0)
51.6b	(/ (+ (* (pow x 3) 3.0) (* (* x (+ (* 3.0 x) 1.0)) (pow x 3))) (pow x 6))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
29×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
19×	`unpow-prod-down`
18×	`associate-r`
16×	`associate-l`
15×	`add-cbrt-cube`
13×	`prod-exp`
7×	`cube-prod` `associate-/r*` `sqr-pow`
6×	`pow1`
5×	`cbrt-unprod` `unswap-sqr`
4×	`pow-to-exp` `associate-*r/` `pow-exp` `add-log-exp`
3×	`flip3-+` `div-exp` `-commutative` `flip-+` `associate-/l`
2×	`cube-mult` `unpow3` `associate-*l/` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 131

Calls

4 calls:

18.0ms	(* (* x (+ (* 3.0 x) 1.0)) (pow x 3))
10.0ms	(* x (+ (* 3.0 x) 1.0))
9.0ms	(* (pow x 3) 3.0)
15.0ms	(/ (+ (* (pow x 3) 3.0) (* (* x (+ (* 3.0 x) 1.0)) (pow x 3))) (pow x 6))

series252.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (* x (+ (* 3.0 x) 1.0)) (pow x 3))
66.0ms	(* x (+ (* 3.0 x) 1.0))
37.0ms	(* (pow x 3) 3.0)
64.0ms	(/ (+ (* (pow x 3) 3.0) (* (* x (+ (* 3.0 x) 1.0)) (pow x 3))) (pow x 6))

simplify1.3s

Counts

143 → 143

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	224	2754
1	555	2580
2	2619	2077
done	5000	2077

prune297.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch85.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	14618.947191620917
10	-64880754058.88788	-2.651420353119469e-05	-11755.062723959316

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	81
1	37	66
2	44	66
3	47	66
done	47	66

end0.0ms

sample527.0ms

Algorithm

intervals

Results

183.0ms	1719×	body	1280	valid
103.0ms	1224×	body	640	valid
95.0ms	4124×	body	80	valid
38.0ms	618×	body	320	valid
13.0ms	315×	body	160	valid