Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
5.0ms	127×	body	80	valid
3.0ms	42×	body	640	valid
1.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify117.0ms

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	137	13
12	141	13
13	143	13
done	143	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite79.0ms

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:

6.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
58.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ 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	1012	1427
3	2729	1416
done	5001	1414

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.0b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `frac-sub` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp`
3×	`cbrt-undiv` `flip3--` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 141

Calls

4 calls:

5.0ms	(/ 1 (- x 1.0))
5.0ms	(/ x (+ x 1.0))
24.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
33.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1.0))
39.0ms	(/ x (+ x 1.0))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
132.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify1.3s

Counts

153 → 153

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	235	2040
1	574	1766
2	1833	1586
done	5001	1580

prune228.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.2b	(/ 3.0 (pow x 3))
0.5b	(/ 1.0 (* x x))
5.4b	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
53×	`times-frac`
37×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
16×	`add-log-exp`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
9×	`unpow3`
7×	`distribute-lft-out`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `distribute-rgt-out` `diff-log` `div-inv` `distribute-lft-out--` `sqr-pow`
3×	`cbrt-undiv` `sum-log` `frac-sub` `distribute-neg-frac`
2×	`distribute-rgt-neg-in` `frac-2neg` `flip3-+` `neg-log` `frac-add` `clear-num` `flip-+`
1×	`+-commutative` `associate--l-` `neg-sub0` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft1-in` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

41.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
6.0ms	(/ 3.0 (pow x 3))
3.0ms	(/ 1.0 (* x x))
133.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
35.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ 1.0 (* x x))
36.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify1.0s

Counts

145 → 145

Iterations

Useful iterations: 2 (393.0ms)

Iter	Nodes	Cost
0	214	1988
1	535	1734
2	2052	1630
done	5001	1630

prune254.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)))
5.3b	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
6.4b	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
25.4b	(- (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

186×	`*-un-lft-identity`
91×	`times-frac`
79×	`add-sqr-sqrt`
56×	`distribute-lft-out`
51×	`associate-r`
44×	`unpow-prod-down` `cube-prod`
36×	`add-cube-cbrt`
19×	`distribute-lft-out--` `difference-of-squares`
13×	`flip3-+` `flip-+`
11×	`add-exp-log` `sum-cubes` `add-cbrt-cube` `add-log-exp`
10×	`frac-sub`
9×	`associate-/l*`
6×	`pow1` `frac-times` `associate-*l/`
5×	`associate-/r*`
4×	`associate-l` `associate-/r/`
3×	`flip3--` `associate-*r/` `flip--`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `sub-neg` `distribute-rgt-out` `frac-2neg` `unpow3` `pow-prod-down` `associate--l+` `clear-num` `*-commutative`

Counts

4 → 186

Calls

4 calls:

79.0ms	(* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)))
44.0ms	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
19.0ms	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
156.0ms	(- (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)))
50.0ms	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
31.0ms	(+ (pow x 3) (* (* 1.0 (- 1.0 x)) x))
173.0ms	(- (+ (pow x 3) (* (* 1.0 (- 1.0 x)) x)) (* (+ x 1.0) (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))))

simplify1.0s

Counts

198 → 198

Iterations

Useful iterations: 2 (288.0ms)

Iter	Nodes	Cost
0	255	4670
1	716	4174
2	3238	3998
done	5000	3998

prune490.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.8b

bsearch87.0ms

Steps

Iters	Range		Point
7	1766.3470775505596	94269.73169533648	10580.433189833957
10	-3752817.331716861	-5.670122129476186e-07	-13568.460963923884

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	81
1	46	66
done	46	66

end0.0ms

sample523.0ms

Algorithm

intervals

Results

182.0ms	1697×	body	1280	valid
106.0ms	1273×	body	640	valid
90.0ms	4049×	body	80	valid
39.0ms	636×	body	320	valid
14.0ms	345×	body	160	valid