Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	3×	body	160	valid

simplify108.0ms

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: 31.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite73.0ms

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:

5.0ms	(/ x (+ x 1.0))
12.0ms	(/ (+ x 1.0) (- x 1.0))
51.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
124.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: 3 (820.0ms)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1012	1427
3	2727	1414
done	5000	1414

prune202.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.2b	(/ 1.0 (* x x))
0.3b	(/ 3.0 (pow x 3))
6.4b	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite169.0ms

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:

37.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
3.0ms	(/ 1.0 (* x x))
4.0ms	(/ 3.0 (pow x 3))
119.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
27.0ms	(/ 1.0 (* x x))
35.0ms	(/ 3.0 (pow x 3))
33.0ms	(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify883.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (363.0ms)

Iter	Nodes	Cost
0	214	1988
1	535	1734
2	2051	1630
done	5000	1630

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

49.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
28.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
109.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ 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))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
332.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
198.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify840.0ms

Counts

341 → 341

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	410	10805
1	1269	9795
done	5001	9593

prune477.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
21.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (/ (+ x 1.0) (- x 1.0)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`frac-times` `swap-sqr`
9×	`flip3--` `frac-sub` `flip--`
8×	`pow1/3` `associate-r/` `associate-r` `associate-l` `associate-l/` `distribute-lft-out--`
6×	`add-exp-log` `add-log-exp` `difference-of-squares`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
19.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (/ (+ x 1.0) (- x 1.0)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- x 1.0))
93.0ms	(cbrt (- x 1.0))
117.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
258.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (/ (+ x 1.0) (- x 1.0)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))

simplify710.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (200.0ms)

Iter	Nodes	Cost
0	248	2621
1	627	2465
2	2115	2110
done	5000	2110

prune311.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch96.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	12679.85899306799
8	-14583263.309321204	-1162.6651869185068	-11931.41196902016

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	97
1	42	82
done	42	82

end0.0ms

sample520.0ms

Algorithm

intervals

Results

190.0ms	1731×	body	1280	valid
100.0ms	1265×	body	640	valid
89.0ms	4084×	body	80	valid
40.0ms	618×	body	320	valid
12.0ms	302×	body	160	valid