Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
3.0ms	20×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	11×	body	1280	valid
1.0ms	12×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	4122
13	3069
12	2474
11	2032
10	1843
9	1602
8	1334
7	972
6	535
5	248
4	118
3	71
2	33
1	16
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

23.0ms	(* (- 1.0 x) y)
18.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
22.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series198.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- 1.0 x) y)
88.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
62.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1286
1	346
0	128

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

72.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
17.0ms	(/ y (+ y 1.0))
9.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series243.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
64.0ms	(/ y (+ y 1.0))
106.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1637
1	425
0	157

prune465.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))
0.2b	(/ 1.0 (/ y x))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
49×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
13×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `div-exp` `associate-/l*` `distribute-lft-out--`
2×	`pow1` `sub-neg` `flip3--` `frac-sub` `flip--` `associate--r+` `difference-of-squares`
1×	`clear-num` `frac-2neg` `associate-/r/` `associate--r-`

Counts

2 → 92

Calls

2 calls:

81.0ms	(- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))
11.0ms	(/ 1.0 (/ y x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))
26.0ms	(/ 1.0 (/ y x))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1798
1	523
0	204

prune498.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))) (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))))
7.2b	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
7.2b	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
7.2b	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
65×	`cbrt-prod`
58×	`add-sqr-sqrt`
52×	`cbrt-div`
33×	`distribute-lft-out--`
26×	`flip3--` `frac-sub` `flip--`
16×	`frac-times` `swap-sqr`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`pow1/3`
7×	`times-frac`
6×	`add-exp-log`
4×	`add-cbrt-cube` `associate-l/` `associate-r/` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 139

Calls

4 calls:

944.0ms	(* (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))) (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))))
109.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
100.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
113.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))

series803.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))) (cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x))))
164.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
193.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))
162.0ms	(cbrt (- (/ 1.0 y) (- (/ 1.0 (/ y x)) x)))

simplify2.3s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	1754
1	613
0	252

prune952.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes399.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 14.3b

bsearch100.0ms

Steps

Iters	Range		Point
10	4.9803363081918155	422514113030.77625	361767606.44001645
5	-2.085807323628561e+25	-8.665460962243007e+24	-8.76265571073903e+24

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

326.0ms	6102×	body	80	valid
185.0ms	538×	body	320	valid
126.0ms	744×	body	640	valid
103.0ms	336×	body	1280	valid
23.0ms	280×	body	160	valid