Details

sample69.0ms

Algorithm

intervals

Results

26.0ms	55×	body	1280	valid
15.0ms	143×	body	80	valid
12.0ms	32×	body	640	valid
6.0ms	21×	body	320	valid
1.0ms	5×	body	160	valid

simplify190.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.8b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

7.0ms	(/ x (+ x 1))
33.0ms	(/ (+ x 1) (- x 1))
86.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ x (+ x 1))
24.0ms	(/ (+ x 1) (- x 1))
107.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
3	2000
2	1074
1	399
0	180

prune402.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))))
0.1b	(/ 1 (sqrt (+ x 1)))
0.1b	(/ x (sqrt (+ x 1)))
7.7b	(- (* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (/ (+ x 1) (- x 1)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
106×	`times-frac`
98×	`*-un-lft-identity`
67×	`sqrt-prod`
64×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
14×	`associate-/r*` `distribute-lft-out`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`flip3-+` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv`
3×	`rec-exp` `1-exp` `frac-sub` `pow-flip`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`
1×	`sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `*-commutative` `flip--` `inv-pow`

Counts

4 → 208

Calls

4 calls:

60.0ms	(* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))))
9.0ms	(/ 1 (sqrt (+ x 1)))
8.0ms	(/ x (sqrt (+ x 1)))
40.0ms	(- (* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (/ (+ x 1) (- x 1)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1))))
30.0ms	(/ 1 (sqrt (+ x 1)))
64.0ms	(/ x (sqrt (+ x 1)))
82.0ms	(- (* (/ 1 (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (/ (+ x 1) (- x 1)))

simplify1.3s

Counts

220 → 220

Iterations

Iter	Nodes
done	2000
3	2000
2	1911
1	752
0	266

prune769.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ 3 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`associate-r`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp` `unswap-sqr`

Counts

1 → 24

Calls

1 calls:

23.0ms

(* x (+ 3 x))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(* x (+ 3 x))

simplify839.0ms

Counts

27 → 27

Iterations

Iter	Nodes
done	2012
3	2012
2	536
1	140
0	44

prune81.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 3 x) (* x x))
0.3b	(/ 1 (* x x))
9.5b	(+ (+ (/ 3 x) (/ 1 (* x x))) (/ (/ 3 x) (* x x)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
28×	`*-un-lft-identity`
26×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/l*`
11×	`pow1`
10×	`div-exp`
8×	`cbrt-undiv` `add-log-exp`
6×	`div-inv` `pow-flip` `distribute-lft-out`
5×	`prod-exp`
4×	`frac-add`
3×	`sum-log` `cbrt-unprod` `insert-posit16`
2×	`rec-exp` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `1-exp` `flip-+`
1×	`pow2` `+-commutative` `associate-+l+` `pow-plus` `distribute-rgt-out` `pow-prod-down` `pow-sqr` `pow-prod-up` `inv-pow` `associate-/l/`

Counts

3 → 101

Calls

3 calls:

10.0ms	(/ (/ 3 x) (* x x))
14.0ms	(/ 1 (* x x))
120.0ms	(+ (+ (/ 3 x) (/ 1 (* x x))) (/ (/ 3 x) (* x x)))

series130.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (/ 3 x) (* x x))
37.0ms	(/ 1 (* x x))
41.0ms	(+ (+ (/ 3 x) (/ 1 (* x x))) (/ (/ 3 x) (* x x)))

simplify1.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	2001
2	2001
1	571
0	195

prune373.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.2b

bsearch136.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	48819.349325626084	9532.068405488257
9	-6838974.188497498	-0.005838610583870787	-0.9996091570601888

simplify17.0ms

Iterations

Iter	Nodes
done	48
3	48
2	42
1	36
0	24

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	1679×	body	1280	valid
498.0ms	1288×	body	640	valid
375.0ms	4120×	body	80	valid
151.0ms	608×	body	320	valid
107.0ms	305×	body	160	valid