Details

sample73.0ms

Algorithm

intervals

Results

29.0ms	53×	body	1280	valid
16.0ms	50×	body	640	valid
11.0ms	128×	body	80	valid
5.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify118.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.6b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite87.0ms

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:

8.0ms	(/ x (+ x 1))
21.0ms	(/ (+ x 1) (- x 1))
56.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ x (+ x 1))
33.0ms	(/ (+ x 1) (- x 1))
101.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify981.0ms

Counts

126 → 126

Iterations

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

prune956.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.6b	(/ -3 (* x (* x x)))
0.8b	(/ 1 (* x x))
5.8b	(- (/ -3 (* x (* x x))) (+ (/ 3 x) (/ 1 (* x x))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
26×	`pow1`
23×	`add-cbrt-cube`
18×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`prod-exp` `add-cube-cbrt` `add-log-exp`
8×	`times-frac`
7×	`div-exp` `cbrt-unprod`
6×	`pow-prod-up` `pow-flip` `associate-/l*`
5×	`cbrt-undiv`
4×	`pow-prod-down` `insert-posit16` `div-inv` `distribute-lft-out--`
3×	`associate-l` `frac-sub`
2×	`pow2` `rec-exp` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `diff-log` `1-exp` `frac-add` `pow-sqr` `distribute-lft-out`
1×	`sum-log` `sub-neg` `flip3-+` `distribute-rgt-out` `flip3--` `cube-unmult` `associate-r` `*-commutative` `flip-+` `flip--` `associate--r+` `inv-pow` `sub-div` `difference-of-squares` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

27.0ms	(* x (* x x))
26.0ms	(/ -3 (* x (* x x)))
12.0ms	(/ 1 (* x x))
113.0ms	(- (/ -3 (* x (* x x))) (+ (/ 3 x) (/ 1 (* x x))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* x (* x x))
52.0ms	(/ -3 (* x (* x x)))
26.0ms	(/ 1 (* x x))
32.0ms	(- (/ -3 (* x (* x x))) (+ (/ 3 x) (/ 1 (* x x))))

simplify890.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	2002
2	2002
1	501
0	171

prune878.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ 1 (/ (- x 1) (+ x 1)))
0.0b	(/ (- x 1) (+ x 1))
2.6b	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

275×	`times-frac`
268×	`*-un-lft-identity`
226×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
52×	`difference-of-squares`
42×	`associate-/r*`
41×	`distribute-lft-out`
25×	`distribute-lft-out--`
21×	`difference-of-sqr-1`
19×	`add-exp-log`
13×	`add-cbrt-cube` `associate-/r/` `associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 280

Calls

4 calls:

9.0ms	(/ x (+ x 1))
17.0ms	(/ 1 (/ (- x 1) (+ x 1)))
20.0ms	(/ (- x 1) (+ x 1))
63.0ms	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x (+ x 1))
29.0ms	(/ 1 (/ (- x 1) (+ x 1)))
30.0ms	(/ (- x 1) (+ x 1))
89.0ms	(- (/ x (+ x 1)) (/ 1 (/ (- x 1) (+ x 1))))

simplify1.1s

Counts

292 → 292

Iterations

Iter	Nodes
done	2000
2	2000
1	853
0	336

prune2.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
0.0b	(/ (+ 1 x) (- x 1))
2.6b	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
2.6b	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
88×	`times-frac`
76×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod` `distribute-lft-out`
22×	`difference-of-squares`
20×	`add-cube-cbrt`
17×	`log-pow`
9×	`add-log-exp`
7×	`associate-/r*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `log-prod` `difference-of-sqr-1`
4×	`exp-sum` `insert-posit16` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `frac-sub` `flip-+` `div-inv`

Counts

4 → 144

Calls

4 calls:

145.0ms	(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
37.0ms	(/ (+ 1 x) (- x 1))
176.0ms	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
88.0ms	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))
49.0ms	(/ (+ 1 x) (- x 1))
91.0ms	(log (exp (- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))))
89.0ms	(- (/ x (+ 1 x)) (/ (+ 1 x) (- x 1)))

simplify1.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	2032
3	2032
2	1152
1	443
0	195

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch111.0ms

Steps

Iters	Range		Point
11	5.037382729650074e-10	1937402784720.5117	11259.474582447798
8	-44481.00103279522	-87.25999490770408	-9516.22025087149

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	1741×	body	1280	valid
408.0ms	1232×	body	640	valid
284.0ms	4052×	body	80	valid
133.0ms	652×	body	320	valid
68.0ms	323×	body	160	valid