Details

sample75.0ms

Algorithm

intervals

Results

35.0ms	76×	body	1280	valid
16.0ms	56×	body	640	valid
6.0ms	19×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	60×	body	80	valid
2.0ms	19×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	9
1	9
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
3.9b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 42

Calls

3 calls:

27.0ms	(+ x (sqrt (+ (* x x) 1.0)))
13.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms	(sqrt (+ (* x x) 1.0))

series341.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ x (sqrt (+ (* x x) 1.0)))
208.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify689.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
2	1377
1	320
0	134

prune267.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
0.1b	(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
106×	`times-frac`
76×	`associate-l`
52×	`*-un-lft-identity` `add-cube-cbrt`
44×	`sqrt-prod`
26×	`add-exp-log`
22×	`unpow-prod-down` `cube-prod`
18×	`unswap-sqr`
14×	`add-cbrt-cube`
13×	`associate-r`
10×	`div-exp` `sqr-pow`
8×	`prod-exp`
6×	`cube-mult` `unpow3` `frac-sub` `add-log-exp`
4×	`pow1` `cbrt-undiv` `cbrt-unprod`
3×	`frac-times` `flip3-+` `associate-l/` `associate-r/` `flip-+`
2×	`pow-to-exp` `diff-log` `pow-exp` `div-inv`
1×	`sum-log` `sub-neg` `flip3--` `pow-prod-down` `associate--l+` `*-commutative` `flip--`

Counts

2 → 151

Calls

2 calls:

202.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
68.0ms	(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

series248.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
89.0ms	(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

simplify1.7s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	3791
1	733
0	236

prune757.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (pow x 3))
15.6b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.3b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `pow-exp` `flip-+` `div-inv` `flip--`
1×	`sum-log` `sub-neg` `rem-log-exp` `log-pow` `associate--r+`

Counts

4 → 160

Calls

4 calls:

10.0ms	(/ 0.0625 (pow x 5))
12.0ms	(/ 0.125 (pow x 3))
123.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
204.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 0.0625 (pow x 5))
45.0ms	(/ 0.125 (pow x 3))
283.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
67.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.7s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
2	3244
1	721
0	316

prune761.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 0.125 (pow x 3))
13.1b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`associate-/r*` `unpow-prod-down` `cube-prod`
8×	`add-exp-log`
6×	`log-prod`
4×	`cube-mult` `add-cbrt-cube` `unpow3` `distribute-lft-out` `sqr-pow`
3×	`pow1` `div-exp` `associate-/l*`
2×	`log-div` `distribute-lft-out--` `add-log-exp`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `rem-log-exp` `pow-exp` `log-pow` `flip-+` `div-inv`

Counts

2 → 82

Calls

2 calls:

10.0ms	(/ 0.125 (pow x 3))
151.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series336.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ 0.125 (pow x 3))
268.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify878.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1571
1	350
0	164

prune339.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.3b

bsearch131.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	0.886715197951362
10	-1138.2876542095912	-1.6260248627107784e-07	-1.0218942286122286

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	34

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	2336×	body	1280	valid
1.1s	1547×	body	640	valid
365.0ms	816×	body	2560	valid
206.0ms	778×	body	320	valid
110.0ms	2122×	body	80	valid
52.0ms	401×	body	160	valid