Details

sample63.0ms

Algorithm

intervals

Results

32.0ms	77×	body	1280	valid
12.0ms	54×	body	640	valid
6.0ms	21×	body	2560	valid
2.0ms	78×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b	(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series275.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1.0)))
173.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms	(sqrt (+ (* x x) 1.0))

simplify1.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (611.0ms)

Iter	Nodes	Cost
0	133	761
1	308	691
2	853	618
3	3211	602
done	5001	602

prune152.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

113.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series290.0ms

Counts

2 → 6

Calls

2 calls:

151.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
139.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.1s

Counts

292 → 292

Iterations

Useful iterations: 2 (502.0ms)

Iter	Nodes	Cost
0	336	4436
1	860	3364
2	2949	2955
done	5001	2955

prune438.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 0.125 (pow x 3))
10.2b	(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`times-frac`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
9×	`log-prod`
8×	`add-exp-log`
5×	`difference-of-squares` `sqr-pow`
4×	`cube-mult` `log-div` `unpow3` `add-cbrt-cube`
3×	`pow1` `div-exp` `associate-/l*`
2×	`frac-sub` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 87

Calls

2 calls:

4.0ms	(/ 0.125 (pow x 3))
37.0ms	(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

series194.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 0.125 (pow x 3))
154.0ms	(log (- (+ (* 2 x) (/ 0.5 x)) (/ 0.125 (pow x 3))))

simplify561.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (184.0ms)

Iter	Nodes	Cost
0	204	1459
1	443	1276
2	1348	1216
done	5000	1216

prune194.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (pow x 3))
12.2b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.0b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite193.0ms

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×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 160

Calls

4 calls:

3.0ms	(/ 0.0625 (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
82.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
96.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 0.0625 (pow x 5))
34.0ms	(/ 0.125 (pow x 3))
188.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
51.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify930.0ms

Counts

172 → 172

Iterations

Useful iterations: 2 (357.0ms)

Iter	Nodes	Cost
0	318	2936
1	689	2663
2	2120	2507
done	5001	2507

prune397.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes90.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch91.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	0.9004884393655546
9	-5.7596417613087905	-6.7357437175194845e-09	-1.03811431304858

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	57
1	40	57
done	40	57

end0.0ms

sample1.8s

Algorithm

intervals

Results

930.0ms	2308×	body	1280	valid
364.0ms	1563×	body	640	valid
208.0ms	786×	body	2560	valid
105.0ms	767×	body	320	valid
68.0ms	2171×	body	80	valid
36.0ms	405×	body	160	valid