Details

sample64.0ms

Algorithm

intervals

Results

33.0ms	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

localize6.0ms

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))

rewrite22.0ms

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

series292.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ x (sqrt (+ (* x x) 1.0)))
183.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify2.0s

Counts

51 → 51

Iterations

Useful iterations: 3 (629.0ms)

Iter	Nodes	Cost
0	133	761
1	308	691
2	902	618
3	4411	602
done	5000	602

prune139.0ms

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:

115.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
70.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series339.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
180.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.4s

Counts

292 → 292

Iterations

Useful iterations: 2 (553.0ms)

Iter	Nodes	Cost
0	336	4436
1	860	3364
2	3589	2955
done	5000	2955

prune420.0ms

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 (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
30×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
8×	`add-exp-log`
4×	`cube-mult` `log-div` `log-prod` `unpow3` `add-cbrt-cube` `sqr-pow`
3×	`pow1` `div-exp` `associate-/l*`
2×	`frac-add` `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 → 82

Calls

2 calls:

4.0ms	(/ 0.125 (pow x 3))
35.0ms	(log (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

series193.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 0.125 (pow x 3))
151.0ms	(log (+ (/ 0.5 x) (- (* 2 x) (/ 0.125 (pow x 3)))))

simplify547.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	187	1303
1	428	1116
2	1669	1056
done	5000	1056

prune168.0ms

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))))

rewrite199.0ms

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))
4.0ms	(/ 0.125 (pow x 3))
86.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
99.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 0.0625 (pow x 5))
41.0ms	(/ 0.125 (pow x 3))
185.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
56.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify953.0ms

Counts

172 → 172

Iterations

Useful iterations: 2 (305.0ms)

Iter	Nodes	Cost
0	318	2936
1	689	2663
2	2658	2507
done	5001	2507

prune384.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch86.0ms

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

946.0ms	2308×	body	1280	valid
362.0ms	1563×	body	640	valid
215.0ms	786×	body	2560	valid
106.0ms	767×	body	320	valid
64.0ms	2171×	body	80	valid
31.0ms	405×	body	160	valid