Details

sample157.0ms

Algorithm

intervals

Results

74.0ms	114×	body	1280	valid
31.0ms	78×	body	640	valid
20.0ms	262×	body	80	nan
10.0ms	42×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	18	12
2	25	12
3	40	12
4	61	12
5	88	12
6	102	12
7	106	12
done	106	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 x) (- 1.0 x))
5.6b	(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/r*`
4×	`associate-/r/` `add-cbrt-cube` `associate-/l*`
3×	`pow1`
2×	`flip3--` `div-exp` `rem-log-exp` `flip--` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 82

Calls

2 calls:

309.0ms	(/ (+ 1.0 x) (- 1.0 x))
11.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

series227.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ 1.0 x) (- 1.0 x))
182.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

simplify1.7s

Counts

88 → 88

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	142	1276
1	319	1221
2	803	1150
3	1966	1108
done	5000	1104

prune182.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune5.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
5.5b	(log (sqrt (+ 1.0 x)))
5.6b	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
70×	`times-frac`
52×	`sqrt-prod`
48×	`log-prod`
45×	`add-cube-cbrt`
15×	`distribute-lft-out--` `difference-of-squares`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`pow1`
7×	`associate-/l*`
6×	`sqrt-div` `add-cbrt-cube`
5×	`associate-/r*`
4×	`associate-/r/` `log-pow` `add-log-exp`
3×	`log-div` `flip3-+` `rem-log-exp` `flip-+`
2×	`flip3--` `sqrt-pow1` `pow1/2` `div-exp` `flip--` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `clear-num`

Counts

4 → 151

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 x))
23.0ms	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
6.0ms	(log (sqrt (+ 1.0 x)))
12.0ms	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ 1.0 x))
109.0ms	(/ (sqrt (+ 1.0 x)) (- 1.0 x))
81.0ms	(log (sqrt (+ 1.0 x)))
214.0ms	(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))

simplify2.4s

Counts

163 → 163

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	261	2622
1	562	2416
2	1420	2270
3	4565	2225
done	5001	2225

prune360.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))
0.0b	(/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x))
5.5b	(log (sqrt (+ 1.0 x)))
5.6b	(log (/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x)))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

1572×	`times-frac`
1548×	`*-un-lft-identity`
997×	`sqrt-prod`
887×	`add-sqr-sqrt`
572×	`add-cube-cbrt`
403×	`log-prod`
331×	`distribute-lft-out`
264×	`unpow-prod-down` `cube-prod`
157×	`distribute-lft-out--` `difference-of-squares`
78×	`associate-/l*`
66×	`sum-cubes`
26×	`sqrt-div` `associate-/r/`
16×	`add-exp-log`
13×	`flip3-+` `flip-+` `div-inv`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`div-exp`
5×	`associate-/r*`
4×	`rem-log-exp` `log-pow` `add-log-exp`
3×	`cbrt-undiv` `log-div`
2×	`flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 933

Calls

4 calls:

16.0ms	(sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))
117.0ms	(/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x))
6.0ms	(log (sqrt (+ 1.0 x)))
65.0ms	(log (/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))
196.0ms	(/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x))
109.0ms	(log (sqrt (+ 1.0 x)))
284.0ms	(log (/ (/ (sqrt (+ (pow 1.0 3) (pow x 3))) (sqrt (+ (* x (- x 1.0)) (* 1.0 1.0)))) (- 1.0 x)))

simplify2.0s

Counts

945 → 945

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	838	43149
1	1931	38874
2	4378	38415
done	5000	38415

prune2.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	18	20
done	18	20

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.9s	3498×	body	1280	valid
1.3s	2438×	body	640	valid
1.0s	7984×	body	80	nan
366.0ms	1245×	body	320	valid
131.0ms	619×	body	160	valid
15.0ms	200×	body	80	valid