Details

sample149.0ms

Algorithm

intervals

Results

89.0ms	103×	body	1280	valid
37.0ms	91×	body	640	valid
6.0ms	33×	body	320	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.6b	(log (+ 1.0 x))
6.6b	(log (- 1.0 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms	(log (+ 1.0 x))
5.0ms	(log (- 1.0 x))

series213.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (+ 1.0 x))
47.0ms	(log (- 1.0 x))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: 3 (839.0ms)

Iter	Nodes	Cost
0	186	1203
1	426	1150
2	1221	1064
3	4251	1008
done	5000	1008

prune202.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.6b	(log (- 1.0 x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
83×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`pow1` `div-exp` `prod-exp` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-r/` `associate-l` `associate-/r` `flip--` `add-log-exp`
2×	`cbrt-undiv` `div-sub` `frac-sub` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 163

Calls

3 calls:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
58.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.0ms	(log (- 1.0 x))

series243.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
142.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
43.0ms	(log (- 1.0 x))

simplify1.1s

Counts

172 → 172

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	409	3188
1	953	2943
2	2567	2577
done	5001	2564

prune479.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`associate-*r/` `associate-/r/` `log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv` `add-log-exp`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

3 → 266

Calls

3 calls:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
35.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
89.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series241.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
58.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
123.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.2s

Counts

275 → 275

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	334	5394
1	813	4934
2	2201	4280
done	5002	4254

prune750.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* (* 1/2 (/ x 1.0)) (/ x (pow (sqrt 1.0) 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
89×	`add-sqr-sqrt`
68×	`associate-r`
59×	`*-un-lft-identity`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
27×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`div-exp` `prod-exp`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
4×	`associate-/r/` `log-pow` `difference-of-squares`
3×	`associate-r/` `associate-l` `associate-/r`
2×	`cbrt-undiv` `flip3--` `frac-sub` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `clear-num` `*-commutative` `flip-+`

Counts

2 → 156

Calls

2 calls:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
91.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* (* 1/2 (/ x 1.0)) (/ x (pow (sqrt 1.0) 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series306.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
255.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* (* 1/2 (/ x 1.0)) (/ x (pow (sqrt 1.0) 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.1s

Counts

162 → 162

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	356	4235
1	884	3981
2	2451	3351
done	5000	3334

prune497.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes29.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	27	36
done	27	36

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	3441×	body	1280	valid
992.0ms	2504×	body	640	valid
233.0ms	1199×	body	320	valid
95.0ms	8000×	pre	80	true
70.0ms	636×	body	160	valid
10.0ms	220×	body	80	valid