Details

sample148.0ms

Algorithm

intervals

Results

92.0ms	108×	body	1280	valid
34.0ms	85×	body	640	valid
6.0ms	30×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	22×	body	160	valid
1.0ms	11×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 60.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.4b	(log (+ 1.0 x))
5.5b	(log (- 1.0 x))

rewrite15.0ms

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:

8.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms	(log (+ 1.0 x))
3.0ms	(log (- 1.0 x))

series208.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
45.0ms	(log (+ 1.0 x))
42.0ms	(log (- 1.0 x))

simplify431.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	186	1203
1	430	1150
2	1555	1064
done	5001	1064

prune205.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 57.4b

localize13.0ms

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)))))
5.5b	(log (- 1.0 x))

rewrite66.0ms

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:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms	(log (- 1.0 x))

series228.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
130.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
45.0ms	(log (- 1.0 x))

simplify1.9s

Counts

172 → 172

Iterations

Useful iterations: 2 (584.0ms)

Iter	Nodes	Cost
0	409	3188
1	1006	2943
2	4411	2577
done	5000	2577

prune452.0ms

Pruning

5 alts after pruning (5 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)))))

rewrite112.0ms

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:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
39.0ms	(/ (- (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:

62.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
61.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
117.0ms	(/ (- (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)))))

simplify1.5s

Counts

275 → 275

Iterations

Useful iterations: 2 (346.0ms)

Iter	Nodes	Cost
0	334	5394
1	860	4926
2	3875	4280
done	5001	4280

prune765.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- (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))))))
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)))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

196×	`times-frac`
175×	`add-sqr-sqrt`
136×	`associate-r`
114×	`*-un-lft-identity`
112×	`unpow-prod-down`
93×	`add-cube-cbrt`
52×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
26×	`exp-prod`
20×	`prod-exp`
19×	`div-exp`
16×	`add-cbrt-cube`
15×	`pow1`
14×	`distribute-lft-out--`
12×	`pow-to-exp` `pow-exp`
8×	`associate-/r/`
7×	`log-pow` `difference-of-squares`
6×	`associate-r/` `associate-l` `associate-/l`
5×	`add-log-exp`
4×	`frac-sub` `cbrt-unprod` `div-inv`
3×	`cbrt-undiv` `flip3--` `associate-/r*` `flip--`
2×	`flip3-+` `div-sub` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/`
1×	`frac-2neg` `exp-diff` `clear-num` `rem-exp-log`

Counts

4 → 301

Calls

4 calls:

69.0ms	(exp (/ (- (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))))))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
42.0ms	(/ (- (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)))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(exp (/ (- (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))))))
53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
120.0ms	(/ (- (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)))))

simplify1.6s

Counts

313 → 313

Iterations

Useful iterations: 2 (361.0ms)

Iter	Nodes	Cost
0	380	6747
1	942	6262
2	4114	5660
done	5000	5660

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	53
1	23	53
done	23	53

end0.0ms

sample4.5s

Algorithm

intervals

Results

3.0s	3536×	body	1280	valid
952.0ms	2396×	body	640	valid
247.0ms	1238×	body	320	valid
99.0ms	8000×	pre	80	true
64.0ms	587×	body	160	valid
11.0ms	243×	body	80	valid