Details

sample152.0ms

Algorithm

intervals

Results

91.0ms	108×	body	1280	valid
36.0ms	85×	body	640	valid
9.0ms	42×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
0.0ms	5×	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: 62.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.3b	(log (- 1.0 x))
4.6b	(log (+ 1.0 x))

rewrite30.0ms

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:

15.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series214.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
43.0ms	(log (- 1.0 x))
42.0ms	(log (+ 1.0 x))

simplify2.0s

Counts

78 → 78

Iterations

Useful iterations: 3 (798.0ms)

Iter	Nodes	Cost
0	186	1203
1	426	1150
2	1219	1064
3	4241	1008
done	5001	1008

prune189.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 60.2b

localize17.0ms

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)))))
4.3b	(log (- 1.0 x))

rewrite105.0ms

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:

35.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
57.0ms	(/ (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))

series237.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
131.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
47.0ms	(log (- 1.0 x))

simplify985.0ms

Counts

172 → 172

Iterations

Useful iterations: done (980.0ms)

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

prune473.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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:

35.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
86.0ms	(/ (- (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)))))

series226.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
119.0ms	(/ (- (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)))))

simplify913.0ms

Counts

275 → 275

Iterations

Useful iterations: done (905.0ms)

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

prune748.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 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	(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	(/ (- (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)))))

rewrite322.0ms

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:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
35.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
146.0ms	(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))))))
88.0ms	(/ (- (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)))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
152.0ms	(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))))))
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)))))

simplify955.0ms

Counts

313 → 313

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	380	6747
1	894	6254
2	2396	5532
done	5000	5506

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	21	35
done	21	35

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.1s	3507×	body	1280	valid
1.0s	2448×	body	640	valid
270.0ms	1239×	body	320	valid
98.0ms	8000×	pre	80	true
72.0ms	608×	body	160	valid
10.0ms	198×	body	80	valid