Details

sample168.0ms

Algorithm

intervals

Results

105.0ms	119×	body	1280	valid
33.0ms	78×	body	640	valid
8.0ms	35×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
0.0ms	8×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0b	(log (- 1.0 x))
5.3b	(log (+ 1.0 x))

rewrite70.0ms

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:

29.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
8.0ms	(log (- 1.0 x))
7.0ms	(log (+ 1.0 x))

series328.0ms

Counts

3 → 9

Calls

3 calls:

187.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
69.0ms	(log (- 1.0 x))
71.0ms	(log (+ 1.0 x))

simplify856.0ms

Counts

78 → 78

Iterations

Useful iterations: done (853.0ms)

Iter	Nodes	Cost
0	186	1203
1	432	1150
2	1725	1066
done	5001	1024

prune287.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.0b

localize41.0ms

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)))))
5.0b	(log (- 1.0 x))

rewrite143.0ms

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:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
72.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.0ms	(log (- 1.0 x))

series393.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
225.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
61.0ms	(log (- 1.0 x))

simplify745.0ms

Counts

172 → 172

Iterations

Useful iterations: done (735.0ms)

Iter	Nodes	Cost
0	409	3188
1	1090	2943
done	5000	2587

prune845.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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)))))

rewrite254.0ms

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:

40.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
162.0ms	(/ (- (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)))))

series313.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
71.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
167.0ms	(/ (- (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)))))

simplify2.8s

Counts

275 → 275

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	334	5394
1	944	4934
2	4527	4280
done	5001	4278

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

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

rewrite732.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
124×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
70×	`add-cube-cbrt`
68×	`associate-r`
56×	`unpow-prod-down`
52×	`exp-prod`
37×	`log-pow`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-lft-out--`
17×	`pow1` `unswap-sqr`
12×	`associate-/r/`
11×	`add-cbrt-cube`
10×	`div-exp` `prod-exp` `difference-of-squares`
7×	`associate-*r/`
6×	`pow-to-exp` `pow-exp` `frac-sub` `associate-/l*`
5×	`add-log-exp`
4×	`flip3--` `flip--` `div-inv`
3×	`log-prod` `flip3-+` `div-sub` `associate-l` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `exp-diff` `cbrt-unprod` `associate-/l/`
1×	`log-div` `frac-2neg` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `rem-exp-log`

Counts

4 → 230

Calls

4 calls:

44.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
96.0ms	(/ (- (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)))))
306.0ms	(log (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)))))))
272.0ms	(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))))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
160.0ms	(/ (- (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)))))
155.0ms	(log (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)))))))
211.0ms	(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))))))

simplify2.8s

Counts

242 → 242

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	413	6898
1	1066	6521
2	4790	5925
done	5000	5924

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	33
1	19	33
done	19	33

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.4s	3362×	body	1280	valid
1.5s	2529×	body	640	valid
403.0ms	1300×	body	320	valid
150.0ms	605×	body	160	valid
137.0ms	8000×	pre	80	true
13.0ms	204×	body	80	valid