Details

sample212.0ms

Algorithm

intervals

Results

125.0ms	103×	body	1280	valid
48.0ms	82×	body	640	valid
14.0ms	46×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	16×	body	160	valid
1.0ms	9×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	262
1	10	262
2	11	262
done	11	262

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.8b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

14.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms	(log (- 1.0 x))
4.0ms	(log (+ 1.0 x))

series293.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
57.0ms	(log (- 1.0 x))
71.0ms	(log (+ 1.0 x))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	185	32125
1	432	27184
2	1758	26299
done	5000	26189

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 58.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -1/2 (* (/ x 1.0) (/ x 1.0)))
0.0b	(/ (log (- 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
5.0b	(log (- 1.0 x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

26.0ms	(* -1/2 (* (/ x 1.0) (/ x 1.0)))
107.0ms	(/ (log (- 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
4.0ms	(log (- 1.0 x))

series245.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* -1/2 (* (/ x 1.0) (/ x 1.0)))
146.0ms	(/ (log (- 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
66.0ms	(log (- 1.0 x))

simplify2.7s

Counts

94 → 94

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	269	48023
1	724	41916
2	3433	40627
done	5001	40627

prune488.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
18×	`prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt`
13×	`pow1` `-un-lft-identity` `associate-r/` `add-cube-cbrt`
9×	`cbrt-undiv` `times-frac` `div-exp`
8×	`associate-/r/`
7×	`associate-*l/`
6×	`pow-prod-down` `frac-add`
4×	`frac-times` `flip3-+` `associate-r` `associate-l` `flip-+`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `div-inv` `flip--`

Counts

3 → 94

Calls

3 calls:

40.0ms	(* -1/2 (* (/ x 1.0) (/ x 1.0)))
52.0ms	(* (* (/ x 1.0) (/ x 1.0)) 1/2)
155.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))

series255.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* -1/2 (* (/ x 1.0) (/ x 1.0)))
52.0ms	(* (* (/ x 1.0) (/ x 1.0)) 1/2)
149.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))

simplify3.2s

Counts

103 → 103

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	214	44105
1	675	38563
2	3912	36710
done	5001	36708

prune532.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
58×	`times-frac`
54×	`associate-*r/`
48×	`*-un-lft-identity` `associate-/r/` `add-cube-cbrt`
36×	`frac-add`
24×	`flip3-+` `flip-+`
21×	`swap-sqr` `associate-r` `associate-l`
20×	`add-cbrt-cube` `add-exp-log`
18×	`frac-times`
16×	`associate-*l/`
11×	`pow1`
7×	`cbrt-div`
6×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `div-sub` `flip--`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `cube-unmult` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 184

Calls

4 calls:

205.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
189.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
413.0ms	(cbrt (* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))))))
466.0ms	(* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
169.0ms	(/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x))))
159.0ms	(cbrt (* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))))))
213.0ms	(* (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))) (/ (- (- (log 1.0) (* (* (/ x 1.0) (/ x 1.0)) 1/2)) (* 1.0 x)) (+ (* -1/2 (* (/ x 1.0) (/ x 1.0))) (+ (log 1.0) (* 1.0 x)))))

simplify2.2s

Counts

196 → 196

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	271	147525
1	1028	137274
done	5001	134023

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes42.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	21	794
1	28	794
done	28	794

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.3s	3464×	body	1280	valid
1.5s	2480×	body	640	valid
456.0ms	1238×	body	320	valid
177.0ms	8000×	pre	80	true
99.0ms	599×	body	160	valid
15.0ms	219×	body	80	valid