Details

sample49.0ms

Algorithm

intervals

Results

16.0ms	58×	body	1280	valid
8.0ms	139×	body	80	valid
8.0ms	36×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify196.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

11.0ms	(/ x (+ x 1.0))
26.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series270.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
184.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.7s

Counts

605 → 605

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune663.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.9b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite958.0ms

Algorithm

rewrite-expression-head

Rules

1898×	`*-un-lft-identity`
1428×	`times-frac`
1132×	`add-sqr-sqrt`
936×	`prod-diff`
810×	`add-cube-cbrt`
473×	`log-prod`
470×	`exp-sum`
365×	`distribute-lft-out`
182×	`associate-/r/`
175×	`distribute-lft-out--`
157×	`difference-of-squares`
91×	`div-inv`
55×	`flip3-+` `flip-+`
38×	`flip3--` `flip--`
18×	`fma-neg`
17×	`log-pow`
16×	`exp-prod`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 1097

Calls

4 calls:

50.0ms	(/ (+ x 1.0) (- x 1.0))
21.0ms	(/ x (+ x 1.0))
515.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
188.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- x 1.0))
35.0ms	(/ x (+ x 1.0))
142.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
181.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.3s

Counts

1109 → 1109

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1136	69094
1	1825	60490
2	3748	44278
done	5000	44276

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.9b	(log (exp (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1219×	`*-un-lft-identity`
824×	`times-frac`
639×	`add-sqr-sqrt`
468×	`prod-diff`
411×	`add-cube-cbrt`
227×	`distribute-lft-out`
163×	`distribute-lft-out--`
100×	`difference-of-squares`
90×	`associate-/r/`
76×	`cbrt-prod`
48×	`unpow-prod-down` `cube-prod`
45×	`div-inv`
42×	`log-pow`
41×	`exp-prod`
27×	`flip3-+` `flip-+`
21×	`flip3--` `flip--`
18×	`fma-neg`
6×	`pow1` `cube-div` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-unpow` `cbrt-div` `log-prod` `unpow3` `frac-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 675

Calls

4 calls:

194.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
170.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
729.0ms	(log (exp (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))))
181.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
173.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
182.0ms	(log (exp (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))))
187.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts

687 → 687

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	615	37131
1	1364	32989
2	3225	24669
done	5001	23785

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

2721×	`*-un-lft-identity`
1732×	`times-frac`
1190×	`add-sqr-sqrt`
936×	`prod-diff`
805×	`add-cube-cbrt`
510×	`distribute-lft-out`
405×	`distribute-lft-out--`
202×	`sqrt-prod`
180×	`associate-/r/`
172×	`difference-of-squares`
90×	`div-inv`
79×	`swap-sqr`
54×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
36×	`fma-neg`
27×	`sqrt-div`
20×	`pow1`
19×	`associate-r` `associate-l`
11×	`frac-sub`
9×	`frac-times` `sqrt-pow1` `pow1/2`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1222

Calls

4 calls:

196.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
641.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
150.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
179.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
162.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
159.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
472.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.4s

Counts

1234 → 1234

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	599	73421
1	1278	63936
2	3006	47608
done	5000	40300

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch146.0ms

Steps

Iters	Range		Point
8	1902.9075791774285	6884452.324493753	11573.998562574065
9	-3592450.023809973	-45.38980787391071	-12435.329388671693

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	58
1	34	43
done	34	43

end0.0ms

sample1.3s

Algorithm

intervals

Results

366.0ms	1673×	body	1280	valid
342.0ms	4157×	body	80	valid
199.0ms	1264×	body	640	valid
101.0ms	602×	body	320	valid
60.0ms	304×	body	160	valid