Details

sample344.0ms

Algorithm

intervals

Results

129.0ms	67×	body	10240	exit
90.0ms	77×	body	2560	valid
79.0ms	114×	body	1280	valid
14.0ms	36×	body	640	valid
6.0ms	323×	pre	80	true
2.0ms	8×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	5×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 5 (1.2s)

Iter	Nodes	Cost
0	17	614
1	40	614
2	95	614
3	237	614
4	629	559
5	2307	544
done	5000	544

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.9b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* b eps)) 1.0)
4.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l`

Counts

4 → 117

Calls

4 calls:

74.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
17.0ms	(- (exp (* a eps)) 1.0)
17.0ms	(- (exp (* b eps)) 1.0)
20.0ms	(- (exp (* (+ a b) eps)) 1.0)

series413.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
52.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* b eps)) 1.0)
76.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify3.2s

Counts

129 → 129

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	228	59672
1	619	52053
2	2353	46542
done	5012	46349

prune781.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

26.0ms

(+ (/ 1 a) (/ 1 b))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(+ (/ 1 a) (/ 1 b))

simplify5.2s

Counts

37 → 37

Iterations

Useful iterations: 3 (257.0ms)

Iter	Nodes	Cost
0	42	4698
1	110	4101
2	316	4076
3	692	4052
4	1680	4052
5	4525	4052
done	5000	4052

prune243.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt a) (cbrt a))
0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

18.0ms	(* (cbrt a) (cbrt a))
1.0ms	(cbrt a)
1.0ms	(cbrt a)
2.0ms	(cbrt a)

series1.2s

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (cbrt a) (cbrt a))
313.0ms	(cbrt a)
270.0ms	(cbrt a)
300.0ms	(cbrt a)

simplify4.9s

Counts

93 → 93

Iterations

Useful iterations: 3 (467.0ms)

Iter	Nodes	Cost
0	65	18502
1	140	15989
2	382	15714
3	1072	15034
4	4108	15034
done	5000	15034

prune529.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (cbrt a))
0.3b	(/ 1 (pow (* a a) 1/3))
0.6b	(cbrt a)
33.7b	(pow (* a a) 1/3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
31×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`add-exp-log`
15×	`cbrt-prod`
13×	`pow1`
11×	`associate-/r*`
10×	`div-exp`
8×	`add-cbrt-cube` `pow-exp`
6×	`pow-pow` `associate-/l*`
5×	`rec-exp` `unpow-prod-down` `1-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow-to-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `pow-flip`
2×	`clear-num` `frac-2neg` `unpow1/3` `pow1/3` `div-inv` `inv-pow`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up`

Counts

4 → 134

Calls

4 calls:

10.0ms	(/ 1 (cbrt a))
16.0ms	(/ 1 (pow (* a a) 1/3))
1.0ms	(cbrt a)
10.0ms	(pow (* a a) 1/3)

series1.4s

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ 1 (cbrt a))
281.0ms	(/ 1 (pow (* a a) 1/3))
604.0ms	(cbrt a)
218.0ms	(pow (* a a) 1/3)

simplify2.6s

Counts

146 → 146

Iterations

Useful iterations: 3 (662.0ms)

Iter	Nodes	Cost
0	167	43513
1	329	29130
2	726	28494
3	1576	27374
done	5000	27374

prune757.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes258.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	123
1	9	123
done	9	123

end0.0ms

sample14.9s

Algorithm

intervals

Results

5.2s	2560×	body	2560	valid
4.0s	3481×	body	1280	valid
3.1s	1968×	body	10240	exit
938.0ms	9969×	pre	80	true
574.0ms	1033×	body	640	valid
434.0ms	145×	body	160	valid
116.0ms	325×	body	320	valid
45.0ms	457×	body	80	valid