Details

sample240.0ms

Algorithm

intervals

Results

91.0ms	96×	body	2560	valid
61.0ms	66×	body	10240	exit
50.0ms	102×	body	1280	valid
9.0ms	31×	body	640	valid
5.0ms	322×	pre	80	true
2.0ms	9×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	2×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	258	24
4	760	24
5	3738	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.5b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* a eps)) 1.0)
6.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

60.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
14.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* a eps)) 1.0)
18.0ms	(- (exp (* (+ a b) eps)) 1.0)

series325.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
33.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
53.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify894.0ms

Counts

129 → 129

Iterations

Useful iterations: done (888.0ms)

Iter	Nodes	Cost
0	228	2725
1	598	2432
2	2211	1949
done	5000	1847

prune422.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

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×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

28.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify2.8s

Counts

37 → 37

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	251	211
3	523	210
4	1465	210
5	3712	210
done	5000	210

prune93.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt b) (cbrt b))
0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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:

11.0ms	(* (cbrt b) (cbrt b))
1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series745.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (cbrt b) (cbrt b))
186.0ms	(cbrt b)
179.0ms	(cbrt b)
178.0ms	(cbrt b)

simplify3.5s

Counts

93 → 93

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune239.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

15.1b

(/ (+ a b) (* a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

21.0ms

(/ (+ a b) (* a b))

series40.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(/ (+ a b) (* a b))

simplify2.4s

Counts

30 → 30

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	57	304
1	147	298
2	499	256
3	1835	256
done	5000	256

prune44.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

0% (2.9b remaining)

Error of 3.2b against oracle of 0.3b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2551×	body	2560	valid
1.7s	1952×	body	10240	exit
1.7s	3461×	body	1280	valid
284.0ms	1037×	body	640	valid
159.0ms	9954×	pre	80	true
69.0ms	377×	body	320	valid
27.0ms	436×	body	80	valid
17.0ms	140×	body	160	valid