Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	62×	body	1280	valid
6.0ms	62×	body	640	valid
3.0ms	183×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

13.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	501	542
3	1228	537
4	3918	536
done	5000	536

prune110.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

10.0ms	(* x (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)

series70.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* x (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)

simplify1.7s

Counts

46 → 46

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	70	356
1	182	328
2	462	298
3	1382	298
done	5000	298

prune67.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (exp x) 1.0))
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
0.0b	(* (exp x) (exp x))
3.9b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `exp-prod`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`pow-prod-down`
4×	`times-frac` `associate-r/` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

13.0ms	(* x (+ (exp x) 1.0))
25.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
7.0ms	(* (exp x) (exp x))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series154.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* x (+ (exp x) 1.0))
79.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
13.0ms	(* (exp x) (exp x))
25.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify790.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (254.0ms)

Iter	Nodes	Cost
0	160	1376
1	418	1216
2	1585	1053
done	5000	1053

prune207.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
0.0b	(pow (exp x) 2)
3.9b	(- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

39×	`exp-prod`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
8×	`pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`add-exp-log` `pow-pow`
3×	`unpow-prod-down` `pow-unpow`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2` `difference-of-squares` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

8.0ms	(* (exp x) (exp x))
7.0ms	(* (exp x) (exp x))
2.0ms	(pow (exp x) 2)
53.0ms	(- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (* 1.0 1.0) (* 1.0 1.0)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (exp x) (exp x))
18.0ms	(* (exp x) (exp x))
13.0ms	(pow (exp x) 2)
38.0ms	(- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: 3 (842.0ms)

Iter	Nodes	Cost
0	111	1087
1	246	751
2	804	646
3	2951	590
done	5000	590

prune246.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.0b

bsearch41.0ms

Steps

Iters	Range		Point
10	-3752817.331716861	-5.670122129476186e-07	-0.0001664903813288805

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	58
1	39	58
done	39	58

end0.0ms

sample893.0ms

Algorithm

intervals

Results

380.0ms	2216×	body	1280	valid
185.0ms	1666×	body	640	valid
109.0ms	5558×	body	80	valid
57.0ms	814×	body	320	valid
18.0ms	398×	body	160	valid