Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	67×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	191×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite17.0ms

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:

11.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	501	542
3	1229	537
4	4072	536
done	5001	536

prune113.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x 1/6) 1/2)
0.1b	(* x (+ (* x 1/6) 1/2))
0.4b	(* x 1/6)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

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

series106.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x 1/6) 1/2)
60.0ms	(* x (+ (* x 1/6) 1/2))
15.0ms	(* x 1/6)

simplify1.9s

Counts

60 → 60

Iterations

Useful iterations: 3 (310.0ms)

Iter	Nodes	Cost
0	78	480
1	204	439
2	502	399
3	1461	397
done	5000	397

prune95.0ms

Pruning

3 alts after pruning (2 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))
4.1b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite54.0ms

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))
23.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
8.0ms	(* (exp x) (exp x))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series161.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (+ (exp x) 1.0))
84.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
13.0ms	(* (exp x) (exp x))
30.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify761.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	160	1376
1	418	1216
2	1585	1053
done	5001	1053

prune217.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 1.0) x)
0.0b	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
0.0b	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
3.4b	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

16.0ms	(* (+ (exp x) 1.0) x)
7.0ms	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
7.0ms	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
23.0ms	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (+ (exp x) 1.0) x)
50.0ms	(/ (* 1.0 1.0) (* x (+ (exp x) 1.0)))
44.0ms	(/ (exp (* 2 x)) (* (+ (exp x) 1.0) x))
107.0ms	(- (/ (exp (* 2 x)) (* (+ (exp x) 1.0) x)) (/ (* 1.0 1.0) (* x (+ (exp x) 1.0))))

simplify833.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (244.0ms)

Iter	Nodes	Cost
0	175	1675
1	474	1575
2	2018	1381
done	5000	1381

prune213.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes23.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch33.0ms

Steps

Iters	Range		Point
8	-0.04390830018224924	-1.7961213486546931e-06	-0.00010015840142054043

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	35
1	32	35
done	32	35

end0.0ms

sample871.0ms

Algorithm

intervals

Results

385.0ms	2235×	body	1280	valid
172.0ms	1635×	body	640	valid
99.0ms	5418×	body	80	valid
59.0ms	846×	body	320	valid
19.0ms	430×	body	160	valid