Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	62×	body	1280	valid
10.0ms	47×	body	640	valid
7.0ms	172×	body	80	valid
5.0ms	31×	body	320	valid
2.0ms	16×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.8b	(- (exp x) 1.0)

rewrite56.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1.0) x)
25.0ms	(- (exp x) 1.0)

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	4953
2	817
1	227
0	99

prune276.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

4.0ms	(+ 1/2 (* 1/6 x))
15.0ms	(* x (+ 1/2 (* 1/6 x)))
6.0ms	(* 1/6 x)

series155.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ 1/2 (* 1/6 x))
90.0ms	(* x (+ 1/2 (* 1/6 x)))
24.0ms	(* 1/6 x)

simplify607.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
2	936
1	227
0	78

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.5b	(- (/ (exp x) x) (/ 1.0 x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

9.0ms	(/ (exp x) x)
39.0ms	(- (/ (exp x) x) (/ 1.0 x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) x)
61.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify2.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	4150
2	731
1	226
0	105

prune219.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
0.0b	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
4.8b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`pow1` `sqrt-pow1` `difference-of-squares`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`associate-l`
4×	`frac-times` `flip3--` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `pow1/2` `associate-l/` `associate-r/` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

2.0ms	(sqrt (exp x))
2.0ms	(sqrt (exp x))
118.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
15.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series195.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (exp x))
23.0ms	(sqrt (exp x))
105.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
52.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify662.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1521
1	274
0	109

prune389.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch42.0ms

Steps

Iters	Range		Point
9	-0.0007095347148853646	-4.632829109756021e-12	-0.00022388012385775216

simplify9.0ms

Iterations

Iter	Nodes
done	34
2	34
1	33
0	24

end0.0ms

sample2.2s

Algorithm

intervals

Results

654.0ms	2190×	body	1280	valid
441.0ms	436×	body	160	valid
402.0ms	1688×	body	640	valid
269.0ms	5514×	body	80	valid
157.0ms	889×	body	320	valid