Details

sample37.0ms

Algorithm

intervals

Results

14.0ms	66×	body	1280	valid
6.0ms	49×	body	640	valid
5.0ms	176×	body	80	valid
3.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.7b	(- (exp x) 1.0)

rewrite52.0ms

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:

36.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

series76.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
35.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

58 → 58

Iterations

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

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)

rewrite36.0ms

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:

8.0ms	(+ 1/2 (* 1/6 x))
19.0ms	(* x (+ 1/2 (* 1/6 x)))
8.0ms	(* 1/6 x)

series148.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ 1/2 (* 1/6 x))
77.0ms	(* x (+ 1/2 (* 1/6 x)))
21.0ms	(* 1/6 x)

simplify465.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
2	936
1	227
0	78

prune268.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (* 1/6 x))
0.0b	(pow (exp x) (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)
4.0b	(log (pow (exp x) (+ 1/2 (* 1/6 x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`log-prod`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `rem-log-exp` `associate-r` `associate-l`
2×	`pow-to-exp` `unpow-prod-up` `pow-exp` `sqr-pow`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

8.0ms	(+ 1/2 (* 1/6 x))
10.0ms	(pow (exp x) (+ 1/2 (* 1/6 x)))
5.0ms	(* 1/6 x)
6.0ms	(log (pow (exp x) (+ 1/2 (* 1/6 x))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ 1/2 (* 1/6 x))
23.0ms	(pow (exp x) (+ 1/2 (* 1/6 x)))
29.0ms	(* 1/6 x)
464.0ms	(log (pow (exp x) (+ 1/2 (* 1/6 x))))

simplify714.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1469
1	314
0	110

prune440.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
3.3b	(- (/ (exp x) x) (/ 1.0 x))

rewrite39.0ms

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:

12.0ms	(/ (exp x) x)
26.0ms	(- (/ (exp x) x) (/ 1.0 x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (exp x) x)
61.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify1.7s

Counts

56 → 56

Iterations

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

prune250.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch54.0ms

Steps

Iters	Range		Point
8	-0.003292329160956242	-2.923395978885857e-06	-0.00013003875479750078

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

612.0ms	2297×	body	1280	valid
406.0ms	1626×	body	640	valid
245.0ms	5476×	body	80	valid
91.0ms	803×	body	320	valid
30.0ms	424×	body	160	valid