Details

sample46.0ms

Algorithm

intervals

Results

16.0ms	71×	body	1280	valid
8.0ms	57×	body	640	valid
4.0ms	161×	body	80	valid
3.0ms	33×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 41.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.4b	(- (exp x) 1.0)

rewrite34.0ms

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:

23.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
19.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

58 → 58

Iterations

Useful iterations: 4 (773.0ms)

Iter	Nodes	Cost
0	99	596
1	221	572
2	503	542
3	1095	537
4	2836	536
done	5001	536

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

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:

5.0ms	(+ 1/2 (* 1/6 x))
15.0ms	(* x (+ 1/2 (* 1/6 x)))
7.0ms	(* 1/6 x)

series107.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ 1/2 (* 1/6 x))
60.0ms	(* x (+ 1/2 (* 1/6 x)))
15.0ms	(* 1/6 x)

simplify1.5s

Counts

60 → 60

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	78	480
1	204	439
2	572	397
3	1768	397
done	5000	397

prune91.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

49.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
10.0ms	(+ (exp x) 1.0)
29.0ms	(* x (+ (exp x) 1.0))
16.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series153.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
33.0ms	(* x (+ (exp x) 1.0))
29.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify691.0ms

Counts

88 → 88

Iterations

Useful iterations: done (689.0ms)

Iter	Nodes	Cost
0	136	1231
1	378	1140
2	1346	991
done	5001	871

prune167.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
3.3b	(- (pow (exp x) 2) (* 1.0 1.0))
3.3b	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-cube-cbrt` `log-pow` `add-log-exp` `difference-of-squares`
7×	`pow1` `exp-prod`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`associate-r`
3×	`associate-l`
2×	`sub-neg` `unpow-prod-down` `flip3-+` `associate-*r/` `exp-sum` `flip-+` `distribute-lft-out` `unpow2` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `log-div` `flip3--` `distribute-lft-in` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

29.0ms	(* x (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
23.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
43.0ms	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* x (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
26.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
28.0ms	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

simplify1.4s

Counts

85 → 85

Iterations

Useful iterations: 3 (540.0ms)

Iter	Nodes	Cost
0	139	906
1	305	819
2	799	723
3	2565	715
done	5002	715

prune195.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes22.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 20.9b

bsearch21.0ms

Steps

Iters	Range		Point
5	-0.0002772006047103471	-9.588134368690297e-05	-0.00016816552986419862

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	30
1	30	30
done	30	30

end0.0ms

sample911.0ms

Algorithm

intervals

Results

391.0ms	2352×	body	1280	valid
169.0ms	1649×	body	640	valid
99.0ms	5259×	body	80	valid
53.0ms	818×	body	320	valid
17.0ms	412×	body	160	valid