Details

sample60.0ms

Algorithm

intervals

Results

22.0ms	68×	body	1280	valid
10.0ms	178×	body	80	valid
9.0ms	47×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	10×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.6b	(- (exp x) 1.0)

rewrite36.0ms

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:

24.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series102.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- (exp x) 1.0) x)
32.0ms	(- (exp x) 1.0)

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.2s)

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

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)

rewrite41.0ms

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:

6.0ms	(+ 1/2 (* 1/6 x))
20.0ms	(* x (+ 1/2 (* 1/6 x)))
14.0ms	(* 1/6 x)

series136.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ 1/2 (* 1/6 x))
69.0ms	(* x (+ 1/2 (* 1/6 x)))
22.0ms	(* 1/6 x)

simplify2.1s

Counts

60 → 60

Iterations

Useful iterations: 2 (154.0ms)

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

prune125.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (* x x) (+ 1/2 (* 1/6 x))))
0.1b	(* (* x x) (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)
2.4b	(/ (+ x (* (* x x) (+ 1/2 (* 1/6 x)))) x)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 83

Calls

4 calls:

7.0ms	(+ x (* (* x x) (+ 1/2 (* 1/6 x))))
49.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
7.0ms	(* 1/6 x)
29.0ms	(/ (+ x (* (* x x) (+ 1/2 (* 1/6 x)))) x)

series184.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ x (* (* x x) (+ 1/2 (* 1/6 x))))
83.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
18.0ms	(* 1/6 x)
47.0ms	(/ (+ x (* (* x x) (+ 1/2 (* 1/6 x)))) x)

simplify1.3s

Counts

95 → 95

Iterations

Useful iterations: 2 (419.0ms)

Iter	Nodes	Cost
0	141	1382
1	356	1280
2	1337	1168
done	5000	1168

prune204.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (+ 1/2 (* 1/6 x)))
0.1b	(/ 1 (/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x))))))
0.3b	(* 1/6 x)
2.6b	(/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
62×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
18×	`associate-/r*` `add-cbrt-cube`
12×	`pow1`
11×	`associate-/r/`
8×	`div-exp`
6×	`flip3-+` `associate-r` `flip-+` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `inv-pow`

Counts

4 → 154

Calls

4 calls:

28.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
15.0ms	(/ 1 (/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x))))))
7.0ms	(* 1/6 x)
19.0ms	(/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x)))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
50.0ms	(/ 1 (/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x))))))
14.0ms	(* 1/6 x)
55.0ms	(/ x (+ x (* (* x x) (+ 1/2 (* 1/6 x)))))

simplify1.7s

Counts

166 → 166

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	257	3560
1	605	3204
2	1786	2925
done	5000	2897

prune358.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch50.0ms

Steps

Iters	Range		Point
8	-0.1517943218839364	-1.6640733670284383e-05	-0.00013926054794957644

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	41
1	36	41
done	36	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

502.0ms	2218×	body	1280	valid
250.0ms	1716×	body	640	valid
137.0ms	5418×	body	80	valid
74.0ms	823×	body	320	valid
23.0ms	397×	body	160	valid