Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	63×	body	1280	valid
9.0ms	62×	body	640	valid
5.0ms	169×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid

simplify13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (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-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:

42.0ms	(/ (- (exp x) 1.0) x)
12.0ms	(- (exp x) 1.0)

series68.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 3 (812.0ms)

Iter	Nodes	Cost
0	99	596
1	227	572
2	802	544
3	4675	537
done	5002	537

prune204.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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)

rewrite38.0ms

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))
18.0ms	(* x (+ 1/2 (* 1/6 x)))
13.0ms	(* 1/6 x)

series145.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ 1/2 (* 1/6 x))
70.0ms	(* x (+ 1/2 (* 1/6 x)))
29.0ms	(* 1/6 x)

simplify638.0ms

Counts

60 → 60

Iterations

Useful iterations: done (636.0ms)

Iter	Nodes	Cost
0	78	480
1	227	445
2	936	405
done	5000	399

prune157.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (* x 1/6))
0.1b	(* (* x x) (+ 1/2 (* x 1/6)))
0.4b	(* x 1/6)
4.2b	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) x)

rewrite124.0ms

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×	`associate-r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 81

Calls

4 calls:

8.0ms	(+ 1/2 (* x 1/6))
32.0ms	(* (* x x) (+ 1/2 (* x 1/6)))
18.0ms	(* x 1/6)
64.0ms	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) x)

series231.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1/2 (* x 1/6))
100.0ms	(* (* x x) (+ 1/2 (* x 1/6)))
23.0ms	(* x 1/6)
70.0ms	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) x)

simplify2.9s

Counts

93 → 93

Iterations

Useful iterations: 2 (828.0ms)

Iter	Nodes	Cost
0	139	1236
1	415	1172
2	3106	1052
done	5001	1052

prune277.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x))
3.9b	(* (/ 1 (* (cbrt x) (cbrt x))) (/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
51×	`add-exp-log` `times-frac`
39×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `associate-/r*`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip-+`

Counts

4 → 133

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
43.0ms	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x))
104.0ms	(* (/ 1 (* (cbrt x) (cbrt x))) (/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x)))

series874.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(cbrt x)
284.0ms	(cbrt x)
141.0ms	(/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x))
110.0ms	(* (/ 1 (* (cbrt x) (cbrt x))) (/ (+ x (* (* x x) (+ 1/2 (* x 1/6)))) (cbrt x)))

simplify3.1s

Counts

145 → 145

Iterations

Useful iterations: 2 (769.0ms)

Iter	Nodes	Cost
0	213	3374
1	691	3230
2	4955	2658
done	5001	2658

prune476.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes39.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch51.0ms

Steps

Iters	Range		Point
10	-1106898266.2167518	-2.9526231381329305e-09	-0.00015289388879205097

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	28
1	27	28
done	27	28

end0.0ms

sample1.7s

Algorithm

intervals

Results

656.0ms	2203×	body	1280	valid
386.0ms	1750×	body	640	valid
245.0ms	5512×	body	80	valid
91.0ms	816×	body	320	valid
33.0ms	412×	body	160	valid