Details

sample83.0ms

Algorithm

intervals

Results

23.0ms	66×	body	1280	valid
18.0ms	48×	body	640	valid
17.0ms	70×	body	10240	exit
4.0ms	29×	body	320	valid
4.0ms	95×	body	80	valid
2.0ms	18×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
5.5b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
21.0ms	(- (exp x) 1.0)

series65.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (exp x) (- (exp x) 1.0))
31.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (719.0ms)

Iter	Nodes	Cost
0	91	640
1	191	614
2	648	581
3	3086	577
done	5000	577

prune199.0ms

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `associate-l`
9×	`times-frac` `add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`flip3-+` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

27.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
65.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
14.0ms	(* x 1/6)

series190.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
102.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
30.0ms	(* x 1/6)

simplify1.9s

Counts

87 → 87

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	161	1282
1	428	1215
2	2112	1112
done	5002	1110

prune331.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`associate-r`
30×	`add-cube-cbrt` `*-un-lft-identity`
26×	`cbrt-prod`
25×	`add-exp-log`
20×	`times-frac`
18×	`pow1` `associate-l`
14×	`add-cbrt-cube`
12×	`unswap-sqr`
11×	`prod-exp`
9×	`cbrt-unprod`
6×	`pow1/3` `swap-sqr` `pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`associate-*r/`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `flip-+` `unpow2` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-plus` `pow-exp` `div-inv`

Counts

4 → 136

Calls

4 calls:

101.0ms	(* (* (cbrt (exp x)) (cbrt (exp x))) (/ (cbrt (exp x)) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
16.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
43.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
7.0ms	(* x 1/6)

series302.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* (cbrt (exp x)) (cbrt (exp x))) (/ (cbrt (exp x)) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
153.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
75.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
17.0ms	(* x 1/6)

simplify539.0ms

Counts

148 → 148

Iterations

Useful iterations: done (533.0ms)

Iter	Nodes	Cost
0	240	2424
1	739	2270
done	5000	1978

prune607.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

14.0ms	(+ (* 1/12 x) (/ 1 x))
7.0ms	(* 1/12 x)

series73.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(+ (* 1/12 x) (/ 1 x))
20.0ms	(* 1/12 x)

simplify2.8s

Counts

35 → 35

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	51	269
1	137	247
2	491	225
3	3072	225
done	5002	225

prune110.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	2500×	body	10240	exit
707.0ms	2237×	body	1280	valid
331.0ms	1639×	body	640	valid
142.0ms	2848×	body	80	valid
99.0ms	839×	body	320	valid
33.0ms	439×	body	160	valid