Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	83×	body	1280	valid
16.0ms	74×	body	10240	exit
9.0ms	42×	body	640	valid
3.0ms	87×	body	80	valid
3.0ms	24×	body	320	valid
2.0ms	20×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
5.8b	(- (exp x) 1.0)

rewrite62.0ms

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:

41.0ms	(/ (exp x) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)

series54.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (678.0ms)

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

prune179.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

11.0ms	(+ (* x 1/6) 1/2)
40.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
36.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
7.0ms	(* x 1/6)

series205.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* x 1/6) 1/2)
47.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
83.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
18.0ms	(* x 1/6)

simplify1.6s

Counts

101 → 101

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	169	1406
1	450	1326
2	2168	1213
done	5000	1211

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 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)

rewrite20.0ms

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:

12.0ms	(+ (* 1/12 x) (/ 1 x))
7.0ms	(* 1/12 x)

series64.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (* 1/12 x) (/ 1 x))
15.0ms	(* 1/12 x)

simplify2.3s

Counts

35 → 35

Iterations

Useful iterations: 2 (65.0ms)

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

prune93.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (* 1/12 x) (/ 1 x)))
0.2b	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
0.3b	(* 1/12 x)
0.3b	(* 1/12 x)

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`pow1`
21×	`sqrt-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-div`
12×	`associate-r` `associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
7×	`flip3-+` `flip-+`
6×	`unswap-sqr`
5×	`pow-prod-down` `pow-prod-up`
4×	`frac-times` `add-log-exp`
3×	`prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 108

Calls

4 calls:

22.0ms	(sqrt (+ (* 1/12 x) (/ 1 x)))
152.0ms	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
13.0ms	(* 1/12 x)
8.0ms	(* 1/12 x)

series143.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* 1/12 x) (/ 1 x)))
56.0ms	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
15.0ms	(* 1/12 x)
17.0ms	(* 1/12 x)

simplify1.3s

Counts

120 → 120

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	122	1865
1	287	1269
2	1278	1135
done	5000	1106

prune331.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 21.1b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	30
1	27	30
done	27	30

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	2503×	body	10240	exit
822.0ms	2290×	body	1280	valid
315.0ms	1663×	body	640	valid
99.0ms	2805×	body	80	valid
98.0ms	804×	body	320	valid
36.0ms	440×	body	160	valid