Details

sample82.0ms

Algorithm

intervals

Results

24.0ms	64×	body	1280	valid
20.0ms	76×	body	10240	exit
12.0ms	49×	body	640	valid
5.0ms	29×	body	320	valid
5.0ms	98×	body	80	valid
2.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	152
1	7	152
2	8	152
done	8	152

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize7.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ (exp x) (- (exp x) 1.0))
3.7b	(- (exp x) 1.0)

rewrite50.0ms

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` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 51

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
23.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (817.0ms)

Iter	Nodes	Cost
0	91	16288
1	191	14948
2	645	14868
3	2908	14828
done	5000	14828

prune190.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 1 x) 1/2)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

12.0ms	(+ (/ 1 x) 1/2)
41.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
9.0ms	(* 1/12 x)

series52.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ (/ 1 x) 1/2)
16.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
15.0ms	(* 1/12 x)

simplify993.0ms

Counts

53 → 53

Iterations

Useful iterations: done (988.0ms)

Iter	Nodes	Cost
0	73	9092
1	209	7900
2	774	7900
done	5000	7860

prune198.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

21.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
5.0ms	(cbrt (* 1/12 x))
5.0ms	(cbrt (* 1/12 x))
5.0ms	(cbrt (* 1/12 x))

series1.2s

Counts

4 → 12

Calls

4 calls:

312.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
266.0ms	(cbrt (* 1/12 x))
272.0ms	(cbrt (* 1/12 x))
303.0ms	(cbrt (* 1/12 x))

simplify812.0ms

Counts

70 → 70

Iterations

Useful iterations: done (804.0ms)

Iter	Nodes	Cost
0	55	15843
1	137	12565
2	575	12562
done	5000	11882

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

12.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (cbrt x) (cbrt x))
284.0ms	(cbrt x)
272.0ms	(cbrt x)
258.0ms	(cbrt x)

simplify1.5s

Counts

85 → 85

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	61	17134
1	138	14621
2	727	14346
done	5000	13666

prune321.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

regimes143.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 21.6b

bsearch2.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	28	1066
1	40	1066
done	40	1066

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2289×	body	1280	valid
756.0ms	2544×	body	10240	exit
312.0ms	1611×	body	640	valid
171.0ms	2894×	body	80	valid
102.0ms	792×	body	320	valid
35.0ms	417×	body	160	valid