Details

sample62.0ms

Algorithm

intervals

Results

38.0ms	231×	body	10240	exit
6.0ms	208×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	19×	body	160	valid
1.0ms	7×	body	640	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 5 (147.0ms)

Iter	Nodes	Cost
0	8	16
1	20	15
2	48	15
3	105	15
4	190	14
5	621	12
6	2585	12
done	5001	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- wj (/ x (exp wj)))
0.0b	(/ (- wj (/ x (exp wj))) (+ wj 1))
0.0b	(/ x (exp wj))
4.8b	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
40×	`times-frac`
24×	`add-cube-cbrt`
14×	`difference-of-squares`
9×	`associate-/l*`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log` `associate-/r*` `distribute-lft-out` `distribute-lft-out--`
4×	`pow1`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`flip3-+` `flip-+` `associate--r-`

Counts

4 → 109

Calls

4 calls:

13.0ms	(- wj (/ x (exp wj)))
41.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
8.0ms	(/ x (exp wj))
50.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- wj (/ x (exp wj)))
42.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
27.0ms	(/ x (exp wj))
47.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: 3 (655.0ms)

Iter	Nodes	Cost
0	182	1772
1	431	1678
2	1031	1613
3	2469	1608
done	5000	1608

prune249.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* wj (- wj (* 2 x)))
0.0b	(+ (* wj (- wj (* 2 x))) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

17.0ms	(* wj (- wj (* 2 x)))
14.0ms	(+ (* wj (- wj (* 2 x))) x)

series73.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* wj (- wj (* 2 x)))
24.0ms	(+ (* wj (- wj (* 2 x))) x)

simplify912.0ms

Counts

45 → 45

Iterations

Useful iterations: 3 (337.0ms)

Iter	Nodes	Cost
0	71	519
1	189	487
2	519	445
3	1897	439
done	5000	439

prune82.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt wj) (cbrt wj))
0.6b	(cbrt wj)
0.6b	(cbrt wj)
0.6b	(cbrt wj)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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:

11.0ms	(* (cbrt wj) (cbrt wj))
1.0ms	(cbrt wj)
1.0ms	(cbrt wj)
1.0ms	(cbrt wj)

series710.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (cbrt wj) (cbrt wj))
175.0ms	(cbrt wj)
170.0ms	(cbrt wj)
172.0ms	(cbrt wj)

simplify3.2s

Counts

85 → 85

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	61	524
1	115	417
2	319	397
3	1092	379
4	4423	374
done	5000	364

prune195.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* wj wj) 1/3) (* (cbrt wj) (- wj (* 2 x))))
0.3b	(* (cbrt wj) (- wj (* 2 x)))
0.6b	(cbrt wj)
30.6b	(pow (* wj wj) 1/3)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
16×	`prod-exp`
14×	`pow1` `add-sqr-sqrt`
11×	`associate-l` `add-cbrt-cube`
10×	`distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in`
7×	`cbrt-prod` `cbrt-unprod`
6×	`sub-neg` `pow-pow` `associate-*r/` `pow-exp`
4×	`associate-r` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `unpow1/3`
2×	`unpow-prod-down` `flip3--` `pow-prod-down` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`
1×	`pow2` `pow-plus` `pow1/3` `pow-sqr` `pow-prod-up`

Counts

4 → 97

Calls

4 calls:

37.0ms	(* (pow (* wj wj) 1/3) (* (cbrt wj) (- wj (* 2 x))))
19.0ms	(* (cbrt wj) (- wj (* 2 x)))
1.0ms	(cbrt wj)
6.0ms	(pow (* wj wj) 1/3)

series557.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (pow (* wj wj) 1/3) (* (cbrt wj) (- wj (* 2 x))))
141.0ms	(* (cbrt wj) (- wj (* 2 x)))
173.0ms	(cbrt wj)
175.0ms	(pow (* wj wj) 1/3)

simplify803.0ms

Counts

109 → 109

Iterations

Useful iterations: done (800.0ms)

Iter	Nodes	Cost
0	153	1341
1	371	1175
2	1334	1051
done	5000	1018

prune212.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes78.0ms

Accuracy

66.4% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.1b

bsearch30.0ms

Steps

Iters	Range		Point
8	1.424245324695418e-11	2.4229076172777078e-08	6.4440943861943365e-09

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	25	29
done	25	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s	7541×	body	10240	exit
178.0ms	6326×	body	80	valid
68.0ms	781×	body	320	valid
60.0ms	437×	body	640	valid
32.0ms	543×	body	160	valid