Details

sample112.0ms

Algorithm

intervals

Results

58.0ms	228×	body	10240	exit
26.0ms	192×	body	80	valid
3.0ms	19×	body	640	valid
3.0ms	27×	body	320	valid
2.0ms	24×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 5 (191.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- wj (/ x (exp wj))) (+ wj 1))
0.3b	(/ x (exp wj))
5.6b	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
39×	`times-frac`
23×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`associate-/l*`
7×	`associate-/r*` `add-cbrt-cube` `distribute-lft-out`
6×	`add-exp-log` `distribute-lft-out--`
5×	`add-log-exp`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `associate-/r/` `flip--` `div-inv` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `flip-+` `associate--r-`

Counts

3 → 94

Calls

3 calls:

62.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
14.0ms	(/ x (exp wj))
83.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
50.0ms	(/ x (exp wj))
83.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

simplify2.2s

Counts

103 → 103

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	174	1576
1	409	1496
2	960	1436
3	2267	1431
done	5000	1431

prune383.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `distribute-rgt-in` `add-cube-cbrt` `sub-neg` `associate-+r+` `*-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:

18.0ms	(* wj (- wj (* x 2)))
9.0ms	(+ x (* wj (- wj (* x 2))))

series145.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(* wj (- wj (* x 2)))
56.0ms	(+ x (* wj (- wj (* x 2))))

simplify1.6s

Counts

45 → 45

Iterations

Useful iterations: 2 (158.0ms)

Iter	Nodes	Cost
0	70	507
1	186	473
2	543	431
3	2129	431
done	5001	431

prune174.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (- wj (* x 2))) (cbrt (- wj (* x 2))))
0.6b	(cbrt (- wj (* x 2)))
0.6b	(cbrt (- wj (* x 2)))
0.6b	(cbrt (- wj (* x 2)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

44.0ms	(* (cbrt (- wj (* x 2))) (cbrt (- wj (* x 2))))
3.0ms	(cbrt (- wj (* x 2)))
3.0ms	(cbrt (- wj (* x 2)))
4.0ms	(cbrt (- wj (* x 2)))

series954.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (cbrt (- wj (* x 2))) (cbrt (- wj (* x 2))))
237.0ms	(cbrt (- wj (* x 2)))
239.0ms	(cbrt (- wj (* x 2)))
246.0ms	(cbrt (- wj (* x 2)))

simplify3.7s

Counts

99 → 99

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	129	1635
1	274	1504
2	679	1418
3	1593	1281
4	3928	1225
done	5001	1180

prune412.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- wj (* x 2)))
0.6b	(cbrt (- wj (* x 2)))
0.6b	(cbrt (- wj (* x 2)))
0.6b	(cbrt (- wj (* x 2)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (- wj (* x 2)))
9.0ms	(cbrt (- wj (* x 2)))
3.0ms	(cbrt (- wj (* x 2)))
4.0ms	(cbrt (- wj (* x 2)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (- wj (* x 2)))
203.0ms	(cbrt (- wj (* x 2)))
203.0ms	(cbrt (- wj (* x 2)))
211.0ms	(cbrt (- wj (* x 2)))

simplify2.7s

Counts

64 → 64

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	68	856
1	156	828
2	365	780
3	875	732
4	1896	680
done	5000	668

prune302.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.5b

regimes175.0ms

Accuracy

59.8% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.1b

bsearch46.0ms

Steps

Iters	Range		Point
7	1.1362596833603348e-09	1.5244367550608482e-07	5.6200684172778545e-09

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	31
1	26	31
done	26	31

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.5s	7477×	body	10240	exit
534.0ms	820×	body	320	valid
461.0ms	6222×	body	80	valid
400.0ms	547×	body	160	valid
156.0ms	492×	body	640	valid