Details

sample205.0ms

Algorithm

intervals

Results

155.0ms	234×	body	10240	exit
18.0ms	212×	body	80	valid
6.0ms	21×	body	320	valid
5.0ms	11×	body	640	valid
3.0ms	17×	body	160	valid

simplify13.3s

Counts

1 → 1

Iterations

Iter	Nodes
7	13238
6	1755
5	573
4	251
3	154
2	76
1	36
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* wj (exp wj))
0.0b	(* wj (exp wj))
0.3b	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
4.5b	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-cbrt-cube`
8×	`pow1` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`associate-/r*`
4×	`distribute-rgt-out` `distribute-rgt1-in` `insert-posit16`
3×	`associate-/l*`
2×	`flip3--` `div-sub` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `flip-+` `div-inv` `distribute-lft-out--` `associate--r-`

Counts

4 → 96

Calls

4 calls:

9.0ms	(* wj (exp wj))
10.0ms	(* wj (exp wj))
37.0ms	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
37.0ms	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* wj (exp wj))
52.0ms	(* wj (exp wj))
54.0ms	(/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj))))
80.0ms	(- wj (/ (- (* wj (exp wj)) x) (+ (exp wj) (* wj (exp wj)))))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
3	3756
2	1453
1	641
0	153

prune964.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `insert-posit16`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

10.0ms	(+ x (* wj (+ wj (* -2 x))))
22.0ms	(* wj (+ wj (* -2 x)))

series98.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ x (* wj (+ wj (* -2 x))))
64.0ms	(* wj (+ wj (* -2 x)))

simplify1.0s

Counts

43 → 43

Iterations

Iter	Nodes
3	3837
2	892
1	340
0	74

prune250.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* wj (+ wj (* -2 x)))) (cbrt (* wj (+ wj (* -2 x)))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (cbrt (* wj (+ wj (* -2 x)))) (cbrt (* wj (+ wj (* -2 x)))))
4.0ms	(cbrt (* wj (+ wj (* -2 x))))
5.0ms	(cbrt (* wj (+ wj (* -2 x))))
4.0ms	(cbrt (* wj (+ wj (* -2 x))))

series1.6s

Counts

4 → 12

Calls

4 calls:

369.0ms	(* (cbrt (* wj (+ wj (* -2 x)))) (cbrt (* wj (+ wj (* -2 x)))))
415.0ms	(cbrt (* wj (+ wj (* -2 x))))
404.0ms	(cbrt (* wj (+ wj (* -2 x))))
391.0ms	(cbrt (* wj (+ wj (* -2 x))))

simplify823.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2042
2	948
1	464
0	109

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (* wj (+ wj (* -2 x))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))
8.9b	(cbrt (* wj (+ wj (* -2 x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div` `associate-*r/`
4×	`cbrt-prod` `add-sqr-sqrt` `pow1` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `add-cube-cbrt` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

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

series1.6s

Counts

4 → 12

Calls

4 calls:

374.0ms	(cbrt (* wj (+ wj (* -2 x))))
425.0ms	(cbrt (* wj (+ wj (* -2 x))))
387.0ms	(cbrt (* wj (+ wj (* -2 x))))
418.0ms	(cbrt (* wj (+ wj (* -2 x))))

simplify774.0ms

Counts

60 → 60

Iterations

Iter	Nodes
4	2093
3	1060
2	479
1	246
0	57

prune846.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

regimes217.0ms

Accuracy

59.5% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 2.1b

bsearch76.0ms

Steps

Iters	Range		Point
8	639.0488776514559	7213346.136357025	706.4071446376307
7	6.338303524804038e-10	3.3590593015773896e-08	9.034798015591916e-09

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	25

end0.0ms

sample9.3s

Algorithm

intervals

Results

7.6s	7615×	body	10240	exit
735.0ms	6289×	body	80	valid
322.0ms	794×	body	320	valid
218.0ms	462×	body	640	valid
105.0ms	531×	body	160	valid