Details

sample183.0ms

Algorithm

intervals

Results

103.0ms	232×	body	10240	exit
25.0ms	22×	body	160	valid
14.0ms	191×	body	80	valid
6.0ms	19×	body	640	valid
5.0ms	24×	body	320	valid

simplify491.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	398
3	109
2	48
1	20
0	8

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj))
6.2b	(+ wj (/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj)))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
98×	`times-frac`
94×	`*-un-lft-identity`
30×	`difference-of-squares`
28×	`add-cube-cbrt`
14×	`associate-/l*`
13×	`distribute-lft-out`
10×	`distribute-lft-out--`
7×	`associate-/r*` `add-cbrt-cube`
6×	`add-exp-log`
5×	`add-log-exp`
3×	`pow1` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-sub` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3--` `frac-sub` `flip--`

Counts

3 → 117

Calls

3 calls:

9.0ms	(/ x (exp wj))
106.0ms	(/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj))
116.0ms	(+ wj (/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ x (exp wj))
63.0ms	(/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj))
54.0ms	(+ wj (/ (- (/ x (exp wj)) (/ wj 1)) (+ 1 wj)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	2113
1	536
0	216

prune532.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

37.0ms	(+ (+ x (* wj wj)) (* -2 (* wj x)))
24.0ms	(* -2 (* wj x))
9.0ms	(+ x (* wj wj))

series114.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (+ x (* wj wj)) (* -2 (* wj x)))
26.0ms	(* -2 (* wj x))
47.0ms	(+ x (* wj wj))

simplify902.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	1425
1	269
0	84

prune254.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

66.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
13.0ms	(cbrt (+ x (pow wj 2)))
12.0ms	(cbrt (+ x (pow wj 2)))
6.0ms	(cbrt (+ x (pow wj 2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

443.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
501.0ms	(cbrt (+ x (pow wj 2)))
442.0ms	(cbrt (+ x (pow wj 2)))
454.0ms	(cbrt (+ x (pow wj 2)))

simplify807.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1056
1	280
0	119

prune744.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize109.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ (* wj wj) x))
0.9b	(pow (cbrt (cbrt (+ (* wj wj) x))) (+ 3 1))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
17×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`unpow-prod-down`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow-unpow` `add-cbrt-cube` `pow1/3` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out`
2×	`pow-pow`
1×	`pow-to-exp` `unpow-prod-up` `pow-exp` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

11.0ms	(cbrt (+ x (pow wj 2)))
11.0ms	(cbrt (+ x (pow wj 2)))
8.0ms	(cbrt (+ (* wj wj) x))
32.0ms	(pow (cbrt (cbrt (+ (* wj wj) x))) (+ 3 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

519.0ms	(cbrt (+ x (pow wj 2)))
459.0ms	(cbrt (+ x (pow wj 2)))
99.0ms	(cbrt (+ (* wj wj) x))
177.0ms	(pow (cbrt (cbrt (+ (* wj wj) x))) (+ 3 1))

simplify694.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1453
1	403
0	150

prune696.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes164.0ms

Accuracy

68.9% (0.6b remaining)

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

bsearch47.0ms

Steps

Iters	Range		Point
7	1.9673231826388637e-10	1.2857563411330803e-08	6.728609179253454e-09

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample6.9s

Algorithm

intervals

Results

4.9s	7579×	body	10240	exit
885.0ms	6305×	body	80	valid
205.0ms	795×	body	320	valid
165.0ms	440×	body	640	valid
98.0ms	550×	body	160	valid