Details

sample138.0ms

Algorithm

intervals

Results

93.0ms	262×	body	10240	exit
10.0ms	193×	body	80	valid
6.0ms	21×	body	640	valid
4.0ms	28×	body	320	valid
2.0ms	18×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 5 (618.0ms)

Iter	Nodes	Cost
0	8	16
1	21	15
2	52	15
3	111	15
4	206	14
5	686	12
6	2789	12
done	5001	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp wj))
0.0b	(/ (- wj (/ x (exp wj))) (+ 1 wj))
5.0b	(- wj (/ (- wj (/ x (exp wj))) (+ 1 wj)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-sqr-sqrt`
173×	`*-un-lft-identity`
123×	`times-frac`
90×	`prod-diff`
87×	`add-cube-cbrt`
36×	`difference-of-squares`
25×	`distribute-lft-out`
18×	`distribute-lft-out--`
9×	`associate-/l*`
8×	`associate-/r/`
7×	`associate-/r*` `add-cbrt-cube`
6×	`add-exp-log`
5×	`div-inv` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `associate--r-`

Counts

3 → 193

Calls

3 calls:

14.0ms	(/ x (exp wj))
102.0ms	(/ (- wj (/ x (exp wj))) (+ 1 wj))
131.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ 1 wj)))

series209.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ x (exp wj))
64.0ms	(/ (- wj (/ x (exp wj))) (+ 1 wj))
91.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ 1 wj)))

simplify2.2s

Counts

202 → 202

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	331	8699
1	824	7901
2	2232	5818
done	5001	4977

prune456.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (* wj x) -2 (fma wj wj x))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(fma (* wj x) -2 (fma wj wj x))

simplify2.3s

Counts

13 → 13

Iterations

Useful iterations: 4 (770.0ms)

Iter	Nodes	Cost
0	21	158
1	40	155
2	106	134
3	457	134
4	2765	108
done	5000	108

prune80.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- wj (/ x (exp wj))) (fma wj (- wj) 1))
0.0b	(/ x (exp wj))
0.0b	(/ x (exp wj))
5.0b	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`times-frac`
39×	`*-un-lft-identity`
31×	`add-cube-cbrt`
12×	`associate-/l*`
10×	`add-cbrt-cube`
9×	`associate-/r*`
8×	`add-exp-log` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`associate-/l/`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

4 → 112

Calls

4 calls:

82.0ms	(/ (- wj (/ x (exp wj))) (fma wj (- wj) 1))
23.0ms	(/ x (exp wj))
14.0ms	(/ x (exp wj))
1.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

series258.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- wj (/ x (exp wj))) (fma wj (- wj) 1))
34.0ms	(/ x (exp wj))
31.0ms	(/ x (exp wj))
79.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

simplify2.6s

Counts

124 → 124

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	167	1751
1	355	1710
2	861	1592
3	2154	1586
done	5000	1584

prune578.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj))
5.0b	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
5.0b	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
5.0b	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj))
0.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
0.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
0.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

series426.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj))
89.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
71.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)
87.0ms	(fma (- wj 1) (/ (- wj (/ x (exp wj))) (fma wj (- wj) 1)) wj)

simplify3.3s

Counts

55 → 55

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	79	1220
1	174	1213
2	425	1068
3	1114	1039
4	3916	1026
done	5000	1022

prune370.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes83.0ms

Accuracy

66.9% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.0b

bsearch60.0ms

Steps

Iters	Range		Point
7	1.0710839719517313e-09	3.960545047166202e-08	5.8018913561244524e-09

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	51
1	28	51
done	28	51

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.7s	7666×	body	10240	exit
832.0ms	6262×	body	80	valid
139.0ms	797×	body	320	valid
124.0ms	461×	body	640	valid
65.0ms	565×	body	160	valid