Details

sample140.0ms

Algorithm

intervals

Results

91.0ms	232×	body	10240	exit
13.0ms	207×	body	80	valid
5.0ms	16×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 5 (235.0ms)

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: 11.6b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite222.0ms

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:

14.0ms	(/ x (exp wj))
87.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
114.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ x (exp wj))
57.0ms	(/ (- wj (/ x (exp wj))) (+ wj 1))
91.0ms	(- wj (/ (- wj (/ x (exp wj))) (+ wj 1)))

simplify1.9s

Counts

103 → 103

Iterations

Useful iterations: 3 (889.0ms)

Iter	Nodes	Cost
0	174	1576
1	409	1496
2	960	1436
3	2266	1431
done	5001	1431

prune322.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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:

23.0ms	(* wj (- wj (* 2 x)))
8.0ms	(+ x (* wj (- wj (* 2 x))))

series103.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(* wj (- wj (* 2 x)))
37.0ms	(+ x (* wj (- wj (* 2 x))))

simplify1.5s

Counts

45 → 45

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	70	507
1	186	473
2	543	431
3	2135	431
done	5000	431

prune142.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt wj) (cbrt wj))
0.7b	(cbrt wj)
0.7b	(cbrt wj)
0.7b	(cbrt wj)

rewrite37.0ms

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:

22.0ms	(* (cbrt wj) (cbrt wj))
2.0ms	(cbrt wj)
2.0ms	(cbrt wj)
2.0ms	(cbrt wj)

series1.2s

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (cbrt wj) (cbrt wj))
237.0ms	(cbrt wj)
273.0ms	(cbrt wj)
323.0ms	(cbrt wj)

simplify5.0s

Counts

85 → 85

Iterations

Useful iterations: done (4.9s)

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

prune603.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (* wj wj)) (* (cbrt wj) (- wj (* 2 x))))
0.3b	(* (cbrt wj) (- wj (* 2 x)))
0.7b	(cbrt wj)
30.9b	(cbrt (* wj wj))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

37.0ms	(* (cbrt (* wj wj)) (* (cbrt wj) (- wj (* 2 x))))
19.0ms	(* (cbrt wj) (- wj (* 2 x)))
1.0ms	(cbrt wj)
4.0ms	(cbrt (* wj wj))

series800.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (cbrt (* wj wj)) (* (cbrt wj) (- wj (* 2 x))))
161.0ms	(* (cbrt wj) (- wj (* 2 x)))
260.0ms	(cbrt wj)
295.0ms	(cbrt (* wj wj))

simplify4.5s

Counts

89 → 89

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	127	1045
1	308	997
2	1061	903
3	4938	879
done	5000	879

prune274.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes122.0ms

Accuracy

31.5% (1.2b remaining)

Error of 1.5b against oracle of 0.3b and baseline of 2.1b

bsearch52.0ms

Steps

Iters	Range		Point
9	-1.9918553488737634e-08	-1.2276846442872278e-14	-5.00771993997508e-09

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	21	29
done	21	29

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.5s	7577×	body	10240	exit
616.0ms	747×	body	320	valid
406.0ms	6323×	body	80	valid
177.0ms	482×	body	640	valid
59.0ms	513×	body	160	valid