Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	80×	body	1280	valid
6.0ms	45×	body	640	valid
4.0ms	174×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
3	15
2	13
1	10
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.8b	(- (exp x) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

20.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

series90.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- (exp x) 1.0) x)
24.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	1947
2	569
1	224
0	99

prune241.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

37.0ms	(* x (+ (* 1/6 x) 1/2))
6.0ms	(* 1/6 x)

series86.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* x (+ (* 1/6 x) 1/2))
24.0ms	(* 1/6 x)

simplify3.6s

Counts

46 → 46

Iterations

Iter	Nodes
done	5019
3	3635
2	646
1	204
0	70

prune161.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
3.8b	(- (exp x) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)
15.0ms	(- (exp x) 1.0)

series795.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt x)
285.0ms	(cbrt x)
239.0ms	(cbrt x)
26.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
4	1842
3	680
2	284
1	123
0	62

prune296.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.1b

bsearch44.0ms

Steps

Iters	Range		Point
9	-0.03438460291724579	-3.2432757514909933e-09	-0.00016689112366788532

simplify4.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

692.0ms	2256×	body	1280	valid
305.0ms	1712×	body	640	valid
249.0ms	5394×	body	80	valid
144.0ms	830×	body	320	valid
76.0ms	402×	body	160	valid