Details

sample48.0ms

Algorithm

intervals

Results

15.0ms	62×	body	1280	valid
11.0ms	67×	body	640	valid
6.0ms	177×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	15×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.8b	(- (exp x) 1.0)

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

72.0ms	(/ (- (exp x) 1.0) x)
25.0ms	(- (exp x) 1.0)

series76.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- (exp x) 1.0) x)
27.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	127	854
1	281	745
2	612	665
3	1785	619
done	5001	605

prune206.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma 1/6 x 1/2) 1)
0.1b	(fma 1/6 x 1/2)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

1.0ms	(fma x (fma 1/6 x 1/2) 1)
1.0ms	(fma 1/6 x 1/2)

series92.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(fma x (fma 1/6 x 1/2) 1)
44.0ms	(fma 1/6 x 1/2)

simplify2.9s

Counts

26 → 26

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	33	213
1	53	204
2	114	176
3	381	175
4	1753	175
done	5001	175

prune59.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma x (fma 1/6 x 1/2) 1))
0.0b	(fma x (fma 1/6 x 1/2) 1)
0.1b	(fma 1/6 x 1/2)
0.3b	(log (exp (fma x (fma 1/6 x 1/2) 1)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

4.0ms	(exp (fma x (fma 1/6 x 1/2) 1))
1.0ms	(fma x (fma 1/6 x 1/2) 1)
1.0ms	(fma 1/6 x 1/2)
6.0ms	(log (exp (fma x (fma 1/6 x 1/2) 1)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (fma x (fma 1/6 x 1/2) 1))
28.0ms	(fma x (fma 1/6 x 1/2) 1)
54.0ms	(fma 1/6 x 1/2)
39.0ms	(log (exp (fma x (fma 1/6 x 1/2) 1)))

simplify2.6s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	71	656
1	111	596
2	225	524
3	710	519
4	3345	518
done	5000	518

prune198.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.5b	(- (/ (exp x) x) (/ 1.0 x))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
213×	`add-sqr-sqrt`
209×	`*-un-lft-identity`
201×	`add-cube-cbrt`
169×	`prod-diff`
30×	`div-inv`
13×	`fma-neg`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`add-exp-log` `associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`

Counts

2 → 236

Calls

2 calls:

11.0ms	(/ (exp x) x)
56.0ms	(- (/ (exp x) x) (/ 1.0 x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (exp x) x)
67.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify4.5s

Counts

242 → 242

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	342	8500
1	750	7453
2	1637	5470
3	4974	3248
done	5000	3248

prune220.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes30.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.9b

bsearch21.0ms

Steps

Iters	Range		Point
5	-0.00021785999598854965	-9.497075983896804e-05	-0.00012192187032837518

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	18	21
done	18	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

649.0ms	5367×	body	80	valid
638.0ms	2197×	body	1280	valid
379.0ms	1692×	body	640	valid
99.0ms	852×	body	320	valid
31.0ms	417×	body	160	valid