Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	75×	body	1280	valid
8.0ms	49×	body	640	valid
6.0ms	182×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	9×	body	160	valid

simplify15.0ms

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: 38.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.0b	(- (exp x) 1.0)

rewrite57.0ms

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:

39.0ms	(/ (- (exp x) 1.0) x)
13.0ms	(- (exp x) 1.0)

series96.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- (exp x) 1.0) x)
28.0ms	(- (exp x) 1.0)

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: done (2.0s)

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

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(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)

series91.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(fma x (fma 1/6 x 1/2) 1)
60.0ms	(fma 1/6 x 1/2)

simplify2.7s

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

prune111.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 x 1/2)
0.1b	(fma 1/6 x 1/2)
10.6b	(sqrt (fma x (fma 1/6 x 1/2) 1))
10.6b	(sqrt (fma x (fma 1/6 x 1/2) 1))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma 1/6 x 1/2)
1.0ms	(fma 1/6 x 1/2)
3.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
3.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

series278.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma 1/6 x 1/2)
35.0ms	(fma 1/6 x 1/2)
77.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
110.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

simplify4.7s

Counts

62 → 62

Iterations

Useful iterations: 5 (3.4s)

Iter	Nodes	Cost
0	57	634
1	114	552
2	276	524
3	700	516
4	1691	512
5	4865	492
done	5000	492

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma x 5/96 1/4) 1)
0.1b	(fma x 5/96 1/4)
0.1b	(fma 1/6 x 1/2)
10.6b	(sqrt (fma x (fma 1/6 x 1/2) 1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

0.0ms	(fma x (fma x 5/96 1/4) 1)
1.0ms	(fma x 5/96 1/4)
0.0ms	(fma 1/6 x 1/2)
3.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

series217.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma x (fma x 5/96 1/4) 1)
45.0ms	(fma x 5/96 1/4)
45.0ms	(fma 1/6 x 1/2)
82.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

simplify2.2s

Counts

57 → 57

Iterations

Useful iterations: 3 (262.0ms)

Iter	Nodes	Cost
0	81	530
1	145	480
2	346	436
3	1006	431
4	3361	431
done	5000	431

prune204.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes21.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.3b

bsearch33.0ms

Steps

Iters	Range		Point
9	-0.00046903783504091863	-4.353488769003373e-11	-0.00017507561591521617

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	20	27
done	20	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

671.0ms	2351×	body	1280	valid
352.0ms	1603×	body	640	valid
213.0ms	5455×	body	80	valid
126.0ms	819×	body	320	valid
30.0ms	399×	body	160	valid