Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	74×	body	1280	valid
8.0ms	56×	body	640	valid
4.0ms	169×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	14×	body	160	valid

simplify9.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.4b	(- (exp x) 1.0)

rewrite82.0ms

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:

55.0ms	(/ (- (exp x) 1.0) x)
23.0ms	(- (exp x) 1.0)

series86.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- (exp x) 1.0) x)
27.0ms	(- (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

prune227.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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:

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

series72.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(fma x (fma 1/6 x 1/2) 1)
49.0ms	(fma 1/6 x 1/2)

simplify3.0s

Counts

26 → 26

Iterations

Useful iterations: 3 (482.0ms)

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

prune85.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 x 1/2)
0.1b	(fma 1/6 x 1/2)
8.9b	(sqrt (fma x (fma 1/6 x 1/2) 1))
8.9b	(sqrt (fma x (fma 1/6 x 1/2) 1))

rewrite6.0ms

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)
0.0ms	(fma 1/6 x 1/2)
2.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
3.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

series269.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma 1/6 x 1/2)
47.0ms	(fma 1/6 x 1/2)
96.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
87.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))

simplify4.6s

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

prune275.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3)
8.9b	(sqrt (fma x (fma 1/6 x 1/2) 1))
8.9b	(sqrt (fma x (fma 1/6 x 1/2) 1))
10.6b	(cbrt (pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `add-sqr-sqrt` `sqrt-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
8×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2`
2×	`cube-mult` `rem-sqrt-square` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

6.0ms	(pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3)
2.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
2.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
6.0ms	(cbrt (pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3))

series475.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3)
104.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
99.0ms	(sqrt (fma x (fma 1/6 x 1/2) 1))
102.0ms	(cbrt (pow (sqrt (fma x (fma 1/6 x 1/2) 1)) 3))

simplify2.7s

Counts

105 → 105

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	114	1743
1	259	1257
2	684	1248
3	3391	1220
done	5000	1210

prune365.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

regimes38.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 21.7b

bsearch35.0ms

Steps

Iters	Range		Point
6	-0.0008047768791668974	-9.640722949014248e-05	-0.00019073022953316793

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	31
1	27	31
done	27	31

end0.0ms

sample1.6s

Algorithm

intervals

Results

670.0ms	2258×	body	1280	valid
265.0ms	1649×	body	640	valid
215.0ms	5485×	body	80	valid
126.0ms	811×	body	320	valid
28.0ms	416×	body	160	valid