Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	66×	body	1280	valid
6.0ms	49×	body	640	valid
4.0ms	176×	body	80	valid
3.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.7b	(- (exp x) 1.0)

rewrite33.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

21.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
27.0ms	(- (exp x) 1.0)

simplify676.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1006
1	296
0	127

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series102.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(fma x 1/2 (fma 1/6 (* x x) 1))
71.0ms	(fma 1/6 (* x x) 1)

simplify983.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1360
2	200
1	54
0	33

prune161.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)
0.0ms	(fma 1/6 x 1/2)

series59.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma x (fma 1/6 x 1/2) 1)
35.0ms	(fma 1/6 x 1/2)

simplify525.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5001
3	764
2	170
1	57
0	33

prune120.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fma (* x x) 1/6 1)) (cbrt (fma (* x x) 1/6 1)))
10.2b	(cbrt (fma (* x x) 1/6 1))
10.2b	(cbrt (fma (* x x) 1/6 1))
10.2b	(cbrt (fma (* x x) 1/6 1))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

15.0ms	(* (cbrt (fma (* x x) 1/6 1)) (cbrt (fma (* x x) 1/6 1)))
1.0ms	(cbrt (fma (* x x) 1/6 1))
1.0ms	(cbrt (fma (* x x) 1/6 1))
2.0ms	(cbrt (fma (* x x) 1/6 1))

series669.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (cbrt (fma (* x x) 1/6 1)) (cbrt (fma (* x x) 1/6 1)))
155.0ms	(cbrt (fma (* x x) 1/6 1))
186.0ms	(cbrt (fma (* x x) 1/6 1))
151.0ms	(cbrt (fma (* x x) 1/6 1))

simplify974.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	885
1	250
0	112

prune755.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch49.0ms

Steps

Iters	Range		Point
8	-0.003292329160956242	-2.923395978885857e-06	-0.00013003875479750078

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

707.0ms	2297×	body	1280	valid
338.0ms	1626×	body	640	valid
208.0ms	5476×	body	80	valid
129.0ms	803×	body	320	valid
31.0ms	424×	body	160	valid