Details

sample64.0ms

Algorithm

intervals

Results

29.0ms	66×	body	1280	valid
11.0ms	49×	body	640	valid
7.0ms	176×	body	80	valid
5.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	152
1	10	152
2	13	152
3	15	152
done	15	152

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)

series61.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
21.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	127	21628
1	296	19412
2	1006	17610
done	5000	17521

prune357.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

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

series101.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma 1/2 x (fma 1/6 (* x x) 1))
77.0ms	(fma 1/6 (* x x) 1)

simplify1.9s

Counts

26 → 26

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	32	5719
1	57	4468
2	200	4468
3	1322	4288
done	5000	3988

prune123.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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×	`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)
1.0ms	(fma 1/6 x 1/2)

series104.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma x (fma 1/6 x 1/2) 1)
64.0ms	(fma 1/6 x 1/2)

simplify1.0s

Counts

26 → 26

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	33	4382
1	57	3644
2	170	3644
3	764	3644
done	5001	3524

prune189.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

9.0ms	(* (cbrt (fma 1/6 (* x x) 1)) (cbrt (fma 1/6 (* x x) 1)))
1.0ms	(cbrt (fma 1/6 (* x x) 1))
1.0ms	(cbrt (fma 1/6 (* x x) 1))
1.0ms	(cbrt (fma 1/6 (* x x) 1))

series628.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (cbrt (fma 1/6 (* x x) 1)) (cbrt (fma 1/6 (* x x) 1)))
146.0ms	(cbrt (fma 1/6 (* x x) 1))
168.0ms	(cbrt (fma 1/6 (* x x) 1))
126.0ms	(cbrt (fma 1/6 (* x x) 1))

simplify1.6s

Counts

93 → 93

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	112	33644
1	250	28163
2	877	28088
done	5000	26673

prune507.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99% (0.2b remaining)

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

bsearch56.0ms

Steps

Iters	Range		Point
8	-0.003292329160956242	-2.923395978885857e-06	-0.00010910993504645059

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	777
1	27	777
done	27	777

end0.0ms

sample1.8s

Algorithm

intervals

Results

683.0ms	2297×	body	1280	valid
490.0ms	1626×	body	640	valid
255.0ms	5476×	body	80	valid
109.0ms	803×	body	320	valid
70.0ms	424×	body	160	valid