Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	74×	body	1280	valid
11.0ms	56×	body	640	valid
6.0ms	169×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	14×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	14	6
2	15	6
done	15	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite102.0ms

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:

73.0ms	(/ (- (exp x) 1.0) x)
25.0ms	(- (exp x) 1.0)

series86.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- (exp x) 1.0) x)
24.0ms	(- (exp x) 1.0)

simplify4.9s

Counts

74 → 74

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	127	854
1	1723	720
done	5000	667

prune206.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

0.0ms

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

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

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

simplify3.3s

Counts

13 → 13

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	23	158
1	66	152
2	716	132
done	5000	107

prune68.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x 1/6 1/2)
0.1b	(fma x 1/6 1/2)
8.9b	(sqrt (fma x (fma x 1/6 1/2) 1))
8.9b	(sqrt (fma x (fma x 1/6 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 x 1/6 1/2)
0.0ms	(fma x 1/6 1/2)
2.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
2.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))

series251.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma x 1/6 1/2)
40.0ms	(fma x 1/6 1/2)
81.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
88.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))

simplify721.0ms

Counts

62 → 62

Iterations

Useful iterations: done (718.0ms)

Iter	Nodes	Cost
0	58	634
1	212	572
done	5000	520

prune285.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

7.0ms	(pow (sqrt (fma x (fma x 1/6 1/2) 1)) 3)
3.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
2.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
4.0ms	(cbrt (pow (sqrt (fma x (fma x 1/6 1/2) 1)) 3))

series431.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(pow (sqrt (fma x (fma x 1/6 1/2) 1)) 3)
83.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
88.0ms	(sqrt (fma x (fma x 1/6 1/2) 1))
93.0ms	(cbrt (pow (sqrt (fma x (fma x 1/6 1/2) 1)) 3))

simplify2.2s

Counts

105 → 105

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	114	1743
1	842	1283
done	5001	1243

prune376.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch42.0ms

Steps

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	30
1	26	30
done	26	30

end0.0ms

sample1.7s

Algorithm

intervals

Results

683.0ms	2258×	body	1280	valid
334.0ms	1649×	body	640	valid
260.0ms	5485×	body	80	valid
91.0ms	811×	body	320	valid
30.0ms	416×	body	160	valid