Details

sample66.0ms

Algorithm

intervals

Results

22.0ms	65×	body	1280	valid
14.0ms	62×	body	640	valid
8.0ms	200×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize40.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.4b	(- (exp x) 1.0)

rewrite77.0ms

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:

51.0ms	(/ (- (exp x) 1.0) x)
22.0ms	(- (exp x) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (- (exp x) 1.0) x)
23.0ms	(- (exp x) 1.0)

simplify4.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	2400
2	723
1	293
0	127

prune449.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)

series107.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(fma x (fma 1/6 x 1/2) 1)
64.0ms	(fma 1/6 x 1/2)

simplify4.1s

Counts

26 → 26

Iterations

Iter	Nodes
done	5008
4	1916
3	420
2	122
1	57
0	33

prune191.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 x 1/2)
0.1b	(fma 1/6 x 1/2)
0.1b	(fma 1/6 x 1/2)
8.7b	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 42

Calls

4 calls:

1.0ms	(fma 1/6 x 1/2)
1.0ms	(fma 1/6 x 1/2)
1.0ms	(fma 1/6 x 1/2)
41.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma 1/6 x 1/2)
77.0ms	(fma 1/6 x 1/2)
62.0ms	(fma 1/6 x 1/2)
46.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))

simplify5.7s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
4	2508
3	477
2	130
1	61
0	37

prune462.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

8.7b	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
8.7b	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
9.6b	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))
9.6b	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `cbrt-prod` `expm1-log1p-u` `sqrt-pow1` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow1/2` `pow3` `rem-cbrt-cube`

Counts

4 → 58

Calls

4 calls:

33.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
41.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
9.0ms	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))
10.0ms	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
41.0ms	(cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1)))
118.0ms	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))
113.0ms	(sqrt (cbrt (* (* (fma x (fma 1/6 x 1/2) 1) (fma x (fma 1/6 x 1/2) 1)) (fma x (fma 1/6 x 1/2) 1))))

simplify6.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
4	4324
3	1121
2	344
1	134
0	65

prune575.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes179.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 21.5b

bsearch4.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample2.7s

Algorithm

intervals

Results

895.0ms	2289×	body	1280	valid
549.0ms	450×	body	160	valid
418.0ms	5474×	body	80	valid
381.0ms	1599×	body	640	valid
145.0ms	845×	body	320	valid