Details

sample65.0ms

Algorithm

intervals

Results

18.0ms	68×	body	1280	valid
17.0ms	94×	body	10240	exit
9.0ms	54×	body	640	valid
4.0ms	92×	body	80	valid
3.0ms	31×	body	320	valid
1.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 67

Calls

2 calls:

39.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (exp x) (- (exp x) 1.0))
25.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	2050
2	672
1	252
0	117

prune333.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

5.0ms	(/ (exp x) (fma (* x x) (fma x 1/6 1/2) x))
0.0ms	(fma (* x x) (fma x 1/6 1/2) x)
0.0ms	(fma x 1/6 1/2)

series133.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (exp x) (fma (* x x) (fma x 1/6 1/2) x))
42.0ms	(fma (* x x) (fma x 1/6 1/2) x)
47.0ms	(fma x 1/6 1/2)

simplify2.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5023
3	2404
2	586
1	191
0	98

prune326.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma x 1/12 (/ 1 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

0.0ms

(fma x 1/12 (/ 1 x))

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(fma x 1/12 (/ 1 x))

simplify2.5s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
5	2167
4	457
3	130
2	40
1	23
0	17

prune45.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (fma x 1/12 (/ 1 x)))
0.1b	(fma x 1/12 (/ 1 x))
1.7b	(expm1 (log1p (fma x 1/12 (/ 1 x))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p (fma x 1/12 (/ 1 x)))
0.0ms	(fma x 1/12 (/ 1 x))
0.0ms	(expm1 (log1p (fma x 1/12 (/ 1 x))))

series174.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(log1p (fma x 1/12 (/ 1 x)))
70.0ms	(fma x 1/12 (/ 1 x))
68.0ms	(expm1 (log1p (fma x 1/12 (/ 1 x))))

simplify4.1s

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
4	4611
3	1582
2	506
1	192
0	87

prune241.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes53.0ms

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
0	8

end0.0ms

sample2.6s

Algorithm

intervals

Results

744.0ms	1560×	body	640	valid
728.0ms	2334×	body	1280	valid
671.0ms	2597×	body	10240	exit
128.0ms	2820×	body	80	valid
109.0ms	868×	body	320	valid
31.0ms	419×	body	160	valid