Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
9.0ms	94×	body	10240	exit
5.0ms	53×	body	640	valid
2.0ms	29×	body	320	valid
2.0ms	84×	body	80	valid
1.0ms	15×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4
done	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.7b	(- (exp x) 1.0)

rewrite32.0ms

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

Counts

2 → 67

Calls

2 calls:

18.0ms	(/ (exp x) (- (exp x) 1.0))
12.0ms	(- (exp x) 1.0)

series47.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify186.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404
done	5001	404

prune150.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0b	(fma 1/6 (pow x 3) x)
9.3b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

7.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series145.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
78.0ms	(fma 1/6 (pow x 3) x)
28.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify95.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414
done	5002	414

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

9.3b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
12.0b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
12.0b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
12.0b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
66.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
66.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
61.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

simplify65.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	145	578
1	408	536
2	1953	530
3	5001	530
done	5001	530

prune266.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

6.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms	(fma 1/12 x (/ 1 x))

series67.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
51.0ms	(fma 1/12 x (/ 1 x))

simplify38.0ms

Counts

34 → 34

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116
done	5001	116

prune60.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 11.5b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19
done	30	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

371.0ms	2263×	body	1280	valid
250.0ms	2511×	body	10240	exit
172.0ms	1710×	body	640	valid
53.0ms	2801×	body	80	valid
51.0ms	794×	body	320	valid
21.0ms	433×	body	160	valid