Details

sample66.0ms

Algorithm

intervals

Results

28.0ms	75×	body	1280	valid
11.0ms	47×	body	640	valid
7.0ms	174×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify16.0ms

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

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (exp x) 1.0)

rewrite78.0ms

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:

54.0ms	(/ (- (exp x) 1.0) x)
19.0ms	(- (exp x) 1.0)

series72.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- (exp x) 1.0) x)
23.0ms	(- (exp x) 1.0)

simplify2.6s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	2361
2	721
1	292
0	127

prune292.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(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)

series72.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(fma x (fma 1/6 x 1/2) 1)
49.0ms	(fma 1/6 x 1/2)

simplify2.9s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
4	2796
3	498
2	133
1	57
0	33

prune110.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
3.2b	(- (/ (exp x) x) (/ 1.0 x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
213×	`add-sqr-sqrt`
209×	`*-un-lft-identity`
201×	`add-cube-cbrt`
169×	`prod-diff`
30×	`div-inv`
13×	`fma-neg`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `add-exp-log` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `div-exp` `frac-sub` `flip--` `sub-div`

Counts

2 → 236

Calls

2 calls:

6.0ms	(/ (exp x) x)
40.0ms	(- (/ (exp x) x) (/ 1.0 x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (exp x) x)
58.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify2.2s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	1919
1	782
0	342

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
0.0b	(/ (sqrt (exp x)) x)
3.6b	(fma (/ (sqrt (exp x)) 1) (/ (sqrt (exp x)) x) (- (/ 1.0 x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
8×	`sqrt-pow1`
6×	`pow1` `exp-prod` `add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`rem-sqrt-square` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 87

Calls

4 calls:

5.0ms	(sqrt (exp x))
5.0ms	(sqrt (exp x))
15.0ms	(/ (sqrt (exp x)) x)
0.0ms	(fma (/ (sqrt (exp x)) 1) (/ (sqrt (exp x)) x) (- (/ 1.0 x)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (exp x))
21.0ms	(sqrt (exp x))
67.0ms	(/ (sqrt (exp x)) x)
138.0ms	(fma (/ (sqrt (exp x)) 1) (/ (sqrt (exp x)) x) (- (/ 1.0 x)))

simplify3.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
4	4542
3	1184
2	429
1	199
0	110

prune568.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch34.0ms

Steps

Iters	Range		Point
9	-0.1501579911863904	-8.136897775944376e-09	-0.000197609785676648

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2249×	body	1280	valid
426.0ms	1655×	body	640	valid
259.0ms	5531×	body	80	valid
111.0ms	838×	body	320	valid
35.0ms	423×	body	160	valid