Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	62×	body	1280	valid
11.0ms	47×	body	640	valid
8.0ms	172×	body	80	valid
5.0ms	31×	body	320	valid
2.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.8b	(- (exp x) 1.0)

rewrite46.0ms

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:

27.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- (exp x) 1.0) x)
18.0ms	(- (exp x) 1.0)

simplify757.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1006
1	296
0	127

prune331.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

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

series131.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(fma x 1/2 (fma 1/6 (* x x) 1))
92.0ms	(fma 1/6 (* x x) 1)

simplify1.1s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1360
2	200
1	54
0	33

prune128.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.5b	(- (/ (exp x) x) (/ 1.0 x))

rewrite78.0ms

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

series87.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) x)
62.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify1.7s

Counts

242 → 242

Iterations

Iter	Nodes
done	5001
2	2598
1	783
0	342

prune663.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
0.0b	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
4.8b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

131×	`sqrt-prod`
108×	`prod-diff`
104×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
84×	`add-cube-cbrt`
38×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
8×	`pow1` `sqrt-pow1` `difference-of-squares`
6×	`exp-prod` `add-cbrt-cube` `fma-neg` `add-exp-log` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `flip3--` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `pow1/2` `associate-l/` `associate-r/` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 210

Calls

4 calls:

5.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
121.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
30.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series249.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (exp x))
20.0ms	(sqrt (exp x))
144.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0)))
72.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify2.0s

Counts

222 → 222

Iterations

Iter	Nodes
done	5000
2	4093
1	709
0	224

prune532.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch41.0ms

Steps

Iters	Range		Point
9	-0.0007095347148853646	-4.632829109756021e-12	-0.00022388012385775216

simplify5.0ms

Iterations

Iter	Nodes
done	29
2	29
1	28
0	23

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2190×	body	1280	valid
323.0ms	1688×	body	640	valid
197.0ms	5514×	body	80	valid
114.0ms	889×	body	320	valid
35.0ms	436×	body	160	valid