Details

sample69.0ms

Algorithm

intervals

Results

27.0ms	70×	body	1280	valid
15.0ms	59×	body	640	valid
7.0ms	161×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	16×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.9b	(- (exp x) 1.0)

rewrite88.0ms

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:

57.0ms	(/ (- (exp x) 1.0) x)
27.0ms	(- (exp x) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (- (exp x) 1.0) x)
29.0ms	(- (exp x) 1.0)

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	127	854
1	281	745
2	612	665
3	1785	619
done	5001	605

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)

series113.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(fma x (fma 1/6 x 1/2) 1)
72.0ms	(fma 1/6 x 1/2)

simplify3.0s

Counts

26 → 26

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	33	213
1	53	204
2	114	176
3	381	175
4	1753	175
done	5001	175

prune75.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
0.0b	(+ 1.0 (exp x))
5.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite596.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
139×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
44×	`difference-of-squares`
31×	`associate-/l*`
27×	`distribute-lft-out`
24×	`exp-sum`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `fma-neg` `div-exp` `prod-diff` `log1p-expm1-u`
3×	`fma-def` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 214

Calls

4 calls:

206.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
231.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
7.0ms	(+ 1.0 (exp x))
125.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series195.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x))) x)
59.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
9.0ms	(+ 1.0 (exp x))
33.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.2s

Counts

226 → 226

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	319	4871
1	771	4677
2	2342	4400
done	5001	4386

prune772.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ 1.0 (exp x)))
0.6b	(cbrt (+ 1.0 (exp x)))
0.6b	(cbrt (+ 1.0 (exp x)))
5.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`cbrt-prod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-neg` `prod-diff` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `pow1/3` `exp-sum` `flip-+` `distribute-lft-out`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

10.0ms	(cbrt (+ 1.0 (exp x)))
7.0ms	(cbrt (+ 1.0 (exp x)))
6.0ms	(cbrt (+ 1.0 (exp x)))
102.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series544.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (+ 1.0 (exp x)))
165.0ms	(cbrt (+ 1.0 (exp x)))
173.0ms	(cbrt (+ 1.0 (exp x)))
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts

84 → 84

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	104	943
1	233	889
2	619	793
3	1975	756
done	5000	728

prune290.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

98.9% (0.2b remaining)

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

bsearch66.0ms

Steps

Iters	Range		Point
9	-0.002338049553438653	-8.574655782360099e-11	-0.0001245218611780339

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	56
1	31	56
done	31	56

end0.0ms

sample1.7s

Algorithm

intervals

Results

773.0ms	2297×	body	1280	valid
354.0ms	1617×	body	640	valid
178.0ms	5435×	body	80	valid
98.0ms	808×	body	320	valid
37.0ms	436×	body	160	valid