Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	76×	body	1280	valid
6.0ms	59×	body	640	valid
3.0ms	188×	body	80	valid
1.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (exp x) 1.0)

rewrite23.0ms

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:

15.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series54.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify3.2s

Counts

74 → 74

Iterations

Useful iterations: 3 (468.0ms)

Iter	Nodes	Cost
0	127	854
1	288	745
2	888	656
3	4814	637
done	5000	637

prune138.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

0.0ms

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

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

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

simplify3.0s

Counts

13 → 13

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	23	158
1	39	152
2	106	134
3	479	107
4	3504	107
done	5000	107

prune33.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)) x)
0.2b	(sqrt (exp x))
0.2b	(sqrt (exp x))
3.9b	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

2.0ms	(/ (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)) x)
1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

series154.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)) x)
11.0ms	(sqrt (exp x))
14.0ms	(sqrt (exp x))
47.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

simplify990.0ms

Counts

87 → 87

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	99	912
1	176	593
2	539	561
3	2134	560
done	5000	560

prune184.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch25.0ms

Steps

Iters	Range		Point
9	-5.7596417613087905	-8.638519114283913e-09	-0.0002022345445868293

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	18	24
done	18	24

end0.0ms

sample883.0ms

Algorithm

intervals

Results

381.0ms	2245×	body	1280	valid
179.0ms	1677×	body	640	valid
109.0ms	5529×	body	80	valid
57.0ms	839×	body	320	valid
19.0ms	432×	body	160	valid