Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	76×	body	1280	valid
6.0ms	59×	body	640	valid
3.0ms	188×	body	80	valid
2.0ms	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)

rewrite19.0ms

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:

12.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: 3 (515.0ms)

Iter	Nodes	Cost
0	127	854
1	277	745
2	613	665
3	1989	637
done	5000	637

prune142.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

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))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify2.0s

Counts

13 → 13

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	23	158
1	38	152
2	100	134
3	414	107
4	2798	107
done	5000	107

prune34.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

51×	`sqrt-prod`
46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
36×	`add-cube-cbrt` `prod-diff`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1` `associate-/l/`
6×	`pow1` `exp-prod` `fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `flip--` `log1p-expm1-u` `difference-of-squares`
3×	`flip3-+` `times-frac` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `rem-sqrt-square` `pow1/2` `associate-r/` `div-exp` `associate-l/` `distribute-lft-out--`
1×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 129

Calls

4 calls:

36.0ms	(/ (* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0))) x)
1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
10.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series214.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (* (+ (sqrt 1.0) (sqrt (exp x))) (- (sqrt (exp x)) (sqrt 1.0))) x)
16.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
37.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify685.0ms

Counts

141 → 141

Iterations

Useful iterations: done (681.0ms)

Iter	Nodes	Cost
0	179	2355
1	439	1602
2	1455	1295
done	5000	1294

prune268.0ms

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

bsearch35.0ms

Steps

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	22	28
done	22	28

end0.0ms

sample841.0ms

Algorithm

intervals

Results

375.0ms	2245×	body	1280	valid
171.0ms	1677×	body	640	valid
95.0ms	5529×	body	80	valid
54.0ms	839×	body	320	valid
18.0ms	432×	body	160	valid