Details

sample79.0ms

Algorithm

intervals

Results

55.0ms	185×	body	1280	valid
6.0ms	272×	body	80	valid
6.0ms	37×	body	640	valid
2.0ms	22×	body	320	valid
0.0ms	8×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	52	8
5	62	8
6	87	8
7	146	8
8	241	8
9	773	8
done	5000	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.9b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

5.0ms	(- (exp x) 2.0)
29.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series67.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
54.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify2.3s

Counts

71 → 71

Iterations

Useful iterations: 3 (612.0ms)

Iter	Nodes	Cost
0	124	914
1	277	729
2	815	619
3	4125	557
done	5000	557

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
6.0ms	(* 1/12 (pow x 4))

series211.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
123.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify1.6s

Counts

56 → 56

Iterations

Useful iterations: 3 (420.0ms)

Iter	Nodes	Cost
0	80	619
1	147	581
2	454	529
3	2370	526
done	5001	526

prune135.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- 2.0 (exp (- x)))
3.3b	(- (exp x) (- 2.0 (exp (- x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`prod-diff`
24×	`add-cube-cbrt`
11×	`associate--r+`
9×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`fma-neg`
5×	`difference-of-squares`
4×	`diff-log`
3×	`sub-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`associate--r-`

Counts

2 → 76

Calls

2 calls:

5.0ms	(- 2.0 (exp (- x)))
20.0ms	(- (exp x) (- 2.0 (exp (- x))))

series73.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- 2.0 (exp (- x)))
60.0ms	(- (exp x) (- 2.0 (exp (- x))))

simplify2.8s

Counts

82 → 82

Iterations

Useful iterations: 3 (677.0ms)

Iter	Nodes	Cost
0	149	1666
1	327	1248
2	916	986
3	4836	714
done	5000	714

prune126.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (- x)) 2.0)
0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
3.6b	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x)) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`sqrt-pow1`
6×	`pow1` `exp-prod` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`rem-sqrt-square` `pow1/2`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 74

Calls

4 calls:

12.0ms	(- (exp (- x)) 2.0)
1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x)) 2.0))

series146.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (exp (- x)) 2.0)
11.0ms	(sqrt (exp x))
11.0ms	(sqrt (exp x))
106.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x)) 2.0))

simplify1.5s

Counts

86 → 86

Iterations

Useful iterations: 3 (374.0ms)

Iter	Nodes	Cost
0	120	819
1	222	649
2	590	555
3	2918	512
done	5001	512

prune175.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes13.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5631×	body	1280	valid
196.0ms	1250×	body	640	valid
181.0ms	8069×	body	80	valid
59.0ms	652×	body	320	valid
17.0ms	294×	body	160	valid