Details

sample75.0ms

Algorithm

intervals

Results

52.0ms	187×	body	1280	valid
5.0ms	259×	body	80	valid
5.0ms	34×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	38	8
4	49	8
5	54	8
6	63	8
7	80	8
8	99	8
9	106	8
10	110	8
11	114	8
done	114	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.2b	(+ (- (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)
28.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series75.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
61.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.4s

Counts

71 → 71

Iterations

Useful iterations: 3 (445.0ms)

Iter	Nodes	Cost
0	124	914
1	283	729
2	715	628
3	2777	595
done	5000	595

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite8.0ms

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))

series234.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
128.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
44.0ms	(* 1/12 (pow x 4))

simplify1.6s

Counts

56 → 56

Iterations

Useful iterations: 3 (247.0ms)

Iter	Nodes	Cost
0	80	619
1	147	581
2	345	529
3	1348	526
done	5000	526

prune148.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- 2.0 (exp (- x)))
4.7b	(- (exp x) (- 2.0 (exp (- x))))

rewrite31.0ms

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:

6.0ms	(- 2.0 (exp (- x)))
22.0ms	(- (exp x) (- 2.0 (exp (- x))))

series77.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(- 2.0 (exp (- x)))
63.0ms	(- (exp x) (- 2.0 (exp (- x))))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	149	1666
1	335	1248
2	875	986
3	3719	912
done	5000	906

prune145.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (- x)))
0.0b	(* (sqrt (exp (- x))) (sqrt (exp (- x))))
3.3b	(- (+ (exp (- x)) (exp x)) 2.0)
4.1b	(fma (- (sqrt (exp (- x)))) (sqrt (exp (- x))) (* (sqrt (exp (- x))) (sqrt (exp (- x)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

95×	`sqrt-pow1`
86×	`exp-prod`
69×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
27×	`distribute-rgt-neg-in`
23×	`distribute-lft-neg-in`
21×	`sqrt-prod`
20×	`pow1`
17×	`pow-prod-down` `pow-prod-up`
15×	`pow-sqr`
14×	`sqrt-div`
12×	`prod-diff`
9×	`neg-mul-1` `pow1/2` `add-log-exp`
8×	`swap-sqr`
7×	`neg-sub0` `exp-neg` `exp-diff`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `fma-neg` `log1p-expm1-u` `unswap-sqr`
2×	`diff-log` `associate-r/` `associate-l/` `distribute-lft-out--`
1×	`pow2` `sub-neg` `rem-sqrt-square` `flip3--` `pow-plus` `sqrt-unprod` `prod-exp` `associate--l+` `sum-log` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

4.0ms	(sqrt (exp (- x)))
40.0ms	(* (sqrt (exp (- x))) (sqrt (exp (- x))))
82.0ms	(- (+ (exp (- x)) (exp x)) 2.0)
0.0ms	(fma (- (sqrt (exp (- x)))) (sqrt (exp (- x))) (* (sqrt (exp (- x))) (sqrt (exp (- x)))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (exp (- x)))
7.0ms	(* (sqrt (exp (- x))) (sqrt (exp (- x))))
63.0ms	(- (+ (exp (- x)) (exp x)) 2.0)
110.0ms	(fma (- (sqrt (exp (- x)))) (sqrt (exp (- x))) (* (sqrt (exp (- x))) (sqrt (exp (- x)))))

simplify2.2s

Counts

181 → 181

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	221	2089
1	418	1391
2	974	1199
3	3590	1065
done	5000	1053

prune368.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes17.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.6s	5613×	body	1280	valid
185.0ms	1213×	body	640	valid
174.0ms	8100×	body	80	valid
60.0ms	693×	body	320	valid
18.0ms	325×	body	160	valid