Details

sample77.0ms

Algorithm

intervals

Results

53.0ms	178×	body	1280	valid
6.0ms	284×	body	80	valid
5.0ms	36×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	19×	body	160	valid

simplify96.0ms

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: 29.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite34.0ms

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)
27.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series71.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
58.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.6s

Counts

71 → 71

Iterations

Useful iterations: 3 (415.0ms)

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

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

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

Counts

2 → 37

Calls

2 calls:

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

series167.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
41.0ms	(* 1/12 (pow x 4))

simplify3.7s

Counts

43 → 43

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	67	403
1	126	371
2	284	345
3	1028	342
4	4792	338
done	5000	338

prune106.0ms

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)))
5.3b	(- (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:

5.0ms	(- 2.0 (exp (- x)))
23.0ms	(- (exp x) (- 2.0 (exp (- x))))

series74.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 2.0 (exp (- x)))
55.0ms	(- (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

prune139.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(+ (sqrt (exp x)) (sqrt 2.0))
1.6b	(- (sqrt (exp x)) (sqrt 2.0))
60.1b	(fma (+ (sqrt (exp x)) (sqrt 2.0)) (- (sqrt (exp x)) (sqrt 2.0)) (exp (- x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

53×	`sqrt-prod`
43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`fma-def` `fma-neg`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod`
2×	`distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `pow1/2` `diff-log` `sum-log` `flip--` `flip-+` `fma-udef`

Counts

4 → 111

Calls

4 calls:

1.0ms	(sqrt (exp x))
7.0ms	(+ (sqrt (exp x)) (sqrt 2.0))
10.0ms	(- (sqrt (exp x)) (sqrt 2.0))
0.0ms	(fma (+ (sqrt (exp x)) (sqrt 2.0)) (- (sqrt (exp x)) (sqrt 2.0)) (exp (- x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
38.0ms	(+ (sqrt (exp x)) (sqrt 2.0))
36.0ms	(- (sqrt (exp x)) (sqrt 2.0))
148.0ms	(fma (+ (sqrt (exp x)) (sqrt 2.0)) (- (sqrt (exp x)) (sqrt 2.0)) (exp (- x)))

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	2006
1	314	1431
2	696	1130
3	2537	992
done	5001	986

prune239.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes17.0ms

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	5681×	body	1280	valid
189.0ms	1254×	body	640	valid
177.0ms	8261×	body	80	valid
55.0ms	603×	body	320	valid
18.0ms	295×	body	160	valid