Details

sample82.0ms

Algorithm

intervals

Results

57.0ms	187×	body	1280	valid
7.0ms	259×	body	80	valid
5.0ms	34×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify92.0ms

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

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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)
26.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (402.0ms)

Iter	Nodes	Cost
0	124	914
1	277	729
2	717	628
3	2799	595
done	5000	595

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

series226.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
129.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
37.0ms	(* 1/12 (pow x 4))

simplify1.2s

Counts

56 → 56

Iterations

Useful iterations: 3 (308.0ms)

Iter	Nodes	Cost
0	80	619
1	147	581
2	359	529
3	1485	526
done	5000	526

prune155.0ms

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))))

rewrite32.0ms

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)))
24.0ms	(- (exp x) (- 2.0 (exp (- x))))

series76.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 2.0 (exp (- x)))
58.0ms	(- (exp x) (- 2.0 (exp (- x))))

simplify1.9s

Counts

82 → 82

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	149	1666
1	327	1248
2	873	986
3	3753	813
done	5000	807

prune148.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))
0.0b	(- (exp (- x)) 2.0)
4.1b	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x)) 2.0))

rewrite17.0ms

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:

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

series154.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
11.0ms	(sqrt (exp x))
15.0ms	(- (exp (- x)) 2.0)
116.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x)) 2.0))

simplify846.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (232.0ms)

Iter	Nodes	Cost
0	120	819
1	222	649
2	484	564
3	1724	530
done	5000	530

prune208.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes19.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b 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

sample2.4s

Algorithm

intervals

Results

1.7s	5613×	body	1280	valid
202.0ms	8100×	body	80	valid
199.0ms	1213×	body	640	valid
72.0ms	693×	body	320	valid
21.0ms	325×	body	160	valid