Details

sample80.0ms

Algorithm

intervals

Results

55.0ms	185×	body	1280	valid
6.0ms	37×	body	640	valid
6.0ms	272×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	8×	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: 29.2b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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)
25.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (404.0ms)

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)))
5.0ms	(* 1/12 (pow x 4))

series235.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
130.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
43.0ms	(* 1/12 (pow x 4))

simplify1.4s

Counts

56 → 56

Iterations

Useful iterations: 3 (312.0ms)

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

prune141.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 2.0) (+ 1 (* (exp x) (- (exp x) 2.0)))) (* (+ (exp x) 2.0) (exp x)))
0.0b	(+ (exp x) 2.0)
0.0b	(+ (exp x) 2.0)
2.7b	(+ 1 (* (exp x) (- (exp x) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`associate-+r+`
19×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`prod-diff`
16×	`add-cbrt-cube`
14×	`add-exp-log`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`flip3-+` `flip-+` `add-log-exp`
9×	`fma-def`
8×	`associate-/l/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`+-commutative` `sum-log`
2×	`sub-neg` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 105

Calls

4 calls:

15.0ms	(/ (* (+ (exp x) 2.0) (+ 1 (* (exp x) (- (exp x) 2.0)))) (* (+ (exp x) 2.0) (exp x)))
4.0ms	(+ (exp x) 2.0)
4.0ms	(+ (exp x) 2.0)
7.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (* (+ (exp x) 2.0) (+ 1 (* (exp x) (- (exp x) 2.0)))) (* (+ (exp x) 2.0) (exp x)))
8.0ms	(+ (exp x) 2.0)
9.0ms	(+ (exp x) 2.0)
61.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

simplify1.2s

Counts

117 → 117

Iterations

Useful iterations: 2 (410.0ms)

Iter	Nodes	Cost
0	195	1937
1	543	1647
2	2151	1173
done	5000	1173

prune278.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (* (- (exp x) 2.0) (exp x)) (fma (exp x) (- (exp x) 2.0) -1) 1) (* (exp x) (- (pow (exp x) 2) (* 2.0 2.0))))
0.0b	(* (exp x) (exp x))
0.0b	(pow (exp x) 2)
2.6b	(+ (pow 1 3) (pow (* (exp x) (- (exp x) 2.0)) 3))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

40×	`distribute-rgt-in` `distribute-lft-in`
32×	`*-un-lft-identity` `prod-diff`
31×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
21×	`exp-prod`
18×	`unpow-prod-down`
17×	`pow1`
12×	`fma-def`
11×	`add-cbrt-cube`
8×	`add-exp-log`
7×	`pow-prod-down`
6×	`associate-l` `add-log-exp` `sqr-pow`
5×	`unpow2`
4×	`expm1-log1p-u` `sub-neg` `pow-pow` `associate-r/` `associate-r*` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `cube-prod` `swap-sqr`
2×	`cube-mult` `*-commutative` `distribute-lft-out`
1×	`+-commutative` `pow2` `pow-to-exp` `flip3--` `flip3-+` `pow-plus` `unpow3` `pow-exp` `sum-log` `sum-cubes` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

39.0ms	(* (fma (* (- (exp x) 2.0) (exp x)) (fma (exp x) (- (exp x) 2.0) -1) 1) (* (exp x) (- (pow (exp x) 2) (* 2.0 2.0))))
8.0ms	(* (exp x) (exp x))
2.0ms	(pow (exp x) 2)
13.0ms	(+ (pow 1 3) (pow (* (exp x) (- (exp x) 2.0)) 3))

series409.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (fma (* (- (exp x) 2.0) (exp x)) (fma (exp x) (- (exp x) 2.0) -1) 1) (* (exp x) (- (pow (exp x) 2) (* 2.0 2.0))))
14.0ms	(* (exp x) (exp x))
14.0ms	(pow (exp x) 2)
232.0ms	(+ (pow 1 3) (pow (* (exp x) (- (exp x) 2.0)) 3))

simplify1.2s

Counts

161 → 161

Iterations

Useful iterations: 2 (561.0ms)

Iter	Nodes	Cost
0	277	4204
1	652	3836
2	2556	3551
done	5000	3551

prune481.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b 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
192.0ms	1250×	body	640	valid
180.0ms	8069×	body	80	valid
60.0ms	652×	body	320	valid
17.0ms	294×	body	160	valid