Details

sample80.0ms

Algorithm

intervals

Results

54.0ms	185×	body	1280	valid
8.0ms	272×	body	80	valid
6.0ms	37×	body	640	valid
2.0ms	22×	body	320	valid
0.0ms	8×	body	160	valid

simplify2.8s

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	83	8
7	130	8
8	208	8
9	701	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)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
28.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series74.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.2s

Counts

41 → 41

Iterations

Useful iterations: 3 (392.0ms)

Iter	Nodes	Cost
0	93	511
1	212	465
2	596	445
3	2518	432
done	5001	432

prune92.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

3.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
13.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
6.0ms	(* 1/360 (pow x 6))
9.0ms	(* 1/12 (pow x 4))

series286.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
60.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
53.0ms	(* 1/360 (pow x 6))
38.0ms	(* 1/12 (pow x 4))

simplify528.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	133	1068
1	334	934
2	1113	888
done	5000	888

prune222.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube`
16×	`add-exp-log`
15×	`flip3-+` `flip-+`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `frac-times` `associate-/l/` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `associate-*l/`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `associate-+l+` `associate-r/` `div-exp` `associate-l*`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
2×	`+-commutative` `sub-neg` `sum-log` `associate-/r/` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

23.0ms	(/ (* (+ 2.0 (exp x)) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
45.0ms	(* (+ 2.0 (exp x)) (+ (* (exp x) (- (exp x) 2.0)) 1))
4.0ms	(+ (exp x) 2.0)
9.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series269.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (* (+ 2.0 (exp x)) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
97.0ms	(* (+ 2.0 (exp x)) (+ (* (exp x) (- (exp x) 2.0)) 1))
8.0ms	(+ (exp x) 2.0)
61.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	176	2146
1	574	2050
2	3007	1700
done	5001	1689

prune245.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (pow x 3))
0.1b	(* 3.25 (pow x 4))
0.1b	(/ (+ (* 3.0 (pow x 2)) (+ (* 4.0 (pow x 3)) (* 3.25 (pow x 4)))) (* (+ (exp x) 2.0) (exp x)))
0.1b	(* 3.0 (pow x 2))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`associate-r`
23×	`add-exp-log`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
12×	`unpow-prod-down`
11×	`unswap-sqr`
10×	`prod-exp`
9×	`associate-l`
6×	`sqr-pow`
4×	`pow1` `cube-prod` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `times-frac` `pow-exp` `-commutative` `associate-/l`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip-+` `associate-/l/` `unpow2`
1×	`cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* 4.0 (pow x 3))
6.0ms	(* 3.25 (pow x 4))
41.0ms	(/ (+ (* 3.0 (pow x 2)) (+ (* 4.0 (pow x 3)) (* 3.25 (pow x 4)))) (* (+ (exp x) 2.0) (exp x)))
6.0ms	(* 3.0 (pow x 2))

series183.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 4.0 (pow x 3))
42.0ms	(* 3.25 (pow x 4))
77.0ms	(/ (+ (* 3.0 (pow x 2)) (+ (* 4.0 (pow x 3)) (* 3.25 (pow x 4)))) (* (+ (exp x) 2.0) (exp x)))
26.0ms	(* 3.0 (pow x 2))

simplify823.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (258.0ms)

Iter	Nodes	Cost
0	222	1719
1	562	1617
2	2119	1398
done	5000	1398

prune327.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	17	15
done	17	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5631×	body	1280	valid
193.0ms	1250×	body	640	valid
178.0ms	8069×	body	80	valid
58.0ms	652×	body	320	valid
17.0ms	294×	body	160	valid