Details

sample177.0ms

Algorithm

intervals

Results

122.0ms	177×	body	1280	valid
15.0ms	40×	body	640	valid
12.0ms	222×	body	80	valid
5.0ms	24×	body	320	valid
2.0ms	11×	body	160	valid

simplify147.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	49	8
5	54	8
6	63	8
7	80	8
8	95	8
9	103	8
10	111	8
done	111	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.1b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite106.0ms

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:

11.0ms	(- (exp x) 2.0)
94.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series97.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
75.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.8s

Counts

41 → 41

Iterations

Useful iterations: 3 (662.0ms)

Iter	Nodes	Cost
0	93	511
1	204	465
2	579	445
3	2107	432
done	5000	432

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:

42.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
12.0ms	(* 1/360 (pow x 6))
12.0ms	(* 1/12 (pow x 4))

series456.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
213.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
77.0ms	(* 1/360 (pow x 6))
70.0ms	(* 1/12 (pow x 4))

simplify4.1s

Counts

87 → 87

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	133	1068
1	331	934
2	950	888
3	4360	870
done	5001	868

prune311.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x))))
0.0b	(+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))
0.1b	(pow (exp x) 3)
4.9b	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

rewrite800.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
75×	`times-frac`
64×	`difference-of-squares`
51×	`unpow-prod-down` `cube-prod`
38×	`add-cube-cbrt`
33×	`sqr-pow`
25×	`associate-/l*`
20×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1`
4×	`difference-cubes` `pow-pow`
3×	`pow-unpow` `exp-prod` `flip3-+` `associate-/r*` `flip-+`
2×	`+-commutative` `associate-+l+` `div-sub` `frac-add` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `distribute-rgt-in` `exp-neg` `cube-mult` `pow-to-exp` `associate-+l-` `flip3--` `frac-2neg` `distribute-lft-in` `exp-diff` `unpow3` `div-exp` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 174

Calls

4 calls:

172.0ms	(/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x))))
50.0ms	(+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))
5.0ms	(pow (exp x) 3)
563.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x))))
37.0ms	(+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))
36.0ms	(pow (exp x) 3)
259.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

simplify2.0s

Counts

186 → 186

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	292	5623
1	681	5307
2	2484	5140
done	5001	5139

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
4.9b	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
4.9b	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
4.9b	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`frac-add`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `pow-pow`
3×	`+-commutative` `neg-sub0` `exp-neg` `associate-+l-` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3-+` `exp-diff` `div-sub` `cube-prod` `sum-log` `flip-+` `distribute-lft-out`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

10.0ms	(pow (exp x) 3)
472.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
537.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
506.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (exp x) 3)
260.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
257.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
279.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))

simplify959.0ms

Counts

83 → 83

Iterations

Useful iterations: done (955.0ms)

Iter	Nodes	Cost
0	111	2175
1	267	2090
2	852	1901
done	5000	1821

prune551.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.8s	5582×	body	1280	valid
848.0ms	1264×	body	640	valid
518.0ms	8085×	body	80	valid
142.0ms	651×	body	320	valid
77.0ms	324×	body	160	valid