Details

sample131.0ms

Algorithm

intervals

Results

88.0ms	180×	body	1280	valid
13.0ms	44×	body	640	valid
10.0ms	233×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.9s

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	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.6b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite66.0ms

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

series110.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (exp x) 2.0)
86.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify546.0ms

Counts

41 → 41

Iterations

Useful iterations: done (544.0ms)

Iter	Nodes	Cost
0	93	511
1	215	465
2	832	445
done	5001	433

prune167.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite74.0ms

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:

26.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
18.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
13.0ms	(* 1/360 (pow x 6))
13.0ms	(* 1/12 (pow x 4))

series420.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
199.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
60.0ms	(* 1/360 (pow x 6))
81.0ms	(* 1/12 (pow x 4))

simplify1.0s

Counts

87 → 87

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	133	1068
1	343	934
2	1423	888
done	5002	879

prune276.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
25.6b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

24.0ms	(* 1/360 (pow x 6))
21.0ms	(* 1/12 (pow x 4))
78.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
57.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series338.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* 1/360 (pow x 6))
52.0ms	(* 1/12 (pow x 4))
106.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
87.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify1.9s

Counts

114 → 114

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	181	2128
1	485	1863
2	2423	1645
done	5001	1636

prune437.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))
0.0b	(* (exp x) (+ 2.0 (exp x)))
0.1b	(pow (exp x) 3)
3.9b	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))) (exp (- x)))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

19.0ms	(+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))
47.0ms	(* (exp x) (+ 2.0 (exp x)))
9.0ms	(pow (exp x) 3)
396.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))) (exp (- x)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))
26.0ms	(* (exp x) (+ 2.0 (exp x)))
35.0ms	(pow (exp x) 3)
279.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* (exp x) (+ 2.0 (exp x))) (* 2.0 2.0))) (exp (- x)))

simplify3.4s

Counts

89 → 89

Iterations

Useful iterations: 2 (705.0ms)

Iter	Nodes	Cost
0	165	1375
1	513	1282
2	3227	1173
done	5000	1173

prune393.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.5s	5691×	body	1280	valid
656.0ms	647×	body	320	valid
323.0ms	8043×	body	80	valid
308.0ms	1205×	body	640	valid
32.0ms	309×	body	160	valid