Details

sample75.0ms

Algorithm

intervals

Results

51.0ms	182×	body	1280	valid
5.0ms	37×	body	640	valid
5.0ms	240×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify210.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5
done	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite60.0ms

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:

10.0ms	(- (exp x) 2.0)
49.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify90.0ms

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260
done	5001	260

prune93.0ms

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

rewrite60.0ms

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:

9.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
26.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
11.0ms	(* 1/360 (pow x 6))
12.0ms	(* 1/12 (pow x 4))

series281.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
54.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
53.0ms	(* 1/360 (pow x 6))
37.0ms	(* 1/12 (pow x 4))

simplify49.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423
done	5001	423

prune205.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
30.8b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.8b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.8b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

146.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
17.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
20.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
17.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
136.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
141.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
138.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify52.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	358	2077
1	1236	1956
2	5002	1780
done	5002	1780

prune368.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1))
0.0b	(* (exp x) (- (exp x) 2.0))
0.0b	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
3.7b	(+ (* (exp x) (- (exp x) 2.0)) 1)

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube`
17×	`add-exp-log`
14×	`add-sqr-sqrt` `flip3-+` `flip-+`
12×	`*-un-lft-identity`
8×	`pow1` `frac-times` `add-cube-cbrt` `associate-r` `associate-/l/`
7×	`associate-l`
6×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`cbrt-undiv` `sub-neg` `associate-+l+` `div-exp`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `times-frac` `clear-num` `associate-/r` `sum-log` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

93.0ms	(* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1))
37.0ms	(* (exp x) (- (exp x) 2.0))
61.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
20.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series287.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1))
34.0ms	(* (exp x) (- (exp x) 2.0))
101.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
60.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify117.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	604	1296
1	3967	1029
2	5001	1018
done	5001	1018

prune234.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes19.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7
done	17	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5700×	body	1280	valid
181.0ms	1220×	body	640	valid
171.0ms	7908×	body	80	valid
53.0ms	612×	body	320	valid
17.0ms	312×	body	160	valid