Details

sample134.0ms

Algorithm

intervals

Results

90.0ms	179×	body	1280	valid
11.0ms	274×	body	80	valid
8.0ms	36×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid

simplify133.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite84.0ms

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:

20.0ms	(- (exp x) 2.0)
61.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series90.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(- (exp x) 2.0)
76.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.8s

Counts

41 → 41

Iterations

Useful iterations: 3 (570.0ms)

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

prune171.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite93.0ms

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)))
47.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
23.0ms	(* 1/360 (pow x 6))
12.0ms	(* 1/12 (pow x 4))

series372.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
70.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
70.0ms	(* 1/360 (pow x 6))
41.0ms	(* 1/12 (pow x 4))

simplify4.3s

Counts

87 → 87

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	133	1068
1	331	934
2	952	888
3	4364	870
done	5001	868

prune378.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

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))))))
29.9b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite299.0ms

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:

206.0ms	(* (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))))))
24.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
39.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
25.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (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))))))
223.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
208.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
195.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify2.3s

Counts

107 → 107

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	4106
1	360	3755
2	946	3511
3	2935	3006
done	5000	2940

prune599.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.2b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
17.5b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite149.0ms

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:

18.0ms	(* 1/360 (pow x 6))
11.0ms	(* 1/12 (pow x 4))
46.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
69.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series286.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 1/360 (pow x 6))
44.0ms	(* 1/12 (pow x 4))
112.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
66.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify943.0ms

Counts

114 → 114

Iterations

Useful iterations: done (939.0ms)

Iter	Nodes	Cost
0	181	2128
1	424	1835
2	1216	1643
done	5001	1627

prune433.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes37.0ms

Accuracy

49% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.6b

bsearch57.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.03372358286109268

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	42
1	33	42
done	33	42

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.6s	5661×	body	1280	valid
521.0ms	1239×	body	640	valid
445.0ms	7952×	body	80	valid
173.0ms	634×	body	320	valid
35.0ms	318×	body	160	valid