Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
10.0ms	32×	body	640	valid
9.0ms	144×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	15×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3510
6	440
5	117
4	53
3	30
2	22
1	15
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
4.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

5.0ms	(+ 1.0 (exp (* -2.0 x)))
17.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
75.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series166.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1.0 (exp (* -2.0 x)))
51.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
96.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.3s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4667
2	926
1	261
0	116

prune419.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
4.1b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
304×	`*-un-lft-identity`
229×	`sqrt-prod`
212×	`add-sqr-sqrt`
188×	`add-cube-cbrt`
57×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
14×	`associate-/r*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
10×	`div-inv`
8×	`add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 317

Calls

4 calls:

6.0ms	(+ 1.0 (exp (* -2.0 x)))
62.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
25.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
286.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series325.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ 1.0 (exp (* -2.0 x)))
70.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
118.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
106.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify2.3s

Counts

329 → 329

Iterations

Iter	Nodes
done	5000
2	3691
1	831
0	351

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.4b	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
26.9b	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

8630×	`times-frac`
8145×	`sqrt-prod`
5504×	`*-un-lft-identity`
3686×	`add-sqr-sqrt`
3564×	`add-cube-cbrt`
969×	`distribute-lft-out`
406×	`sqrt-div`
405×	`associate-/l*`
204×	`associate-/r/`
102×	`flip3-+` `flip-+` `div-inv`
27×	`associate-/r*` `difference-of-squares`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 3474

Calls

4 calls:

241.0ms	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
58.0ms	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
20.0ms	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
2.4s	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series476.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
88.0ms	(/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
205.0ms	(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
132.0ms	(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify4.6s

Counts

3486 → 3486

Iterations

Iter	Nodes
done	5001
1	4727
0	1994

prune7.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 0.33333333333333337)
0.1b	(* (* x x) (* (* x x) 5.551115123125783e-17))
1.5b	(* (* x x) 5.551115123125783e-17)
13.3b	(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1` `add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate--l+`
3×	`sub-neg` `associate-l` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`flip3--` `diff-log` `flip--`

Counts

4 → 82

Calls

4 calls:

15.0ms	(* (* x x) 0.33333333333333337)
64.0ms	(* (* x x) (* (* x x) 5.551115123125783e-17))
17.0ms	(* (* x x) 5.551115123125783e-17)
23.0ms	(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* x x) 0.33333333333333337)
40.0ms	(* (* x x) (* (* x x) 5.551115123125783e-17))
31.0ms	(* (* x x) 5.551115123125783e-17)
53.0ms	(- (* x (- 1.0 (* (* x x) 0.33333333333333337))) (* (* x x) (* (* x x) 5.551115123125783e-17)))

simplify2.4s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2722
1	351
0	119

prune354.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes235.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

635.0ms	4070×	body	80	valid
590.0ms	1709×	body	1280	valid
315.0ms	1268×	body	640	valid
179.0ms	637×	body	320	valid
31.0ms	316×	body	160	valid