Details

sample101.0ms

Algorithm

intervals

Results

25.0ms	61×	body	10240	exit
22.0ms	319×	body	80	valid
19.0ms	43×	body	1280	valid
11.0ms	43×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	309	27
4	1045	27
5	4482	27
done	5000	27

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
2.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
46×	`times-frac`
26×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out--`
10×	`add-cbrt-cube` `associate-/l*`
8×	`add-exp-log`
7×	`distribute-lft-out`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-l` `associate-/l/`
3×	`associate-r`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `associate-*l/` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `associate--r-` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

10.0ms	(* (+ 1.0 eps) x)
27.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
29.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
117.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (+ 1.0 eps) x)
44.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
43.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
177.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify600.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (202.0ms)

Iter	Nodes	Cost
0	245	2879
1	574	2745
2	1606	2586
done	5000	2586

prune365.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
6.2b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

7.0ms	(* 0.6666666666666667 (pow x 3))
27.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series79.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify390.0ms

Counts

51 → 51

Iterations

Useful iterations: done (389.0ms)

Iter	Nodes	Cost
0	84	590
1	210	548
2	779	498
done	5000	462

prune112.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

6.2b	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 41

Calls

4 calls:

108.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
38.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify745.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (171.0ms)

Iter	Nodes	Cost
0	56	882
1	135	861
2	449	561
3	1755	469
done	5000	469

prune169.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))
46.8b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
38.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
39.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify1.6s

Counts

48 → 48

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	21	360
1	37	344
2	68	296
3	100	284
4	184	284
5	502	284
6	1671	284
done	5000	284

prune181.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

regimes71.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.7b

bsearch144.0ms

Steps

Iters	Range		Point
10	0.0005333266348582408	2757715261.7841525	201.1922359123358

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	54
1	44	54
2	46	54
done	46	54

end0.0ms

sample3.0s

Algorithm

intervals

Results

821.0ms	1969×	body	10240	exit
767.0ms	1714×	body	1280	valid
584.0ms	10167×	body	80	valid
342.0ms	1269×	body	640	valid
114.0ms	652×	body	320	valid
34.0ms	290×	body	160	valid