Details

sample166.0ms

Algorithm

intervals

Results

98.0ms	109×	body	1280	valid
24.0ms	20×	body	2560	valid
20.0ms	56×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

59.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series104.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

simplify3.1s

Counts

30 → 30

Iterations

Useful iterations: 4 (392.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune115.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

36.0ms	(+ (+ x eps) x)
18.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
59.0ms	(cos (/ (+ (+ x eps) x) 2))

series126.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
66.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
34.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.2s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	91	656
1	213	646
2	546	566
3	1366	548
4	4627	540
done	5000	540

prune228.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

34.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
3.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
81.0ms	(cos (/ (+ (+ x eps) x) 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
33.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
77.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
34.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.9s

Counts

97 → 97

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	117	1733
1	247	1447
2	705	1279
3	3806	1245
done	5000	1245

prune273.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos (/ (+ (+ x eps) x) 2)) 2)
0.5b	(cbrt (* (pow (cos (/ (+ (+ x eps) x) 2)) 2) (cos (/ (+ (+ x eps) x) 2))))
3.8b	(cos (/ (+ (+ x eps) x) 2))
3.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
2×	`unpow2`
1×	`cbrt-prod` `pow-to-exp` `pow-pow` `pow1/3` `pow3` `pow-exp` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 42

Calls

4 calls:

5.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 2)
11.0ms	(cbrt (* (pow (cos (/ (+ (+ x eps) x) 2)) 2) (cos (/ (+ (+ x eps) x) 2))))
85.0ms	(cos (/ (+ (+ x eps) x) 2))
70.0ms	(cos (/ (+ (+ x eps) x) 2))

series137.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 2)
31.0ms	(cbrt (* (pow (cos (/ (+ (+ x eps) x) 2)) 2) (cos (/ (+ (+ x eps) x) 2))))
40.0ms	(cos (/ (+ (+ x eps) x) 2))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.7s

Counts

54 → 54

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	60	787
1	127	610
2	239	527
3	577	509
4	2317	509
done	5001	509

prune228.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes158.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.4b

bsearch149.0ms

Steps

Iters	Range		Point
8	2.4141069970017172e-21	1.1811762867881907e-17	1.1645375548633762e-17
8	-1550992.7687819407	-108.06719872485291	-109.79102272340833

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.8s	3289×	body	1280	valid
1.1s	1870×	body	640	valid
820.0ms	663×	body	2560	valid
230.0ms	764×	body	320	valid
126.0ms	1086×	body	80	valid
51.0ms	328×	body	160	valid