Details

sample95.0ms

Algorithm

intervals

Results

42.0ms	98×	body	1280	valid
20.0ms	24×	body	2560	valid
14.0ms	62×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
5.1b	(sin (+ x eps))

rewrite59.0ms

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:

48.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify137.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164
done	5001	164

prune82.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
4.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

17.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
12.0ms	(* (sin x) (cos eps))
13.0ms	(* (cos x) (sin eps))
57.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (cos eps))
48.0ms	(* (cos x) (sin eps))
116.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify39.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543
done	5001	543

prune232.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
2.2b	(- (cos eps) 1)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

24.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
32.0ms	(* (sin x) (- (cos eps) 1))
12.0ms	(* (cos x) (sin eps))
7.0ms	(- (cos eps) 1)

series232.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms	(* (sin x) (- (cos eps) 1))
48.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify47.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499
done	5001	499

prune258.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
2.2b	(- (cos eps) 1)
2.2b	(log (exp (- (cos eps) 1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`log-pow`
15×	`log-prod`
14×	`exp-prod` `associate-r`
13×	`add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `exp-sum` `add-log-exp` `difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg`
3×	`difference-of-sqr-1` `distribute-lft-out--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 92

Calls

4 calls:

13.0ms	(* (cos x) (sin eps))
65.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
8.0ms	(- (cos eps) 1)
16.0ms	(log (exp (- (cos eps) 1)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos x) (sin eps))
49.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
20.0ms	(- (cos eps) 1)
23.0ms	(log (exp (- (cos eps) 1)))

simplify131.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	287	592
1	1044	493
2	4516	482
3	5002	482
done	5002	482

prune300.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes123.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10
done	15	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	3276×	body	1280	valid
576.0ms	646×	body	2560	valid
454.0ms	1856×	body	640	valid
123.0ms	758×	body	320	valid
60.0ms	1092×	body	80	valid
38.0ms	372×	body	160	valid