Details

sample2.3s

Algorithm

intervals

Results

2.1s	105×	body	1280	valid
58.0ms	75×	body	640	valid
42.0ms	16×	body	2560	valid
6.0ms	15×	body	320	valid
3.0ms	32×	body	80	valid
3.0ms	13×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize61.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
4.5b	(sin (+ x eps))

rewrite965.0ms

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:

882.0ms	(- (sin (+ x eps)) (sin x))
46.0ms	(sin (+ x eps))

series535.0ms

Counts

2 → 6

Calls

2 calls:

350.0ms	(- (sin (+ x eps)) (sin x))
184.0ms	(sin (+ x eps))

simplify11.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
5	4290
4	1664
3	743
2	304
1	135
0	64

prune498.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* eps 1/2)) (cos (/ (+ (+ x x) eps) 2)))
4.6b	(cos (/ (+ (+ x x) eps) 2))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `unswap-sqr`

Counts

2 → 26

Calls

2 calls:

47.0ms	(* (sin (* eps 1/2)) (cos (/ (+ (+ x x) eps) 2)))
118.0ms	(cos (/ (+ (+ x x) eps) 2))

series186.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(* (sin (* eps 1/2)) (cos (/ (+ (+ x x) eps) 2)))
73.0ms	(cos (/ (+ (+ x x) eps) 2))

simplify10.7s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
4	2517
3	1007
2	365
1	150
0	67

prune558.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize123.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (+ x (/ eps 2))) (cos (+ x (/ eps 2)))) (cos (+ x (/ eps 2)))))
4.6b	(cos (+ x (/ eps 2)))
4.6b	(cos (+ x (/ eps 2)))
4.6b	(cos (+ x (/ eps 2)))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-sum`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 35

Calls

4 calls:

98.0ms	(cbrt (* (* (cos (+ x (/ eps 2))) (cos (+ x (/ eps 2)))) (cos (+ x (/ eps 2)))))
45.0ms	(cos (+ x (/ eps 2)))
38.0ms	(cos (+ x (/ eps 2)))
74.0ms	(cos (+ x (/ eps 2)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (* (* (cos (+ x (/ eps 2))) (cos (+ x (/ eps 2)))) (cos (+ x (/ eps 2)))))
87.0ms	(cos (+ x (/ eps 2)))
313.0ms	(cos (+ x (/ eps 2)))
113.0ms	(cos (+ x (/ eps 2)))

simplify11.6s

Counts

47 → 47

Iterations

Iter	Nodes
done	5002
5	3042
4	790
3	346
2	146
1	81
0	47

prune996.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (+ x (/ eps 2))))
0.2b	(* (sin (* eps 1/2)) (log (exp (cos (+ x (/ eps 2))))))
0.5b	(log (exp (cos (+ x (/ eps 2)))))
4.6b	(cos (+ x (/ eps 2)))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

43.0ms	(exp (cos (+ x (/ eps 2))))
232.0ms	(* (sin (* eps 1/2)) (log (exp (cos (+ x (/ eps 2))))))
87.0ms	(log (exp (cos (+ x (/ eps 2)))))
124.0ms	(cos (+ x (/ eps 2)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(exp (cos (+ x (/ eps 2))))
292.0ms	(* (sin (* eps 1/2)) (log (exp (cos (+ x (/ eps 2))))))
83.0ms	(log (exp (cos (+ x (/ eps 2)))))
190.0ms	(cos (+ x (/ eps 2)))

simplify11.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
4	3563
3	1403
2	539
1	231
0	114

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes432.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end4.0ms

sample31.1s

Algorithm

intervals

Results

17.5s	3290×	body	1280	valid
6.0s	646×	body	2560	valid
3.8s	1849×	body	640	valid
1.5s	1140×	body	80	valid
913.0ms	338×	body	160	valid
577.0ms	737×	body	320	valid