Details

sample173.0ms

Algorithm

intervals

Results

72.0ms	110×	body	1280	valid
55.0ms	22×	body	2560	valid
19.0ms	50×	body	640	valid
8.0ms	28×	body	320	valid
4.0ms	18×	body	160	valid
2.0ms	28×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

419.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series69.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify3.2s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
5	4797
4	1781
3	755
2	305
1	135
0	63

prune163.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

18.0ms	(+ x (+ x eps))
20.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
36.0ms	(cos (/ (+ x (+ x eps)) 2))

series166.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ x (+ x eps))
108.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (* 1/2 eps)))
32.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.3s

Counts

49 → 49

Iterations

Iter	Nodes
done	5011
3	2895
2	636
1	209
0	84

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

25.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

series135.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
45.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.7s

Counts

44 → 44

Iterations

Iter	Nodes
done	5005
5	3259
4	1040
3	384
2	137
1	81
0	43

prune373.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (+ (* 1/2 eps) x)))
0.3b	(* (log (exp (cos (+ (* 1/2 eps) x)))) (sin (* 1/2 eps)))
0.5b	(log (exp (cos (+ (* 1/2 eps) x))))
2.9b	(cos (+ (* 1/2 eps) x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

14.0ms	(exp (cos (+ (* 1/2 eps) x)))
42.0ms	(* (log (exp (cos (+ (* 1/2 eps) x)))) (sin (* 1/2 eps)))
30.0ms	(log (exp (cos (+ (* 1/2 eps) x))))
28.0ms	(cos (+ (* 1/2 eps) x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(exp (cos (+ (* 1/2 eps) x)))
61.0ms	(* (log (exp (cos (+ (* 1/2 eps) x)))) (sin (* 1/2 eps)))
22.0ms	(log (exp (cos (+ (* 1/2 eps) x))))
30.0ms	(cos (+ (* 1/2 eps) x))

simplify2.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
4	2671
3	1170
2	490
1	199
0	102

prune402.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes152.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	3302×	body	1280	valid
1.3s	1847×	body	640	valid
920.0ms	655×	body	2560	valid
243.0ms	772×	body	320	valid
152.0ms	1102×	body	80	valid
56.0ms	322×	body	160	valid