Details

sample92.0ms

Algorithm

intervals

Results

45.0ms	143×	body	1280	valid
20.0ms	24×	body	2560	valid
11.0ms	57×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

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:

0.7b	(- (cos (+ x eps)) (cos x))
5.0b	(cos (+ x eps))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

16.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series78.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify114.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164
done	5002	164

prune100.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite113.0ms

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`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

12.0ms	(* (cos x) (cos eps))
19.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
13.0ms	(* (sin x) (sin eps))
66.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series320.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos x) (cos eps))
89.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms	(* (sin x) (sin eps))
137.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	601
2	4487	583
3	5002	583
done	5002	583

prune276.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.2b	(* (sin x) (sin eps))
3.4b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

124.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
14.0ms	(* (sin x) (sin eps))
76.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
66.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series464.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
47.0ms	(* (sin x) (sin eps))
137.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify72.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	239	889
1	732	805
2	2888	794
3	5001	794
done	5001	794

prune321.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.2b	(* (sin x) (sin eps))
3.4b	(log (* 1 (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))))
3.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-log-exp`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`pow1`
8×	`add-exp-log`
7×	`add-cube-cbrt`
6×	`diff-log` `add-cbrt-cube`
5×	`exp-prod`
4×	`sub-neg` `exp-sum` `associate--l+`
3×	`rem-log-exp` `associate-r` `associate-l` `prod-exp` `rem-exp-log`
2×	`exp-diff` `pow-prod-down` `log-pow` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `log-div` `log-prod` `flip3--` `1-exp` `associate-r/` `-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

122.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
13.0ms	(* (sin x) (sin eps))
182.0ms	(log (* 1 (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))))
65.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series462.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
52.0ms	(* (sin x) (sin eps))
133.0ms	(log (* 1 (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))))
133.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify91.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	236	762
1	797	687
2	3798	677
3	5002	677
done	5002	677

prune263.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.7b

regimes202.0ms

Accuracy

76.1% (2.4b remaining)

Error of 17.3b against oracle of 14.9b and baseline of 24.9b

bsearch110.0ms

Steps

Iters	Range		Point
7	4.000715157667192e-13	8.957781355231878e-11	8.78089823303509e-11
8	-8.072282243414738e-50	-4.0445797790301095e-54	-7.952525266384432e-50

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	64
1	50	64
2	50	64
done	50	64

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4477×	body	1280	valid
541.0ms	646×	body	2560	valid
383.0ms	1850×	body	640	valid
88.0ms	646×	body	320	valid
28.0ms	294×	body	160	valid
5.0ms	87×	body	80	valid