Details

sample94.0ms

Algorithm

intervals

Results

48.0ms	149×	body	1280	valid
19.0ms	18×	body	2560	valid
11.0ms	56×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	11×	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

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite23.0ms

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:

14.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify106.0ms

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

prune83.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

12.0ms	(+ (* (sin x) (sin eps)) (cos x))
12.0ms	(* (cos x) (cos eps))
11.0ms	(* (sin x) (sin eps))
26.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* (sin x) (sin eps)) (cos x))
41.0ms	(* (cos x) (cos eps))
51.0ms	(* (sin x) (sin eps))
132.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify40.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	576
2	5002	567
done	5002	567

prune228.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
2.8b	(- (* (cos x) (cos eps)) (* 1 (+ (* (sin x) (sin eps)) (cos x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
6×	`associate-r` `associate-l`
3×	`cos-mult`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `frac-sub` `cbrt-unprod` `flip-+` `associate--r+` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `sum-log` `flip--` `sin-mult`

Counts

4 → 65

Calls

4 calls:

11.0ms	(+ (* (sin x) (sin eps)) (cos x))
11.0ms	(* (cos x) (cos eps))
11.0ms	(* (sin x) (sin eps))
26.0ms	(- (* (cos x) (cos eps)) (* 1 (+ (* (sin x) (sin eps)) (cos x))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* (sin x) (sin eps)) (cos x))
40.0ms	(* (cos x) (cos eps))
50.0ms	(* (sin x) (sin eps))
131.0ms	(- (* (cos x) (cos eps)) (* 1 (+ (* (sin x) (sin eps)) (cos x))))

simplify44.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	360	620
1	1514	581
2	5002	571
done	5002	571

prune256.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))))
0.2b	(* (sin x) (sin eps))
2.8b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))
2.9b	(log (exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

70.0ms	(exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))))
11.0ms	(* (sin x) (sin eps))
26.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))
49.0ms	(log (exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))))
46.0ms	(* (sin x) (sin eps))
142.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))
137.0ms	(log (exp (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify43.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	302	858
1	1147	780
2	5001	773
done	5001	773

prune230.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 14.4b

regimes196.0ms

Accuracy

87.4% (1.2b remaining)

Error of 16.1b against oracle of 14.9b and baseline of 24.6b

bsearch88.0ms

Steps

Iters	Range		Point
8	4.11075536510938e-11	9.85435867085541e-08	3.130998694967744e-08
6	-1.6640733670284383e-05	-3.4900073017642136e-06	-3.6584498918211995e-06

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	17
1	44	17
2	44	17
done	44	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4421×	body	1280	valid
579.0ms	673×	body	2560	valid
405.0ms	1889×	body	640	valid
106.0ms	662×	body	320	valid
28.0ms	280×	body	160	valid
4.0ms	75×	body	80	valid