Details

sample95.0ms

Algorithm

intervals

Results

53.0ms	151×	body	1280	valid
15.0ms	65×	body	640	valid
14.0ms	10×	body	2560	valid
2.0ms	14×	body	320	valid
2.0ms	15×	body	160	valid
0.0ms	1×	body	80	valid

simplify13.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite40.0ms

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:

13.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series67.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.5s

Counts: 30 → 30

prune83.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

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))
3.2b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite96.0ms

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:

11.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
11.0ms	(* (sin x) (sin eps))
56.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
128.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify1.3s

Counts: 82 → 82

prune230.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
3.2b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite64.0ms

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:

10.0ms	(* (cos eps) (cos x))
11.0ms	(+ (* (sin x) (sin eps)) (cos x))
11.0ms	(* (sin x) (sin eps))
30.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos eps) (cos x))
51.0ms	(+ (* (sin x) (sin eps)) (cos x))
49.0ms	(* (sin x) (sin eps))
138.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify1.5s

Counts: 77 → 77

prune241.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
3.2b	(- (* (cos eps) (cos x)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
25.3b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow-unpow` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cos-mult` `frac-sub` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `flip3-+` `pow1/3` `sum-log` `*-commutative` `flip--` `rem-cbrt-cube` `flip-+` `associate--r+` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

11.0ms	(* (sin x) (sin eps))
8.0ms	(pow (* (sin x) (sin eps)) 3)
38.0ms	(- (* (cos eps) (cos x)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
4.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series296.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin x) (sin eps))
67.0ms	(pow (* (sin x) (sin eps)) 3)
135.0ms	(- (* (cos eps) (cos x)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
49.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify565.0ms

Counts: 88 → 88

prune220.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 14.0b

regimes204.0ms

Accuracy

87.2% (1.3b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 24.5b

bsearch129.0ms

Steps

Iters	Range		Point
7	6.296057712345076e-10	4.2024004726508306e-08	2.004511153324394e-08
10	-66313704.61781203	-0.0001727236275851095	-0.0001750220631805364

simplify392.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.4s	4507×	body	1280	valid
687.0ms	1822×	body	640	valid
632.0ms	594×	body	2560	valid
113.0ms	685×	body	320	valid
33.0ms	312×	body	160	valid
4.0ms	80×	body	80	valid