Details

sample131.0ms

Algorithm

intervals

Results

72.0ms	146×	body	1280	valid
22.0ms	22×	body	2560	valid
17.0ms	57×	body	640	valid
5.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify24.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize16.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.2b	(cos (+ x eps))

rewrite72.0ms

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:

60.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series103.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

simplify1.2s

Counts: 30 → 30

prune139.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.0b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite88.0ms

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:

11.0ms	(* (cos x) (cos eps))
13.0ms	(+ (* (sin x) (sin eps)) (cos x))
18.0ms	(* (sin x) (sin eps))
45.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos x) (cos eps))
66.0ms	(+ (* (sin x) (sin eps)) (cos x))
66.0ms	(* (sin x) (sin eps))
199.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify741.0ms

Counts: 77 → 77

prune370.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.6b

localize16.0ms

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))
2.0b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite114.0ms

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))
19.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
70.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series402.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos x) (cos eps))
112.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
62.0ms	(* (sin x) (sin eps))
176.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify1.8s

Counts: 82 → 82

prune414.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.0b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
28.2b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

14.0ms	(* (sin x) (sin eps))
9.0ms	(pow (* (sin x) (sin eps)) 3)
99.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
5.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series479.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin x) (sin eps))
92.0ms	(pow (* (sin x) (sin eps)) 3)
220.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
84.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify728.0ms

Counts: 90 → 90

prune377.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.6b

regimes284.0ms

Accuracy

84.3% (1.6b remaining)

Error of 16.4b against oracle of 14.8b and baseline of 24.9b

bsearch169.0ms

Steps

Iters	Range		Point
9	5.617255490710578e-12	0.0026080803058150265	1.8759082039949294e-09
6	-1.7104155354788486e-05	-1.486794689715045e-06	-1.7256400847951869e-06

simplify1.1s

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.7s	4490×	body	1280	valid
1.3s	1828×	body	640	valid
1.0s	641×	body	2560	valid
171.0ms	666×	body	320	valid
102.0ms	281×	body	160	valid
9.0ms	94×	body	80	valid