Details

sample111.0ms

Algorithm

intervals

Results

62.0ms	144×	body	1280	valid
17.0ms	19×	body	2560	valid
14.0ms	57×	body	640	valid
5.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify1.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize11.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.5b	(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:

54.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series101.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

simplify107.0ms

Counts: 30 → 30

prune140.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.4b

localize31.0ms

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))
2.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite178.0ms

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:

21.0ms	(* (cos x) (cos eps))
37.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
24.0ms	(* (sin x) (sin eps))
93.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series437.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos x) (cos eps))
116.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
68.0ms	(* (sin x) (sin eps))
192.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify100.0ms

Counts: 82 → 82

prune367.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.3b

localize17.0ms

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))
2.9b	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sum-log` `cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `pow-prod-down` `neg-log` `frac-add` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate--l-` `neg-sub0` `associate-+r-` `flip3-+` `flip-+` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

13.0ms	(* (cos x) (cos eps))
16.0ms	(- (- (* (sin x) (sin eps))) (cos x))
13.0ms	(* (sin x) (sin eps))
38.0ms	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos x) (cos eps))
80.0ms	(- (- (* (sin x) (sin eps))) (cos x))
85.0ms	(* (sin x) (sin eps))
207.0ms	(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify64.0ms

Counts: 84 → 84

prune440.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
2.6b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
3.7b	(log (exp (* (sin x) (sin eps))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

22.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
16.0ms	(* (sin x) (sin eps))
82.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
5.0ms	(log (exp (* (sin x) (sin eps))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
68.0ms	(* (sin x) (sin eps))
235.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
86.0ms	(log (exp (* (sin x) (sin eps))))

simplify92.0ms

Counts: 78 → 78

prune321.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.2b

regimes306.0ms

Accuracy

85.2% (1.5b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 24.5b

bsearch172.0ms

Steps

Iters	Range		Point
9	9.904262439501984e-16	3.244205803610274e-06	2.126123295417241e-07
9	-0.002338049553438653	-4.347782938444816e-12	-4.2327309977810814e-09

simplify57.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.8s	4523×	body	1280	valid
1.4s	611×	body	2560	valid
787.0ms	1821×	body	640	valid
270.0ms	670×	body	320	valid
52.0ms	292×	body	160	valid
52.0ms	83×	body	80	valid