Details

sample161.0ms

Algorithm

intervals

Results

90.0ms	109×	body	1280	valid
26.0ms	21×	body	2560	valid
16.0ms	44×	body	640	valid
6.0ms	25×	body	320	valid
4.0ms	42×	body	80	valid
3.0ms	15×	body	160	valid

simplify27.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize21.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

77.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

series95.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify1.4s

Counts: 30 → 30

prune144.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
3.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite131.0ms

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

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (sin x) (cos eps))
13.0ms	(* (cos x) (sin eps))
28.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
74.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series439.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin x) (cos eps))
81.0ms	(* (cos x) (sin eps))
119.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
153.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify690.0ms

Counts: 76 → 76

prune371.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
1.7b	(- (cos eps) 1)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

17.0ms	(* (cos x) (sin eps))
25.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
43.0ms	(* (sin x) (- (cos eps) 1))
15.0ms	(- (cos eps) 1)

series326.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos x) (sin eps))
158.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
71.0ms	(* (sin x) (- (cos eps) 1))
34.0ms	(- (cos eps) 1)

simplify2.2s

Counts: 89 → 89

prune450.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
0.3b	(cbrt (pow (- (cos eps) 1) 3))
0.4b	(pow (- (cos eps) 1) 3)
1.7b	(- (cos eps) 1)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
44×	`cbrt-prod`
36×	`*-un-lft-identity`
23×	`associate-r`
22×	`unpow-prod-down` `cube-prod`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
7×	`pow1` `add-exp-log` `difference-of-sqr-1` `distribute-lft-out--`
6×	`cube-div` `add-cbrt-cube` `add-log-exp`
5×	`unswap-sqr`
4×	`cbrt-div` `flip3--` `flip--` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
2×	`associate-*r/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 124

Calls

4 calls:

105.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
11.0ms	(cbrt (pow (- (cos eps) 1) 3))
11.0ms	(pow (- (cos eps) 1) 3)
13.0ms	(- (cos eps) 1)

series194.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin x) (cbrt (pow (- (cos eps) 1) 3)))
32.0ms	(cbrt (pow (- (cos eps) 1) 3))
66.0ms	(pow (- (cos eps) 1) 3)
37.0ms	(- (cos eps) 1)

simplify610.0ms

Counts: 136 → 136

prune486.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes194.0ms

Accuracy

10.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify702.0ms

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.8s	3226×	body	1280	valid
1.1s	1823×	body	640	valid
1.0s	709×	body	2560	valid
191.0ms	769×	body	320	valid
86.0ms	1115×	body	80	valid
61.0ms	358×	body	160	valid