Details

sample151.0ms

Algorithm

intervals

Results

75.0ms	103×	body	1280	valid
26.0ms	19×	body	2560	valid
24.0ms	55×	body	640	valid
6.0ms	26×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	9×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize52.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.4b	(sin (+ x eps))

rewrite89.0ms

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:

69.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (sin (+ x eps)) (sin x))
27.0ms	(sin (+ x eps))

simplify104.0ms

Counts: 30 → 30

prune109.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.4b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite123.0ms

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:

18.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
14.0ms	(* (sin x) (cos eps))
75.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series461.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
83.0ms	(* (cos x) (sin eps))
61.0ms	(* (sin x) (cos eps))
155.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify134.0ms

Counts: 76 → 76

prune287.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
2.1b	(- (cos eps) 1)

rewrite100.0ms

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:

31.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
44.0ms	(* (sin x) (- (cos eps) 1))
12.0ms	(- (cos eps) 1)

series327.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
79.0ms	(* (cos x) (sin eps))
77.0ms	(* (sin x) (- (cos eps) 1))
21.0ms	(- (cos eps) 1)

simplify150.0ms

Counts: 89 → 89

prune480.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (cos eps) 3) (pow 1 3)) (+ (* (cos eps) (+ (cos eps) 1)) 1))
0.4b	(pow (cos eps) 3)
0.5b	(+ (cos eps) 1)
2.0b	(- (pow (cos eps) 3) (pow 1 3))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
120×	`difference-of-squares`
102×	`times-frac`
93×	`unpow-prod-down` `cube-prod`
51×	`sqr-pow`
46×	`add-cube-cbrt`
34×	`associate-/l*`
30×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-mult`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 234

Calls

4 calls:

116.0ms	(/ (- (pow (cos eps) 3) (pow 1 3)) (+ (* (cos eps) (+ (cos eps) 1)) 1))
3.0ms	(pow (cos eps) 3)
20.0ms	(+ (cos eps) 1)
40.0ms	(- (pow (cos eps) 3) (pow 1 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- (pow (cos eps) 3) (pow 1 3)) (+ (* (cos eps) (+ (cos eps) 1)) 1))
44.0ms	(pow (cos eps) 3)
12.0ms	(+ (cos eps) 1)
79.0ms	(- (pow (cos eps) 3) (pow 1 3))

simplify140.0ms

Counts: 246 → 246

prune910.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify66.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.9s	3371×	body	1280	valid
1.1s	611×	body	2560	valid
1.0s	1842×	body	640	valid
210.0ms	720×	body	320	valid
102.0ms	1114×	body	80	valid
65.0ms	342×	body	160	valid