Details

sample221.0ms

Algorithm

intervals

Results

94.0ms	111×	body	1280	valid
46.0ms	34×	body	80	valid
31.0ms	60×	body	640	valid
27.0ms	19×	body	2560	valid
7.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid

simplify9.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize23.0ms

Local error

Found 2 expressions with local error:

3.1b	(sin (+ x eps))
1.2b	(- (sin (+ x eps)) (sin x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

Slowest

45.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series78.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

53.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify1.6s

Counts: 32 → 32

prune389.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize61.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (/ (+ x (+ x eps)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
0.2b	(/ (+ x (+ x eps)) 2)
0.0b	(+ x (+ x eps))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-cos-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

Slowest

58.0ms	(/ (+ x (+ x eps)) 2)
24.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
19.0ms	(cos (/ (+ x (+ x eps)) 2))
11.0ms	(+ x (+ x eps))

series184.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

63.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
51.0ms	(/ (+ x (+ x eps)) 2)
37.0ms	(+ x (+ x eps))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify966.0ms

Counts: 94 → 94

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 2 expressions with local error:

2.9b	(cos (+ x (* 1/2 eps)))
0.2b	(* (sin (/ eps 2)) (cos (+ x (* 1/2 eps))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`insert-posit16` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

Slowest

32.0ms	(* (sin (/ eps 2)) (cos (+ x (* 1/2 eps))))
12.0ms	(cos (+ x (* 1/2 eps)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(* (sin (/ eps 2)) (cos (+ x (* 1/2 eps))))
38.0ms	(cos (+ x (* 1/2 eps)))

simplify1.7s

Counts: 35 → 35

prune477.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
0.2b	(* (sin x) (sin (* 1/2 eps)))
0.1b	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
0.1b	(* (cos x) (cos (* 1/2 eps)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-*r/` `insert-posit16`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`diff-log`

Counts

4 → 82

Calls

4 calls:

Slowest

116.0ms	(* (sin (/ eps 2)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
35.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
31.0ms	(* (cos x) (cos (* 1/2 eps)))
18.0ms	(* (sin x) (sin (* 1/2 eps)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

182.0ms	(* (sin (/ eps 2)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
137.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
75.0ms	(* (cos x) (cos (* 1/2 eps)))
69.0ms	(* (sin x) (sin (* 1/2 eps)))

simplify1.4s

Counts: 94 → 94

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch6.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.5s	3321×	body	1280	valid
1.3s	615×	body	2560	valid
1.3s	1827×	body	640	valid
650.0ms	726×	body	320	valid
178.0ms	1145×	body	80	valid
120.0ms	366×	body	160	valid