Details

sample242.0ms

Algorithm

intervals

Results

134.0ms	146×	body	1280	valid
46.0ms	19×	body	2560	valid
33.0ms	56×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	3×	body	80	valid

simplify14.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize67.0ms

Local error

Found 2 expressions with local error:

3.0b	(cos (+ x eps))
1.1b	(- (cos (+ x eps)) (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

Slowest

22.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series159.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

112.0ms	(- (cos (+ x eps)) (cos x))
46.0ms	(cos (+ x eps))

simplify1.3s

Counts: 32 → 32

prune400.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize41.0ms

Local error

Found 4 expressions with local error:

2.9b	(sin (/ (+ x (+ x eps)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.2b	(/ (+ x (+ x eps)) 2)
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-out`
11×	`pow1`
6×	`associate-l`
5×	`associate-/l*`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative` `sin-mult` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-*r/` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

Slowest

76.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
70.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
51.0ms	(/ (+ x (+ x eps)) 2)
34.0ms	(sin (/ (+ x (+ x eps)) 2))

series274.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
79.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
56.0ms	(sin (/ (+ x (+ x eps)) 2))
45.0ms	(/ (+ x (+ x eps)) 2)

simplify1.4s

Counts: 98 → 98

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 3 expressions with local error:

2.9b	(sin (+ x (* 1/2 eps)))
0.3b	(* (sin (/ eps 2)) (sin (+ x (* 1/2 eps))))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (+ x (* 1/2 eps)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`sin-sum`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`insert-posit16` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

Slowest

56.0ms	(* -2 (* (sin (/ eps 2)) (sin (+ x (* 1/2 eps)))))
26.0ms	(* (sin (/ eps 2)) (sin (+ x (* 1/2 eps))))
9.0ms	(sin (+ x (* 1/2 eps)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

94.0ms	(* (sin (/ eps 2)) (sin (+ x (* 1/2 eps))))
78.0ms	(* -2 (* (sin (/ eps 2)) (sin (+ x (* 1/2 eps)))))
30.0ms	(sin (+ x (* 1/2 eps)))

simplify899.0ms

Counts: 64 → 64

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))))
0.2b	(* (sin x) (cos (* 1/2 eps)))
0.1b	(* (cos x) (sin (* 1/2 eps)))
0.1b	(+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps))))

rewrite185.0ms

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`
4×	`insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `sin-cos-mult`

Counts

4 → 74

Calls

4 calls:

Slowest

100.0ms	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))))
42.0ms	(+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps))))
26.0ms	(* (cos x) (sin (* 1/2 eps)))
16.0ms	(* (sin x) (cos (* 1/2 eps)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

204.0ms	(* (sin (/ eps 2)) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))))
133.0ms	(+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps))))
85.0ms	(* (cos x) (sin (* 1/2 eps)))
64.0ms	(* (sin x) (cos (* 1/2 eps)))

simplify2.1s

Counts: 86 → 86

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes296.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.1s	4478×	body	1280	valid
1.3s	1840×	body	640	valid
1.1s	615×	body	2560	valid
339.0ms	691×	body	320	valid
77.0ms	291×	body	160	valid
11.0ms	85×	body	80	valid