Details

Time bar (total: 20.5s)

sample289.0ms

Algorithm
intervals
Results
127.0ms126×body1280valid
75.0ms66×body640valid
57.0ms27×body2560valid
11.0ms23×body320valid
3.0ms9×body160valid
1.0ms5×body80valid

simplify16.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize27.0ms

Local error

Found 2 expressions with local error:

4.6b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite21.0ms

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
11.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(- (cos (+ x eps)) (cos x))
38.0ms
(cos (+ x eps))

simplify1.4s

Counts
32 → 32

prune299.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

4.8b
(sin (/ (+ x (+ x eps)) 2))
0.3b
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.0b
(+ x (+ x eps))
0.0b
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×sum-log distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 64
Calls
4 calls:
Slowest
63.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
57.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
30.0ms
(sin (/ (+ x (+ x eps)) 2))
11.0ms
(+ x (+ x eps))

series302.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
104.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
41.0ms
(+ x (+ x eps))
41.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts
76 → 76

prune871.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 2 expressions with local error:

4.8b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt *-un-lft-identity sin-sum associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
2 → 30
Calls
2 calls:
Slowest
42.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
21.0ms
(sin (+ x (* eps 1/2)))

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
28.0ms
(sin (+ x (* eps 1/2)))

simplify3.2s

Counts
36 → 36

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-cbrt-cube add-exp-log
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l*
4×insert-posit16
3×*-commutative
2×sin-cos-mult
1×+-commutative sum-log flip3-+ associate-*r/ flip-+ distribute-lft-out unswap-sqr
Counts
4 → 80
Calls
4 calls:
Slowest
142.0ms
(+ (* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
88.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
68.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
34.0ms
(* (sin x) (cos (* eps 1/2)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(+ (* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
101.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
78.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
70.0ms
(* (sin x) (cos (* eps 1/2)))

simplify877.0ms

Counts
92 → 92

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes260.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
4.7s4438×body1280valid
1.7s635×body2560valid
1.6s1939×body640valid
312.0ms631×body320valid
72.0ms282×body160valid
44.0ms75×body80valid