Details

Time bar (total: 26.3s)

sample206.0ms

Algorithm
intervals
Results
122.0ms146×body1280valid
33.0ms65×body640valid
28.0ms17×body2560valid
8.0ms19×body320valid
2.0ms6×body160valid
0.0ms3×body80valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(- (cos (+ x eps)) (cos x))

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize25.0ms

Local error

Found 2 expressions with local error:

4.4b
(cos (+ x eps))
0.5b
(- (cos (+ x eps)) (cos x))

rewrite19.0ms

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
12.0ms
(- (cos (+ x eps)) (cos x))
7.0ms
(cos (+ x eps))

series120.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
90.0ms
(- (cos (+ x eps)) (cos x))
30.0ms
(cos (+ x eps))

simplify481.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
177.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
145.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
55.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
34.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
16.0ms
(- (cos (+ x eps)) (cos x))

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 4 expressions with local error:

4.2b
(sin (/ (+ x (+ eps x)) 2))
0.2b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite175.0ms

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
78.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
56.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
22.0ms
(+ x (+ eps x))
19.0ms
(sin (/ (+ x (+ eps x)) 2))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
99.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
43.0ms
(+ x (+ eps x))
42.0ms
(sin (/ (+ x (+ eps x)) 2))

simplify3.4s

Counts
36 → 76
Calls
36 calls:
Slowest
735.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
516.0ms
(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
476.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
285.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
283.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune871.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

4.2b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite62.0ms

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
54.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
8.0ms
(sin (+ x (* eps 1/2)))

series135.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
102.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
32.0ms
(sin (+ x (* eps 1/2)))

simplify2.0s

Counts
18 → 36
Calls
18 calls:
Slowest
542.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
460.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (sin (+ x (* eps 1/2))) (sin (+ x (* eps 1/2)))) (sin (+ x (* eps 1/2)))))
285.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
268.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
80.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))))
0.2b
(* (cos x) (sin (* 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)))))

rewrite314.0ms

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
1×+-commutative sum-log flip3-+ associate-*r/ flip-+ sin-cos-mult distribute-lft-out unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
100.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
95.0ms
(+ (* (* -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))) (* (sin x) (cos (* eps 1/2))))
29.0ms
(* (cos x) (sin (* eps 1/2)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(+ (* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
137.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
94.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
69.0ms
(* (cos x) (sin (* eps 1/2)))

simplify6.6s

Counts
51 → 91
Calls
51 calls:
Slowest
450.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
406.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
385.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
318.0ms
(- (+ (* 2 (* (sin x) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))))
311.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2)))))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 1.3b

bsearch4.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.8s4453×body1280valid
1.7s1900×body640valid
1.2s618×body2560valid
311.0ms689×body320valid
65.0ms253×body160valid
12.0ms87×body80valid