Details

Time bar (total: 24.7s)

sample220.0ms

Algorithm
intervals
Results
129.0ms133×body1280valid
43.0ms75×body640valid
25.0ms16×body2560valid
9.0ms22×body320valid
2.0ms8×body160valid
0.0ms2×body80valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize22.0ms

Local error

Found 2 expressions with local error:

4.4b
(cos (+ x eps))
0.8b
(- (cos (+ x eps)) (cos x))

rewrite50.0ms

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
37.0ms
(cos (+ x eps))
13.0ms
(- (cos (+ x eps)) (cos x))

series126.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
96.0ms
(- (cos (+ x eps)) (cos x))
30.0ms
(cos (+ x eps))

simplify502.0ms

Counts
13 → 32
Calls
13 calls:
Slowest
171.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
144.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
63.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
41.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
18.0ms
(- (sqrt (cos (+ x eps))) (sqrt (cos x)))

prune337.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 4 expressions with local error:

4.4b
(sin (/ (+ x (+ eps x)) 2))
0.3b
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b
(+ x (+ eps x))
0.0b
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite131.0ms

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
55.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
41.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
23.0ms
(sin (/ (+ x (+ eps x)) 2))
11.0ms
(+ x (+ eps x))

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
121.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
55.0ms
(sin (/ (+ x (+ eps x)) 2))
33.0ms
(+ x (+ eps x))

simplify3.3s

Counts
36 → 76
Calls
36 calls:
Slowest
718.0ms
(* (* (* -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)))))
480.0ms
(* (* (* -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)))))
406.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
291.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
247.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))

prune764.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 2 expressions with local error:

4.4b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite51.0ms

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
43.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
8.0ms
(sin (+ x (* eps 1/2)))

series134.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
91.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
43.0ms
(sin (+ x (* eps 1/2)))

simplify1.8s

Counts
18 → 36
Calls
18 calls:
Slowest
559.0ms
(* (* (* (* -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)))))
467.0ms
(* (* (* (* -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)))))
217.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
172.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
77.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

prune388.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-cbrt-cube add-exp-log
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×*-commutative insert-posit16 add-log-exp
2×sin-cos-mult unswap-sqr
1×associate-*r/
Counts
4 → 86
Calls
4 calls:
Slowest
115.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
72.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
35.0ms
(* (cos x) (sin (* eps 1/2)))
26.0ms
(* (sin x) (cos (* eps 1/2)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(* (* -2 (sin (* eps 1/2))) (* (sin x) (cos (* eps 1/2))))
98.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
82.0ms
(* (cos x) (sin (* eps 1/2)))
67.0ms
(* (sin x) (cos (* eps 1/2)))

simplify5.8s

Counts
59 → 98
Calls
59 calls:
Slowest
478.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
442.0ms
(* -2 (* (cos x) (pow (sin (* 1/2 eps)) 2)))
412.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))
367.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
344.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2)))) (* (* (* (cos x) (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (* (cos x) (sin (* eps 1/2)))))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.8s4462×body1280valid
1.6s1908×body640valid
1.2s619×body2560valid
603.0ms676×body320valid
111.0ms264×body160valid
10.0ms71×body80valid