Details

Time bar (total: 17.6s)

sample188.0ms

Algorithm
intervals
Results
114.0ms148×body1280valid
34.0ms25×body2560valid
23.0ms49×body640valid
6.0ms21×body320valid
2.0ms8×body160valid
1.0ms5×body80valid

simplify8.0ms

Calls
1 calls:
Slowest
7.0ms
(- (cos (+ x eps)) (cos x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.8b
(cos (+ x eps))
1.2b
(- (cos (+ x eps)) (cos x))

rewrite8.0ms

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
Calls
2 calls:
Slowest
5.0ms
(- (cos (+ x eps)) (cos x))
2.0ms
(cos (+ x eps))

series94.0ms

Calls
2 calls:
Slowest
57.0ms
(- (cos (+ x eps)) (cos x))
37.0ms
(cos (+ x eps))

simplify661.0ms

Calls
13 calls:
Slowest
355.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
155.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
47.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
35.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
15.0ms
(- (cos (+ x eps)) (cos x))

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b
(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))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×associate-*r* insert-posit16 add-log-exp
3×associate-*l*
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp associate-*r/ cbrt-unprod flip-+
Calls
4 calls:
Slowest
13.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
8.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
5.0ms
(sin (/ (+ x (+ eps x)) 2))
1.0ms
(+ x (+ eps x))

series228.0ms

Calls
4 calls:
Slowest
105.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
84.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
25.0ms
(sin (/ (+ x (+ eps x)) 2))
14.0ms
(+ x (+ eps x))

simplify1.4s

Calls
22 calls:
Slowest
349.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
293.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
126.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
109.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
83.0ms
(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune736.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 2 expressions with local error:

1.6b
(sin (+ x (* eps 1/2)))
0.3b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt *-un-lft-identity sin-sum associate-*r* add-cube-cbrt
2×insert-posit16 add-log-exp
1×distribute-rgt-in distribute-lft-in associate-*l* pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
2 calls:
Slowest
21.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
5.0ms
(sin (+ x (* eps 1/2)))

series73.0ms

Calls
2 calls:
Slowest
51.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
21.0ms
(sin (+ x (* eps 1/2)))

simplify1.1s

Calls
15 calls:
Slowest
425.0ms
(* (* (* (* -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)))))
204.0ms
(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
124.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
75.0ms
(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))
65.0ms
(* (* -2 (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

prune394.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
4×insert-posit16
3×pow-prod-down prod-exp *-commutative cbrt-unprod
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in sin-cos-mult
Calls
4 calls:
Slowest
35.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
26.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
14.0ms
(* (sin x) (cos (* eps 1/2)))
13.0ms
(* (cos x) (sin (* eps 1/2)))

series371.0ms

Calls
4 calls:
Slowest
155.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
104.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
70.0ms
(* (cos x) (sin (* eps 1/2)))
43.0ms
(* (sin x) (cos (* eps 1/2)))

simplify3.0s

Calls
40 calls:
Slowest
491.0ms
(* (* (* (* -2 (sin (* eps 1/2))) (* -2 (sin (* eps 1/2)))) (* -2 (sin (* eps 1/2)))) (* (* (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))
373.0ms
(- x (+ (* 1/8 (* x (pow eps 2))) (* 1/6 (pow x 3))))
312.0ms
(- (* 1/2 eps) (+ (* 1/4 (* (pow x 2) eps)) (* 1/48 (pow eps 3))))
233.0ms
(* -2 (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 eps))))
221.0ms
(+ (* (* (sin x) (cos (* eps 1/2))) (* (sin x) (cos (* eps 1/2)))) (- (* (* (cos x) (sin (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))) (* (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))))

prune996.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes212.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.4s4405×body1280valid
1.5s1850×body640valid
1.2s715×body2560valid
357.0ms662×body320valid
68.0ms284×body160valid
11.0ms84×body80valid