Details

Time bar (total: 24.8s)

sample250.0ms

Algorithm
intervals
Results
155.0ms150×body1280valid
35.0ms59×body640valid
35.0ms19×body2560valid
10.0ms17×body320valid
2.0ms8×body160valid
0.0ms3×body80valid

simplify16.0ms

Calls
1 calls:
Slowest
15.0ms
(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize26.0ms

Local error

Found 2 expressions with local error:

3.5b
(cos (+ x eps))
0.9b
(- (cos (+ x eps)) (cos x))

rewrite47.0ms

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
35.0ms
(- (cos (+ x eps)) (cos x))
12.0ms
(cos (+ x eps))

series89.0ms

Calls
2 calls:
Slowest
64.0ms
(- (cos (+ x eps)) (cos x))
25.0ms
(cos (+ x eps))

simplify524.0ms

Calls
13 calls:
Slowest
198.0ms
(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
173.0ms
(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
43.0ms
(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms
(/ (exp (cos (+ x eps))) (exp (cos x)))
16.0ms
(- (cos (+ x eps)) (cos x))

prune400.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

3.3b
(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))))

rewrite179.0ms

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
Calls
4 calls:
Slowest
85.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
58.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
19.0ms
(sin (/ (+ x (+ eps x)) 2))
16.0ms
(+ x (+ eps x))

series330.0ms

Calls
4 calls:
Slowest
148.0ms
(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
92.0ms
(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
52.0ms
(sin (/ (+ x (+ eps x)) 2))
38.0ms
(+ x (+ eps x))

simplify3.3s

Calls
36 calls:
Slowest
676.0ms
(* (* (* -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)))))
566.0ms
(* (* (* -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)))))
378.0ms
(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
262.0ms
(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
246.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune834.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

3.3b
(sin (+ x (* eps 1/2)))
0.2b
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
0.0b
(* -2 (sin (* eps 1/2)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×*-un-lft-identity associate-*r* add-cube-cbrt
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sin-sum insert-posit16 add-log-exp
2×*-commutative
1×distribute-rgt-in distribute-lft-in unswap-sqr
Calls
3 calls:
Slowest
65.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
17.0ms
(* -2 (sin (* eps 1/2)))
8.0ms
(sin (+ x (* eps 1/2)))

series176.0ms

Calls
3 calls:
Slowest
106.0ms
(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
36.0ms
(* -2 (sin (* eps 1/2)))
35.0ms
(sin (+ x (* eps 1/2)))

simplify2.5s

Calls
31 calls:
Slowest
557.0ms
(* (* (* (* -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)))))
529.0ms
(* (* (* (* -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)))))
324.0ms
(- (* 1/24 (pow eps 3)) (+ (* 1/1920 (pow eps 5)) eps))
200.0ms
(* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
199.0ms
(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))

prune601.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16
3×*-commutative
2×flip3-+ associate-*r/ flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in sin-cos-mult
Calls
4 calls:
Slowest
127.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
34.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
17.0ms
(* (cos x) (sin (* eps 1/2)))
17.0ms
(* (sin x) (cos (* eps 1/2)))

series489.0ms

Calls
4 calls:
Slowest
240.0ms
(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
128.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
61.0ms
(* (sin x) (cos (* eps 1/2)))
60.0ms
(* (cos x) (sin (* eps 1/2)))

simplify5.1s

Calls
47 calls:
Slowest
631.0ms
(- (* 1/2 eps) (+ (* 1/4 (* (pow x 2) eps)) (* 1/48 (pow eps 3))))
585.0ms
(* (* (* (* -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))))))
478.0ms
(* (* (* (* -2 -2) -2) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (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))))))
452.0ms
(* (* (* (cos x) (cos x)) (cos x)) (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))))
366.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))))

prune994.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch3.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
4.8s4391×body1280valid
1.7s660×body2560valid
1.3s1891×body640valid
306.0ms679×body320valid
81.0ms295×body160valid
11.0ms84×body80valid