Details

Time bar (total: 47.7s)

sample180.0ms

Algorithm
intervals
Results
53.0ms37×body2560valid
49.0ms59×body640valid
41.0ms54×body1280valid
12.0ms30×body320valid
8.0ms57×body80valid
5.0ms19×body160valid

simplify60.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
60.0ms
(/ (- 1 (cos x)) (* x x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize21.0ms

Local error

Found 2 expressions with local error:

11.7b
(/ (- 1 (cos x)) (* x x))
2.5b
(- 1 (cos x))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-cube-cbrt add-log-exp
3×distribute-lft-out--
2×pow1 cbrt-undiv flip3-- div-exp insert-posit16 flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 47
Calls
2 calls:
Slowest
44.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series97.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
72.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify2.5s

Counts
35 → 53
Calls
35 calls:
Slowest
673.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
664.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
223.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
137.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
81.0ms
(- (pow 1 3) (pow (cos x) 3))

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

11.7b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
13×*-un-lft-identity prod-exp cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×associate-*l* pow-prod-down associate-*r/ insert-posit16
3×flip3-+ swap-sqr flip-+
2×associate-/r/ *-commutative sqr-sin sin-mult distribute-lft-out unswap-sqr
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 96
Calls
4 calls:
Slowest
31.0ms
(* (* x x) (+ 1 (cos x)))
26.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
11.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
43.0ms
(* (* x x) (+ 1 (cos x)))
29.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify12.0s

Counts
73 → 108
Calls
73 calls:
Slowest
1.4s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.1s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.0s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
993.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))

prune930.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1)
0.2b
(* (/ (sin x) x) (/ (sin x) x))
0.2b
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
0.1b
(/ (sin x) x)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
48×*-un-lft-identity
42×add-cube-cbrt
36×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×prod-exp cbrt-unprod
7×associate-/r*
6×div-inv add-log-exp
4×insert-posit16 associate-/l* unswap-sqr
3×distribute-lft-out associate-/l/
2×frac-times clear-num frac-2neg flip3-+ associate-*l/ associate-*r/ associate-/r/ flip-+
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 144
Calls
4 calls:
Slowest
31.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
17.0ms
(* (/ (sin x) x) (/ (sin x) x))
8.0ms
(/ (sin x) x)
5.0ms
(+ (cos x) 1)

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (* (/ (sin x) x) (/ (sin x) x)) (+ (cos x) 1))
66.0ms
(* (/ (sin x) x) (/ (sin x) x))
57.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify9.4s

Counts
142 → 156
Calls
142 calls:
Slowest
549.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
544.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
510.0ms
(/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
508.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
488.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1)
0.2b
(* (/ (sin x) x) (sin x))
0.1b
(* (+ (cos x) 1) x)
0.1b
(/ (* (/ (sin x) x) (sin x)) (* (+ (cos x) 1) x))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
21×add-sqr-sqrt
18×*-un-lft-identity
17×associate-*l*
14×add-cube-cbrt
11×times-frac
10×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
8×pow1
6×associate-*r* associate-*l/ add-log-exp
4×insert-posit16
3×flip3-+ flip-+ unswap-sqr
2×pow-prod-down associate-/r/ *-commutative div-inv distribute-lft-out
1×+-commutative clear-num associate-/r* sum-log frac-2neg associate-/l* associate-/l/
Counts
4 → 97
Calls
4 calls:
Slowest
40.0ms
(/ (* (/ (sin x) x) (sin x)) (* (+ (cos x) 1) x))
19.0ms
(* (+ (cos x) 1) x)
13.0ms
(* (/ (sin x) x) (sin x))
10.0ms
(+ (cos x) 1)

series234.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(/ (* (/ (sin x) x) (sin x)) (* (+ (cos x) 1) x))
67.0ms
(* (+ (cos x) 1) x)
56.0ms
(* (/ (sin x) x) (sin x))
22.0ms
(+ (cos x) 1)

simplify13.1s

Counts
68 → 109
Calls
68 calls:
Slowest
1.3s
(/ (* (* (* (/ (sin x) x) (sin x)) (* (/ (sin x) x) (sin x))) (* (/ (sin x) x) (sin x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.2s
(/ (* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.2s
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.1s
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x)))
1.0s
(/ (* (* (* (/ (sin x) x) (sin x)) (* (/ (sin x) x) (sin x))) (* (/ (sin x) x) (sin x))) (* (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)) (* (* x x) x)))

prune940.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.8s1534×body2560valid
1.7s1504×body640valid
1.0s1249×body1280valid
453.0ms940×body320valid
296.0ms2277×body80valid
162.0ms496×body160valid