Details

Time bar (total: 1.0m)

sample98.0ms

Algorithm
intervals
Results
32.0ms48×body2560valid
26.0ms51×body640valid
15.0ms37×body1280valid
9.0ms31×body320valid
6.0ms77×body80valid
2.0ms12×body160valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize11.0ms

Local error

Found 2 expressions with local error:

13.8b
(/ (- 1 (cos x)) (* x x))
1.8b
(- 1 (cos x))

rewrite52.0ms

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
40.0ms
(/ (- 1 (cos x)) (* x x))
10.0ms
(- 1 (cos x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
74.0ms
(/ (- 1 (cos x)) (* x x))
31.0ms
(- 1 (cos x))

simplify2.5s

Counts
35 → 53
Calls
35 calls:
Slowest
717.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
672.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
247.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
141.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
68.0ms
(/ (- 1 (cos x)) (pow x 2))

prune405.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.7b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite100.0ms

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
34.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
28.0ms
(* (* x x) (+ 1 (cos x)))
27.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
64.0ms
(* (* x x) (+ 1 (cos x)))
32.0ms
(* (sin x) (sin x))
19.0ms
(+ 1 (cos x))

simplify11.2s

Counts
73 → 108
Calls
73 calls:
Slowest
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)))))
975.0ms
(/ (* (* (* (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)))))
975.0ms
(/ (* (* (* (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)))))
944.0ms
(/ (* (* (* (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)))))

prune674.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×times-frac
50×*-un-lft-identity
48×add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
6×cbrt-undiv associate-/r* div-exp div-inv associate-/l* add-log-exp
4×prod-exp cbrt-unprod insert-posit16 unswap-sqr
2×clear-num frac-2neg
1×pow2 frac-times +-commutative sum-log flip3-+ pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ distribute-lft-out
Counts
4 → 137
Calls
4 calls:
Slowest
14.0ms
(* (/ (sin x) x) (/ (sin x) x))
10.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)
5.0ms
(+ (cos x) 1)

series118.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(* (/ (sin x) x) (/ (sin x) x))
33.0ms
(/ (sin x) x)
31.0ms
(/ (sin x) x)
10.0ms
(+ (cos x) 1)

simplify4.4s

Counts
138 → 149
Calls
138 calls:
Slowest
386.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
349.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
346.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
187.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt x)))
136.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

13.4b
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
0.4b
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
23×times-frac
21×add-sqr-sqrt *-un-lft-identity
19×cbrt-undiv add-cube-cbrt cbrt-unprod
12×pow1
7×rec-exp associate-/r* 1-exp
6×associate-/r/ div-inv sin-mult add-log-exp
4×insert-posit16 associate-/l*
3×swap-sqr associate-*r* associate-*l*
2×clear-num frac-2neg flip3-+ associate-*r/ flip-+ associate-/l/
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up sqr-sin pow-flip distribute-lft-out inv-pow unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
48.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
46.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
20.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series213.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
68.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
29.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify34.2s

Counts
121 → 151
Calls
121 calls:
Slowest
1.5s
(/ (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))))
1.4s
(/ (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))))
1.3s
(/ (* (* 1 1) 1) (/ (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x)))))
1.3s
(/ (* (* 1 1) 1) (/ (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x)))))
1.2s
(/ (* (* 1 1) 1) (/ (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x)))))

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.8s1548×body2560valid
937.0ms1289×body1280valid
877.0ms1505×body640valid
659.0ms2265×body80valid
409.0ms936×body320valid
102.0ms457×body160valid