Details

Time bar (total: 1.0m)

sample162.0ms

Algorithm
intervals
Results
65.0ms64×body2560valid
46.0ms37×body1280valid
19.0ms44×body640valid
12.0ms33×body320valid
8.0ms72×body80valid
1.0ms6×body160valid

simplify62.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
61.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize22.0ms

Local error

Found 2 expressions with local error:

17.9b
(/ (- 1 (cos x)) (* x x))
0.9b
(- 1 (cos x))

rewrite34.0ms

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
28.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series98.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
59.0ms
(/ (- 1 (cos x)) (* x x))
39.0ms
(- 1 (cos x))

simplify2.5s

Counts
35 → 53
Calls
35 calls:
Slowest
738.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
733.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
237.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
108.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
84.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

17.7b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite88.0ms

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
37.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
33.0ms
(* (* x x) (+ 1 (cos x)))
11.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series188.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
53.0ms
(* (* x x) (+ 1 (cos x)))
23.0ms
(* (sin x) (sin x))
15.0ms
(+ 1 (cos x))

simplify12.0s

Counts
73 → 108
Calls
73 calls:
Slowest
1.3s
(/ (* (* (* (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)))))
1.1s
(/ (* (* (* (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)))))
974.0ms
(/ (* (* (* (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)))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

17.6b
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))

rewrite145.0ms

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
68.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
43.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
25.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
78.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
35.0ms
(* (sin x) (sin x))
19.0ms
(+ 1 (cos x))

simplify34.7s

Counts
121 → 151
Calls
121 calls:
Slowest
1.6s
(/ (* (* (* (* 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))))
1.3s
(/ (* (* (* (* 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)))))
1.2s
(/ (* (* 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)))))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

17.4b
(/ (sin x) (* x x))
0.2b
(* (/ (sin x) (* x x)) (tan (/ x 2)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
7×*-un-lft-identity times-frac associate-*l* add-cube-cbrt
5×prod-exp cbrt-unprod
4×pow1 cbrt-undiv div-exp
3×associate-*r* associate-/l*
2×tan-quot insert-posit16 div-inv add-log-exp unswap-sqr
1×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
2 → 53
Calls
2 calls:
Slowest
36.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
11.0ms
(/ (sin x) (* x x))

series195.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
128.0ms
(* (/ (sin x) (* x x)) (tan (/ x 2)))
67.0ms
(/ (sin x) (* x x))

simplify2.9s

Counts
42 → 59
Calls
42 calls:
Slowest
341.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) x) (* (* x x) x))) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))
328.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) (* x x)) (* x x)))
322.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* (* x x) x) (* (* x x) x)))
255.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))
239.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))

prune494.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s1533×body2560valid
878.0ms1243×body1280valid
816.0ms1527×body640valid
661.0ms2280×body80valid
365.0ms944×body320valid
102.0ms473×body160valid