Details

Time bar (total: 1.1m)

sample177.0ms

Algorithm
intervals
Results
84.0ms64×body2560valid
30.0ms37×body1280valid
26.0ms44×body640valid
14.0ms33×body320valid
10.0ms72×body80valid
2.0ms6×body160valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(/ (- 1 (cos x)) (* x x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-log-exp
3×fma-neg distribute-lft-out--
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 63
Calls
2 calls:
Slowest
16.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series128.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
90.0ms
(/ (- 1 (cos x)) (* x x))
38.0ms
(- 1 (cos x))

simplify3.8s

Counts
55 → 69
Calls
55 calls:
Slowest
676.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
608.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
340.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
199.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
157.0ms
(fma (- (cbrt (cos x))) (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x)))))

prune539.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
14×*-un-lft-identity
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×fma-def 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 → 107
Calls
4 calls:
Slowest
44.0ms
(* (* x x) (+ 1 (cos x)))
25.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
19.0ms
(* (sin x) (sin x))
7.0ms
(+ 1 (cos x))

series154.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
52.0ms
(* (* x x) (+ 1 (cos x)))
21.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify12.3s

Counts
75 → 119
Calls
75 calls:
Slowest
1.6s
(/ (* (* (* (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) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos 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)))))
1.0s
(/ (* (* (* (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)))))
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)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize37.0ms

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))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
23×times-frac
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×cbrt-undiv cbrt-unprod
12×pow1
7×rec-exp associate-/r* 1-exp
6×associate-/r/ div-inv sin-mult add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×fma-def 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 → 150
Calls
4 calls:
Slowest
43.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
36.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
22.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x)))
81.0ms
(/ 1 (/ (* (* x x) (+ 1 (cos x))) (* (sin x) (sin x))))
33.0ms
(* (sin x) (sin x))
22.0ms
(+ 1 (cos x))

simplify33.1s

Counts
123 → 162
Calls
123 calls:
Slowest
1.6s
(/ (* (* 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)))))
1.2s
(/ (* (* (* (* 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
(/ (* (* (* (* 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))))
1.1s
(/ (* (* 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)))))
1.1s
(/ (* (* 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)))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
49×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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
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 → 148
Calls
4 calls:
Slowest
15.0ms
(* (/ (sin x) x) (/ (sin x) x))
8.0ms
(/ (sin x) x)
8.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series141.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
46.0ms
(* (/ (sin x) x) (/ (sin x) x))
35.0ms
(/ (sin x) x)
34.0ms
(/ (sin x) x)
26.0ms
(+ (cos x) 1)

simplify4.9s

Counts
140 → 160
Calls
140 calls:
Slowest
415.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
410.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
382.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
214.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
197.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.8s1533×body2560valid
955.0ms1243×body1280valid
836.0ms1527×body640valid
816.0ms2280×body80valid
443.0ms944×body320valid
112.0ms473×body160valid