Details

Time bar (total: 22.4s)

sample215.0ms

Algorithm
intervals
Results
99.0ms57×body2560valid
65.0ms82×body1280valid
21.0ms58×body640valid
10.0ms38×body320valid
2.0ms13×body160valid
1.0ms8×body80valid

simplify15.0ms

Counts
1 → 1
Iterations
IterNodes
done16
316
214
111
06

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.3b
(- 1.0 (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 52
Calls
2 calls:
17.0ms
(/ (- 1.0 (cos x)) (sin x))
10.0ms
(- 1.0 (cos x))

series110.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(/ (- 1.0 (cos x)) (sin x))
44.0ms
(- 1.0 (cos x))

simplify1.6s

Counts
58 → 58
Iterations
IterNodes
done5002
31941
2596
1240
0106

prune404.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sin x))
0.2b
(/ (cos x) (sin x))
1.5b
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
28×times-frac
21×add-cube-cbrt
7×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
5×add-log-exp
4×div-inv distribute-lft-out-- difference-of-squares
3×pow1
2×cbrt-undiv clear-num frac-2neg div-exp
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 77
Calls
3 calls:
9.0ms
(/ 1.0 (sin x))
15.0ms
(/ (cos x) (sin x))
37.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series189.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(/ 1.0 (sin x))
24.0ms
(/ (cos x) (sin x))
137.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.6s

Counts
86 → 86
Iterations
IterNodes
done5000
32129
2783
1302
0146

prune459.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
1.2b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
12×pow1
11×add-cube-cbrt
9×sqr-pow
8×add-log-exp
7×add-cbrt-cube add-exp-log
5×distribute-lft-out--
3×pow-unpow swap-sqr associate-*r* associate-*l*
1×pow2 cube-mult pow-to-exp difference-cubes +-commutative sqr-cos sum-log sub-neg pow-pow flip3-+ pow-plus flip3-- diff-log unpow3 pow-prod-down pow-exp prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod flip-+ flip-- distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 96
Calls
4 calls:
16.0ms
(* (cos x) (cos x))
6.0ms
(pow (cos x) 3)
5.0ms
(+ 1.0 (cos x))
23.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series181.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (cos x) (cos x))
54.0ms
(pow (cos x) 3)
17.0ms
(+ 1.0 (cos x))
83.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.9s

Counts
108 → 108
Iterations
IterNodes
done5009
33848
21174
1407
0152

prune737.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cos x) (cos x)) (* (cos x) (cos x)))
0.3b
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
0.4b
(+ 1.0 (cos x))
1.2b
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
115×pow1
36×cos-mult pow-prod-up
27×associate-*l/
23×pow-prod-down
22×pow-sqr
18×frac-times pow-plus
16×add-cbrt-cube add-exp-log
15×cbrt-div
13×pow2
12×associate-*r/
11×add-sqr-sqrt
8×*-un-lft-identity prod-exp cbrt-unprod add-log-exp
4×add-cube-cbrt difference-of-squares
2×sqr-cos
1×cbrt-prod distribute-rgt-in +-commutative sum-log sub-neg unpow-prod-down distribute-lft-in flip3-+ flip3-- pow1/3 diff-log cube-prod swap-sqr associate-*r* associate-*l* *-commutative flip-+ flip-- distribute-lft-out distribute-lft-out-- unswap-sqr sqr-pow
Counts
4 → 121
Calls
4 calls:
42.0ms
(* (* (cos x) (cos x)) (* (cos x) (cos x)))
1.6s
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
5.0ms
(+ 1.0 (cos x))
19.0ms
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* (cos x) (cos x)) (* (cos x) (cos x)))
61.0ms
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
18.0ms
(+ 1.0 (cos x))
73.0ms
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x))))

simplify1.8s

Counts
133 → 133
Iterations
IterNodes
done5000
21498
1502
0204

prune543.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes331.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.8b

bsearch210.0ms

Steps
ItersRangePoint
11
3.4817375791661903e-26
573579.0075499975
0.02105783752125853
10
-84463.33967257517
-3.2432757514909933e-09
-0.02231715051571105

simplify20.0ms

Iterations
IterNodes
done69
169
053

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.7s1642×body2560valid
3.4s2753×body1280valid
946.0ms1876×body640valid
271.0ms927×body320valid
146.0ms452×body160valid
37.0ms345×body80valid
36.0ms5×body5120valid