Details

Time bar (total: 23.1s)

sample210.0ms

Algorithm
intervals
Results
107.0ms57×body2560valid
57.0ms82×body1280valid
22.0ms58×body640valid
10.0ms38×body320valid
2.0ms13×body160valid
1.0ms8×body80valid

simplify13.0ms

Counts
1 → 1
Iterations
IterNodes
done16
316
214
111
06

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize65.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:
18.0ms
(/ (- 1.0 (cos x)) (sin x))
10.0ms
(- 1.0 (cos x))

series74.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (- 1.0 (cos x)) (sin x))
22.0ms
(- 1.0 (cos x))

simplify1.5s

Counts
58 → 58
Iterations
IterNodes
done5002
31941
2596
1240
0106

prune369.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite41.0ms

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:
4.0ms
(/ 1.0 (sin x))
7.0ms
(/ (cos x) (sin x))
28.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(/ 1.0 (sin x))
28.0ms
(/ (cos x) (sin x))
106.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.8s

Counts
86 → 86
Iterations
IterNodes
done5000
32129
2783
1302
0146

prune493.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

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))

rewrite48.0ms

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:
10.0ms
(* (cos x) (cos x))
5.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
20.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series152.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cos x) (cos x))
37.0ms
(pow (cos x) 3)
16.0ms
(+ 1.0 (cos x))
73.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify3.1s

Counts
108 → 108
Iterations
IterNodes
done5009
33848
21174
1407
0152

prune592.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

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))))

rewrite2.4s

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:
37.0ms
(* (* (cos x) (cos x)) (* (cos x) (cos x)))
2.3s
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
20.0ms
(+ 1.0 (cos x))
25.0ms
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x))))

series178.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* (cos x) (cos x)) (* (cos x) (cos x)))
46.0ms
(cbrt (* (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (* (cos x) (cos x)) (* (cos x) (cos x)))) (cos x)))
14.0ms
(+ 1.0 (cos x))
87.0ms
(- (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

prune514.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes386.0ms

Accuracy

98.7% (0.4b remaining)

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

bsearch143.0ms

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

simplify32.0ms

Iterations
IterNodes
done69
169
053

end0.0ms

sample8.9s

Algorithm
intervals
Results
4.0s1642×body2560valid
2.6s2753×body1280valid
1.1s1876×body640valid
483.0ms452×body160valid
390.0ms927×body320valid
47.0ms345×body80valid
46.0ms5×body5120valid