Details

Time bar (total: 22.2s)

sample237.0ms

Algorithm
intervals
Results
111.0ms48×body2560valid
73.0ms89×body1280valid
27.0ms62×body640valid
8.0ms27×body320valid
4.0ms19×body160valid
1.0ms11×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06202
111202
214202
316202
done16202

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
2.1b
(- 1.0 (cos x))

rewrite53.0ms

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:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
10.0ms
(- 1.0 (cos x))

series78.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(/ (- 1.0 (cos x)) (sin x))
24.0ms
(- 1.0 (cos x))

simplify896.0ms

Counts
58 → 58
Iterations

Useful iterations: done (892.0ms)

IterNodesCost
010619054
124017685
280517605
done500017525

prune321.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.3b
(* (cos x) (cos x))
0.5b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
16×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log add-log-exp
6×swap-sqr associate-*r* associate-*l*
5×sqr-cos
2×pow2 pow-plus cube-unmult pow-prod-down prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod associate--r+ unswap-sqr
1×distribute-rgt-in difference-cubes +-commutative associate-+l+ sum-log sub-neg distribute-lft-in flip3-+ distribute-rgt-out flip3-- diff-log flip-+ flip--
Counts
4 → 82
Calls
4 calls:
15.0ms
(* (cos x) (cos x))
18.0ms
(* (cos x) (cos x))
14.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
34.0ms
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (cos x) (cos x))
31.0ms
(* (cos x) (cos x))
78.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
61.0ms
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (* (cos x) (cos x))))

simplify3.3s

Counts
94 → 94
Iterations

Useful iterations: done (3.3s)

IterNodesCost
012122747
135417544
2277717293
done500117213

prune564.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.5b
(log (exp (* (cos x) (cos x))))
0.5b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (log (exp (* (cos x) (cos x))))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×pow1 log-prod
11×*-un-lft-identity add-cube-cbrt
9×add-log-exp
8×associate--r+
6×add-cbrt-cube add-exp-log
5×sqr-cos
4×distribute-rgt-in distribute-lft-in
3×swap-sqr associate-*r* associate-*l* exp-sum log-pow
1×pow2 +-commutative associate-+l+ exp-prod sum-log sub-neg flip3-+ pow-plus distribute-rgt-out flip3-- exp-to-pow diff-log rem-log-exp pow-prod-down prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 75
Calls
4 calls:
9.0ms
(* (cos x) (cos x))
4.0ms
(log (exp (* (cos x) (cos x))))
11.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
49.0ms
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (log (exp (* (cos x) (cos x))))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (cos x) (cos x))
19.0ms
(log (exp (* (cos x) (cos x))))
50.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
61.0ms
(- (* 1.0 (* 1.0 1.0)) (* (cos x) (log (exp (* (cos x) (cos x))))))

simplify3.3s

Counts
87 → 87
Iterations

Useful iterations: done (3.3s)

IterNodesCost
015227784
140518972
2278418519
done500018397

prune576.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) (sin x)))
0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
48×difference-of-squares
41×*-un-lft-identity
39×unpow-prod-down cube-prod
25×times-frac associate-/l* sqr-pow
15×distribute-lft-out--
10×add-cbrt-cube add-exp-log
9×add-cube-cbrt
8×add-log-exp
5×pow1
3×difference-cubes pow-unpow
2×cbrt-undiv flip3-+ flip3-- div-exp associate-*l/ associate-/r/ flip-+ flip-- associate-/l/
1×cube-mult pow-to-exp +-commutative clear-num associate-/r* sum-log sub-neg pow-pow frac-2neg diff-log unpow3 div-sub pow-exp prod-exp cbrt-unprod div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 139
Calls
4 calls:
134.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) (sin x)))
5.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
25.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series409.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) (sin x)))
51.0ms
(pow (cos x) 3)
20.0ms
(+ 1.0 (cos x))
81.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.5s

Counts
151 → 151
Iterations

Useful iterations: 2 (960.0ms)

IterNodesCost
0220120453
163379043
2314075443
done500075443

prune669.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes181.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.2b

bsearch132.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
160.65039477392645
0.021092325268080338
8
-0.9341403346610884
-0.003292329160956242
-0.02266404857182586

simplify17.0ms

Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
0502060
1692060
done692060

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.3s1619×body2560valid
2.7s2702×body1280valid
991.0ms1905×body640valid
654.0ms923×body320valid
96.0ms502×body160valid
37.0ms345×body80valid
24.0ms4×body5120valid