Details

Time bar (total: 9.5s)

sample47.0ms

Algorithm
intervals
Results
19.0ms44×body2560valid
8.0ms37×body1280valid
5.0ms38×body640valid
3.0ms32×body320valid
2.0ms80×body80valid
2.0ms25×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
1138
2218
3268
4298
done298

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
14.8b
(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
9.0ms
(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify1.6s

Counts
48 → 48
Iterations

Useful iterations: done (1.6s)

IterNodesCost
088507
1218489
2636441
32189441
done5000440

prune122.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (/ x (- 1.0 (cos x))))
0.1b
(/ x (- 1.0 (cos x)))
0.2b
(/ 1 (* x (/ x (- 1.0 (cos x)))))
1.9b
(- 1.0 (cos x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
42×*-un-lft-identity
34×times-frac
32×add-exp-log
26×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube
11×div-exp
9×pow1
8×prod-exp distribute-lft-out-- difference-of-squares
6×cbrt-undiv associate-/r* associate-/l* add-log-exp
5×associate-/r/
4×cbrt-unprod
3×rec-exp flip3-- 1-exp associate-*l* flip-- div-inv
2×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num unswap-sqr
1×sub-neg diff-log *-commutative inv-pow
Counts
4 → 124
Calls
4 calls:
17.0ms
(* x (/ x (- 1.0 (cos x))))
6.0ms
(/ x (- 1.0 (cos x)))
12.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
3.0ms
(- 1.0 (cos x))

series155.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* x (/ x (- 1.0 (cos x))))
45.0ms
(/ x (- 1.0 (cos x)))
42.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
22.0ms
(- 1.0 (cos x))

simplify2.3s

Counts
136 → 136
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01841539
14201416
210471282
338761244
done50011243

prune275.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.4b
(pow (cos x) 3)
0.6b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
21×*-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-exp-log add-cbrt-cube
5×distribute-lft-out--
3×pow-unpow swap-sqr associate-*r* associate-*l*
2×sqr-cos
1×difference-cubes +-commutative pow2 cube-mult pow-to-exp sub-neg associate-+l+ distribute-rgt-out flip3-- pow-pow flip3-+ pow-plus diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log pow-sqr cos-mult *-commutative pow-prod-up flip-- cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr
Counts
4 → 97
Calls
4 calls:
4.0ms
(* (cos x) (cos x))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
17.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series143.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (cos x) (cos x))
33.0ms
(pow (cos x) 3)
41.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
51.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify755.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
01591253
13641003
21395953
done5001953

prune324.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (* x (/ x (- (pow 1.0 3) (pow (cos x) 3)))) (+ (* 1.0 1.0) (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x)))))))
0.4b
(pow (cos x) 3)
0.6b
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x))))
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
33×add-sqr-sqrt
21×*-un-lft-identity
19×add-cbrt-cube
16×difference-of-squares
15×unpow-prod-down cube-prod prod-exp
11×pow1 div-exp add-log-exp
9×add-cube-cbrt sqr-pow
5×cbrt-undiv associate-*r/ associate-/r/ cbrt-unprod distribute-lft-out--
4×rec-exp 1-exp
3×pow-unpow pow-flip flip3-+ times-frac pow-prod-down sum-log flip-+ associate-/l*
2×frac-times
1×difference-cubes +-commutative cube-mult pow-to-exp sub-neg associate-+r+ flip3-- pow-pow frac-2neg diff-log unpow3 associate-*l/ pow-exp clear-num associate-/r* flip-- div-inv distribute-lft-out inv-pow rem-cube-cbrt
Counts
4 → 113
Calls
4 calls:
204.0ms
(/ 1 (* (* x (/ x (- (pow 1.0 3) (pow (cos x) 3)))) (+ (* 1.0 1.0) (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x)))))))
2.0ms
(pow (cos x) 3)
7.0ms
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x))))
17.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series301.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ 1 (* (* x (/ x (- (pow 1.0 3) (pow (cos x) 3)))) (+ (* 1.0 1.0) (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x)))))))
33.0ms
(pow (cos x) 3)
51.0ms
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* 1.0 (cos x))))
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify931.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (284.0ms)

IterNodesCost
02392805
16702585
224932256
done50002256

prune359.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes69.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.8b

bsearch76.0ms

Steps
ItersRangePoint
9
3.182061564411226e-09
0.0591185632533196
0.03476390489487963
8
-0.04390830018224924
-1.7961213486546931e-06
-0.02915897731694385

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
04367
15665
done5665

end0.0ms

sample1.6s

Algorithm
intervals
Results
751.0ms1610×body2560valid
283.0ms1251×body1280valid
206.0ms1470×body640valid
95.0ms947×body320valid
68.0ms2245×body80valid
39.0ms477×body160valid