Details

Time bar (total: 14.4s)

sample113.0ms

Algorithm
intervals
Results
44.0ms46×body2560valid
21.0ms35×body1280valid
17.0ms48×body640valid
7.0ms29×body320valid
7.0ms87×body80valid
2.0ms11×body160valid

simplify30.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize15.0ms

Local error

Found 2 expressions with local error:

1.1b
(- 1.0 (cos x))
12.9b
(/ (- 1.0 (cos x)) (* x x))

rewrite60.0ms

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:
29.0ms
(- 1.0 (cos x))
30.0ms
(/ (- 1.0 (cos x)) (* x x))

series117.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(- 1.0 (cos x))
80.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts
48 → 48
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
088507
1212489
2548441
31500441
done5000441

prune168.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.1b
(- 1.0 (cos x))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 114
Calls
3 calls:
71.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
17.0ms
(/ (- 1.0 (cos x)) x)
7.0ms
(- 1.0 (cos x))

series167.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
89.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(- 1.0 (cos x))

simplify2.5s

Counts
123 → 123
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01891536
14951379
215381227
done50001226

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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)) x))
0.4b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite187.0ms

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-exp-log add-cbrt-cube
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×+-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub pow-exp prod-exp clear-num associate-/r* sum-log cbrt-unprod div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 139
Calls
4 calls:
118.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
5.0ms
(pow (cos x) 3)
13.0ms
(+ 1.0 (cos x))
43.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series355.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
48.0ms
(pow (cos x) 3)
11.0ms
(+ 1.0 (cos x))
69.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.5s

Counts
151 → 151
Iterations

Useful iterations: 2 (449.0ms)

IterNodesCost
02183004
15572815
221212659
done50012659

prune523.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x) (- (pow 1.0 3) (pow (cos x) 3)))
0.4b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite150.0ms

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-/r* sqr-pow
15×distribute-lft-out--
10×add-exp-log add-cbrt-cube
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×+-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 pow-exp prod-exp clear-num sum-log cbrt-unprod div-inv distribute-lft-out associate-/l* rem-cube-cbrt
Counts
4 → 138
Calls
4 calls:
84.0ms
(/ (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x) (- (pow 1.0 3) (pow (cos x) 3)))
4.0ms
(pow (cos x) 3)
7.0ms
(+ 1.0 (cos x))
41.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series333.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x) (- (pow 1.0 3) (pow (cos x) 3)))
33.0ms
(pow (cos x) 3)
17.0ms
(+ 1.0 (cos x))
69.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: 2 (461.0ms)

IterNodesCost
02142939
15232715
220072559
done50012559

prune539.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch118.0ms

Steps
ItersRangePoint
9
0.0033303272193615503
311302.39110615524
0.030278781168554474
9
-7.35943201301068
-4.403108084983288e-07
-0.028173748830909656

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03581
14850
done4850

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s1594×body2560valid
618.0ms1227×body1280valid
434.0ms1421×body640valid
212.0ms964×body320valid
121.0ms2318×body80valid
56.0ms476×body160valid