Details

Time bar (total: 14.3s)

sample72.0ms

Algorithm
intervals
Results
28.0ms46×body2560valid
13.0ms35×body1280valid
10.0ms48×body640valid
5.0ms29×body320valid
4.0ms87×body80valid
1.0ms11×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

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite48.0ms

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:
7.0ms
(- 1.0 (cos x))
38.0ms
(/ (- 1.0 (cos x)) (* x x))

series128.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(- 1.0 (cos x))
91.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts
48 → 48
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
088507
1212489
2548441
31500441
done5000441

prune190.0ms

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))

rewrite79.0ms

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:
46.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
22.0ms
(/ (- 1.0 (cos x)) x)
6.0ms
(- 1.0 (cos x))

series146.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
58.0ms
(/ (- 1.0 (cos x)) x)
24.0ms
(- 1.0 (cos x))

simplify2.6s

Counts
123 → 123
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01891536
14951379
215381227
done50001226

prune378.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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))

rewrite543.0ms

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:
470.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x))
4.0ms
(pow (cos x) 3)
7.0ms
(+ 1.0 (cos x))
50.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series405.0ms

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)) x))
34.0ms
(pow (cos x) 3)
17.0ms
(+ 1.0 (cos x))
96.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.3s

Counts
151 → 151
Iterations

Useful iterations: 2 (494.0ms)

IterNodesCost
02183004
15572815
221212659
done50012659

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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))

rewrite145.0ms

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:
87.0ms
(/ (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x) (- (pow 1.0 3) (pow (cos x) 3)))
6.0ms
(pow (cos x) 3)
12.0ms
(+ 1.0 (cos x))
33.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series335.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (* (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)) x) (- (pow 1.0 3) (pow (cos x) 3)))
47.0ms
(pow (cos x) 3)
16.0ms
(+ 1.0 (cos x))
56.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.4s

Counts
150 → 150
Iterations

Useful iterations: 2 (446.0ms)

IterNodesCost
02142939
15232715
220072559
done50012559

prune438.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch134.0ms

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

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03477
14750
done4750

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s1594×body2560valid
652.0ms1421×body640valid
514.0ms1227×body1280valid
271.0ms964×body320valid
138.0ms2318×body80valid
51.0ms476×body160valid