Details

Time bar (total: 19.4s)

sample252.0ms

Algorithm
intervals
Results
110.0ms51×body2560valid
88.0ms86×body1280valid
27.0ms65×body640valid
8.0ms27×body320valid
3.0ms18×body160valid
1.0ms9×body80valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite34.0ms

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-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
19.0ms
(/ (- 1.0 (cos x)) (sin x))
12.0ms
(- 1.0 (cos x))

series111.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(/ (- 1.0 (cos x)) (sin x))
29.0ms
(- 1.0 (cos x))

simplify2.8s

Counts
58 → 58
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
0106665
1235645
2531609
31194609
43136608
done5000608

prune232.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
125.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
4.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
63.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series298.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
36.0ms
(pow (cos x) 3)
15.0ms
(+ (cos x) 1.0)
64.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.7s

Counts
201 → 201
Iterations

Useful iterations: 2 (538.0ms)

IterNodesCost
02645407
16115084
220384978
done50004978

prune875.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
0.4b
(+ (cos x) 1.0)
1.4b
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
70×times-frac
53×*-un-lft-identity
25×unpow-prod-down cube-prod difference-of-squares
17×add-cube-cbrt
16×distribute-lft-out--
11×sqr-pow
10×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×flip3-+ associate-/r/ flip-+
3×pow-unpow distribute-rgt-out--
2×+-commutative sum-log div-inv distribute-lft-out
1×cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-exp frac-sub flip-- sub-div rem-cube-cbrt
Counts
4 → 105
Calls
4 calls:
4.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
7.0ms
(+ (cos x) 1.0)
322.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(pow (cos x) 3)
19.0ms
(+ (cos x) 1.0)
19.0ms
(+ (cos x) 1.0)
397.0ms
(- (/ (pow 1.0 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (/ (pow (cos x) 3) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))))

simplify1.3s

Counts
117 → 117
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
01883626
14413499
213603379
done50003379

prune661.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
1.4b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
32×difference-of-squares
31×*-un-lft-identity
27×unpow-prod-down cube-prod
26×log-pow
25×exp-prod
17×sqr-pow
10×distribute-lft-out--
9×add-cube-cbrt
8×add-log-exp
6×pow1
5×add-exp-log log-prod add-cbrt-cube
3×pow-unpow
2×difference-cubes sub-neg exp-sum
1×+-commutative cube-mult pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log unpow3 rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 109
Calls
4 calls:
5.0ms
(pow (cos x) 3)
7.0ms
(+ (cos x) 1.0)
31.0ms
(- (pow 1.0 3) (pow (cos x) 3))
120.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series216.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
79.0ms
(- (pow 1.0 3) (pow (cos x) 3))
82.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify900.0ms

Counts
121 → 121
Iterations

Useful iterations: 2 (209.0ms)

IterNodesCost
01691422
13471208
29591152
done50001152

prune442.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

regimes158.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch116.0ms

Steps
ItersRangePoint
9
5.155942382976535e-09
0.21963308938311268
0.022836634539273117
11
-2445851338.3862987
-4.2674702477225e-16
-0.026676798341091105

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04067
14767
done4767

end0.0ms

sample8.0s

Algorithm
intervals
Results
4.1s1589×body2560valid
2.2s2733×body1280valid
1.0s1880×body640valid
266.0ms944×body320valid
150.0ms476×body160valid
40.0ms375×body80valid
10.0ms3×body5120valid