Details

Time bar (total: 13.8s)

sample71.0ms

Algorithm
intervals
Results
28.0ms50×body2560valid
13.0ms36×body1280valid
8.0ms46×body640valid
5.0ms76×body80valid
4.0ms27×body320valid
2.0ms21×body160valid

simplify19.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b
(- 1.0 (cos x))
13.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
12.0ms
(- 1.0 (cos x))
23.0ms
(/ (- 1.0 (cos x)) (* x x))

series128.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(- 1.0 (cos x))
96.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0116808
1269678
2747566
32669526
done5001517

prune183.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
2.3b
(- 1.0 (cos x))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
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×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u 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 → 132
Calls
3 calls:
75.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms
(/ (- 1.0 (cos x)) x)
8.0ms
(- 1.0 (cos x))

series168.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
55.0ms
(/ (- 1.0 (cos x)) x)
38.0ms
(- 1.0 (cos x))

simplify1.8s

Counts
141 → 141
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02191855
15561581
217411364
done50011323

prune416.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
0.4b
(+ 1.0 (cos x))
0.4b
(pow (cos x) 3)
2.1b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
165×*-un-lft-identity
144×prod-diff
138×unpow-prod-down cube-prod
113×add-cube-cbrt
80×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3
25×associate-/l* distribute-lft-out--
12×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp pow-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 354
Calls
4 calls:
136.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
7.0ms
(+ 1.0 (cos x))
8.0ms
(pow (cos x) 3)
65.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series384.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
17.0ms
(+ 1.0 (cos x))
47.0ms
(pow (cos x) 3)
90.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.2s

Counts
366 → 366
Iterations

Useful iterations: done (2.2s)

IterNodesCost
037811554
18167927
223476842
done50016120

prune811.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ 1.0 (cos x))
0.4b
(pow (cos x) 3)
1.2b
(log (exp (pow (cos x) 3)))
2.1b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
192×prod-diff
170×log-pow
156×exp-prod
119×add-sqr-sqrt
117×*-un-lft-identity
112×add-cube-cbrt
94×unpow-prod-down cube-prod
32×sqr-pow
31×cube-mult unpow3
19×pow1
12×fma-neg
7×add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-unpow fma-def associate--r+
2×distribute-lft-out--
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ diff-log rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 295
Calls
4 calls:
7.0ms
(+ 1.0 (cos x))
4.0ms
(pow (cos x) 3)
11.0ms
(log (exp (pow (cos x) 3)))
96.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series145.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ 1.0 (cos x))
30.0ms
(pow (cos x) 3)
30.0ms
(log (exp (pow (cos x) 3)))
72.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify1.8s

Counts
307 → 307
Iterations

Useful iterations: done (1.8s)

IterNodesCost
030910650
16235142
214943447
done50012484

prune456.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes93.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch111.0ms

Steps
ItersRangePoint
9
9.85435867085541e-08
110.15968793260775
0.031416007424221945
8
-0.1517943218839364
-1.6640733670284383e-05
-0.030204237643336285

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
050107
161107
done61107

end0.0ms

sample2.1s

Algorithm
intervals
Results
928.0ms1592×body2560valid
401.0ms1298×body1280valid
281.0ms1478×body640valid
142.0ms894×body320valid
94.0ms2272×body80valid
44.0ms466×body160valid