Details

Time bar (total: 18.4s)

sample118.0ms

Algorithm
intervals
Results
43.0ms45×body2560valid
25.0ms48×body1280valid
16.0ms48×body640valid
7.0ms29×body320valid
5.0ms71×body80valid
4.0ms15×body160valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
12.8b
(/ (- 1.0 (cos x)) (* x x))

rewrite50.0ms

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:
7.0ms
(- 1.0 (cos x))
41.0ms
(/ (- 1.0 (cos x)) (* x x))

series107.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(- 1.0 (cos x))
66.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts
64 → 64
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0116808
1301681
21709566
done5001553

prune206.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
2.0b
(- 1.0 (cos x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×add-sqr-sqrt *-un-lft-identity
76×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
9×prod-diff
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u fma-neg div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 165
Calls
3 calls:
51.0ms
(/ (/ (- 1.0 (cos x)) x) x)
34.0ms
(/ (- 1.0 (cos x)) x)
15.0ms
(- 1.0 (cos x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ (/ (- 1.0 (cos x)) x) x)
69.0ms
(/ (- 1.0 (cos x)) x)
27.0ms
(- 1.0 (cos x))

simplify1.9s

Counts
174 → 174
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02592577
16212361
229992187
done50002152

prune515.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

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) (+ (cos x) 1.0))))
0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite256.0ms

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:
131.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))))
7.0ms
(pow (cos x) 3)
22.0ms
(+ (cos x) 1.0)
58.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series351.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ (cos x) 1.0))))
50.0ms
(pow (cos x) 3)
18.0ms
(+ (cos x) 1.0)
101.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify4.7s

Counts
366 → 366
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
038211554
19478075
248856916
done50006916

prune612.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.5b
(+ (cos x) 1.0)
0.9b
(log (exp (pow (cos x) 3)))
1.8b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite126.0ms

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:
6.0ms
(pow (cos x) 3)
12.0ms
(+ (cos x) 1.0)
12.0ms
(log (exp (pow (cos x) 3)))
67.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series157.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (cos x) 3)
15.0ms
(+ (cos x) 1.0)
31.0ms
(log (exp (pow (cos x) 3)))
79.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

simplify3.9s

Counts
307 → 307
Iterations

Useful iterations: done (3.9s)

IterNodesCost
031010650
17526019
239523447
done50003446

prune475.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch123.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
0.03382760307135756
10
-2676750800.736259
-2.9526231381329305e-09
-0.03237572141906872

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03455
13755
done3755

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s1568×body2560valid
514.0ms1295×body1280valid
365.0ms1433×body640valid
208.0ms2324×body80valid
157.0ms944×body320valid
151.0ms436×body160valid