Details

Time bar (total: 6.8s)

sample142.0ms

Algorithm
intervals
Results
73.0ms56×body2560valid
38.0ms91×body1280valid
15.0ms59×body640valid
4.0ms24×body320valid
2.0ms14×body160valid
1.0ms12×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune10.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.9b
(- 1.0 (cos x))

rewrite11.0ms

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:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series12.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify78.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune202.0ms

Filtered
58 candidates to 42 candidates (27.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New431558
Fresh000
Picked101
Done000
Total441559

Merged error: 0.3b

Counts
59 → 15

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1 sum-log
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult associate-+r+ flip3-+ unpow3 flip-+
Counts
3 → 69
Calls
3 calls:
8.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms
(* 1/240 (pow x 5))
8.0ms
(* 1/24 (pow x 3))

series14.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify45.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0301375
11301346
25002346

prune246.0ms

Filtered
78 candidates to 49 candidates (37.2%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh01414
Picked011
Done000
Total781593

Merged error: 0.3b

Counts
93 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.3b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×associate-*r*
3×pow-unpow associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 92
Calls
4 calls:
6.0ms
(* (cos x) (+ (cos x) 1.0))
4.0ms
(+ (cos x) 1.0)
2.0ms
(pow (cos x) 3)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series18.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (cos x) (+ (cos x) 1.0))
2.0ms
(+ (cos x) 1.0)
5.0ms
(pow (cos x) 3)
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0353593
11734555
25001535

prune533.0ms

Filtered
104 candidates to 61 candidates (41.3%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New977104
Fresh4913
Picked101
Done011
Total10217119

Merged error: 0.2b

Counts
119 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
0.4b
(pow (pow (cos x) 3) 3)
1.7b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
56×unpow-prod-down cube-prod
44×difference-of-squares
40×cbrt-prod
27×sqr-pow
18×*-un-lft-identity
14×add-cube-cbrt
8×add-log-exp
7×add-exp-log
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×cube-mult unpow3
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×+-commutative sub-neg flip3-- flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 135
Calls
4 calls:
4.0ms
(+ (cos x) 1.0)
3.0ms
(pow (cos x) 3)
5.0ms
(pow (pow (cos x) 3) 3)
25.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series23.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(+ (cos x) 1.0)
5.0ms
(pow (cos x) 3)
9.0ms
(pow (pow (cos x) 3) 3)
7.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify63.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04211014
11553953
25002916

prune549.0ms

Filtered
147 candidates to 60 candidates (59.2%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1425147
Fresh41115
Picked101
Done011
Total14717164

Merged error: 0.2b

Counts
164 → 17

regimes256.0ms

Accuracy

98.2% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04535
14535

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s1633×body2560valid
1.2s2748×body1280valid
462.0ms1874×body640valid
159.0ms930×body320valid
54.0ms460×body160valid
25.0ms353×body80valid
8.0ms2×body5120valid

Profiling

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