Details

Time bar (total: 6.4s)

sample154.0ms

Algorithm
intervals
Results
89.0ms62×body2560valid
36.0ms77×body1280valid
13.0ms55×body640valid
4.0ms25×body320valid
2.0ms19×body80valid
2.0ms18×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite12.0ms

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))

series53.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify84.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22654373
35001373

prune150.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New441458
Fresh000
Picked101
Done000
Total451459

Merged error: 0.2b

Counts
59 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×cube-mult associate-+r+ unpow3
Counts
4 → 80
Calls
4 calls:
4.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
8.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series282.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
55.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
52.0ms
(* 1/240 (pow x 5))
39.0ms
(* 1/24 (pow x 3))

simplify53.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0355458
11538430
25002429

prune187.0ms

Filtered
92 candidates to 59 candidates (64.1%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01313
Picked011
Done000
Total9214106

Merged error: 0.2b

Counts
106 → 14

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b
(/ (sin x) (- 1.0 (cos x)))
2.0b
(- 1.0 (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
105×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 159
Calls
3 calls:
9.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms
(/ (sin x) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series95.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
41.0ms
(/ (sin x) (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))

simplify62.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05101595
123961452
250021339

prune228.0ms

Filtered
168 candidates to 85 candidates (50.6%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1635168
Fresh4812
Picked011
Done011
Total16715182

Merged error: 0.2b

Counts
182 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ (cos x) 1.0))
0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.8b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite28.0ms

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:
7.0ms
(* (cos x) (+ (cos x) 1.0))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
13.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series125.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (cos x) (+ (cos x) 1.0))
29.0ms
(pow (cos x) 3)
10.0ms
(+ (cos x) 1.0)
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify70.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0353593
11734555
25001535

prune206.0ms

Filtered
104 candidates to 61 candidates (58.7%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New995104
Fresh4812
Picked101
Done022
Total10415119

Merged error: 0.1b

Counts
119 → 15

regimes327.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 31.7b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03720
13720

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.2s1627×body2560valid
1.2s2716×body1280valid
453.0ms1897×body640valid
159.0ms920×body320valid
54.0ms496×body160valid
22.0ms341×body80valid
10.0ms3×body5120valid

Profiling

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