Details

Time bar (total: 5.7s)

sample151.0ms

Algorithm
intervals
Results
76.0ms56×body2560valid
43.0ms88×body1280valid
15.0ms63×body640valid
4.0ms26×body320valid
1.0ms11×body160valid
1.0ms12×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.1b
(- 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))

series11.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

simplify78.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune129.0ms

Filtered
42 candidates to 58 candidates (-38.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New441458
Fresh000
Picked101
Done000
Total451459

Merged error: 0.1b

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))

rewrite27.0ms

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))
8.0ms
(* 1/24 (pow x 3))

series26.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (* 1/240 (pow x 5)) (* 1/2 x))
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))

simplify52.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0355458
11538429
25002428

prune175.0ms

Filtered
59 candidates to 92 candidates (-55.9%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01313
Picked011
Done000
Total9214106

Merged error: 0.1b

Counts
106 → 14

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)
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite26.0ms

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))
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
11.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series20.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (cos x) (+ (cos x) 1.0))
5.0ms
(pow (cos x) 3)
2.0ms
(+ (cos x) 1.0)
9.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify67.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0353593
11734555
25001535

prune186.0ms

Filtered
61 candidates to 104 candidates (-70.5%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1004104
Fresh21012
Picked101
Done011
Total10315118

Merged error: 0.1b

Counts
118 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.0b
(log (exp (pow (cos x) 3)))
1.9b
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
14×log-pow
12×add-cube-cbrt exp-prod
7×pow1 unpow-prod-down cube-prod add-log-exp
6×log-prod
5×add-exp-log add-cbrt-cube
4×difference-of-squares
3×pow-unpow associate--r+ sqr-pow
2×cube-mult unpow3 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 → 80
Calls
4 calls:
2.0ms
(pow (cos x) 3)
4.0ms
(+ (cos x) 1.0)
4.0ms
(log (exp (pow (cos x) 3)))
15.0ms
(- (pow 1.0 3) (log (exp (pow (cos x) 3))))

series21.0ms

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

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0296446
11109381
25001373

prune153.0ms

Filtered
60 candidates to 92 candidates (-53.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New88492
Fresh21113
Picked101
Done011
Total9116107

Merged error: 0.1b

Counts
107 → 16

regimes206.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04832
14832

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1586×body2560valid
1.2s2740×body1280valid
427.0ms1812×body640valid
165.0ms1008×body320valid
52.0ms477×body160valid
24.0ms373×body80valid
15.0ms4×body5120valid

Profiling

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