Details

Time bar (total: 6.1s)

sample150.0ms

Algorithm
intervals
Results
79.0ms55×body2560valid
38.0ms86×body1280valid
17.0ms63×body640valid
5.0ms29×body320valid
1.0ms12×body160valid
1.0ms11×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0167
1167

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
2.6b
(- 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))

series18.0ms

Counts
2 → 6
Calls
2 calls:
14.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify48.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05700608

prune137.0ms

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: 0.2b

Counts
59 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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)) (* x 1/2))
7.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series29.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (* 1/240 (pow x 5)) (* x 1/2))
8.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify47.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05088875

prune188.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New91192
Fresh11213
Picked101
Done000
Total9313106

Merged error: 0.2b

Counts
106 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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-+l+ unpow3
Counts
4 → 80
Calls
4 calls:
7.0ms
(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* x 1/2))
4.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series27.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5))) (* x 1/2))
12.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify46.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05072909

prune185.0ms

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

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01212
Picked011
Done000
Total9213105

Merged error: 0.2b

Counts
105 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b
(log (- 1.0 (cos x)))
0.3b
(exp (log (- 1.0 (cos x))))
2.6b
(- 1.0 (cos x))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
30×log-prod
25×exp-sum
24×add-cube-cbrt times-frac
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×exp-prod flip3-- exp-diff flip--
3×associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 98
Calls
4 calls:
8.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms
(log (- 1.0 (cos x)))
4.0ms
(exp (log (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))

series29.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
15.0ms
(log (- 1.0 (cos x)))
3.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

simplify41.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050491090

prune121.0ms

Filtered
66 candidates to 110 candidates (-66.7%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1073110
Fresh11011
Picked011
Done011
Total10815123

Merged error: 0.2b

Counts
123 → 15

regimes191.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.2b

bsearch32.0ms

Steps
ItersRangePoint
7
0.003810670139712195
0.06592465963988953
0.024437279157310036
8
-0.6973264211480649
-0.00018277710226217338
-0.021854661524483378

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04355
14355

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.3s1621×body2560valid
1.4s2784×body1280valid
488.0ms1812×body640valid
170.0ms962×body320valid
55.0ms457×body160valid
25.0ms357×body80valid
20.0ms7×body5120valid

Profiling

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