Details

Time bar (total: 6.3s)

sample135.0ms

Algorithm
intervals
Results
68.0ms53×body2560valid
36.0ms83×body1280valid
16.0ms69×body640valid
5.0ms29×body320valid
1.0ms13×body160valid
1.0ms9×body80valid

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: 32.6b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.7b
(- 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))

series58.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify80.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune160.0ms

Filtered
58 candidates to 42 candidates (72.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New431558
Fresh000
Picked101
Done000
Total441559

Merged error: 0.2b

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
(* 1/24 (pow x 3))
0.3b
(* 1/240 (pow x 5))

rewrite25.0ms

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)))
6.0ms
(* 1/24 (pow x 3))
9.0ms
(* 1/240 (pow x 5))

series147.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
40.0ms
(* 1/24 (pow x 3))
47.0ms
(* 1/240 (pow x 5))

simplify45.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0301375
11301346
25001346

prune164.0ms

Filtered
78 candidates to 49 candidates (62.8%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh01414
Picked011
Done000
Total781593

Merged error: 0.2b

Counts
93 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b
(exp (log (- 1.0 (cos x))))
0.3b
(log (- 1.0 (cos x)))
1.7b
(- 1.0 (cos x))

rewrite23.0ms

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))
5.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(log (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series149.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
24.0ms
(exp (log (- 1.0 (cos x))))
73.0ms
(log (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))

simplify82.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0289829
1791761
22667734
35001708

prune211.0ms

Filtered
110 candidates to 66 candidates (60.0%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1037110
Fresh7613
Picked101
Done011
Total11114125

Merged error: 0.2b

Counts
125 → 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)))
1.7b
(- 1.0 (cos x))

rewrite29.0ms

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)))
3.0ms
(- 1.0 (cos x))

series91.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms
(/ (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
05101593
123961450
250021337

prune197.0ms

Filtered
168 candidates to 85 candidates (50.6%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1662168
Fresh21012
Picked011
Done011
Total16814182

Merged error: 0.2b

Counts
182 → 14

regimes124.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.1b

bsearch75.0ms

Steps
ItersRangePoint
9
2.8262556577633816e-09
1.3569245790634763
0.022979987068408314
7
-5.155753157609302
-0.022529268385055725
-0.023966108920839193

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04528
14528

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s1570×body2560valid
1.3s2827×body1280valid
661.0ms1918×body640valid
151.0ms900×body320valid
65.0ms456×body160valid
24.0ms6×body5120valid
22.0ms323×body80valid

Profiling

Loading profile data...