Details

Time bar (total: 9.1s)

analyze5.0ms

Algorithm
search

sample248.0ms

Algorithm
intervals
Results
179.0ms97×body2560valid
45.0ms73×body1280valid
8.0ms48×body640valid
4.0ms256×pre80true
2.0ms21×body320valid
1.0ms17×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
1114
2114

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.0b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (tan x))
4.2b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×*-un-lft-identity
19×times-frac
12×add-cube-cbrt
5×distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
3×associate-/r* div-inv associate-/l*
2×pow1
1×tan-quot cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num associate-/r/ frac-sub flip--
Counts
2 → 50
Calls
2 calls:
4.0ms
(/ 1.0 (tan x))
13.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series31.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(/ 1.0 (tan x))
20.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify52.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0232342
1610327
21880327
35002326

prune88.0ms

Filtered
46 candidates to 56 candidates (-21.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New55156
Fresh000
Picked101
Done000
Total56157

Merged error: 0.3b

Counts
57 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b
(* 0.022222222222222223 (pow x 3))
0.1b
(* 0.0021164021164021165 (pow x 5))

rewrite22.0ms

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
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
6.0ms
(* 0.022222222222222223 (pow x 3))
6.0ms
(* 0.0021164021164021165 (pow x 5))

series16.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms
(* 0.022222222222222223 (pow x 3))
5.0ms
(* 0.0021164021164021165 (pow x 5))

simplify46.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0301381
11298348
25001348

prune141.0ms

Filtered
49 candidates to 78 candidates (-59.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New73578
Fresh000
Picked101
Done000
Total74579

Merged error: 0.2b

Counts
79 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
0.0b
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
0.1b
(* 0.022222222222222223 (pow x 3))
0.1b
(* 0.0021164021164021165 (pow x 5))

rewrite25.0ms

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:
5.0ms
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
7.0ms
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
6.0ms
(* 0.022222222222222223 (pow x 3))
5.0ms
(* 0.0021164021164021165 (pow x 5))

series27.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
6.0ms
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
4.0ms
(* 0.022222222222222223 (pow x 3))
5.0ms
(* 0.0021164021164021165 (pow x 5))

simplify53.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0349485
11525454
25002454

prune151.0ms

Filtered
58 candidates to 92 candidates (-58.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh044
Picked011
Done000
Total92597

Merged error: 0.2b

Counts
97 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
19.0ms
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
6.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series85.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
20.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
20.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
20.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify65.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04962207
119322080
250011862

prune553.0ms

Filtered
75 candidates to 99 candidates (-32.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New90999
Fresh213
Picked011
Done011
Total9212104

Merged error: 0.1b

Counts
104 → 12

regimes129.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0187
1187

end0.0ms

analyze4.0ms

Algorithm
search

sample7.2s

Algorithm
intervals
Results
5.3s3243×body2560valid
1.3s2453×body1280valid
235.0ms1258×body640valid
129.0ms8000×pre80true
76.0ms669×body320valid
27.0ms336×body160valid
2.0ms41×body80valid

Profiling

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