Details

Time bar (total: 10.5s)

sample536.0ms

Algorithm
intervals
Results
130.0ms52×body2560valid
49.0ms74×body1280valid
19.0ms65×body640valid
8.0ms41×body320valid
1.0ms12×body160valid
1.0ms12×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.6b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.1b
(- x (tan x))
1.1b
(- x (sin x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 80
Calls
3 calls:
8.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series204.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(/ (- x (sin x)) (- x (tan x)))
69.0ms
(- x (tan x))
46.0ms
(- x (sin x))

simplify150.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune295.0ms

Filtered
89 candidates to 63 candidates (29.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New86389
Fresh000
Picked101
Done000
Total87390

Merged error: 0.0b

Counts
90 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
12.6b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×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×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- sum-log flip-- associate--r+
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 27/2800 (pow x 4))
5.0ms
(* 9/40 (pow x 2))
6.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series132.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(* 27/2800 (pow x 4))
29.0ms
(* 9/40 (pow x 2))
58.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0273349
11123316
25001313

prune197.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh022
Picked011
Done000
Total75378

Merged error: 0.0b

Counts
78 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (- x (tan x)))
1.0b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.1b
(- x (tan x))
1.1b
(- x (tan x))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
44×add-sqr-sqrt
33×times-frac
18×distribute-lft-out--
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
6×add-exp-log flip3-- associate-/r/ add-cbrt-cube flip--
5×associate-/r*
4×pow1
3×sub-neg distribute-rgt-out-- diff-log div-inv associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num frac-sub sub-div
Counts
4 → 94
Calls
4 calls:
6.0ms
(/ (sin x) (- x (tan x)))
28.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))

series383.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (sin x) (- x (tan x)))
199.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
56.0ms
(- x (tan x))
60.0ms
(- x (tan x))

simplify38.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0376909
11205870
25001870

prune423.0ms

Filtered
106 candidates to 80 candidates (24.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1042106
Fresh011
Picked101
Done011
Total1054109

Merged error: 0.0b

Counts
109 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b
(- x (tan x))
1.1b
(- x (tan x))
1.1b
(- x (tan x))
1.1b
(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
118×add-sqr-sqrt
80×times-frac
68×unpow-prod-down cube-prod
52×distribute-lft-out--
47×difference-of-squares
16×associate-/r/
12×add-cube-cbrt flip3-- distribute-rgt-out-- flip-- add-log-exp sqr-pow
8×div-inv
4×pow1 add-exp-log cube-div sub-neg diff-log add-cbrt-cube
1×difference-cubes frac-sub sub-div
Counts
4 → 138
Calls
4 calls:
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
91.0ms
(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

series440.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- x (tan x))
61.0ms
(- x (tan x))
56.0ms
(- x (tan x))
263.0ms
(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

simplify60.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721887
116961857
250021857

prune670.0ms

Filtered
150 candidates to 78 candidates (48.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1500150
Fresh022
Picked011
Done011
Total1504154

Merged error: 0.0b

Counts
154 → 4

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch85.0ms

Steps
ItersRangePoint
8
3.9971791970784e-05
0.9384348231062936
0.02165258737934737
7
-0.04031575958609914
-0.0011811564698516964
-0.028030499297402853

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04138
14138

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.0s1627×body2560valid
1.6s2736×body1280valid
485.0ms1870×body640valid
160.0ms948×body320valid
53.0ms458×body160valid
25.0ms361×body80valid

Profiling

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