Details

Time bar (total: 9.3s)

sample441.0ms

Algorithm
intervals
Results
101.0ms47×body2560valid
50.0ms83×body1280valid
18.0ms69×body640valid
6.0ms36×body320valid
1.0ms11×body160valid
1.0ms10×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

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: 32.0b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.9b
(- x (sin x))
1.9b
(- x (tan x))

rewrite36.0ms

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)))
4.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series170.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- x (sin x)) (- x (tan x)))
36.0ms
(- x (sin x))
61.0ms
(- x (tan x))

simplify155.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune173.0ms

Filtered
89 candidates to 63 candidates (70.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New86389
Fresh000
Picked101
Done000
Total87390

Merged error: 0.0b

Counts
90 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.2b
(* 9/40 (pow x 2))
14.8b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite22.0ms

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))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series105.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(* 27/2800 (pow x 4))
24.0ms
(* 9/40 (pow x 2))
44.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0273349
11123316
25001313

prune134.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh022
Picked011
Done000
Total75378

Merged error: 0.0b

Counts
78 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
1.8b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b
(- x (tan x))
1.9b
(- 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)))
27.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))

series334.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ (sin x) (- x (tan x)))
172.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms
(- x (tan x))
52.0ms
(- x (tan x))

simplify41.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0376909
11205870
25001870

prune202.0ms

Filtered
106 candidates to 80 candidates (75.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1060106
Fresh011
Picked011
Done011
Total1063109

Merged error: 0.0b

Counts
109 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (tan x) 3)
1.9b
(- (pow x 3) (pow (tan x) 3))
1.9b
(- x (sin x))
34.5b
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
159×add-sqr-sqrt
89×*-un-lft-identity
81×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
26×distribute-lft-out--
25×associate-/l*
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow flip3-- associate-/r* flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×tan-quot cbrt-undiv cube-div cube-mult pow-to-exp pow-pow frac-2neg flip3-+ unpow3 div-sub div-exp pow-exp clear-num flip-+ div-inv rem-cube-cbrt
Counts
4 → 192
Calls
4 calls:
3.0ms
(pow (tan x) 3)
11.0ms
(- (pow x 3) (pow (tan x) 3))
4.0ms
(- x (sin x))
25.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(pow (tan x) 3)
121.0ms
(- (pow x 3) (pow (tan x) 3))
34.0ms
(- x (sin x))
246.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (+ (* (tan x) (+ (tan x) x)) (pow x 2)))

simplify97.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06252980
126042910
250012831

prune412.0ms

Filtered
204 candidates to 106 candidates (52.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2031204
Fresh000
Picked101
Done022
Total2043207

Merged error: 0.0b

Counts
207 → 3

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.5b

bsearch85.0ms

Steps
ItersRangePoint
10
2.2826621327002547e-07
125321.6248081686
0.03348174306025857
9
-0.06461929534003709
-4.410039720853989e-10
-0.020486981416868083

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03014
13014

end0.0ms

sample6.2s

Algorithm
intervals
Results
3.7s1549×body2560valid
1.6s2762×body1280valid
487.0ms1878×body640valid
157.0ms939×body320valid
64.0ms490×body160valid
28.0ms382×body80valid

Profiling

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