Details

Time bar (total: 9.3s)

sample456.0ms

Algorithm
intervals
Results
104.0ms43×body2560valid
53.0ms89×body1280valid
20.0ms68×body640valid
5.0ms31×body320valid
2.0ms15×body160valid
1.0ms10×body80valid

simplify13.0ms

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: 29.3b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
0.7b
(- x (sin x))
0.7b
(- x (tan x))

rewrite39.0ms

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:
25.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
7.0ms
(- x (tan x))

series182.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- x (sin x)) (- x (tan x)))
39.0ms
(- x (sin x))
64.0ms
(- x (tan x))

simplify157.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune185.0ms

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: 0b

Counts
90 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
0.4b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.7b
(- x (tan x))
0.7b
(- x (tan x))

rewrite46.0ms

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))))
6.0ms
(- x (tan x))
3.0ms
(- x (tan x))

series348.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (sin x) (- x (tan x)))
183.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms
(- x (tan x))
56.0ms
(- x (tan x))

simplify42.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0376909
11205870
25001870

prune211.0ms

Filtered
106 candidates to 80 candidates (75.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1060106
Fresh022
Picked011
Done000
Total1063109

Merged error: 0b

Counts
109 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
0.0b
(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.7b
(- x (sin x))
0.7b
(- x (tan x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt *-un-lft-identity
50×times-frac
32×log-pow
31×exp-prod
28×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×associate-/r/
3×log-prod
2×sub-neg diff-log div-sub div-inv associate-/l/
1×cbrt-undiv log-div frac-2neg exp-diff div-exp rem-log-exp clear-num
Counts
4 → 124
Calls
4 calls:
8.0ms
(/ (- x (sin x)) (- x (tan x)))
13.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
4.0ms
(- x (sin x))
3.0ms
(- x (tan x))

series251.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- x (sin x)) (- x (tan x)))
82.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
35.0ms
(- x (sin x))
52.0ms
(- x (tan x))

simplify45.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
04301079
112471026
250011026

prune286.0ms

Filtered
136 candidates to 95 candidates (69.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh011
Picked011
Done011
Total1363139

Merged error: 0b

Counts
139 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.5b
(* 9/40 (pow x 2))
17.1b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite19.0ms

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))

series115.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* 27/2800 (pow x 4))
32.0ms
(* 9/40 (pow x 2))
46.0ms
(- (* 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

prune126.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New75075
Fresh000
Picked011
Done022
Total75378

Merged error: 0b

Counts
78 → 3

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch78.0ms

Steps
ItersRangePoint
9
2.1876360655290875e-05
7233.4722653017725
0.027405454207531866
8
-1.5124741638829355
-8.4755032599275e-05
-0.03196661850967754

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03121
13121

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.0s1577×body2560valid
1.6s2750×body1280valid
510.0ms1922×body640valid
163.0ms920×body320valid
59.0ms471×body160valid
27.0ms360×body80valid

Profiling

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