Details

Time bar (total: 9.4s)

sample437.0ms

Algorithm
intervals
Results
111.0ms46×body2560valid
45.0ms90×body1280valid
16.0ms55×body640valid
7.0ms38×body320valid
2.0ms15×body160valid
1.0ms12×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

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: 28.3b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.7b
(- x (tan x))
1.7b
(- x (sin x))

rewrite37.0ms

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:
24.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series177.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
59.0ms
(- x (tan x))
41.0ms
(- x (sin x))

simplify155.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune181.0ms

Filtered
89 candidates to 63 candidates (70.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh000
Picked101
Done000
Total86490

Merged error: 0.1b

Counts
90 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (- x (tan x)))
1.6b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b
(- x (tan x))
1.7b
(- x (tan x))

rewrite42.0ms

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)))
26.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series335.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (sin x) (- x (tan x)))
177.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
49.0ms
(- x (tan x))
53.0ms
(- x (tan x))

simplify42.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0376909
11205870
25001870

prune209.0ms

Filtered
106 candidates to 80 candidates (75.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1051106
Fresh033
Picked011
Done000
Total1055110

Merged error: 0.0b

Counts
110 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b
(- x (tan x))
1.7b
(- x (tan x))
1.7b
(- x (tan x))
1.7b
(- x (tan x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series207.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- x (tan x))
54.0ms
(- x (tan x))
54.0ms
(- x (tan x))
49.0ms
(- x (tan x))

simplify156.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
091324
1200300
2471300
31247300
44646300
55001300

prune190.0ms

Filtered
68 candidates to 52 candidates (76.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh033
Picked011
Done011
Total68573

Merged error: 0.0b

Counts
73 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 9/40 (pow x 2))
0.3b
(* 27/2800 (pow x 4))
17.8b
(- (* 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
(* 9/40 (pow x 2))
5.0ms
(* 27/2800 (pow x 4))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series114.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* 9/40 (pow x 2))
36.0ms
(* 27/2800 (pow x 4))
48.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0273349
11123316
25002313

prune116.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New74175
Fresh022
Picked011
Done022
Total74680

Merged error: 0.0b

Counts
80 → 6

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch70.0ms

Steps
ItersRangePoint
10
2.7173623733142798e-14
0.17152303280385153
0.033465152062373035
6
-0.06221852409423964
-0.011085094476318487
-0.027581656900530344

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03014
13014

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.3s1627×body2560valid
1.6s2690×body1280valid
505.0ms1902×body640valid
179.0ms948×body320valid
65.0ms484×body160valid
26.0ms349×body80valid

Profiling

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