Details

Time bar (total: 8.3s)

sample492.0ms

Algorithm
intervals
Results
127.0ms57×body2560valid
48.0ms91×body1280valid
17.0ms58×body640valid
4.0ms24×body320valid
2.0ms14×body160valid
1.0ms12×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0135
1175
2195
3195

prune6.0ms

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: 32.2b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.4b
(- x (tan x))
1.4b
(- 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
add-log-exp
add-exp-log associate-/r* add-cbrt-cube associate-/l*
flip3-- flip--
pow1
sub-neg diff-log associate-/r/ associate-/l/
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))

series39.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- x (sin x)) (- x (tan x)))
12.0ms
(- x (tan x))
14.0ms
(- x (sin x))

simplify146.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune291.0ms

Filtered
89 candidates to 63 candidates (29.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New87289
Fresh000
Picked011
Done000
Total87390

Merged error: 0b

Counts
90 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 9/40 (pow x 2))
0.3b
(* 27/2800 (pow x 4))
16.1b
(- (* 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
add-cube-cbrt *-un-lft-identity
unpow-prod-down add-log-exp
add-cbrt-cube unswap-sqr
associate-*l* prod-exp
sqr-pow
pow1
pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
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))

series12.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(* 9/40 (pow x 2))
4.0ms
(* 27/2800 (pow x 4))
6.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify40.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273349
11123316
25002313

prune199.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New75075
Fresh011
Picked011
Done011
Total75378

Merged error: 0b

Counts
78 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (sin x))
1.4b
(- x (sin x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
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))
4.0ms
(- x (sin x))
4.0ms
(- x (sin x))

series33.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- x (tan x))
10.0ms
(- x (tan x))
7.0ms
(- x (sin x))
5.0ms
(- x (sin x))

simplify66.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0150314
1342292
2774292
32023292
45001292

prune193.0ms

Filtered
68 candidates to 50 candidates (26.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New68068
Fresh000
Picked011
Done022
Total68371

Merged error: 0b

Counts
71 → 3

regimes106.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch84.0ms

Steps
ItersRangePoint
10
4.00241138285282e-13
41.84587058567329
1.5574844804023975
7
-0.4867936294477796
-0.0038973504402139516
-0.029703902819011946

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02824
12824

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.1s1642×body2560valid
1.5s2745×body1280valid
459.0ms1871×body640valid
151.0ms938×body320valid
55.0ms451×body160valid
25.0ms353×body80valid

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