Details

Time bar (total: 10.8s)

analyze1.4s

Algorithm
search

sample207.0ms

Algorithm
intervals
Results
115.0ms61×body2560valid
60.0ms95×body1280valid
14.0ms54×body640valid
5.0ms26×body320valid
2.0ms13×body160valid
1.0ms7×body80valid

simplify366.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

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)))
0.6b
(- x (sin x))
0.6b
(- x (tan x))

rewrite20.0ms

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:
7.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
5.0ms
(- x (tan x))

series38.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- x (sin x)) (- x (tan x)))
5.0ms
(- x (sin x))
20.0ms
(- x (tan x))

simplify155.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune85.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
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))
16.3b
(- (* 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))

series15.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(* 27/2800 (pow x 4))
3.0ms
(* 9/40 (pow x 2))
6.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0273349
11123316
25001313

prune102.0ms

Filtered
46 candidates to 75 candidates (-63.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New74175
Fresh022
Picked101
Done000
Total75378

Merged error: 0b

Counts
78 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.2b
(* 9/40 (pow x 2))
16.3b
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite15.0ms

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
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- diff-log flip--
Counts
3 → 64
Calls
3 calls:
5.0ms
(* 27/2800 (pow x 4))
5.0ms
(* 9/40 (pow x 2))
4.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series16.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 27/2800 (pow x 4))
3.0ms
(* 9/40 (pow x 2))
9.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0249308
11003278
25001273

prune96.0ms

Filtered
45 candidates to 73 candidates (-62.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh022
Picked011
Done000
Total73376

Merged error: 0b

Counts
76 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
0.5b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.6b
(- x (tan x))
0.6b
(- x (tan x))

rewrite39.0ms

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

series65.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (sin x) (- x (tan x)))
31.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms
(- x (tan x))
12.0ms
(- x (tan x))

simplify38.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0376909
11205870
25001870

prune85.0ms

Filtered
81 candidates to 106 candidates (-30.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1060106
Fresh011
Picked011
Done011
Total1063109

Merged error: 0b

Counts
109 → 3

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch55.0ms

Steps
ItersRangePoint
10
6.545874801836178e-09
3343307.0532596326
0.029103049480390254
9
-661554.6714150684
-0.0017437851657503233
-0.031011876855453882

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914

end0.0ms

analyze1.1s

Algorithm
search

sample6.7s

Algorithm
intervals
Results
4.1s1643×body2560valid
1.6s2755×body1280valid
499.0ms1820×body640valid
162.0ms911×body320valid
62.0ms495×body160valid
34.0ms376×body80valid

Profiling

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