Details

Time bar (total: 9.5s)

sample515.0ms

Algorithm
intervals
Results
178.0ms60×body2560valid
59.0ms96×body1280valid
15.0ms51×body640valid
4.0ms24×body320valid
2.0ms14×body160valid
1.0ms11×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune5.0ms

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: 34.0b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.3b
(- x (sin x))
1.8b
(- 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:
22.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series173.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ (- x (sin x)) (- x (tan x)))
37.0ms
(- x (sin x))
61.0ms
(- x (tan x))

simplify150.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune233.0ms

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))
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
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))

series108.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 27/2800 (pow x 4))
24.0ms
(* 9/40 (pow x 2))
48.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0273349
11123316
25001313

prune172.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New74175
Fresh022
Picked101
Done000
Total75378

Merged error: 0.0b

Counts
78 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
0.1b
(* 27/2800 (pow x 4))
0.2b
(* 9/40 (pow x 2))
16.1b
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
12×*-un-lft-identity
11×add-log-exp
10×add-cube-cbrt
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 diff-log sqr-pow
3×sub-neg
2×pow-to-exp flip3-- pow-exp associate--l+ *-commutative flip-- cbrt-unprod unpow2
1×associate--l- distribute-lft-out-- difference-of-squares
Counts
4 → 82
Calls
4 calls:
7.0ms
(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
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)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
35.0ms
(* 27/2800 (pow x 4))
30.0ms
(* 9/40 (pow x 2))
105.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify49.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0308474
11219442
25001431

prune215.0ms

Filtered
94 candidates to 59 candidates (62.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh022
Picked011
Done000
Total94397

Merged error: 0.0b

Counts
97 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
1.3b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.8b
(- x (tan x))
1.8b
(- x (tan x))

rewrite41.0ms

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

series340.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (sin x) (- x (tan x)))
183.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
48.0ms
(- x (tan x))
53.0ms
(- x (tan x))

simplify45.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0376909
11205870
25001870

prune270.0ms

Filtered
106 candidates to 81 candidates (76.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1051106
Fresh011
Picked101
Done011
Total1063109

Merged error: 0b

Counts
109 → 3

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch95.0ms

Steps
ItersRangePoint
10
1.4708384485510602e-10
911.8039404667869
0.03188057778463301
8
-4.115764337816432
-0.0035716639301171917
-0.029947781002591788

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04038
14038

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.2s1659×body2560valid
1.6s2733×body1280valid
476.0ms1886×body640valid
159.0ms928×body320valid
51.0ms427×body160valid
28.0ms367×body80valid

Profiling

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