Details

Time bar (total: 8.3s)

sample428.0ms

Algorithm
intervals
Results
347.0ms62×body2560valid
44.0ms78×body1280valid
16.0ms63×body640valid
5.0ms28×body320valid
2.0ms16×body160valid
1.0ms9×body80valid

simplify11.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.1b
(- x (tan x))
1.1b
(- 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
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:
8.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series38.0ms

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

simplify157.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune93.0ms

Filtered
89 candidates to 63 candidates (29.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh000
Picked101
Done000
Total86490

Merged error: 0.0b

Counts
90 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.2b
(* 9/40 (pow x 2))
14.8b
(- (* 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
(* 27/2800 (pow x 4))
6.0ms
(* 9/40 (pow x 2))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series16.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 27/2800 (pow x 4))
7.0ms
(* 9/40 (pow x 2))
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
25001313

prune117.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New73275
Fresh033
Picked101
Done000
Total74579

Merged error: 0.0b

Counts
79 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.2b
(* 9/40 (pow x 2))
14.8b
(- (* 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
(* 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))

series11.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 27/2800 (pow x 4))
3.0ms
(* 9/40 (pow x 2))
5.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273349
11123316
25001313

prune131.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh044
Picked011
Done000
Total75580

Merged error: 0.0b

Counts
80 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

14.8b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.8b
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.8b
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.8b
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3
2×diff-log
1×sub-neg sum-log associate--r+
Counts
4 → 53
Calls
4 calls:
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
6.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

series51.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
17.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))

simplify104.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0227901
1723833
23160827
35001827

prune316.0ms

Filtered
65 candidates to 56 candidates (13.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New64165
Fresh033
Picked101
Done011
Total65570

Merged error: 0.0b

Counts
70 → 5

regimes95.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch42.0ms

Steps
ItersRangePoint
10
6.296263866195351e-10
4429.475794956495
0.02659018566534283
9
-481781.8837170955
-0.012224266776747678
-0.030804876869537152

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03528
13528

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.0s1605×body2560valid
1.6s2743×body1280valid
473.0ms1845×body640valid
162.0ms986×body320valid
56.0ms470×body160valid
25.0ms351×body80valid

Profiling

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