Details

Time bar (total: 10.9s)

analyze1.4s

Algorithm
search

sample230.0ms

Algorithm
intervals
Results
136.0ms48×body2560valid
56.0ms84×body1280valid
18.0ms61×body640valid
5.0ms30×body320valid
3.0ms19×body160valid
1.0ms14×body80valid

simplify345.0ms

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: 32.3b

Counts
2 → 1

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
2.4b
(- x (tan x))
2.4b
(- 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
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))

series39.0ms

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

simplify145.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune108.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
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))
0.1b
(* 9/40 (pow x 2))
15.6b
(- (* 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))

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)) 1/2))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0273349
11123316
25001316

prune119.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New73275
Fresh033
Picked101
Done000
Total74579

Merged error: 0.0b

Counts
79 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
15.6b
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite16.0ms

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
0249323
11084278
25001273

prune109.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh044
Picked011
Done000
Total73578

Merged error: 0.0b

Counts
78 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.6b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.6b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.6b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
6×diff-log
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×cbrt-prod sub-neg sum-log associate--r+
2×cbrt-div
1×pow1/3
Counts
4 → 55
Calls
4 calls:
8.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series31.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
5.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
5.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
5.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify98.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0227719
1723651
23160649
35001649

prune246.0ms

Filtered
48 candidates to 67 candidates (-39.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New66167
Fresh033
Picked101
Done011
Total67572

Merged error: 0.0b

Counts
72 → 5

regimes97.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.4b

bsearch49.0ms

Steps
ItersRangePoint
8
0.019941260639065258
676.3025077532745
1.593823631543573
8
-5.73898230508556
-0.0009362519969224196
-1.5522607823920562

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03019
13019

end0.0ms

analyze1.1s

Algorithm
search

sample6.5s

Algorithm
intervals
Results
3.9s1538×body2560valid
1.7s2756×body1280valid
503.0ms1884×body640valid
184.0ms978×body320valid
62.0ms484×body160valid
28.0ms360×body80valid

Profiling

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