Details

Time bar (total: 8.6s)

sample456.0ms

Algorithm
intervals
Results
135.0ms62×body2560valid
53.0ms77×body1280valid
13.0ms55×body640valid
4.0ms25×body320valid
3.0ms19×body80valid
2.0ms18×body160valid

simplify13.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.5b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.6b
(- x (sin x))
1.6b
(- x (tan 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)))
4.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series188.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- x (sin x)) (- x (tan x)))
36.0ms
(- x (sin x))
78.0ms
(- x (tan x))

simplify151.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148685
24795685
35001685

prune177.0ms

Filtered
89 candidates to 63 candidates (70.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh000
Picked101
Done000
Total86490

Merged error: 0.0b

Counts
90 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 9/40 (pow x 2))
0.1b
(* 27/2800 (pow x 4))
14.1b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite23.0ms

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:
6.0ms
(* 9/40 (pow x 2))
5.0ms
(* 27/2800 (pow x 4))
10.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series108.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 9/40 (pow x 2))
39.0ms
(* 27/2800 (pow x 4))
44.0ms
(- (* 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
11123318
25002315

prune125.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New74175
Fresh033
Picked101
Done000
Total75479

Merged error: 0b

Counts
79 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 9/40 (pow x 2))
0.1b
(* 27/2800 (pow x 4))
14.1b
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite17.0ms

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:
6.0ms
(* 9/40 (pow x 2))
5.0ms
(* 27/2800 (pow x 4))
4.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series166.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 9/40 (pow x 2))
35.0ms
(* 27/2800 (pow x 4))
107.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify41.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0249310
11003281
25002275

prune119.0ms

Filtered
73 candidates to 45 candidates (61.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New73073
Fresh033
Picked011
Done000
Total73477

Merged error: 0b

Counts
77 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- x (sin x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×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:
4.0ms
(- x (sin x))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))

series185.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- x (sin x))
49.0ms
(- x (tan x))
51.0ms
(- x (tan x))
52.0ms
(- x (tan x))

simplify68.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0150319
1342299
2774299
32023299
45001299

prune180.0ms

Filtered
68 candidates to 51 candidates (75.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh022
Picked011
Done011
Total68472

Merged error: 0b

Counts
72 → 4

regimes31.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch83.0ms

Steps
ItersRangePoint
9
0.006602375602419948
2408.9151023461654
0.03184416870118442
10
-7888799.454350161
-0.0014566459989916651
-0.028761646689302346

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03529
13529

end0.0ms

sample6.4s

Algorithm
intervals
Results
4.0s1635×body2560valid
1.5s2712×body1280valid
470.0ms1897×body640valid
143.0ms922×body320valid
54.0ms494×body160valid
22.0ms340×body80valid

Profiling

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