Details

Time bar (total: 11.8s)

analyze2.3s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14

sample137.0ms

Algorithm
intervals
Results
55.0ms66×body1280valid
24.0ms42×body640valid
16.0ms115×body80valid
9.0ms22×body320valid
6.0ms44×body80invalid
6.0ms3×body160invalid
3.0ms11×body160valid
2.0ms5×body320invalid
2.0ms3×body640invalid

simplify78.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0493235
1493235

prune5.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 35.2b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

2.7b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.9b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
15.3b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.8b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log_binary64
58×prod-exp_binary64
52×add-cbrt-cube_binary64
28×times-frac_binary64
26×cbrt-unprod_binary64 add-sqr-sqrt_binary64
24×div-exp_binary64
20×pow1_binary64
19×*-un-lft-identity_binary64
18×associate-*l*_binary64
17×add-cube-cbrt_binary64
16×associate-*l/_binary64
12×associate-/l*_binary64
10×pow-prod-down_binary64 associate-*r*_binary64 unpow-prod-down_binary64 cube-prod_binary64 frac-times_binary64
8×pow-to-exp_binary64 cbrt-undiv_binary64 pow-exp_binary64 tan-quot_binary64
6×associate-*r/_binary64
5×unswap-sqr_binary64
4×flip3-+_binary64 add-log-exp_binary64 sqr-pow_binary64 flip-+_binary64
3×unpow3_binary64 *-commutative_binary64 cube-mult_binary64
2×div-inv_binary64
1×associate-/r*_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 159
Calls
4 calls:
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
10.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
22.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
9.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series653.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
72.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
376.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
29.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify83.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
055653675

prune176.0ms

Filtered
93 candidates to 171 candidates (-83.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1647171
Fresh000
Picked101
Done000
Total1657172

Merged error: 15.2b

Counts
172 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
5.3b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
10.0b
(/.f64 (*.f64 t t) l)
15.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log_binary64 add-cbrt-cube_binary64
65×cbrt-unprod_binary64 prod-exp_binary64
44×associate-*l/_binary64
34×frac-times_binary64
29×pow1_binary64
20×cbrt-undiv_binary64 div-exp_binary64
17×pow-prod-down_binary64
16×tan-quot_binary64
15×add-sqr-sqrt_binary64
14×associate-*r/_binary64
13×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
10×associate-*r*_binary64
9×associate-*l*_binary64
8×flip3-+_binary64 flip-+_binary64
7×times-frac_binary64
4×add-log-exp_binary64
3×associate-/r*_binary64 *-commutative_binary64
2×unswap-sqr_binary64 div-inv_binary64
1×distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64
Counts
4 → 151
Calls
4 calls:
14.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)
26.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series629.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
63.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
16.0ms
(/.f64 (*.f64 t t) l)
376.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify108.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049704010
149704010

prune145.0ms

Filtered
89 candidates to 163 candidates (-83.1%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh156
Picked101
Done000
Total15713170

Merged error: 9.5b

Counts
170 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.7b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
15.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
421×add-exp-log_binary64
304×add-cbrt-cube_binary64
259×prod-exp_binary64
181×cbrt-unprod_binary64
179×frac-times_binary64
178×associate-*l/_binary64
108×div-exp_binary64
81×associate-*r/_binary64
69×cbrt-undiv_binary64
56×tan-quot_binary64
47×associate-/r/_binary64
40×pow1_binary64
32×flip3-+_binary64 flip-+_binary64
26×pow-prod-down_binary64
21×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 1-exp_binary64
16×add-cube-cbrt_binary64
15×associate-*l*_binary64
13×times-frac_binary64
10×associate-*r*_binary64
4×add-log-exp_binary64
3×associate-/l*_binary64 *-commutative_binary64
2×unswap-sqr_binary64 div-inv_binary64
1×associate-/r*_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 308
Calls
4 calls:
34.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
21.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
31.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series891.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
181.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
60.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
373.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify202.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
049679870
149679870

prune266.0ms

Filtered
149 candidates to 320 candidates (-114.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New30911320
Fresh8412
Picked101
Done000
Total31815333

Merged error: 7.9b

Counts
333 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
3.5b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
15.6b
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
193×add-exp-log_binary64 add-cbrt-cube_binary64
87×cbrt-unprod_binary64 prod-exp_binary64
76×times-frac_binary64
64×cbrt-undiv_binary64 div-exp_binary64
53×add-sqr-sqrt_binary64
49×*-un-lft-identity_binary64
43×add-cube-cbrt_binary64
34×associate-*l*_binary64
24×associate-*r*_binary64
17×pow1_binary64
13×associate-/l*_binary64
11×associate-*l/_binary64
10×associate-*r/_binary64
8×pow-prod-down_binary64 associate-/r/_binary64
7×div-inv_binary64
6×tan-quot_binary64
4×add-log-exp_binary64 unswap-sqr_binary64 frac-times_binary64
3×distribute-lft-out_binary64 *-commutative_binary64
1×flip3-+_binary64 associate-/l/_binary64 associate-/r*_binary64 clear-num_binary64 frac-2neg_binary64 flip-+_binary64
Counts
4 → 215
Calls
4 calls:
14.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
11.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
9.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
33.0ms
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
174.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
61.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
240.0ms
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

simplify155.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
049706366
149706366

prune174.0ms

Filtered
127 candidates to 227 candidates (-78.7%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2198227
Fresh7714
Picked101
Done000
Total22715242

Merged error: 7.4b

Counts
242 → 15

regimes238.0ms

Accuracy

49% (3.5b remaining)

Error of 10.6b against oracle of 7.1b and baseline of 14.0b

bsearch163.0ms

Steps
ItersRangePoint
8
4.30935886798751e-32
2.7428418785184186e-29
4.3543219557651655e-32
7
-2.0380112987604354e-28
-4.885973839841103e-30
-4.953282748199605e-30

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05498
15498

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s2033×body1280valid
912.0ms1508×body640valid
472.0ms3313×body80valid
338.0ms782×body320valid
193.0ms1360×body80invalid
111.0ms364×body160valid
82.0ms136×body640invalid
58.0ms136×body320invalid
16.0ms55×body160invalid
15.0ms19×body1280invalid

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