Details

Time bar (total: 11.5s)

analyze2.2s

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

sample134.0ms

Algorithm
intervals
Results
57.0ms66×body1280valid
32.0ms59×body640valid
13.0ms100×body80valid
8.0ms21×body320valid
5.0ms41×body80invalid
3.0ms10×body160valid
2.0ms3×body640invalid
2.0ms3×body320invalid
1.0ms2×body160invalid

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: 32.3b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
3.2b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
12.2b
(*.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)))
18.3b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite64.0ms

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:
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
13.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
26.0ms
(*.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)))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series641.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
177.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
366.0ms
(*.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)))
31.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify85.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
055653675

prune170.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New16011171
Fresh000
Picked101
Done000
Total16111172

Merged error: 14.9b

Counts
172 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.9b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
10.1b
(/.f64 (*.f64 t t) l)
12.2b
(*.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)))

rewrite66.0ms

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:
17.0ms
(*.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)
27.0ms
(*.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)))

series623.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
59.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
13.0ms
(/.f64 (*.f64 t t) l)
369.0ms
(*.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)))

simplify110.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049704010
149704010

prune164.0ms

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

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New15211163
Fresh4610
Picked101
Done000
Total15717174

Merged error: 10.1b

Counts
174 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(/.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))))
3.2b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
4.0b
(*.f64 (/.f64 t l) (sin.f64 k))
12.2b
(*.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)))

rewrite127.0ms

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:
40.0ms
(/.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))))
19.0ms
(*.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))
33.0ms
(*.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)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
279.0ms
(/.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))))
180.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
61.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
381.0ms
(*.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)))

simplify186.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
049679870
149679870

prune265.0ms

Filtered
148 candidates to 320 candidates (-116.2%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New31010320
Fresh10616
Picked101
Done000
Total32116337

Merged error: 7.3b

Counts
337 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.1b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
4.0b
(*.f64 (/.f64 t l) (sin.f64 k))
12.2b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
125×add-exp-log_binary64 add-cbrt-cube_binary64
78×cbrt-unprod_binary64 prod-exp_binary64
49×pow1_binary64
41×associate-*r/_binary64
39×associate-*l/_binary64
35×frac-times_binary64
32×pow-prod-down_binary64
28×associate-*l*_binary64
26×add-sqr-sqrt_binary64
23×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
19×times-frac_binary64
18×tan-quot_binary64
16×cbrt-undiv_binary64 div-exp_binary64
11×associate-*r*_binary64
8×flip3-+_binary64 flip-+_binary64
4×add-log-exp_binary64 *-commutative_binary64
2×unswap-sqr_binary64 div-inv_binary64
1×distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64
Counts
4 → 176
Calls
4 calls:
16.0ms
(*.f64 (/.f64 t l) (*.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))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
28.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
170.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
57.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
369.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

simplify110.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049865129
149865129

prune137.0ms

Filtered
108 candidates to 188 candidates (-74.1%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1835188
Fresh21315
Picked101
Done000
Total18618204

Merged error: 7.3b

Counts
204 → 18

regimes255.0ms

Accuracy

57.4% (3.6b remaining)

Error of 10.8b against oracle of 7.3b and baseline of 15.7b

bsearch210.0ms

Steps
ItersRangePoint
8
1.797503315875472e-75
3.095089891577527e-72
2.543668611609592e-75
10
-7.071645601075058e-46
-4.0051162316101507e-63
-2.792014415073566e-58

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
060131
160131

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s2040×body1280valid
881.0ms1570×body640valid
447.0ms3344×body80valid
276.0ms675×body320valid
177.0ms1364×body80invalid
102.0ms371×body160valid
71.0ms125×body640invalid
55.0ms132×body320invalid
20.0ms75×body160invalid
13.0ms18×body1280invalid

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