Details

Time bar (total: 1.4min)

analyze2.7s (3.2%)

Algorithm
1×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
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14

sample458.0ms (0.5%)

Algorithm
1×intervals
Results
93.0ms43×body2560invalid
90.0ms108×body1280valid
87.0ms23×body5120invalid
49.0ms38×body2560valid
32.0ms57×body640valid
29.0ms31×body1280invalid
18.0ms8×body5120valid
11.0ms22×body640invalid
9.0ms37×body80invalid
7.0ms21×body320invalid
5.0ms11×body320valid
3.0ms12×body160valid
3.0ms22×body80valid
1.0ms5×body160invalid

simplify47.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
0484221
1484221

prune13.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 45.7b

Counts
2 → 1

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.8b
(/.f64 2.0 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0)))
14.5b
(/.f64 (pow.f64 t 3.0) (*.f64 l l))
34.0b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))

rewrite73.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
405×add-exp-log_binary64
237×prod-exp_binary64
115×div-exp_binary64
70×add-cbrt-cube_binary64
56×pow-exp_binary64
38×pow-to-exp_binary64
35×cbrt-unprod_binary64
20×associate-*r*_binary64
19×*-un-lft-identity_binary64 add-cube-cbrt_binary64 unpow-prod-down_binary64 add-sqr-sqrt_binary64 times-frac_binary64
15×associate-*l/_binary64
14×cbrt-undiv_binary64
10×associate-/l*_binary64
9×pow1_binary64
6×tan-quot_binary64
4×add-log-exp_binary64
3×pow-prod-down_binary64 associate-*r/_binary64 sqr-pow_binary64 associate-/r/_binary64 div-inv_binary64 frac-times_binary64
2×associate-/r*_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 195
Calls

4 calls:

19.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))
19.0ms
(/.f64 2.0 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0)))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
6.0ms
(/.f64 (pow.f64 t 3.0) (*.f64 l l))

series449.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

187.0ms
(/.f64 2.0 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0)))
129.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2.0))
87.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3.0) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
45.0ms
(/.f64 (pow.f64 t 3.0) (*.f64 l l))

simplify53.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
053653711

prune350.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New19710207
Fresh000
Picked101
Done000
Total19810208

Merged error: 20.2b

Counts
208 → 10

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b
(/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)))
5.3b
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))
7.4b
(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))
17.2b
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))

rewrite101.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
1424×add-exp-log_binary64
942×prod-exp_binary64
616×pow-exp_binary64
526×div-exp_binary64
316×pow-to-exp_binary64
110×1-exp_binary64 rec-exp_binary64
37×add-sqr-sqrt_binary64
34×add-cbrt-cube_binary64
29×unpow-prod-down_binary64
22×times-frac_binary64
20×*-un-lft-identity_binary64 add-cube-cbrt_binary64
19×associate-*r*_binary64
18×associate-*l*_binary64
13×sqr-pow_binary64
12×cbrt-unprod_binary64 unswap-sqr_binary64
9×associate-/r*_binary64
8×cbrt-undiv_binary64
5×pow1_binary64
4×add-log-exp_binary64 associate-/l*_binary64 div-inv_binary64
3×unpow2_binary64
2×clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×associate-*r/_binary64 inv-pow_binary64 pow-flip_binary64
Counts
4 → 500
Calls

4 calls:

24.0ms
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))
9.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))
7.0ms
(/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)))
7.0ms
(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))

series487.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

193.0ms
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))
134.0ms
(*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0))
132.0ms
(/.f64 1 (*.f64 (pow.f64 k 2.0) (pow.f64 t 1.0)))
28.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))

simplify94.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
512 → 512
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0537810342

prune1.1s (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New5048512
Fresh369
Picked101
Done000
Total50814522

Merged error: 16.2b

Counts
522 → 14

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 k) 2)
0.6b
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))))
5.3b
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))
17.2b
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2))))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))

rewrite236.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
4770×add-exp-log_binary64
3714×prod-exp_binary64
2156×pow-exp_binary64
1555×div-exp_binary64
1226×pow-to-exp_binary64
341×1-exp_binary64 rec-exp_binary64
36×add-cbrt-cube_binary64
23×add-sqr-sqrt_binary64
22×times-frac_binary64
20×unpow-prod-down_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
13×cbrt-unprod_binary64
12×associate-*r*_binary64
11×associate-*l*_binary64
9×associate-/r*_binary64 cbrt-undiv_binary64
6×pow1_binary64 sqr-pow_binary64
4×add-log-exp_binary64 unpow2_binary64 associate-/l*_binary64 div-inv_binary64
3×pow-unpow_binary64 unswap-sqr_binary64
2×clear-num_binary64 frac-2neg_binary64
1×associate-*r/_binary64 pow-pow_binary64 inv-pow_binary64 pow-flip_binary64 *-commutative_binary64
Counts
4 → 1171
Calls

4 calls:

36.0ms
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2))))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))
12.0ms
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))))
10.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))
3.0ms
(pow.f64 (sin.f64 k) 2)

series357.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

194.0ms
(*.f64 (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2))))) 1.0) (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)))
131.0ms
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (*.f64 (pow.f64 t 1.0) (pow.f64 k (/.f64 2.0 2)))))
27.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))
4.0ms
(pow.f64 (sin.f64 k) 2)

simplify200.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1183 → 1183
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0523224974

prune3.4s (4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New117761183
Fresh4913
Picked101
Done000
Total1182151197

Merged error: 15.2b

Counts
1197 → 15

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)))
3.1b
(*.f64 (pow.f64 (/.f64 1 (pow.f64 k (/.f64 2.0 2))) 1.0) (*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0)))
5.3b
(/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2))
14.1b
(*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0))

rewrite938.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
21085×add-exp-log_binary64
15669×prod-exp_binary64
11981×pow-exp_binary64
8476×div-exp_binary64
5102×pow-to-exp_binary64
2303×1-exp_binary64 rec-exp_binary64
52×add-cbrt-cube_binary64
51×unpow-prod-down_binary64
43×times-frac_binary64
41×associate-*l*_binary64
36×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64 add-cube-cbrt_binary64
23×cbrt-unprod_binary64
12×associate-*r*_binary64
11×cbrt-undiv_binary64
9×associate-/r*_binary64 sqr-pow_binary64
5×pow1_binary64 div-inv_binary64
4×add-log-exp_binary64 associate-/l*_binary64
3×unpow2_binary64 unswap-sqr_binary64
2×clear-num_binary64 frac-2neg_binary64 associate-*l/_binary64 *-commutative_binary64
1×associate-*r/_binary64 inv-pow_binary64 pow-flip_binary64
Counts
4 → 4475
Calls

4 calls:

83.0ms
(*.f64 (pow.f64 (/.f64 1 (pow.f64 k (/.f64 2.0 2))) 1.0) (*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0)))
26.0ms
(*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0))
11.0ms
(/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2))
8.0ms
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)))

series433.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

137.0ms
(*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0))
134.0ms
(*.f64 (pow.f64 (/.f64 1 (pow.f64 k (/.f64 2.0 2))) 1.0) (*.f64 (/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2)) (pow.f64 (/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0))) 1.0)))
130.0ms
(/.f64 1 (*.f64 (pow.f64 k (/.f64 2.0 2)) (pow.f64 t 1.0)))
31.0ms
(/.f64 (*.f64 (cos.f64 k) (*.f64 l l)) (pow.f64 (sin.f64 k) 2))

simplify902.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
4487 → 4487
Iterations

Useful iterations: 0 (125.0ms)

IterNodesCost
04970147268
14970147268

prune55.5s (66.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New447984487
Fresh31114
Picked101
Done000
Total4483194502

Merged error: 14.6b

Counts
4502 → 19

regimes539.0ms (0.6%)

Accuracy

Total 4.7b remaining (28%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04765
14765

end0.0ms (0%)

sample15.4s (18.4%)

Algorithm
1×intervals
Results
3.7s1329×body2560invalid
3.5s740×body5120invalid
2.9s3416×body1280valid
1.4s946×body2560valid
1.1s1912×body640valid
673.0ms783×body1280invalid
663.0ms206×body5120valid
292.0ms589×body640invalid
267.0ms638×body320valid
140.0ms958×body80invalid
136.0ms355×body320invalid
88.0ms630×body80valid
69.0ms252×body160valid
48.0ms189×body160invalid

Profiling

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