Details

Time bar (total: 29.2s)

analyze2.7s (9.3%)

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
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
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample369.0ms (1.3%)

Algorithm
intervals
Results
125.0ms34×body4096invalid
74.0ms124×body1024valid
44.0ms26×body2048invalid
28.0ms30×body2048valid
27.0ms16×body4096valid
16.0ms41×body512valid
15.0ms29×body1024invalid
6.0ms15×body512invalid
5.0ms36×body128valid
4.0ms32×body128invalid
2.0msbody256valid
2.0msbody256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify110.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
0518532

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
42.1b
Counts
2 → 1
Compiler

Compiled 42 to 34 computations (19% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
0.2b
(pow.f64 (/.f64 k t) 2)
0.1b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.1b
(/.f64 (pow.f64 t 3) (*.f64 l l))
31.3b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite97.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
405×add-exp-log_binary64_457
237×prod-exp_binary64_468
115×div-exp_binary64_470
70×add-cbrt-cube_binary64_455
56×pow-exp_binary64_487
38×pow-to-exp_binary64_488
35×cbrt-unprod_binary64_452
24×times-frac_binary64_425
21×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r*_binary64_359 add-sqr-sqrt_binary64_441
19×unpow-prod-down_binary64_498
15×associate-*l/_binary64_362 associate-/l*_binary64_364
14×cbrt-undiv_binary64_453
pow1_binary64_480
cube-prod_binary64_447 tan-quot_binary64_578
add-log-exp_binary64_458
pow-prod-down_binary64_490 div-inv_binary64_416 frac-times_binary64_429 sqr-pow_binary64_391 associate-*r/_binary64_361 associate-/r/_binary64_365
clear-num_binary64_418 unpow3_binary64_485 cube-mult_binary64_449 *-commutative_binary64_350 associate-*l*_binary64_360 frac-2neg_binary64_430 associate-/r*_binary64_363
unpow2_binary64_484
Counts
4 → 206
Calls

8 calls:

26.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
21.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))

series1.8s (6.2%)

Counts
4 → 42
Calls

4 calls:

697.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
534.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
482.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
100.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 1612 to 1404 computations (12.9% saved)

simplify121.0ms (0.4%)

Algorithm
egg-herbie
Counts
248 → 248
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049796607
149796607

prune441.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New23711248
Fresh000
Picked101
Done000
Total23811249
Error
17.1b
Counts
249 → 11
Compiler

Compiled 6361 to 3256 computations (48.8% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

3.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
0.4b
(pow.f64 (sin.f64 k) 2)
0.1b
(*.f64 (*.f64 l l) (cos.f64 k))
0.0b
(*.f64 2 (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))))
0.4b
(pow.f64 (sin.f64 k) 2)
3.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
5.3b
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
19.2b
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))

rewrite51.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
163×add-exp-log_binary64_457
102×prod-exp_binary64_468
87×add-cbrt-cube_binary64_455
48×cbrt-unprod_binary64_452
27×div-exp_binary64_470
15×add-sqr-sqrt_binary64_441 cbrt-undiv_binary64_453
10×pow-exp_binary64_487 pow-to-exp_binary64_488 pow1_binary64_480
*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r*_binary64_359
unpow-prod-down_binary64_498
add-log-exp_binary64_458 unswap-sqr_binary64_387 associate-*l*_binary64_360
pow-prod-down_binary64_490 sqr-pow_binary64_391 pow-unpow_binary64_496 unpow2_binary64_484
*-commutative_binary64_350
clear-num_binary64_418 times-frac_binary64_425 div-inv_binary64_416 frac-2neg_binary64_430 pow-pow_binary64_491 associate-/r*_binary64_363 associate-/l*_binary64_364
Counts
4 → 124
Calls

8 calls:

15.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))
10.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
6.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms
(pow.f64 (sin.f64 k) 2)
0.0ms
(*.f64 2 (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))))

series812.0ms (2.8%)

Counts
4 → 36
Calls

4 calls:

523.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))))
156.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
104.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
28.0ms
(pow.f64 (sin.f64 k) 2)
Compiler

Compiled 1200 to 996 computations (17% saved)

simplify79.0ms (0.3%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050023050

prune239.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1528160
Fresh3710
Picked101
Done000
Total15615171
Error
9.8b
Counts
171 → 15
Compiler

Compiled 3890 to 1817 computations (53.3% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
0.2b
(*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
0.1b
(*.f64 (*.f64 l l) (cos.f64 k))
0.0b
(*.f64 2 (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))))
0.2b
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
0.4b
(pow.f64 (sin.f64 k) 2)
3.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
19.2b
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

rewrite45.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
107×add-exp-log_binary64_457
65×add-cbrt-cube_binary64_455
64×prod-exp_binary64_468
34×cbrt-unprod_binary64_452
18×div-exp_binary64_470
16×add-sqr-sqrt_binary64_441
12×cbrt-undiv_binary64_453
10×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
associate-*r*_binary64_359
unpow-prod-down_binary64_498 pow1_binary64_480
pow-exp_binary64_487 pow-to-exp_binary64_488 associate-*l*_binary64_360
add-log-exp_binary64_458 unswap-sqr_binary64_387
sqr-pow_binary64_391 pow-unpow_binary64_496 unpow2_binary64_484
*-commutative_binary64_350
pow-prod-down_binary64_490 clear-num_binary64_418 times-frac_binary64_425 div-inv_binary64_416 frac-2neg_binary64_430 pow-pow_binary64_491 associate-/r*_binary64_363 associate-/l*_binary64_364
Counts
4 → 107
Calls

8 calls:

14.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
9.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
7.0ms
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
3.0ms
(pow.f64 (sin.f64 k) 2)
0.0ms
(*.f64 2 (/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))))

series785.0ms (2.7%)

Counts
4 → 36
Calls

4 calls:

516.0ms
(/.f64 (*.f64 (*.f64 l l) (cos.f64 k)) (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
146.0ms
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
95.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
28.0ms
(pow.f64 (sin.f64 k) 2)
Compiler

Compiled 1208 to 990 computations (18% saved)

simplify95.0ms (0.3%)

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
049522582
149522582

prune199.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1367143
Fresh41014
Picked101
Done000
Total14117158
Error
9.1b
Counts
158 → 17
Compiler

Compiled 3622 to 1787 computations (50.7% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b
(/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
0.4b
(pow.f64 (sin.f64 k) 2)
0.2b
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
0.0b
(*.f64 2 (*.f64 (/.f64 (*.f64 l l) k) (/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))))
0.6b
(/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
3.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
7.6b
(/.f64 (*.f64 l l) k)
12.1b
(*.f64 (/.f64 (*.f64 l l) k) (/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))

rewrite53.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
117×add-exp-log_binary64_457
74×add-cbrt-cube_binary64_455
56×prod-exp_binary64_468
34×div-exp_binary64_470
30×cbrt-unprod_binary64_452
25×add-sqr-sqrt_binary64_441
22×cbrt-undiv_binary64_453
15×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r*_binary64_359
13×times-frac_binary64_425
10×associate-*l*_binary64_360
unswap-sqr_binary64_387 pow1_binary64_480
pow-exp_binary64_487 pow-to-exp_binary64_488
unpow-prod-down_binary64_498 add-log-exp_binary64_458 div-inv_binary64_416 associate-/r*_binary64_363 associate-/l*_binary64_364
clear-num_binary64_418 sqr-pow_binary64_391 *-commutative_binary64_350 frac-2neg_binary64_430 unpow2_binary64_484
associate-*l/_binary64_362 pow-prod-down_binary64_490 frac-times_binary64_429 associate-*r/_binary64_361
Counts
4 → 131
Calls

8 calls:

18.0ms
(*.f64 (/.f64 (*.f64 l l) k) (/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
9.0ms
(/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
7.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
5.0ms
(/.f64 (*.f64 l l) k)
0.0ms
(*.f64 2 (*.f64 (/.f64 (*.f64 l l) k) (/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))))

series939.0ms (3.2%)

Counts
4 → 36
Calls

4 calls:

514.0ms
(*.f64 (/.f64 (*.f64 l l) k) (/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))))
260.0ms
(/.f64 (cos.f64 k) (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
99.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
66.0ms
(/.f64 (*.f64 l l) k)
Compiler

Compiled 1244 to 1032 computations (17% saved)

simplify120.0ms (0.4%)

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
050113277

prune205.0ms (0.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New15611167
Fresh8816
Picked101
Done000
Total16519184
Error
3.7b
Counts
184 → 19
Compiler

Compiled 3823 to 1744 computations (54.4% saved)

simplify59.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
08463571
18463571

regimes882.0ms (3%)

Compiler

Compiled 10890 to 7933 computations (27.2% saved)

bsearch4.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes674.0ms (2.3%)

Compiler

Compiled 7131 to 5447 computations (23.6% saved)

bsearch308.0ms (1.1%)

Steps
ItersRangePoint
7
1.8956564461575922e+205
3.488121964613911e+207
5.655539911333164e+206
1
-2.0202283443693794e+98
-1.8983875135295223e+98
-1.9288477212394867e+98
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes284.0ms (1%)

Compiler

Compiled 2209 to 1712 computations (22.5% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes182.0ms (0.6%)

Compiler

Compiled 1658 to 1281 computations (22.7% saved)

bsearch260.0ms (0.9%)

Steps
ItersRangePoint
9
-1.683875882619071e-49
-7.399793237593248e-59
-6.122936130232856e-54
9
-0.0018941511781248729
-2.1780854095109536e-08
-3.6547036640213393e-07
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes176.0ms (0.6%)

Compiler

Compiled 1582 to 1221 computations (22.8% saved)

bsearch264.0ms (0.9%)

Steps
ItersRangePoint
9
-1.683875882619071e-49
-7.399793237593248e-59
-7.063681446027815e-56
9
-0.0018941511781248729
-2.1780854095109536e-08
-1.1852346881225905e-05
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes176.0ms (0.6%)

Compiler

Compiled 1316 to 1011 computations (23.2% saved)

bsearch254.0ms (0.9%)

Steps
ItersRangePoint
9
-1.683875882619071e-49
-7.399793237593248e-59
-1.3436020588189278e-52
9
-0.0018941511781248729
-2.1780854095109536e-08
-9.151404920080495e-06
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes165.0ms (0.6%)

Compiler

Compiled 1126 to 861 computations (23.5% saved)

bsearch359.0ms (1.2%)

Steps
ItersRangePoint
9
2.8150780433004498e-160
4.0710074064530664e-155
2.167343341657803e-157
8
-1.1263166031459353e+92
-1.7389995373025484e+89
-8.783101688769685e+89
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes159.0ms (0.5%)

Compiler

Compiled 1034 to 797 computations (22.9% saved)

bsearch222.0ms (0.8%)

Steps
ItersRangePoint
9
2.8150780433004498e-160
4.0710074064530664e-155
9.479879216596787e-157
8
-3.617170340213835e-125
-7.209421067556776e-128
-3.575766571680626e-125
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes102.0ms (0.3%)

Compiler

Compiled 297 to 314 computations (-5.7% saved)

bsearch220.0ms (0.8%)

Steps
ItersRangePoint
9
2.8150780433004498e-160
4.0710074064530664e-155
7.777500190582001e-156
8
-3.617170340213835e-125
-7.209421067556776e-128
-2.4575930907319535e-127
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes68.0ms (0.2%)

Compiler

Compiled 207 to 249 computations (-20.3% saved)

bsearch273.0ms (0.9%)

Steps
ItersRangePoint
7
3.913867651201436e-80
7.485197217766062e-78
3.1551806453450644e-78
9
-1.683875882619071e-49
-7.399793237593248e-59
-1.3852239520341363e-58
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes53.0ms (0.2%)

Compiler

Compiled 132 to 184 computations (-39.4% saved)

bsearch0.0ms (0%)

regimes37.0ms (0.1%)

Compiler

Compiled 68 to 114 computations (-67.6% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.1%)

Accuracy

Total 5.3b remaining (69.8%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch25.0ms (0.1%)

Compiler

Compiled 602 to 372 computations (38.2% saved)

simplify9.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0188731
1188731

end0.0ms (0%)

sample14.6s (50%)

Algorithm
intervals
Results
3.9s1182×body4096invalid
2.3s1125×body2048invalid
2.1s3789×body1024valid
1.0s1065×body2048valid
848.0ms453×body4096valid
556.0ms1406×body512valid
404.0ms686×body1024invalid
203.0ms520×body512invalid
144.0ms1070×body128invalid
137.0ms484×body256valid
110.0ms803×body128valid
87.0ms329×body256invalid
Compiler

Compiled 2803 to 2023 computations (27.8% saved)

Pareto

0.5310979781543356

Profiling

Loading profile data...