Details

Time bar (total: 15.8s)

analyze2.0s (12.3%)

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
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
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample107.0ms (0.7%)

Algorithm
1×intervals
Results
56.0ms103×body1024valid
13.0ms36×body512valid
12.0ms100×body128valid
6.0ms49×body128invalid
4.0ms17×body256valid
2.0ms6×body256invalid
2.0ms4×body512invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify151.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 34.0b

Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
2.5b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
16.1b
(/.f64 (pow.f64 t 3) (*.f64 l l))
16.7b
(*.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)))

rewrite76.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_457
58×prod-exp_binary64_468
52×add-cbrt-cube_binary64_455
28×times-frac_binary64_425
26×cbrt-unprod_binary64_452 add-sqr-sqrt_binary64_441
24×div-exp_binary64_470
20×pow1_binary64_480
19×*-un-lft-identity_binary64_419
18×associate-*l*_binary64_360
17×add-cube-cbrt_binary64_454
16×associate-*l/_binary64_362
12×associate-/l*_binary64_364
10×pow-prod-down_binary64_490 unpow-prod-down_binary64_498 associate-*r*_binary64_359 frac-times_binary64_429 cube-prod_binary64_447
8×pow-exp_binary64_487 pow-to-exp_binary64_488 tan-quot_binary64_578 cbrt-undiv_binary64_453
6×associate-*r/_binary64_361
5×unswap-sqr_binary64_387
4×flip3-+_binary64_422 add-log-exp_binary64_458 sqr-pow_binary64_391 flip-+_binary64_393
3×unpow3_binary64_485 cube-mult_binary64_449 *-commutative_binary64_350
2×div-inv_binary64_416
1×clear-num_binary64_418 distribute-rgt-in_binary64_369 distribute-lft-out_binary64_370 distribute-lft-in_binary64_368 frac-2neg_binary64_430 associate-/r*_binary64_363
Counts
4 → 159
Calls

4 calls:

23.0ms
(*.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)))
13.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.3s (8.5%)

Counts
4 → 33
Calls

4 calls:

543.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
487.0ms
(*.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)))
234.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
76.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify99.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
051334249

prune310.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New18210192
Fresh000
Picked101
Done000
Total18310193

Merged error: 19.0b

Counts
193 → 10
Compiler

Compiled 5634 to 3075 computations (45.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
3.6b
(*.f64 (sin.f64 k) (/.f64 t l))
7.9b
(/.f64 (*.f64 t t) l)
16.7b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite82.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
120×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
70×prod-exp_binary64_468 cbrt-unprod_binary64_452
34×frac-times_binary64_429
31×associate-*r/_binary64_361
29×pow1_binary64_480
27×associate-*l/_binary64_362
21×add-sqr-sqrt_binary64_441 div-exp_binary64_470 cbrt-undiv_binary64_453
20×associate-*r*_binary64_359
18×*-un-lft-identity_binary64_419
17×pow-prod-down_binary64_490
16×add-cube-cbrt_binary64_454 tan-quot_binary64_578
13×times-frac_binary64_425
8×flip3-+_binary64_422 flip-+_binary64_393
5×associate-*l*_binary64_360
4×add-log-exp_binary64_458
3×*-commutative_binary64_350 associate-/r*_binary64_363
2×div-inv_binary64_416 unswap-sqr_binary64_387
1×clear-num_binary64_418 distribute-rgt-in_binary64_369 distribute-lft-out_binary64_370 distribute-lft-in_binary64_368 frac-2neg_binary64_430 associate-/l*_binary64_364
Counts
4 → 159
Calls

4 calls:

28.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
19.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
8.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
5.0ms
(/.f64 (*.f64 t t) l)

series1.2s (7.8%)

Counts
4 → 33
Calls

4 calls:

547.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
465.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
168.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
48.0ms
(/.f64 (*.f64 t t) l)

simplify98.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050154563

prune266.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1848192
Fresh639
Picked101
Done000
Total19111202

Merged error: 13.2b

Counts
202 → 11
Compiler

Compiled 5791 to 2845 computations (50.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
2.5b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
3.6b
(*.f64 (sin.f64 k) (/.f64 t l))
16.7b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite106.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
151×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
78×prod-exp_binary64_468 cbrt-unprod_binary64_452
76×times-frac_binary64_425
54×add-sqr-sqrt_binary64_441
51×*-un-lft-identity_binary64_419
49×add-cube-cbrt_binary64_454 associate-*l*_binary64_360
37×div-exp_binary64_470 cbrt-undiv_binary64_453
35×frac-times_binary64_429
34×associate-*r/_binary64_361 pow1_binary64_480
28×associate-*l/_binary64_362
21×associate-*r*_binary64_359
20×pow-prod-down_binary64_490
16×tan-quot_binary64_578
8×flip3-+_binary64_422 flip-+_binary64_393
5×div-inv_binary64_416
4×add-log-exp_binary64_458 *-commutative_binary64_350
2×unswap-sqr_binary64_387
1×distribute-rgt-in_binary64_369 distribute-lft-out_binary64_370 associate-/r/_binary64_365 distribute-lft-in_binary64_368
Counts
4 → 214
Calls

4 calls:

30.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
17.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
11.0ms
(*.f64 (sin.f64 k) (/.f64 t l))

series1.4s (8.7%)

Counts
4 → 36
Calls

4 calls:

532.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
454.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
221.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
169.0ms
(*.f64 (sin.f64 k) (/.f64 t l))

simplify88.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050116026

prune351.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2446250
Fresh5510
Picked101
Done000
Total25011261

Merged error: 11.0b

Counts
261 → 11
Compiler

Compiled 7768 to 3649 computations (53% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))
3.6b
(*.f64 (sin.f64 k) (/.f64 t l))
9.1b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))) (*.f64 (/.f64 l t) (cos.f64 k)))
13.6b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l)))))

rewrite96.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
142×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
79×prod-exp_binary64_468 cbrt-unprod_binary64_452
30×div-exp_binary64_470 cbrt-undiv_binary64_453
29×pow1_binary64_480
24×associate-*r/_binary64_361
19×add-sqr-sqrt_binary64_441
17×pow-prod-down_binary64_490
16×*-un-lft-identity_binary64_419
15×associate-*r*_binary64_359
14×add-cube-cbrt_binary64_454
11×times-frac_binary64_425
10×associate-*l*_binary64_360
5×associate-*l/_binary64_362 associate-/l/_binary64_366
4×flip3-+_binary64_422 add-log-exp_binary64_458 frac-times_binary64_429 flip-+_binary64_393
3×*-commutative_binary64_350
2×div-inv_binary64_416 unswap-sqr_binary64_387
1×clear-num_binary64_418 distribute-lft-out_binary64_370 associate-/r/_binary64_365 frac-2neg_binary64_430 associate-/r*_binary64_363 associate-/l*_binary64_364
Counts
4 → 143
Calls

4 calls:

29.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))) (*.f64 (/.f64 l t) (cos.f64 k)))
22.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l)))))
11.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))
8.0ms
(*.f64 (sin.f64 k) (/.f64 t l))

series1.1s (7%)

Counts
4 → 36
Calls

4 calls:

397.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))) (*.f64 (/.f64 l t) (cos.f64 k)))
296.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l)))))
241.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (sin.f64 k) (/.f64 t l))))
169.0ms
(*.f64 (sin.f64 k) (/.f64 t l))

simplify85.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
053244742

prune229.0ms (1.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1727179
Fresh1910
Picked011
Done000
Total17317190

Merged error: 6.1b

Counts
190 → 17
Compiler

Compiled 5676 to 2516 computations (55.7% saved)

regimes1.5s (9.2%)

Compiler

Compiled 15238 to 11440 computations (24.9% saved)

bsearch126.0ms (0.8%)

Steps
ItersRangePoint
8
993758322.226031
2169021320423.1218
1005420263.9279583
6
-3.149449076880847e-75
-2.3357434235624424e-76
-1.4869480221444148e-75
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053100
153100

end0.0ms (0%)

sample5.0s (31.7%)

Algorithm
1×intervals
Results
1.4s2712×body1024valid
462.0ms1270×body512valid
434.0ms3426×body128valid
176.0ms1409×body128invalid
149.0ms582×body256valid
47.0ms136×body512invalid
37.0ms68×body1024invalid
35.0ms129×body256invalid
7.0ms10×body2048valid
Compiler

Compiled 2488 to 1863 computations (25.1% saved)

Profiling

Loading profile data...