Details

Time bar (total: 15.1s)

analyze2.1s (13.8%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04978140
14978140
033
133
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)

sample98.0ms (0.6%)

Algorithm
1×intervals
Results
46.0ms88×body1024valid
14.0ms117×body128valid
11.0ms30×body512valid
6.0ms54×body128invalid
5.0ms20×body256valid
2.0ms4×body1024invalid
1.0ms1×body2048valid
0.0ms1×body512invalid
0.0ms1×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify59.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
34.6b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.4b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
13.9b
(*.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)))
18.5b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite72.0ms (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:

25.0ms
(*.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)))
12.0ms
(*.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))

series676.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

405.0ms
(*.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)))
180.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
65.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
26.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify75.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
055553677

prune284.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New15912171
Fresh000
Picked101
Done000
Total16012172
Error
13.4b
Counts
172 → 12
Compiler

Compiled 5087 to 2816 computations (44.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
5.5b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
9.3b
(/.f64 (*.f64 t t) l)
13.9b
(*.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)))

rewrite74.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
113×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
65×prod-exp_binary64_468 cbrt-unprod_binary64_452
44×associate-*l/_binary64_362
34×frac-times_binary64_429
29×pow1_binary64_480
20×div-exp_binary64_470 cbrt-undiv_binary64_453
17×pow-prod-down_binary64_490
16×tan-quot_binary64_578
15×add-sqr-sqrt_binary64_441
14×associate-*r/_binary64_361
13×*-un-lft-identity_binary64_419
11×add-cube-cbrt_binary64_454
10×associate-*r*_binary64_359
9×associate-*l*_binary64_360
8×flip3-+_binary64_422 flip-+_binary64_393
7×times-frac_binary64_425
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 → 151
Calls

4 calls:

25.0ms
(*.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)))
14.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series650.0ms (4.3%)

Counts
4 → 12
Calls

4 calls:

394.0ms
(*.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)))
180.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
62.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
15.0ms
(/.f64 (*.f64 t t) l)

simplify91.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049674012
149674012

prune228.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh7411
Picked101
Done000
Total16312175
Error
8.2b
Counts
175 → 12
Compiler

Compiled 5006 to 2515 computations (49.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(/.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))))
2.5b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
3.6b
(*.f64 (/.f64 t l) (sin.f64 k))
13.9b
(*.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)))

rewrite156.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64_457
304×add-cbrt-cube_binary64_455
259×prod-exp_binary64_468
181×cbrt-unprod_binary64_452
179×frac-times_binary64_429
178×associate-*l/_binary64_362
108×div-exp_binary64_470
81×associate-*r/_binary64_361
69×cbrt-undiv_binary64_453
56×tan-quot_binary64_578
47×associate-/r/_binary64_365
40×pow1_binary64_480
32×flip3-+_binary64_422 flip-+_binary64_393
26×pow-prod-down_binary64_490
21×add-sqr-sqrt_binary64_441
18×*-un-lft-identity_binary64_419 1-exp_binary64_463
16×add-cube-cbrt_binary64_454
15×associate-*l*_binary64_360
13×times-frac_binary64_425
10×associate-*r*_binary64_359
4×add-log-exp_binary64_458
3×*-commutative_binary64_350 associate-/l*_binary64_364
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-/r*_binary64_363
Counts
4 → 308
Calls

4 calls:

37.0ms
(*.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)))
35.0ms
(/.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))))
18.0ms
(*.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))

series918.0ms (6.1%)

Counts
4 → 12
Calls

4 calls:

390.0ms
(*.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)))
295.0ms
(/.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))))
178.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
55.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify167.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049629870
149629870

prune537.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New3137320
Fresh3811
Picked101
Done000
Total31715332
Error
5.6b
Counts
332 → 15
Compiler

Compiled 9942 to 5290 computations (46.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.8b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.6b
(*.f64 (/.f64 t l) (sin.f64 k))
14.3b
(*.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))))

rewrite94.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
193×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
87×prod-exp_binary64_468 cbrt-unprod_binary64_452
76×times-frac_binary64_425
64×div-exp_binary64_470 cbrt-undiv_binary64_453
53×add-sqr-sqrt_binary64_441
49×*-un-lft-identity_binary64_419
43×add-cube-cbrt_binary64_454
34×associate-*l*_binary64_360
24×associate-*r*_binary64_359
17×pow1_binary64_480
13×associate-/l*_binary64_364
11×associate-*l/_binary64_362
10×associate-*r/_binary64_361
8×pow-prod-down_binary64_490 associate-/r/_binary64_365
7×div-inv_binary64_416
6×tan-quot_binary64_578
4×add-log-exp_binary64_458 unswap-sqr_binary64_387 frac-times_binary64_429
3×distribute-lft-out_binary64_370 *-commutative_binary64_350
1×flip3-+_binary64_422 clear-num_binary64_418 frac-2neg_binary64_430 flip-+_binary64_393 associate-/r*_binary64_363 associate-/l/_binary64_366
Counts
4 → 215
Calls

4 calls:

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))))
13.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
10.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
9.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series684.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

248.0ms
(*.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))))
204.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
176.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
56.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify129.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
051046374

prune250.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2198227
Fresh7714
Picked101
Done000
Total22715242
Error
5.6b
Counts
242 → 15
Compiler

Compiled 6896 to 2463 computations (64.3% saved)

regimes1.9s (12.9%)

Accuracy

Total 5.0b remaining (42%)

Threshold costs 0b (0%)

Compiler

Compiled 18404 to 13751 computations (25.3% saved)

bsearch340.0ms (2.2%)

Steps
ItersRangePoint
7
2.994501005301103e-165
3.285765990559171e-163
6.839250237191215e-165
10
7.287870877391771e-209
4.823815623800117e-197
2.4659146346821276e-207
10
8.31069825343186e-241
9.476349226392935e-223
6.4743981145055726e-223
5
-1.0569292191251573e-243
-3.469134040243902e-244
-1.0421023210157143e-243
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
083269
183269

end0.0ms (0%)

sample5.4s (35.9%)

Algorithm
1×intervals
Results
1.4s2747×body1024valid
443.0ms1228×body512valid
422.0ms3439×body128valid
173.0ms1429×body128invalid
144.0ms577×body256valid
40.0ms116×body512invalid
32.0ms65×body1024invalid
26.0ms109×body256invalid
7.0ms9×body2048valid
Compiler

Compiled 3121 to 2288 computations (26.7% saved)

Profiling

Loading profile data...