Details

Time bar (total: 13.8s)

analyze2.1s (15.5%)

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)

sample119.0ms (0.9%)

Algorithm
1×intervals
Results
61.0ms91×body1024valid
16.0ms38×body512valid
14.0ms109×body128valid
5.0ms18×body256valid
5.0ms43×body128invalid
2.0ms3×body1024invalid
1.0ms3×body512invalid
1.0ms3×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify220.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0492835
1492835

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 29.2b

Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b
(*.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))
12.6b
(*.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)))
14.2b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite81.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_449
58×prod-exp_binary64_460
52×add-cbrt-cube_binary64_447
28×times-frac_binary64_420
26×cbrt-unprod_binary64_444 add-sqr-sqrt_binary64_435
24×div-exp_binary64_462
20×pow1_binary64_472
19×*-un-lft-identity_binary64_414
18×associate-*l*_binary64_357
17×add-cube-cbrt_binary64_446
16×associate-*l/_binary64_359
12×associate-/l*_binary64_361
10×cube-prod_binary64_439 pow-prod-down_binary64_482 unpow-prod-down_binary64_490 associate-*r*_binary64_356 frac-times_binary64_424
8×cbrt-undiv_binary64_445 pow-exp_binary64_479 pow-to-exp_binary64_480 tan-quot_binary64_570
6×associate-*r/_binary64_358
5×unswap-sqr_binary64_382
4×flip3-+_binary64_417 sqr-pow_binary64_386 add-log-exp_binary64_450 flip-+_binary64_388
3×cube-mult_binary64_441 *-commutative_binary64_347 unpow3_binary64_477
2×div-inv_binary64_411
1×distribute-lft-in_binary64_365 clear-num_binary64_413 distribute-rgt-in_binary64_366 frac-2neg_binary64_425 distribute-lft-out_binary64_367 associate-/r*_binary64_360
Counts
4 → 159
Calls

4 calls:

24.0ms
(*.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))
12.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
8.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.2s (8.8%)

Counts
4 → 12
Calls

4 calls:

712.0ms
(*.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)))
334.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
118.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
56.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify71.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
055863677

prune261.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1629171
Fresh000
Picked101
Done000
Total1639172

Merged error: 14.2b

Counts
172 → 9
Compiler

Compiled 4996 to 2746 computations (45% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
4.0b
(*.f64 (/.f64 t l) (sin.f64 k))
8.5b
(/.f64 (*.f64 t t) l)
12.6b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite80.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
120×add-exp-log_binary64_449 add-cbrt-cube_binary64_447
70×prod-exp_binary64_460 cbrt-unprod_binary64_444
44×associate-*l/_binary64_359
34×frac-times_binary64_424
29×pow1_binary64_472
21×cbrt-undiv_binary64_445 add-sqr-sqrt_binary64_435 div-exp_binary64_462
18×*-un-lft-identity_binary64_414
17×pow-prod-down_binary64_482
16×add-cube-cbrt_binary64_446 tan-quot_binary64_570
15×associate-*l*_binary64_357
14×associate-*r/_binary64_358
13×times-frac_binary64_420
10×associate-*r*_binary64_356
8×flip3-+_binary64_417 flip-+_binary64_388
4×add-log-exp_binary64_450
3×*-commutative_binary64_347 associate-/r*_binary64_360
2×div-inv_binary64_411 unswap-sqr_binary64_382
1×distribute-lft-in_binary64_365 clear-num_binary64_413 distribute-rgt-in_binary64_366 frac-2neg_binary64_425 distribute-lft-out_binary64_367 associate-/l*_binary64_361
Counts
4 → 159
Calls

4 calls:

28.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series1.2s (8.3%)

Counts
4 → 12
Calls

4 calls:

721.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
305.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
99.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
24.0ms
(/.f64 (*.f64 t t) l)

simplify78.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049614094
149614094

prune243.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1647171
Fresh448
Picked101
Done000
Total16911180

Merged error: 10.7b

Counts
180 → 11
Compiler

Compiled 5220 to 2607 computations (50.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.2b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
4.0b
(*.f64 (/.f64 t l) (sin.f64 k))
12.6b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite112.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
151×add-exp-log_binary64_449 add-cbrt-cube_binary64_447
78×prod-exp_binary64_460 cbrt-unprod_binary64_444
76×times-frac_binary64_420
59×associate-*l*_binary64_357
54×add-sqr-sqrt_binary64_435
51×*-un-lft-identity_binary64_414
49×add-cube-cbrt_binary64_446
47×associate-*l/_binary64_359
37×cbrt-undiv_binary64_445 div-exp_binary64_462
35×frac-times_binary64_424
34×pow1_binary64_472
20×pow-prod-down_binary64_482
16×tan-quot_binary64_570
15×associate-*r/_binary64_358
11×associate-*r*_binary64_356
8×flip3-+_binary64_417 flip-+_binary64_388
5×div-inv_binary64_411
4×*-commutative_binary64_347 add-log-exp_binary64_450
2×unswap-sqr_binary64_382
1×associate-/r/_binary64_362 distribute-lft-in_binary64_365 distribute-rgt-in_binary64_366 distribute-lft-out_binary64_367
Counts
4 → 214
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
17.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.3s (9.1%)

Counts
4 → 12
Calls

4 calls:

708.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
324.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
118.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
107.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify108.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049705442
149705442

prune332.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2224226
Fresh3710
Picked011
Done000
Total22512237

Merged error: 7.6b

Counts
237 → 12
Compiler

Compiled 7112 to 3351 computations (52.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
4.0b
(*.f64 (/.f64 t l) (sin.f64 k))
5.4b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
10.6b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite101.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
103×add-exp-log_binary64_449 add-cbrt-cube_binary64_447
53×prod-exp_binary64_460 cbrt-unprod_binary64_444
41×times-frac_binary64_420
33×add-sqr-sqrt_binary64_435
30×*-un-lft-identity_binary64_414
29×pow1_binary64_472
28×add-cube-cbrt_binary64_446
27×associate-*r/_binary64_358
26×associate-*l/_binary64_359
23×cbrt-undiv_binary64_445 div-exp_binary64_462
20×associate-*l*_binary64_357
19×frac-times_binary64_424
17×pow-prod-down_binary64_482
14×tan-quot_binary64_570
13×associate-/r*_binary64_360
11×associate-/l/_binary64_363
8×flip3-+_binary64_417 flip-+_binary64_388
5×associate-*r*_binary64_356
4×div-inv_binary64_411 add-log-exp_binary64_450
3×*-commutative_binary64_347
2×unswap-sqr_binary64_382
1×associate-/r/_binary64_362 clear-num_binary64_413 frac-2neg_binary64_425 distribute-lft-out_binary64_367 associate-/l*_binary64_361
Counts
4 → 169
Calls

4 calls:

29.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
22.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
11.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.5s (10.8%)

Counts
4 → 12
Calls

4 calls:

545.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
523.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
315.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
104.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify83.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049855062
149855062

prune225.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1765181
Fresh7310
Picked101
Done011
Total1849193

Merged error: 3.9b

Counts
193 → 9
Compiler

Compiled 5599 to 2170 computations (61.2% saved)

regimes152.0ms (1.1%)

Compiler

Compiled 1068 to 804 computations (24.7% saved)

bsearch167.0ms (1.2%)

Steps
ItersRangePoint
7
4.402519394390609e-96
2.2107265848568253e-94
1.334877437522025e-94
9
-5.240841532407058e-111
-2.17754598782611e-116
-5.182823860895149e-111
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05196
15196

end0.0ms (0%)

sample4.0s (29.2%)

Algorithm
1×intervals
Results
1.8s2779×body1024valid
523.0ms1243×body512valid
456.0ms3403×body128valid
369.0ms566×body256valid
194.0ms1477×body128invalid
55.0ms133×body512invalid
39.0ms65×body1024invalid
30.0ms109×body256invalid
9.0ms9×body2048valid
Compiler

Compiled 337 to 249 computations (26.1% saved)

Profiling

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