Details

Time bar (total: 13.7s)

analyze2.2s (16%)

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)

sample133.0ms (1%)

Algorithm
1×intervals
Results
68.0ms105×body1024valid
17.0ms40×body512valid
17.0ms92×body128valid
7.0ms48×body128invalid
6.0ms19×body256valid
3.0ms7×body512invalid
1.0ms4×body256invalid
1.0ms1×body1024invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify205.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0492835
1492835

prune4.0ms (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)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
3.3b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.2b
(*.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)))
15.9b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite77.0ms (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:

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)))
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 (9%)

Counts
4 → 12
Calls

4 calls:

727.0ms
(*.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)))
338.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
128.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
42.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify70.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
055863677

prune290.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New16011171
Fresh000
Picked101
Done000
Total16111172

Merged error: 15.1b

Counts
172 → 11
Compiler

Compiled 5123 to 2821 computations (44.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b
(*.f64 (/.f64 t l) (sin.f64 k))
3.3b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.7b
(/.f64 (*.f64 t t) l)
14.2b
(*.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)))

rewrite79.0ms (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 (8.7%)

Counts
4 → 12
Calls

4 calls:

726.0ms
(*.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)))
336.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
106.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
27.0ms
(/.f64 (*.f64 t t) l)

simplify75.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049614094
149614094

prune248.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1656171
Fresh4610
Picked101
Done000
Total17012182

Merged error: 11.0b

Counts
182 → 12
Compiler

Compiled 5264 to 2632 computations (50% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.6b
(*.f64 (/.f64 t l) (sin.f64 k))
3.3b
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
14.2b
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite103.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
151×add-exp-log_binary64_449 add-cbrt-cube_binary64_447
96×prod-exp_binary64_460 cbrt-unprod_binary64_444
61×pow1_binary64_472
47×associate-*l/_binary64_359
41×pow-prod-down_binary64_482
35×frac-times_binary64_424
33×associate-*r/_binary64_358
19×cbrt-undiv_binary64_445 add-sqr-sqrt_binary64_435 div-exp_binary64_462
16×*-un-lft-identity_binary64_414 associate-*l*_binary64_357 tan-quot_binary64_570
14×add-cube-cbrt_binary64_446
11×associate-*r*_binary64_356
10×times-frac_binary64_420
8×flip3-+_binary64_417 flip-+_binary64_388
4×*-commutative_binary64_347 add-log-exp_binary64_450
2×unswap-sqr_binary64_382
1×distribute-lft-in_binary64_365 distribute-rgt-in_binary64_366 div-inv_binary64_411 distribute-lft-out_binary64_367
Counts
4 → 177
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
18.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
13.0ms
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.3s (9.6%)

Counts
4 → 12
Calls

4 calls:

729.0ms
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
347.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
122.0ms
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
113.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify93.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
050034677

prune275.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1836189
Fresh5611
Picked101
Done000
Total18912201

Merged error: 9.7b

Counts
201 → 12
Compiler

Compiled 5721 to 2958 computations (48.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b
(*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k))))
2.6b
(*.f64 (/.f64 t l) (sin.f64 k))
3.3b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
14.2b
(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite95.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
124×add-exp-log_binary64_449 add-cbrt-cube_binary64_447
78×prod-exp_binary64_460 cbrt-unprod_binary64_444
49×pow1_binary64_472
47×associate-*l/_binary64_359
42×associate-*r/_binary64_358
35×frac-times_binary64_424
32×pow-prod-down_binary64_482
20×add-sqr-sqrt_binary64_435
18×associate-*l*_binary64_357
17×*-un-lft-identity_binary64_414
16×cbrt-undiv_binary64_445 tan-quot_binary64_570 div-exp_binary64_462
15×add-cube-cbrt_binary64_446
11×associate-*r*_binary64_356
10×times-frac_binary64_420
8×flip3-+_binary64_417 flip-+_binary64_388
4×*-commutative_binary64_347 add-log-exp_binary64_450
2×unswap-sqr_binary64_382
1×distribute-lft-in_binary64_365 distribute-rgt-in_binary64_366 div-inv_binary64_411 distribute-lft-out_binary64_367
Counts
4 → 164
Calls

4 calls:

29.0ms
(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
13.0ms
(*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.3s (9.4%)

Counts
4 → 12
Calls

4 calls:

732.0ms
(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
331.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
121.0ms
(*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k))))
110.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify92.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
050074309

prune228.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1742176
Fresh2911
Picked101
Done000
Total17711188

Merged error: 7.6b

Counts
188 → 11
Compiler

Compiled 5039 to 2551 computations (49.4% saved)

regimes199.0ms (1.5%)

Compiler

Compiled 1308 to 960 computations (26.6% saved)

bsearch218.0ms (1.6%)

Steps
ItersRangePoint
8
1.238514208247592e+23
1.6260992544432937e+26
2.604016357710232e+25
7
8.957733378832983e-150
1.2796281427062805e-147
1.0610732859761567e-149
0
-1.1370985998610251e-89
-1.1151867640293033e-89
-1.1261426819451643e-89
6
-4.548379915934184e+82
-7.291532268355158e+81
-1.5615747919334984e+82
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
073110
173110

end0.0ms (0%)

sample3.9s (28.5%)

Algorithm
1×intervals
Results
1.7s2680×body1024valid
526.0ms1218×body512valid
504.0ms3539×body128valid
196.0ms1439×body128invalid
159.0ms554×body256valid
66.0ms146×body512invalid
35.0ms55×body1024invalid
30.0ms105×body256invalid
10.0ms9×body2048valid
Compiler

Compiled 404 to 294 computations (27.2% saved)

Profiling

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