Details

Time bar (total: 16.5s)

analyze2.2s (13.2%)

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)

sample120.0ms (0.7%)

Algorithm
1×intervals
Results
57.0ms91×body1024valid
16.0ms38×body512valid
15.0ms109×body128valid
10.0ms43×body128invalid
5.0ms18×body256valid
2.0ms3×body1024invalid
1.0ms3×body512invalid
1.0ms3×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify226.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0492835
1492835

prune11.0ms (0.1%)

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 94 to 78 computations (17% saved)

localize19.0ms (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))

rewrite87.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_461
58×prod-exp_binary64_472
52×add-cbrt-cube_binary64_459
28×times-frac_binary64_429
26×add-sqr-sqrt_binary64_445 cbrt-unprod_binary64_456
24×div-exp_binary64_474
20×pow1_binary64_484
19×*-un-lft-identity_binary64_423
18×associate-*l*_binary64_364
17×add-cube-cbrt_binary64_458
16×associate-*l/_binary64_366
12×associate-/l*_binary64_368
10×pow-prod-down_binary64_494 frac-times_binary64_433 associate-*r*_binary64_363 cube-prod_binary64_451 unpow-prod-down_binary64_502
8×pow-to-exp_binary64_492 pow-exp_binary64_491 tan-quot_binary64_582 cbrt-undiv_binary64_457
6×associate-*r/_binary64_365
5×unswap-sqr_binary64_391
4×flip-+_binary64_397 flip3-+_binary64_426 add-log-exp_binary64_462 sqr-pow_binary64_395
3×unpow3_binary64_489 *-commutative_binary64_354 cube-mult_binary64_453
2×div-inv_binary64_420
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/r*_binary64_367
Counts
4 → 159
Calls

4 calls:

26.0ms
(*.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)))
14.0ms
(*.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 (7.5%)

Counts
4 → 12
Calls

4 calls:

717.0ms
(*.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)))
346.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
124.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
47.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify67.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
055923677

prune539.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New16110171
Fresh000
Picked101
Done000
Total16210172

Merged error: 14.2b

Counts
172 → 10
Compiler

Compiled 9916 to 6708 computations (32.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
5.3b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
8.5b
(/.f64 (*.f64 t t) l)
12.6b
(*.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)))

rewrite85.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
113×add-exp-log_binary64_461 add-cbrt-cube_binary64_459
65×prod-exp_binary64_472 cbrt-unprod_binary64_456
44×associate-*l/_binary64_366
34×frac-times_binary64_433
29×pow1_binary64_484
20×cbrt-undiv_binary64_457 div-exp_binary64_474
17×pow-prod-down_binary64_494
16×tan-quot_binary64_582
15×add-sqr-sqrt_binary64_445
14×associate-*r/_binary64_365
13×*-un-lft-identity_binary64_423
11×add-cube-cbrt_binary64_458
10×associate-*r*_binary64_363
9×associate-*l*_binary64_364
8×flip-+_binary64_397 flip3-+_binary64_426
7×times-frac_binary64_429
4×add-log-exp_binary64_462
3×*-commutative_binary64_354 associate-/r*_binary64_367
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/l*_binary64_368
Counts
4 → 151
Calls

4 calls:

30.0ms
(*.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)))
17.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
9.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series1.2s (7.3%)

Counts
4 → 12
Calls

4 calls:

736.0ms
(*.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)))
342.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
108.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
24.0ms
(/.f64 (*.f64 t t) l)

simplify105.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
050134012

prune526.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh639
Picked101
Done000
Total16211173

Merged error: 10.2b

Counts
173 → 11
Compiler

Compiled 10610 to 6710 computations (36.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(/.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))))
2.2b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.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 l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite185.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64_461
304×add-cbrt-cube_binary64_459
259×prod-exp_binary64_472
181×cbrt-unprod_binary64_456
179×frac-times_binary64_433
178×associate-*l/_binary64_366
108×div-exp_binary64_474
81×associate-*r/_binary64_365
69×cbrt-undiv_binary64_457
56×tan-quot_binary64_582
47×associate-/r/_binary64_369
40×pow1_binary64_484
32×flip-+_binary64_397 flip3-+_binary64_426
26×pow-prod-down_binary64_494
21×add-sqr-sqrt_binary64_445
18×*-un-lft-identity_binary64_423 1-exp_binary64_467
16×add-cube-cbrt_binary64_458
15×associate-*l*_binary64_364
13×times-frac_binary64_429
10×associate-*r*_binary64_363
4×add-log-exp_binary64_462
3×*-commutative_binary64_354 associate-/l*_binary64_368
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/r*_binary64_367
Counts
4 → 308
Calls

4 calls:

41.0ms
(*.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)))
41.0ms
(/.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))))
22.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.7s (10.3%)

Counts
4 → 12
Calls

4 calls:

735.0ms
(*.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)))
525.0ms
(/.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))))
333.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
102.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify158.0ms (1%)

Algorithm
1×egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
049659879
149659879

prune959.0ms (5.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New3137320
Fresh5510
Picked011
Done000
Total31813331

Merged error: 7.1b

Counts
331 → 13
Compiler

Compiled 19207 to 12288 computations (36% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
3.7b
(*.f64 (*.f64 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 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite102.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
125×add-exp-log_binary64_461 add-cbrt-cube_binary64_459
78×prod-exp_binary64_472 cbrt-unprod_binary64_456
49×pow1_binary64_484
41×associate-*r/_binary64_365
39×associate-*l/_binary64_366
35×frac-times_binary64_433
32×pow-prod-down_binary64_494
28×associate-*l*_binary64_364
26×add-sqr-sqrt_binary64_445
23×*-un-lft-identity_binary64_423
21×add-cube-cbrt_binary64_458
19×times-frac_binary64_429
18×tan-quot_binary64_582
16×cbrt-undiv_binary64_457 div-exp_binary64_474
11×associate-*r*_binary64_363
8×flip-+_binary64_397 flip3-+_binary64_426
4×*-commutative_binary64_354 add-log-exp_binary64_462
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374
Counts
4 → 176
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
18.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
12.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.5s (8.9%)

Counts
4 → 12
Calls

4 calls:

711.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
330.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
323.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
103.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify90.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050845129

prune500.0ms (3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1844188
Fresh2911
Picked101
Done011
Total18714201

Merged error: 7.1b

Counts
201 → 14
Compiler

Compiled 11187 to 6152 computations (45% saved)

regimes203.0ms (1.2%)

Compiler

Compiled 1542 to 1199 computations (22.2% saved)

bsearch472.0ms (2.9%)

Steps
ItersRangePoint
9
3.729542458797263e+80
3.396506827762424e+86
3.348442255735602e+86
7
2.2107265848568253e-94
2.8466002320610945e-92
2.7205590739503542e-92
9
8.838866232332503e-197
3.855824379362337e-188
1.3971187596612693e-190
11
-9.661454408626084e-148
-1.7372686647172574e-174
-4.046647252992428e-173
9
-5.240841532407058e-111
-2.17754598782611e-116
-2.3324698848381964e-116
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
083246
183246

end0.0ms (0%)

sample4.2s (25.3%)

Algorithm
1×intervals
Results
2.0s2779×body1024valid
514.0ms1243×body512valid
459.0ms3403×body128valid
192.0ms1477×body128invalid
161.0ms566×body256valid
63.0ms133×body512invalid
42.0ms65×body1024invalid
30.0ms109×body256invalid
9.0ms9×body2048valid
Compiler

Compiled 546 to 391 computations (28.4% saved)

Profiling

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