Details

Time bar (total: 24.9s)

analyze2.6s (10.6%)

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
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample383.0ms (1.5%)

Algorithm
1×intervals
Results
89.0ms33×body4096invalid
81.0ms125×body1024valid
64.0ms36×body2048invalid
44.0ms35×body2048valid
27.0ms12×body4096valid
23.0ms46×body512valid
11.0ms17×body1024invalid
10.0ms26×body512invalid
5.0ms35×body128invalid
4.0ms27×body128valid
3.0ms12×body256invalid
3.0ms11×body256valid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify177.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
0518532

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 41.5b

Counts
2 → 1
Compiler

Compiled 42 to 34 computations (19% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
1.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
17.5b
(/.f64 (pow.f64 t 3) (*.f64 l l))
26.9b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite77.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
228×add-exp-log_binary64_449
139×prod-exp_binary64_460
52×add-cbrt-cube_binary64_447
51×div-exp_binary64_462
37×times-frac_binary64_420
33×add-sqr-sqrt_binary64_435
32×pow-exp_binary64_479
26×cbrt-unprod_binary64_444
24×add-cube-cbrt_binary64_446 *-un-lft-identity_binary64_414 associate-*r*_binary64_356
23×pow-to-exp_binary64_480 unpow-prod-down_binary64_490
18×associate-*l*_binary64_357
12×associate-/l*_binary64_361
11×pow1_binary64_472
10×associate-*l/_binary64_359 cube-prod_binary64_439
8×cbrt-undiv_binary64_445
5×sqr-pow_binary64_386 unswap-sqr_binary64_382
4×pow-prod-down_binary64_482 add-log-exp_binary64_450 tan-quot_binary64_570
3×div-inv_binary64_411 cube-mult_binary64_441 *-commutative_binary64_347 unpow3_binary64_477
2×frac-times_binary64_424 associate-*r/_binary64_358
1×clear-num_binary64_413 frac-2neg_binary64_425 unpow2_binary64_476 associate-/r*_binary64_360
Counts
4 → 187
Calls

4 calls:

21.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (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 (4.8%)

Counts
4 → 12
Calls

4 calls:

703.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
329.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
119.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
43.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify74.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
051584265

prune297.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New18712199
Fresh000
Picked101
Done000
Total18812200

Merged error: 17.0b

Counts
200 → 12
Compiler

Compiled 5295 to 2712 computations (48.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
0.8b
(*.f64 t (pow.f64 (sin.f64 k) 2))
3.4b
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
23.9b
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))

rewrite77.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
320×add-exp-log_binary64_449
183×prod-exp_binary64_460
173×add-cbrt-cube_binary64_447
87×cbrt-unprod_binary64_444
82×div-exp_binary64_462
46×cbrt-undiv_binary64_445
23×add-sqr-sqrt_binary64_435
20×times-frac_binary64_420
17×add-cube-cbrt_binary64_446 *-un-lft-identity_binary64_414
15×pow-exp_binary64_479 pow-to-exp_binary64_480
9×pow1_binary64_472 associate-*r*_binary64_356
6×div-inv_binary64_411 associate-/r*_binary64_360
4×associate-*l*_binary64_357 unpow-prod-down_binary64_490 add-log-exp_binary64_450 unswap-sqr_binary64_382 associate-/l*_binary64_361
3×pow-prod-down_binary64_482
2×clear-num_binary64_413 *-commutative_binary64_347 sqr-pow_binary64_386 frac-2neg_binary64_425 unpow2_binary64_476
1×associate-/r/_binary64_362
Counts
4 → 184
Calls

4 calls:

17.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
16.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))
9.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
7.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

series995.0ms (4%)

Counts
4 → 12
Calls

4 calls:

517.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
301.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))
107.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
69.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify96.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049855216
149855216

prune259.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New18115196
Fresh4711
Picked101
Done000
Total18622208

Merged error: 10.4b

Counts
208 → 22
Compiler

Compiled 5131 to 2437 computations (52.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2 (/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
0.8b
(*.f64 t (pow.f64 (sin.f64 k) 2))
14.3b
(/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))
15.1b
(/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))

rewrite86.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
288×add-exp-log_binary64_449
184×times-frac_binary64_420
173×add-cbrt-cube_binary64_447
157×div-exp_binary64_462
93×cbrt-undiv_binary64_445
80×prod-exp_binary64_460
57×add-sqr-sqrt_binary64_435
51×add-cube-cbrt_binary64_446 *-un-lft-identity_binary64_414
40×cbrt-unprod_binary64_444
36×associate-/r*_binary64_360
21×div-inv_binary64_411
13×associate-/r/_binary64_362
11×pow-exp_binary64_479 pow-to-exp_binary64_480
8×associate-*r*_binary64_356
5×associate-/l*_binary64_361
4×pow1_binary64_472 unpow-prod-down_binary64_490 add-log-exp_binary64_450 unswap-sqr_binary64_382
3×clear-num_binary64_413 associate-*l*_binary64_357 frac-2neg_binary64_425
2×sqr-pow_binary64_386 unpow2_binary64_476
1×*-commutative_binary64_347
Counts
4 → 261
Calls

4 calls:

18.0ms
(/.f64 2 (/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
14.0ms
(/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
10.0ms
(/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))
7.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

series1.0s (4.2%)

Counts
4 → 12
Calls

4 calls:

333.0ms
(/.f64 2 (/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))))
330.0ms
(/.f64 (*.f64 k k) (/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k))))
298.0ms
(/.f64 (*.f64 l l) (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)))
82.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify124.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050898044

prune408.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New26112273
Fresh18321
Picked101
Done000
Total28015295

Merged error: 1.2b

Counts
295 → 15
Compiler

Compiled 7215 to 3583 computations (50.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l)))
0.8b
(*.f64 t (pow.f64 (sin.f64 k) 2))
1.6b
(*.f64 (/.f64 (sqrt.f64 2) (/.f64 k l)) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))))
5.0b
(*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))

rewrite130.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
317×add-exp-log_binary64_449
194×add-cbrt-cube_binary64_447
163×times-frac_binary64_420
145×div-exp_binary64_462
119×prod-exp_binary64_460 add-sqr-sqrt_binary64_435
93×associate-*l*_binary64_357
92×add-cube-cbrt_binary64_446 *-un-lft-identity_binary64_414
87×cbrt-undiv_binary64_445
65×cbrt-unprod_binary64_444
50×sqrt-prod_binary64_429
34×associate-*r*_binary64_356
11×div-inv_binary64_411 pow-exp_binary64_479 pow-to-exp_binary64_480 unswap-sqr_binary64_382
8×pow1_binary64_472
7×associate-/r/_binary64_362
6×associate-/l*_binary64_361
4×associate-*l/_binary64_359 unpow-prod-down_binary64_490 add-log-exp_binary64_450 frac-times_binary64_424 associate-*r/_binary64_358
3×*-commutative_binary64_347
2×sqr-pow_binary64_386 pow-prod-down_binary64_482 unpow2_binary64_476
1×clear-num_binary64_413 frac-2neg_binary64_425 associate-/r*_binary64_360
Counts
4 → 294
Calls

4 calls:

43.0ms
(*.f64 (/.f64 (sqrt.f64 2) (/.f64 k l)) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))))
16.0ms
(*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))
13.0ms
(/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l)))
7.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

series1.4s (5.5%)

Counts
4 → 12
Calls

4 calls:

502.0ms
(/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l)))
487.0ms
(*.f64 (/.f64 (sqrt.f64 2) (/.f64 k l)) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))))
314.0ms
(*.f64 (/.f64 (*.f64 t (pow.f64 (sin.f64 k) 2)) (cos.f64 k)) (/.f64 k l))
73.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))

simplify124.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050009375

prune511.0ms (2.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New3051306
Fresh01414
Picked101
Done000
Total30615321

Merged error: 0.6b

Counts
321 → 15
Compiler

Compiled 8940 to 4809 computations (46.2% saved)

regimes163.0ms (0.7%)

Compiler

Compiled 1492 to 1147 computations (23.1% saved)

bsearch320.0ms (1.3%)

Steps
ItersRangePoint
8
5.525260981863105e-250
7.029153424277228e-246
4.5304118855774756e-246
7
-9.934200142256346e-108
-6.7107443317503e-110
-8.037426128813863e-109
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03572
13572

end0.0ms (0%)

sample14.3s (57.3%)

Algorithm
1×intervals
Results
4.5s1265×body4096invalid
2.5s3766×body1024valid
2.3s1089×body2048invalid
1.2s1059×body2048valid
1.2s465×body4096valid
624.0ms1400×body512valid
420.0ms675×body1024invalid
184.0ms476×body512invalid
147.0ms1053×body128invalid
142.0ms505×body256valid
137.0ms805×body128valid
80.0ms291×body256invalid
Compiler

Compiled 430 to 325 computations (24.4% saved)

Profiling

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