Details

Time bar (total: 18.5s)

analyze2.0s (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
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)

sample102.0ms (0.5%)

Algorithm
1×intervals
Results
50.0ms90×body1024valid
15.0ms117×body128valid
12.0ms33×body512valid
5.0ms42×body128invalid
4.0ms16×body256valid
1.0ms3×body1024invalid
1.0ms3×body512invalid
1.0ms4×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify145.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 33.5b

Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.6b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
12.1b
(*.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)))
16.8b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite77.0ms (0.4%)

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:

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))
11.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))

series2.0s (10.7%)

Counts
4 → 40
Calls

4 calls:

1.0s
(*.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)))
535.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
286.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
114.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 2036 to 1763 computations (13.4% saved)

simplify101.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049724454
149724454

prune325.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New18712199
Fresh000
Picked101
Done000
Total18812200

Merged error: 15.2b

Counts
200 → 12
Compiler

Compiled 5811 to 3222 computations (44.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b
(*.f64 (/.f64 t l) (sin.f64 k))
3.6b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
9.1b
(/.f64 (*.f64 t t) l)
12.1b
(*.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)))

rewrite82.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
120×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
70×prod-exp_binary64_468 cbrt-unprod_binary64_452
44×associate-*l/_binary64_362
34×frac-times_binary64_429
29×pow1_binary64_480
21×add-sqr-sqrt_binary64_441 div-exp_binary64_470 cbrt-undiv_binary64_453
18×*-un-lft-identity_binary64_419
17×pow-prod-down_binary64_490
16×add-cube-cbrt_binary64_454 tan-quot_binary64_578
15×associate-*l*_binary64_360
14×associate-*r/_binary64_361
13×times-frac_binary64_425
10×associate-*r*_binary64_359
8×flip3-+_binary64_422 flip-+_binary64_393
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 → 159
Calls

4 calls:

32.0ms
(*.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)))
16.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series1.8s (10%)

Counts
4 → 42
Calls

4 calls:

1.0s
(*.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)))
531.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
217.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
70.0ms
(/.f64 (*.f64 t t) l)
Compiler

Compiled 2148 to 1779 computations (17.2% saved)

simplify128.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
049774913
149774913

prune295.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1938201
Fresh6511
Picked101
Done000
Total20013213

Merged error: 8.9b

Counts
213 → 13
Compiler

Compiled 6125 to 3091 computations (49.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
3.1b
(*.f64 (/.f64 t l) (sin.f64 k))
3.6b
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
12.1b
(*.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)))

rewrite92.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
151×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
96×prod-exp_binary64_468 cbrt-unprod_binary64_452
61×pow1_binary64_480
47×associate-*l/_binary64_362
41×pow-prod-down_binary64_490
35×frac-times_binary64_429
33×associate-*r/_binary64_361
19×add-sqr-sqrt_binary64_441 div-exp_binary64_470 cbrt-undiv_binary64_453
16×*-un-lft-identity_binary64_419 associate-*l*_binary64_360 tan-quot_binary64_578
14×add-cube-cbrt_binary64_454
11×associate-*r*_binary64_359
10×times-frac_binary64_425
8×flip3-+_binary64_422 flip-+_binary64_393
4×add-log-exp_binary64_458 *-commutative_binary64_350
2×unswap-sqr_binary64_387
1×distribute-rgt-in_binary64_369 div-inv_binary64_416 distribute-lft-out_binary64_370 distribute-lft-in_binary64_368
Counts
4 → 177
Calls

4 calls:

29.0ms
(*.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)))
20.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
12.0ms
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series2.1s (11.1%)

Counts
4 → 46
Calls

4 calls:

1.0s
(*.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)))
544.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
271.0ms
(*.f64 (*.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k)))
217.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
Compiler

Compiled 2324 to 1949 computations (16.1% saved)

simplify104.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049715514
149715514

prune325.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2185223
Fresh3912
Picked101
Done000
Total22214236

Merged error: 7.1b

Counts
236 → 14
Compiler

Compiled 6647 to 3476 computations (47.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k))))
3.1b
(*.f64 (/.f64 t l) (sin.f64 k))
3.6b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
12.1b
(*.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)))

rewrite90.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
124×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
78×prod-exp_binary64_468 cbrt-unprod_binary64_452
49×pow1_binary64_480
47×associate-*l/_binary64_362
42×associate-*r/_binary64_361
35×frac-times_binary64_429
32×pow-prod-down_binary64_490
20×add-sqr-sqrt_binary64_441
18×associate-*l*_binary64_360
17×*-un-lft-identity_binary64_419
16×div-exp_binary64_470 tan-quot_binary64_578 cbrt-undiv_binary64_453
15×add-cube-cbrt_binary64_454
11×associate-*r*_binary64_359
10×times-frac_binary64_425
8×flip3-+_binary64_422 flip-+_binary64_393
4×add-log-exp_binary64_458 *-commutative_binary64_350
2×unswap-sqr_binary64_387
1×distribute-rgt-in_binary64_369 div-inv_binary64_416 distribute-lft-out_binary64_370 distribute-lft-in_binary64_368
Counts
4 → 164
Calls

4 calls:

28.0ms
(*.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)))
16.0ms
(*.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))))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series2.1s (11.1%)

Counts
4 → 46
Calls

4 calls:

1.0s
(*.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)))
542.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
267.0ms
(*.f64 t (*.f64 (/.f64 t l) (*.f64 (/.f64 t l) (sin.f64 k))))
217.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
Compiler

Compiled 2324 to 1949 computations (16.1% saved)

simplify123.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049675213
149675213

prune294.0ms (1.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New2073210
Fresh11213
Picked011
Done000
Total20816224

Merged error: 6.2b

Counts
224 → 16
Compiler

Compiled 5978 to 3015 computations (49.6% saved)

regimes1.2s (6.5%)

Compiler

Compiled 13218 to 10229 computations (22.6% saved)

bsearch214.0ms (1.2%)

Steps
ItersRangePoint
8
4.994361764765953e-101
4.9509333156362976e-98
3.4832430358521343e-99
9
-5.202478802985146e-37
-1.9374592084565792e-42
-9.309408527201053e-42
6
-1.7193770730774465e+119
-4.017531635208098e+118
-4.0656703024351655e+118
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
062158
162158

end0.0ms (0%)

sample4.8s (26.1%)

Algorithm
1×intervals
Results
1.4s2715×body1024valid
453.0ms1232×body512valid
432.0ms3510×body128valid
177.0ms1441×body128invalid
133.0ms533×body256valid
47.0ms122×body512invalid
34.0ms61×body1024invalid
24.0ms100×body256invalid
8.0ms10×body2048valid
Compiler

Compiled 2193 to 1676 computations (23.6% saved)

Profiling

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