Details

Time bar (total: 12.2min)

analyze2.1s (0.3%)

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)

sample109.0ms (0%)

Algorithm
1×intervals
Results
43.0ms79×body1024valid
17.0ms45×body512valid
15.0ms111×body128valid
6.0ms44×body128invalid
6.0ms21×body256valid
2.0ms6×body256invalid
2.0ms4×body512invalid
1.0ms1×body1024invalid
Compiler

Compiled 54 to 52 computations (3.7% saved)

simplify150.0ms (0%)

Algorithm
1×egg-herbie
Counts
4 → 4
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0493238
1493238

prune5.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New044
Fresh044
Picked000
Done000
Total088
Error
24.4b
Counts
8 → 5
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

2.0b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
1.5b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (/.f64 k t) 2)
1.5b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
2.0b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.9b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
17.5b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite81.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_798
58×prod-exp_binary64_809
52×add-cbrt-cube_binary64_796
28×times-frac_binary64_766
26×cbrt-unprod_binary64_793 add-sqr-sqrt_binary64_782
24×div-exp_binary64_811
22×*-un-lft-identity_binary64_760
20×pow1_binary64_821
18×associate-*l*_binary64_701
17×add-cube-cbrt_binary64_795
16×associate-*l/_binary64_703
12×associate-/l*_binary64_705
11×associate-*r*_binary64_700
10×frac-times_binary64_770 cube-prod_binary64_788 pow-prod-down_binary64_831 unpow-prod-down_binary64_839
8×cbrt-undiv_binary64_794 pow-exp_binary64_828 pow-to-exp_binary64_829 tan-quot_binary64_919
6×associate-*r/_binary64_702
5×unswap-sqr_binary64_728
4×flip3-+_binary64_763 add-log-exp_binary64_799 flip-+_binary64_734 sqr-pow_binary64_732
3×cube-mult_binary64_790 distribute-lft-out_binary64_711 unpow3_binary64_826 *-commutative_binary64_691
2×div-inv_binary64_757
1×frac-2neg_binary64_771 distribute-lft-in_binary64_709 associate-/r*_binary64_704 distribute-rgt-in_binary64_710 clear-num_binary64_759
Counts
4 → 160
Calls

8 calls:

31.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
13.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
8.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(pow.f64 (/.f64 k t) 2)

series1.7s (0.2%)

Counts
4 → 41
Calls

4 calls:

947.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
459.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
243.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
99.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 2143 to 1844 computations (14% saved)

simplify101.0ms (0%)

Algorithm
1×egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
051254588

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

2.0b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
1.5b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
0.3b
(/.f64 2 (*.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))))
0.2b
(pow.f64 (/.f64 k t) 2)
1.5b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
2.0b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
14.9b
(*.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)))
17.5b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite75.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_798
58×prod-exp_binary64_809
52×add-cbrt-cube_binary64_796
28×times-frac_binary64_766
26×cbrt-unprod_binary64_793 add-sqr-sqrt_binary64_782
24×div-exp_binary64_811
20×pow1_binary64_821
19×*-un-lft-identity_binary64_760
18×associate-*l*_binary64_701
17×add-cube-cbrt_binary64_795
16×associate-*l/_binary64_703
12×associate-/l*_binary64_705
10×frac-times_binary64_770 associate-*r*_binary64_700 cube-prod_binary64_788 pow-prod-down_binary64_831 unpow-prod-down_binary64_839
8×cbrt-undiv_binary64_794 pow-exp_binary64_828 pow-to-exp_binary64_829 tan-quot_binary64_919
6×associate-*r/_binary64_702
5×unswap-sqr_binary64_728
4×flip3-+_binary64_763 add-log-exp_binary64_799 flip-+_binary64_734 sqr-pow_binary64_732
3×cube-mult_binary64_790 unpow3_binary64_826 *-commutative_binary64_691
2×div-inv_binary64_757
1×frac-2neg_binary64_771 distribute-lft-out_binary64_711 distribute-lft-in_binary64_709 associate-/r*_binary64_704 distribute-rgt-in_binary64_710 clear-num_binary64_759
Counts
4 → 159
Calls

8 calls:

23.0ms
(*.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)))
18.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(pow.f64 (/.f64 k t) 2)

series1.7s (0.2%)

Counts
4 → 41
Calls

4 calls:

933.0ms
(*.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)))
437.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
242.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
98.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 2045 to 1746 computations (14.6% saved)

simplify100.0ms (0%)

Algorithm
1×egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
051084484

prune1.9s (0.3%)

Pruning

124 alts after pruning (124 fresh and 0 done)

PrunedKeptTotal
New280121401
Fresh033
Picked000
Done202
Total282124406
Error
13.5b
Counts
406 → 124
Compiler

Compiled 9537 to 6098 computations (36.1% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

2.0b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
0.4b
(*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k)))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (/.f64 k t) 2)
2.0b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
8.9b
(/.f64 (*.f64 t t) l)
14.9b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite83.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
120×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
70×prod-exp_binary64_809 cbrt-unprod_binary64_793
44×associate-*l/_binary64_703
34×frac-times_binary64_770
29×pow1_binary64_821
21×cbrt-undiv_binary64_794 *-un-lft-identity_binary64_760 div-exp_binary64_811 add-sqr-sqrt_binary64_782
17×pow-prod-down_binary64_831
16×add-cube-cbrt_binary64_795 tan-quot_binary64_919
15×associate-*l*_binary64_701
14×associate-*r/_binary64_702
13×times-frac_binary64_766
11×associate-*r*_binary64_700
8×flip3-+_binary64_763 flip-+_binary64_734
4×add-log-exp_binary64_799
3×distribute-lft-out_binary64_711 associate-/r*_binary64_704 *-commutative_binary64_691
2×unswap-sqr_binary64_728 div-inv_binary64_757
1×frac-2neg_binary64_771 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 associate-/l*_binary64_705 clear-num_binary64_759
Counts
4 → 160
Calls

8 calls:

29.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
14.0ms
(*.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)
0.0ms
(pow.f64 (/.f64 k t) 2)

series1.6s (0.2%)

Counts
4 → 43
Calls

4 calls:

904.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
430.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
167.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
67.0ms
(/.f64 (*.f64 t t) l)
Compiler

Compiled 2249 to 1854 computations (17.6% saved)

simplify87.0ms (0%)

Algorithm
1×egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050674967

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

6.7b
(/.f64 l (/.f64 (pow.f64 t 3) l))
5.5b
(/.f64 (pow.f64 t 3) l)
0.2b
(/.f64 2 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))))
0.0b
(*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l))))
0.2b
(/.f64 2 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))))
5.5b
(/.f64 (pow.f64 t 3) l)
6.7b
(/.f64 l (/.f64 (pow.f64 t 3) l))
20.3b
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))

rewrite153.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
884×times-frac_binary64_766
374×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
169×associate-/r*_binary64_704
118×add-exp-log_binary64_798
102×cube-prod_binary64_788 unpow-prod-down_binary64_839
70×add-cbrt-cube_binary64_796 div-exp_binary64_811
36×cbrt-undiv_binary64_794
34×cube-mult_binary64_790 unpow3_binary64_826 sqr-pow_binary64_732
21×prod-exp_binary64_809
19×associate-/l*_binary64_705
16×div-inv_binary64_757
13×cbrt-unprod_binary64_793
6×pow-exp_binary64_828 pow-to-exp_binary64_829
5×associate-/r/_binary64_706
4×frac-2neg_binary64_771 add-log-exp_binary64_799 pow1_binary64_821 clear-num_binary64_759
1×associate-*r/_binary64_702
Counts
4 → 561
Calls

8 calls:

27.0ms
(/.f64 2 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))))
26.0ms
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))
16.0ms
(/.f64 l (/.f64 (pow.f64 t 3) l))
6.0ms
(/.f64 (pow.f64 t 3) l)
0.0ms
(*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l))))

series618.0ms (0.1%)

Counts
4 → 30
Calls

4 calls:

232.0ms
(/.f64 2 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))))
203.0ms
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))
104.0ms
(/.f64 l (/.f64 (pow.f64 t 3) l))
78.0ms
(/.f64 (pow.f64 t 3) l)
Compiler

Compiled 828 to 792 computations (4.3% saved)

simplify181.0ms (0%)

Algorithm
1×egg-herbie
Counts
591 → 591
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
0512711474

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b
(*.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))) (tan.f64 k))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
0.2b
(pow.f64 (/.f64 k t) 2)
0.1b
(*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k)))
2.4b
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))
4.4b
(/.f64 (pow.f64 t (/.f64 3 2)) l)
4.4b
(/.f64 (pow.f64 t 3/2) l)
7.5b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite82.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
143×add-exp-log_binary64_798
83×prod-exp_binary64_809
66×times-frac_binary64_766
62×add-sqr-sqrt_binary64_782
54×*-un-lft-identity_binary64_760
52×add-cube-cbrt_binary64_795
51×add-cbrt-cube_binary64_796
36×div-exp_binary64_811
35×associate-*l/_binary64_703
34×unpow-prod-down_binary64_839
29×frac-times_binary64_770
27×cbrt-unprod_binary64_793
26×associate-*l*_binary64_701
20×pow1_binary64_821
14×associate-/l*_binary64_705
12×pow-exp_binary64_828 pow-to-exp_binary64_829 tan-quot_binary64_919 sqr-pow_binary64_732
11×associate-*r/_binary64_702 pow-prod-down_binary64_831
8×cbrt-undiv_binary64_794 flip3-+_binary64_763 flip-+_binary64_734
7×associate-*r*_binary64_700
6×associate-/r*_binary64_704
4×unswap-sqr_binary64_728 add-log-exp_binary64_799
3×div-inv_binary64_757
2×frac-2neg_binary64_771 clear-num_binary64_759 *-commutative_binary64_691
1×distribute-lft-out_binary64_711 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 210
Calls

8 calls:

29.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
10.0ms
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))
5.0ms
(/.f64 (pow.f64 t (/.f64 3 2)) l)
5.0ms
(/.f64 (pow.f64 t 3/2) l)
0.0ms
(*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k)))

series1.4s (0.2%)

Counts
4 → 39
Calls

4 calls:

1.1s
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
214.0ms
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sin.f64 k))
89.0ms
(/.f64 (pow.f64 t 3/2) l)
85.0ms
(/.f64 (pow.f64 t (/.f64 3 2)) l)
Compiler

Compiled 2279 to 1880 computations (17.5% saved)

simplify130.0ms (0%)

Algorithm
1×egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049805588
149805588

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (sqrt.f64 t) 3)
0.2b
(pow.f64 (/.f64 k t) 2)
0.1b
(*.f64 t (sqrt.f64 t))
1.3b
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k))
2.9b
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l)))
4.4b
(/.f64 (*.f64 t (sqrt.f64 t)) l)
7.5b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite262.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1041×times-frac_binary64_766
414×*-un-lft-identity_binary64_760
409×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
197×add-exp-log_binary64_798
162×sqrt-prod_binary64_776 cube-prod_binary64_788 unpow-prod-down_binary64_839
85×add-cbrt-cube_binary64_796
83×div-exp_binary64_811
79×prod-exp_binary64_809
78×div-inv_binary64_757
33×cbrt-unprod_binary64_793
29×cbrt-undiv_binary64_794 associate-/r*_binary64_704
27×cube-mult_binary64_790 unpow3_binary64_826 sqr-pow_binary64_732
20×associate-/r/_binary64_706
19×associate-/l*_binary64_705
18×pow1_binary64_821
15×associate-*l/_binary64_703
12×pow-exp_binary64_828 pow-to-exp_binary64_829
10×frac-times_binary64_770
9×pow-prod-down_binary64_831
8×associate-*r*_binary64_700 tan-quot_binary64_919
6×associate-*r/_binary64_702
4×flip3-+_binary64_763 add-log-exp_binary64_799 flip-+_binary64_734
3×distribute-lft-out_binary64_711
2×frac-2neg_binary64_771 associate-*l*_binary64_701 clear-num_binary64_759 *-commutative_binary64_691
1×distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 649
Calls

8 calls:

59.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
44.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k))
27.0ms
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l)))
5.0ms
(/.f64 (*.f64 t (sqrt.f64 t)) l)
0.0ms
(*.f64 t (sqrt.f64 t))

series1.4s (0.2%)

Counts
4 → 36
Calls

4 calls:

836.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
404.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k))
92.0ms
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (*.f64 t (sqrt.f64 t)) l)))
86.0ms
(/.f64 (*.f64 t (sqrt.f64 t)) l)
Compiler

Compiled 2036 to 1737 computations (14.7% saved)

simplify264.0ms (0%)

Algorithm
1×egg-herbie
Counts
685 → 685
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0502222409

localize49.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 31/180 (/.f64 (pow.f64 k 6) (/.f64 l (/.f64 (pow.f64 t 3) l))))
0.0b
(+.f64 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))) (+.f64 (*.f64 1/6 (/.f64 (pow.f64 k 6) (/.f64 l (/.f64 t l)))) (+.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))) (*.f64 1/3 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 (pow.f64 t 3) l))))) (*.f64 31/180 (/.f64 (pow.f64 k 6) (/.f64 l (/.f64 (pow.f64 t 3) l)))))))
0.0b
(+.f64 (*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))) (*.f64 1/3 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 (pow.f64 t 3) l)))))
0.0b
(*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l))))
18.4b
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
20.3b
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))
23.6b
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 (pow.f64 t 3) l)))
24.3b
(/.f64 (pow.f64 k 6) (/.f64 l (/.f64 (pow.f64 t 3) l)))

rewrite954.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
6815×times-frac_binary64_766
2804×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
1377×unpow-prod-down_binary64_839
486×cube-prod_binary64_788
459×sqr-pow_binary64_732
419×associate-/r*_binary64_704
162×cube-mult_binary64_790 unpow3_binary64_826
151×add-exp-log_binary64_798
114×div-exp_binary64_811
108×div-inv_binary64_757
52×add-cbrt-cube_binary64_796
30×cbrt-undiv_binary64_794 associate-/r/_binary64_706
22×associate-/l*_binary64_705
21×pow-exp_binary64_828 pow-to-exp_binary64_829
5×prod-exp_binary64_809
4×frac-2neg_binary64_771 add-log-exp_binary64_799 pow1_binary64_821 clear-num_binary64_759
3×cbrt-unprod_binary64_793
Counts
4 → 1000
Calls

8 calls:

49.0ms
(/.f64 (pow.f64 k 6) (/.f64 l (/.f64 (pow.f64 t 3) l)))
42.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 (pow.f64 t 3) l)))
34.0ms
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))
18.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
0.0ms
(*.f64 2 (/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l))))

series1.0s (0.1%)

Counts
4 → 36
Calls

4 calls:

298.0ms
(/.f64 (pow.f64 k 6) (/.f64 l (/.f64 (pow.f64 t 3) l)))
271.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 (pow.f64 t 3) l)))
240.0ms
(/.f64 (*.f64 k k) (/.f64 l (/.f64 (pow.f64 t 3) l)))
218.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
Compiler

Compiled 4680 to 3366 computations (28.1% saved)

simplify372.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1036 → 1036
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0571036392

prune1.5min (12.2%)

Pruning

725 alts after pruning (724 fresh and 1 done)

PrunedKeptTotal
New21296352764
Fresh3089119
Picked000
Done415
Total21637252888
Error
9.0b
Counts
2888 → 725
Compiler

Compiled 99058 to 57180 computations (42.3% saved)

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (/.f64 k t) 2)
0.2b
(/.f64 t (/.f64 l t))
0.4b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.0b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
14.9b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite108.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
151×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
78×prod-exp_binary64_809 cbrt-unprod_binary64_793
76×times-frac_binary64_766
59×associate-*l*_binary64_701
54×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
49×add-cube-cbrt_binary64_795
47×associate-*l/_binary64_703
37×cbrt-undiv_binary64_794 div-exp_binary64_811
35×frac-times_binary64_770
34×pow1_binary64_821
20×pow-prod-down_binary64_831
16×tan-quot_binary64_919
15×associate-*r/_binary64_702
12×associate-*r*_binary64_700
8×flip3-+_binary64_763 flip-+_binary64_734
5×div-inv_binary64_757
4×add-log-exp_binary64_799 *-commutative_binary64_691
3×distribute-lft-out_binary64_711
2×unswap-sqr_binary64_728
1×associate-/r/_binary64_706 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 215
Calls

8 calls:

32.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
17.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
16.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
0.0ms
(/.f64 t (/.f64 l t))

series1.8s (0.2%)

Counts
4 → 47
Calls

4 calls:

930.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
460.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
237.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
158.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
Compiler

Compiled 2439 to 2038 computations (16.4% saved)

simplify104.0ms (0%)

Algorithm
1×egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051816441

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

9.0b
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
2.7b
(*.f64 (/.f64 k l) (/.f64 t l))
0.2b
(/.f64 2 (*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))))
0.0b
(*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))
0.2b
(/.f64 2 (*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))))
2.7b
(*.f64 (/.f64 k l) (/.f64 t l))
9.0b
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
11.7b
(*.f64 k (*.f64 t t))

rewrite69.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
194×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
107×prod-exp_binary64_809 cbrt-unprod_binary64_793
45×cbrt-undiv_binary64_794 div-exp_binary64_811
34×add-sqr-sqrt_binary64_782
32×pow1_binary64_821
25×times-frac_binary64_766
21×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
19×pow-prod-down_binary64_831
17×associate-*l*_binary64_701
15×associate-*r*_binary64_700
12×associate-*r/_binary64_702
5×unswap-sqr_binary64_728
4×add-log-exp_binary64_799
3×associate-*l/_binary64_703 associate-/r/_binary64_706 div-inv_binary64_757 associate-/l*_binary64_705 frac-times_binary64_770 *-commutative_binary64_691
1×frac-2neg_binary64_771 associate-/r*_binary64_704 clear-num_binary64_759
Counts
4 → 172
Calls

8 calls:

18.0ms
(/.f64 2 (*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))))
13.0ms
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
11.0ms
(*.f64 (/.f64 k l) (/.f64 t l))
6.0ms
(*.f64 k (*.f64 t t))
0.0ms
(*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))

series634.0ms (0.1%)

Counts
4 → 33
Calls

4 calls:

241.0ms
(/.f64 2 (*.f64 2 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))))
204.0ms
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
130.0ms
(*.f64 (/.f64 k l) (/.f64 t l))
58.0ms
(*.f64 k (*.f64 t t))
Compiler

Compiled 978 to 888 computations (9.2% saved)

simplify75.0ms (0%)

Algorithm
1×egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
052163245

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

1.6b
(exp.f64 (log.f64 (*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
0.8b
(*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
0.2b
(/.f64 2 (exp.f64 (log.f64 (*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))))
0.2b
(pow.f64 (/.f64 k t) 2)
5.7b
(/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l)
6.0b
(/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l)
15.3b
(log.f64 (*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
16.6b
(*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

rewrite84.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
135×add-exp-log_binary64_798
66×times-frac_binary64_766
54×prod-exp_binary64_809
50×add-cbrt-cube_binary64_796
49×div-exp_binary64_811
36×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
25×associate-*l*_binary64_701
18×frac-times_binary64_770 associate-*r/_binary64_702
17×cbrt-undiv_binary64_794
16×cbrt-unprod_binary64_793
15×pow1_binary64_821
13×rem-log-exp_binary64_801
12×tan-quot_binary64_919
11×log-div_binary64_847
10×div-inv_binary64_757
8×flip3-+_binary64_763 flip-+_binary64_734 associate-/l*_binary64_705
6×associate-*l/_binary64_703 associate-/r*_binary64_704 pow-exp_binary64_828 pow-to-exp_binary64_829 pow-prod-down_binary64_831
4×distribute-lft-in_binary64_709 add-log-exp_binary64_799 distribute-rgt-in_binary64_710
3×log-pow_binary64_849
2×frac-2neg_binary64_771 clear-num_binary64_759
1×associate-/l/_binary64_707 associate-*r*_binary64_700 *-commutative_binary64_691 log-prod_binary64_846
Counts
4 → 179
Calls

8 calls:

27.0ms
(*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
20.0ms
(log.f64 (*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
8.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l)
6.0ms
(/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l)
0.0ms
(pow.f64 (/.f64 k t) 2)

series2.2s (0.3%)

Counts
4 → 53
Calls

4 calls:

895.0ms
(*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
805.0ms
(log.f64 (*.f64 (/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
254.0ms
(/.f64 (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l) l)
229.0ms
(/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l)
Compiler

Compiled 2736 to 2355 computations (13.9% saved)

simplify107.0ms (0%)

Algorithm
1×egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050456421

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(pow.f64 (/.f64 k t) 2)
0.1b
(/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
0.1b
(/.f64 t (sqrt.f64 l))
0.1b
(*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))
0.6b
(cbrt.f64 l)
0.6b
(cbrt.f64 l)
0.8b
(*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
8.0b
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite205.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1031×add-exp-log_binary64_798
598×prod-exp_binary64_809
383×add-cbrt-cube_binary64_796
334×div-exp_binary64_811
234×cbrt-unprod_binary64_793
130×cbrt-undiv_binary64_794
123×associate-*l/_binary64_703
98×frac-times_binary64_770
46×associate-*r/_binary64_702
40×rec-exp_binary64_810 1-exp_binary64_804
38×pow1_binary64_821
32×tan-quot_binary64_919
25×pow-prod-down_binary64_831
16×flip3-+_binary64_763 flip-+_binary64_734
13×*-un-lft-identity_binary64_760
8×add-cube-cbrt_binary64_795 associate-*r*_binary64_700 add-sqr-sqrt_binary64_782
6×cbrt-prod_binary64_791
4×add-log-exp_binary64_799
3×distribute-lft-out_binary64_711
2×pow1/3_binary64_842 associate-*l*_binary64_701 *-commutative_binary64_691
1×distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 311
Calls

8 calls:

65.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
53.0ms
(*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
1.0ms
(cbrt.f64 l)
1.0ms
(cbrt.f64 l)
0.0ms
(*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))

series1.8s (0.2%)

Counts
4 → 31
Calls

4 calls:

1.2s
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
445.0ms
(*.f64 (*.f64 (*.f64 (/.f64 1 (/.f64 (sqrt.f64 l) (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (*.f64 (/.f64 t (sqrt.f64 l)) (/.f64 t (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
77.0ms
(cbrt.f64 l)
72.0ms
(cbrt.f64 l)
Compiler

Compiled 1969 to 1611 computations (18.2% saved)

simplify199.0ms (0%)

Algorithm
1×egg-herbie
Counts
342 → 342
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0516711193

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))
0.1b
(/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))))
0.1b
(/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))
0.0b
(*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))))
0.2b
(/.f64 2 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.3b
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k))
0.3b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k))
4.1b
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite1.5s (0.2%)

Algorithm
1×rewrite-expression-head
Rules
3034×add-exp-log_binary64_798
1544×div-exp_binary64_811
1316×prod-exp_binary64_809
514×add-cbrt-cube_binary64_796
240×pow-exp_binary64_828 pow-to-exp_binary64_829
224×cbrt-unprod_binary64_793
212×cbrt-undiv_binary64_794
95×associate-*l/_binary64_703
64×frac-times_binary64_770
32×pow1_binary64_821
28×tan-quot_binary64_919
26×associate-*r/_binary64_702
23×associate-/r/_binary64_706
19×pow-prod-down_binary64_831
16×flip3-+_binary64_763 flip-+_binary64_734
14×*-un-lft-identity_binary64_760
11×associate-*r*_binary64_700
9×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
4×add-log-exp_binary64_799
3×distribute-lft-out_binary64_711 associate-/l*_binary64_705 associate-*l*_binary64_701 times-frac_binary64_766 *-commutative_binary64_691
1×frac-2neg_binary64_771 distribute-lft-in_binary64_709 associate-/r*_binary64_704 div-inv_binary64_757 distribute-rgt-in_binary64_710 clear-num_binary64_759
Counts
4 → 606
Calls

8 calls:

341.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
322.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
308.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k))
288.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k))
0.0ms
(*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))))

series2.0s (0.3%)

Counts
4 → 44
Calls

4 calls:

823.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
520.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
415.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k)) (tan.f64 k))
228.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l)))) (/.f64 (pow.f64 (sqrt.f64 t) 3/2) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))) (sin.f64 k))
Compiler

Compiled 2525 to 2141 computations (15.2% saved)

simplify376.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
650 → 650
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
0494932943
1494932943

prune1.3min (10.5%)

Pruning

1055 alts after pruning (1052 fresh and 3 done)

PrunedKeptTotal
New13083831691
Fresh50669719
Picked000
Done336
Total136110552416
Error
6.7b
Counts
2416 → 1055
Compiler

Compiled 69073 to 42673 computations (38.2% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

4.2b
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
0.3b
(/.f64 2 (/.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)))
0.2b
(*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))
0.2b
(pow.f64 (/.f64 k t) 2)
4.2b
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
7.2b
(/.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))
12.9b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite93.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
103×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
53×prod-exp_binary64_809 cbrt-unprod_binary64_793
41×times-frac_binary64_766
33×add-sqr-sqrt_binary64_782
30×*-un-lft-identity_binary64_760
29×pow1_binary64_821
28×add-cube-cbrt_binary64_795
27×associate-*r/_binary64_702
26×associate-*l/_binary64_703
23×cbrt-undiv_binary64_794 div-exp_binary64_811
20×associate-*l*_binary64_701
19×frac-times_binary64_770
17×pow-prod-down_binary64_831
14×tan-quot_binary64_919
13×associate-/r*_binary64_704
11×associate-/l/_binary64_707
8×flip3-+_binary64_763 flip-+_binary64_734
5×associate-*r*_binary64_700
4×add-log-exp_binary64_799 div-inv_binary64_757
3×*-commutative_binary64_691
2×unswap-sqr_binary64_728
1×frac-2neg_binary64_771 distribute-lft-out_binary64_711 associate-/r/_binary64_706 associate-/l*_binary64_705 clear-num_binary64_759
Counts
4 → 169
Calls

8 calls:

27.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
27.0ms
(/.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))
10.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
0.0ms
(pow.f64 (/.f64 k t) 2)

series2.4s (0.3%)

Counts
4 → 57
Calls

4 calls:

932.0ms
(/.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))
899.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
439.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
160.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
Compiler

Compiled 2810 to 2221 computations (21% saved)

simplify116.0ms (0%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050266581

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

11.7b
(*.f64 k (*.f64 t t))
9.0b
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
2.7b
(*.f64 (/.f64 k l) (/.f64 t l))
0.2b
(/.f64 1 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))
0.2b
(/.f64 1 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))
2.7b
(*.f64 (/.f64 k l) (/.f64 t l))
9.0b
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
11.7b
(*.f64 k (*.f64 t t))

rewrite73.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
316×add-exp-log_binary64_798
176×add-cbrt-cube_binary64_796
175×prod-exp_binary64_809
91×cbrt-unprod_binary64_793
84×div-exp_binary64_811
54×pow1_binary64_821
44×cbrt-undiv_binary64_794
34×pow-prod-down_binary64_831 add-sqr-sqrt_binary64_782
25×times-frac_binary64_766
21×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
17×associate-*l*_binary64_701
16×rec-exp_binary64_810 1-exp_binary64_804
15×associate-*r*_binary64_700
9×associate-*r/_binary64_702
7×pow-flip_binary64_834
5×unswap-sqr_binary64_728
4×add-log-exp_binary64_799
3×associate-*l/_binary64_703 associate-/r/_binary64_706 div-inv_binary64_757 associate-/l*_binary64_705 frac-times_binary64_770 *-commutative_binary64_691
1×frac-2neg_binary64_771 associate-/r*_binary64_704 inv-pow_binary64_845 clear-num_binary64_759
Counts
4 → 210
Calls

8 calls:

17.0ms
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
15.0ms
(/.f64 1 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))
12.0ms
(*.f64 (/.f64 k l) (/.f64 t l))
5.0ms
(*.f64 k (*.f64 t t))
0.0ms
(/.f64 1 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))

series618.0ms (0.1%)

Counts
4 → 33
Calls

4 calls:

228.0ms
(/.f64 1 (*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l))))
201.0ms
(*.f64 (*.f64 k (*.f64 t t)) (*.f64 (/.f64 k l) (/.f64 t l)))
129.0ms
(*.f64 (/.f64 k l) (/.f64 t l))
59.0ms
(*.f64 k (*.f64 t t))
Compiler

Compiled 882 to 792 computations (10.2% saved)

simplify120.0ms (0%)

Algorithm
1×egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
050653834

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (/.f64 k t) 2)
0.1b
(/.f64 (sqrt.f64 t) l)
0.1b
(*.f64 t (/.f64 (sqrt.f64 t) l))
0.3b
(*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))
1.3b
(*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k))
5.0b
(*.f64 (/.f64 t l) (sin.f64 k))
7.5b
(*.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite216.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1164×add-exp-log_binary64_798
763×prod-exp_binary64_809
484×add-cbrt-cube_binary64_796
323×div-exp_binary64_811
303×cbrt-unprod_binary64_793
103×cbrt-undiv_binary64_794 associate-*l/_binary64_703
100×1-exp_binary64_804
99×frac-times_binary64_770
81×associate-*r/_binary64_702
76×pow1_binary64_821
54×pow-prod-down_binary64_831
40×rec-exp_binary64_810
32×tan-quot_binary64_919
19×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
16×flip3-+_binary64_763 flip-+_binary64_734 associate-*l*_binary64_701
14×add-cube-cbrt_binary64_795
12×associate-*r*_binary64_700
10×times-frac_binary64_766
4×add-log-exp_binary64_799 *-commutative_binary64_691
3×distribute-lft-out_binary64_711
2×unswap-sqr_binary64_728
1×distribute-lft-in_binary64_709 div-inv_binary64_757 distribute-rgt-in_binary64_710
Counts
4 → 396
Calls

8 calls:

60.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
35.0ms
(*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k))
12.0ms
(*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
0.0ms
(*.f64 t (/.f64 (sqrt.f64 t) l))

series1.6s (0.2%)

Counts
4 → 45
Calls

4 calls:

845.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
402.0ms
(*.f64 (*.f64 (/.f64 (sqrt.f64 t) (/.f64 1 1)) (*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))) (tan.f64 k))
219.0ms
(*.f64 (*.f64 (/.f64 t l) (sin.f64 k)) (*.f64 t (/.f64 (sqrt.f64 t) l)))
169.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
Compiler

Compiled 2740 to 2276 computations (16.9% saved)

simplify222.0ms (0%)

Algorithm
1×egg-herbie
Counts
441 → 441
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
0492013813
1492013813

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (sqrt.f64 t) l)
0.1b
(*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
0.1b
(/.f64 (sqrt.f64 t) (cbrt.f64 l))
0.1b
(*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))
0.8b
(*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
0.8b
(*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k))
1.3b
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
7.5b
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite213.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
548×add-exp-log_binary64_798
476×add-cbrt-cube_binary64_796
354×prod-exp_binary64_809 cbrt-unprod_binary64_793
136×associate-*l/_binary64_703
108×frac-times_binary64_770
104×cbrt-undiv_binary64_794 div-exp_binary64_811
96×associate-*r/_binary64_702
92×pow1_binary64_821
66×pow-prod-down_binary64_831
32×tan-quot_binary64_919
16×flip3-+_binary64_763 flip-+_binary64_734
12×*-un-lft-identity_binary64_760 associate-*r*_binary64_700
7×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
4×add-log-exp_binary64_799 associate-*l*_binary64_701 *-commutative_binary64_691
3×distribute-lft-out_binary64_711
1×distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 320
Calls

8 calls:

53.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
31.0ms
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
26.0ms
(*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
25.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k))
0.0ms
(*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))

series1.8s (0.2%)

Counts
4 → 40
Calls

4 calls:

893.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
489.0ms
(*.f64 (*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k)) (tan.f64 k))
279.0ms
(*.f64 (*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))) (sin.f64 k))
137.0ms
(*.f64 (*.f64 t (/.f64 t (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (*.f64 (/.f64 (sqrt.f64 t) l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
Compiler

Compiled 2243 to 1937 computations (13.6% saved)

simplify197.0ms (0%)

Algorithm
1×egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0521911975

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (sqrt.f64 t) (sqrt.f64 l))
0.1b
(*.f64 t (sqrt.f64 t))
0.1b
(/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))
0.0b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0))
1.4b
(*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0))
1.4b
(/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))
4.2b
(*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))))))
10.1b
(/.f64 (*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))))) (*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0)))

rewrite569.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
1408×times-frac_binary64_766
797×sqrt-prod_binary64_776
753×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
614×add-sqr-sqrt_binary64_782
592×*-un-lft-identity_binary64_760
590×add-cube-cbrt_binary64_795
378×prod-exp_binary64_809 cbrt-unprod_binary64_793
268×cbrt-undiv_binary64_794 div-exp_binary64_811
246×associate-/r*_binary64_704
138×associate-*l*_binary64_701
102×frac-times_binary64_770
80×associate-*r/_binary64_702
52×associate-*l/_binary64_703 flip3-+_binary64_763 flip-+_binary64_734
36×tan-quot_binary64_919
35×associate-/l/_binary64_707
27×pow1_binary64_821
23×div-inv_binary64_757
16×pow-prod-down_binary64_831
9×associate-/r/_binary64_706
7×unswap-sqr_binary64_728
5×associate-*r*_binary64_700
4×add-log-exp_binary64_799
2×frac-2neg_binary64_771 associate-/l*_binary64_705 clear-num_binary64_759 *-commutative_binary64_691
1×distribute-lft-out_binary64_711 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 976
Calls

8 calls:

110.0ms
(/.f64 (*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))))) (*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0)))
81.0ms
(*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))))))
53.0ms
(*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0))
43.0ms
(/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))
0.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0))

series1.9s (0.3%)

Counts
4 → 45
Calls

4 calls:

836.0ms
(/.f64 (*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))))) (*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0)))
768.0ms
(*.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (+.f64 (pow.f64 (/.f64 k t) 2) 0)) (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l)))))))
192.0ms
(*.f64 (/.f64 (sqrt.f64 l) (/.f64 t (sqrt.f64 l))) (+.f64 (pow.f64 (/.f64 k t) 2) 0))
76.0ms
(/.f64 (*.f64 t (sqrt.f64 t)) (/.f64 (sqrt.f64 l) (/.f64 (sqrt.f64 t) (sqrt.f64 l))))
Compiler

Compiled 3468 to 2598 computations (25.1% saved)

simplify417.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1021 → 1021
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0533842501

prune3.5min (28.4%)

Pruning

1438 alts after pruning (1434 fresh and 4 done)

PrunedKeptTotal
New18304612291
Fresh749731047
Picked000
Done448
Total190814383346
Error
6.5b
Counts
3346 → 1438
Compiler

Compiled 46773 to 18738 computations (59.9% saved)

simplify4.5s (0.6%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
015519212851

regimes2.0min (16%)

Compiler

Compiled 816092 to 559077 computations (31.5% saved)

bsearch382.0ms (0.1%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
4.9188446717816575e-52
7
-9.21225149433616e-49
-5.560572296628899e-50
-7.590115960093544e-49
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes26.3s (3.6%)

Compiler

Compiled 159550 to 122698 computations (23.1% saved)

bsearch201.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
1.2217593768261278e-53
7
-9.21225149433616e-49
-5.560572296628899e-50
-2.290681488355177e-49
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes22.4s (3.1%)

Compiler

Compiled 147456 to 113956 computations (22.7% saved)

bsearch218.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
6.010803212440071e-52
10
-2.6091665265566725e-61
-7.980882786746329e-72
-2.3146038142536228e-69
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.5s (0.5%)

Compiler

Compiled 26271 to 20224 computations (23% saved)

bsearch197.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
2.7346199221904777e-52
10
-7.980882786746329e-72
-6.349498978716704e-84
-1.6282454218159167e-82
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.1s (0.4%)

Compiler

Compiled 21824 to 16863 computations (22.7% saved)

bsearch188.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
3.159270465779861e-52
10
-2.6091665265566725e-61
-7.980882786746329e-72
-2.277556820959288e-66
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.1s (0.4%)

Compiler

Compiled 20924 to 16183 computations (22.7% saved)

bsearch188.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
1.3104733160998375e-51
10
-2.6091665265566725e-61
-7.980882786746329e-72
-1.2842414582231446e-63
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.0s (0.4%)

Compiler

Compiled 20724 to 16031 computations (22.6% saved)

bsearch155.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
2.916613012300213e-52
7
-9.21225149433616e-49
-5.560572296628899e-50
-9.73272946386767e-50
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes3.3s (0.4%)

Compiler

Compiled 20524 to 15879 computations (22.6% saved)

bsearch179.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
2.127976288491358e-52
10
-491996311.4352942
-0.0002992355378657526
-0.45837407220548676
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes2.3s (0.3%)

Compiler

Compiled 15570 to 12253 computations (21.3% saved)

bsearch105.0ms (0%)

Steps
ItersRangePoint
11
2.0092709877334266e-16
11580681.145643713
26.46224254970775
4
-7.946948966911184e+59
-4.781282715448954e+59
-4.880209785807149e+59
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.4s (0.2%)

Compiler

Compiled 15475 to 12178 computations (21.3% saved)

bsearch0.0ms (0%)

regimes1.6s (0.2%)

Compiler

Compiled 13267 to 10462 computations (21.1% saved)

bsearch193.0ms (0%)

Steps
ItersRangePoint
9
1.1429711350888233e-60
1.0286371713109099e-53
4.786932960485934e-57
10
-2.6091665265566725e-61
-7.980882786746329e-72
-3.496607597689733e-69
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.5s (0.2%)

Compiler

Compiled 8826 to 7217 computations (18.2% saved)

bsearch169.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
4.554858491562186e-52
10
-2.6091665265566725e-61
-7.980882786746329e-72
-1.354451279343827e-71
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes234.0ms (0%)

Compiler

Compiled 1683 to 1336 computations (20.6% saved)

bsearch163.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
1.0700984684013482e-53
10
-2.6091665265566725e-61
-7.980882786746329e-72
-1.168471794670234e-69
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes112.0ms (0%)

Compiler

Compiled 348 to 325 computations (6.6% saved)

bsearch162.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
3.2805991925196846e-52
10
-2.6091665265566725e-61
-7.980882786746329e-72
-4.6903813489031153e-66
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes100.0ms (0%)

Compiler

Compiled 228 to 237 computations (-3.9% saved)

bsearch160.0ms (0%)

Steps
ItersRangePoint
8
1.0286371713109099e-53
6.774196905011623e-51
3.2805991925196846e-52
10
-2.6091665265566725e-61
-7.980882786746329e-72
-5.554707144313222e-68
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes26.0ms (0%)

Accuracy

Total 4.0b remaining (42%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch37.0ms (0%)

Compiler

Compiled 962 to 566 computations (41.2% saved)

simplify14.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02461163
12461163

end0.0ms (0%)

sample2.0min (16.6%)

Algorithm
1×intervals
Results
1.4s2625×body1024valid
496.0ms3580×body128valid
468.0ms1197×body512valid
196.0ms1455×body128invalid
162.0ms589×body256valid
54.0ms142×body512invalid
34.0ms62×body1024invalid
23.0ms86×body256invalid
7.0ms9×body2048valid
Compiler

Compiled 135946 to 92951 computations (31.6% saved)

Pareto

0.7476252169907559

Profiling

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