Details

Time bar (total: 14.3s)

analyze2.3s (15.9%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04978140
14978140
033
133
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 (0.8%)

Algorithm
1×intervals
Results
49.0ms85×body1024valid
18.0ms47×body512valid
13.0ms104×body128valid
6.0ms50×body128invalid
5.0ms20×body256valid
2.0ms5×body512invalid
1.0ms2×body1024invalid
1.0ms3×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify59.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
35.6b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.9b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
14.1b
(*.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)))
18.8b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite75.0ms (0.5%)

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

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)))
16.0ms
(*.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))

series665.0ms (4.7%)

Counts
4 → 12
Calls

4 calls:

391.0ms
(*.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)))
183.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
65.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
27.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify74.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
055553677

prune285.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New16110171
Fresh000
Picked101
Done000
Total16210172
Error
16.7b
Counts
172 → 10
Compiler

Compiled 5033 to 2764 computations (45.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
10.7b
(/.f64 (*.f64 t t) l)
14.1b
(*.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)))

rewrite79.0ms (0.6%)

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 div-exp_binary64_811 add-sqr-sqrt_binary64_782
18×*-un-lft-identity_binary64_760
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
10×associate-*r*_binary64_700
8×flip3-+_binary64_763 flip-+_binary64_734
4×add-log-exp_binary64_799
3×associate-/r*_binary64_704 *-commutative_binary64_691
2×unswap-sqr_binary64_728 div-inv_binary64_757
1×frac-2neg_binary64_771 distribute-lft-out_binary64_711 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 associate-/l*_binary64_705 clear-num_binary64_759
Counts
4 → 159
Calls

4 calls:

29.0ms
(*.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))
8.0ms
(/.f64 (*.f64 t t) l)
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series649.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

395.0ms
(*.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)))
184.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
56.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
14.0ms
(/.f64 (*.f64 t t) l)

simplify96.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049814094
149814094

prune257.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1638171
Fresh369
Picked101
Done000
Total16714181
Error
10.7b
Counts
181 → 14
Compiler

Compiled 5322 to 2673 computations (49.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.3b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
14.1b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite106.0ms (0.7%)

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×add-sqr-sqrt_binary64_782
51×*-un-lft-identity_binary64_760
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
11×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
2×unswap-sqr_binary64_728
1×distribute-lft-out_binary64_711 associate-/r/_binary64_706 distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710
Counts
4 → 214
Calls

4 calls:

31.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
18.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
17.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series676.0ms (4.7%)

Counts
4 → 12
Calls

4 calls:

385.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
174.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
61.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify105.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049795442
149795442

prune344.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2206226
Fresh5813
Picked101
Done000
Total22614240
Error
7.8b
Counts
240 → 14
Compiler

Compiled 7205 to 3413 computations (52.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
8.1b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
12.0b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite92.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
142×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
79×prod-exp_binary64_809 cbrt-unprod_binary64_793
30×cbrt-undiv_binary64_794 div-exp_binary64_811
29×pow1_binary64_821
20×associate-*l*_binary64_701
19×add-sqr-sqrt_binary64_782
17×pow-prod-down_binary64_831
16×*-un-lft-identity_binary64_760 associate-*r/_binary64_702
14×add-cube-cbrt_binary64_795
13×associate-*l/_binary64_703
11×times-frac_binary64_766
5×associate-/l/_binary64_707 associate-*r*_binary64_700
4×flip3-+_binary64_763 add-log-exp_binary64_799 flip-+_binary64_734 frac-times_binary64_770
3×*-commutative_binary64_691
2×unswap-sqr_binary64_728 div-inv_binary64_757
1×frac-2neg_binary64_771 distribute-lft-out_binary64_711 associate-/r/_binary64_706 associate-/r*_binary64_704 associate-/l*_binary64_705 clear-num_binary64_759
Counts
4 → 143
Calls

4 calls:

31.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
22.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
11.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series594.0ms (4.1%)

Counts
4 → 12
Calls

4 calls:

262.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (*.f64 (/.f64 l t) (cos.f64 k)))
184.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
93.0ms
(*.f64 (sin.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify79.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
055554174

prune225.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1478155
Fresh6713
Picked101
Done000
Total15415169
Error
5.1b
Counts
169 → 15
Compiler

Compiled 5020 to 2253 computations (55.1% saved)

regimes1.6s (11.4%)

Accuracy

Total 6.5b remaining (59.6%)

Threshold costs 0b (0%)

Compiler

Compiled 15443 to 11482 computations (25.6% saved)

bsearch300.0ms (2.1%)

Steps
ItersRangePoint
8
2.880148921520459e+227
8.097579111254507e+231
3.8305734146775315e+227
7
8.247022942557457e+193
1.349953017170864e+195
1.1117120927669026e+194
8
3.5472835416240585e-81
1.0907382914714864e-77
6.597454098759182e-81
9
-1.246814367568544e-147
-7.808800158176141e-154
-1.5767169438438566e-152
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
080245
180245

end0.0ms (0%)

sample5.4s (38.1%)

Algorithm
1×intervals
Results
1.4s2675×body1024valid
504.0ms1287×body512valid
444.0ms3427×body128valid
190.0ms1457×body128invalid
161.0ms602×body256valid
46.0ms115×body512invalid
27.0ms105×body256invalid
25.0ms48×body1024invalid
7.0ms9×body2048valid
Compiler

Compiled 2655 to 1944 computations (26.8% saved)

Profiling

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