Details

Time bar (total: 13.0s)

analyze1.9s (14.9%)

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)

sample107.0ms (0.8%)

Algorithm
1×intervals
Results
52.0ms106×body1024valid
12.0ms97×body128valid
11.0ms32×body512valid
9.0ms20×body256valid
7.0ms55×body128invalid
1.0ms5×body256invalid
1.0ms3×body512invalid
1.0ms2×body1024invalid
1.0ms1×body2048valid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify142.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
34.5b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize20.0ms (0.2%)

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))
4.4b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
12.9b
(*.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)))
18.0b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite70.0ms (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:

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)))
12.0ms
(*.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))

series666.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

392.0ms
(*.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))
26.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify72.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
055553677

prune264.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New16011171
Fresh000
Picked101
Done000
Total16111172
Error
15.4b
Counts
172 → 11
Compiler

Compiled 5056 to 2787 computations (44.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
2.3b
(*.f64 (/.f64 t l) (sin.f64 k))
7.4b
(/.f64 (*.f64 t t) l)
12.9b
(*.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)))

rewrite73.0ms (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:

26.0ms
(*.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)))
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)

series643.0ms (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)))
177.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
57.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
13.0ms
(/.f64 (*.f64 t t) l)

simplify97.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049814094
149814094

prune239.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1647171
Fresh6410
Picked101
Done000
Total17111182
Error
11.0b
Counts
182 → 11
Compiler

Compiled 5216 to 2605 computations (50.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.2b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
2.3b
(*.f64 (/.f64 t l) (sin.f64 k))
12.9b
(*.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)))

rewrite102.0ms (0.8%)

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:

30.0ms
(*.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)))
19.0ms
(*.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))

series700.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

387.0ms
(*.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)))
182.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
76.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
56.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify108.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049795442
149795442

prune324.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2206226
Fresh3710
Picked101
Done000
Total22413237
Error
6.9b
Counts
237 → 13
Compiler

Compiled 7180 to 3393 computations (52.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
2.3b
(*.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))
10.5b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite91.0ms (0.7%)

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

4 calls:

30.0ms
(/.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))
21.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
11.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series821.0ms (6.3%)

Counts
4 → 12
Calls

4 calls:

300.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
294.0ms
(/.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))
172.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify85.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
051325062

prune223.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1774181
Fresh5712
Picked101
Done000
Total18311194
Error
5.0b
Counts
194 → 11
Compiler

Compiled 5599 to 2170 computations (61.2% saved)

regimes1.2s (9.6%)

Accuracy

Total 4.2b remaining (45.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13591 to 10119 computations (25.5% saved)

bsearch133.0ms (1%)

Steps
ItersRangePoint
8
1.0201540763878502e-99
3.30552484343457e-97
3.267593914085643e-97
6
-5.708449964234855e-92
-7.85050282213969e-93
-3.3282816177892314e-92
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053129
153129

end0.0ms (0%)

sample4.8s (36.7%)

Algorithm
1×intervals
Results
1.4s2755×body1024valid
427.0ms3468×body128valid
416.0ms1166×body512valid
180.0ms1494×body128invalid
150.0ms599×body256valid
51.0ms139×body512invalid
33.0ms68×body1024invalid
23.0ms94×body256invalid
9.0ms12×body2048valid
Compiler

Compiled 2269 to 1674 computations (26.2% saved)

Profiling

Loading profile data...