Details

Time bar (total: 10.0min)

analyze2.8s (0.5%)

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)

sample131.0ms (0%)

Algorithm
1×intervals
Results
52.0ms68×body1024valid
19.0ms123×body128valid
19.0ms39×body512valid
8.0ms26×body256valid
5.0ms34×body128invalid
4.0ms6×body1024invalid
2.0ms5×body512invalid
2.0ms7×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify232.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
0493135
1493135

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.2b

Counts
2 → 2
Compiler

Compiled 71 to 59 computations (16.9% saved)

localize31.0ms (0%)

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))
5.0b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
13.3b
(*.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))
16.9b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite130.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_1139
58×prod-exp_binary64_1150
52×add-cbrt-cube_binary64_1137
28×times-frac_binary64_1107
26×add-sqr-sqrt_binary64_1123 cbrt-unprod_binary64_1134
24×div-exp_binary64_1152
22×*-un-lft-identity_binary64_1101
20×pow1_binary64_1162
18×associate-*l*_binary64_1042
17×add-cube-cbrt_binary64_1136
16×associate-*l/_binary64_1044
12×associate-/l*_binary64_1046
11×associate-*r*_binary64_1041
10×cube-prod_binary64_1129 unpow-prod-down_binary64_1180 frac-times_binary64_1111 pow-prod-down_binary64_1172
8×pow-exp_binary64_1169 tan-quot_binary64_1260 cbrt-undiv_binary64_1135 pow-to-exp_binary64_1170
6×associate-*r/_binary64_1043
5×unswap-sqr_binary64_1069
4×add-log-exp_binary64_1140 flip3-+_binary64_1104 flip-+_binary64_1075 sqr-pow_binary64_1073
3×*-commutative_binary64_1032 cube-mult_binary64_1131 distribute-lft-out_binary64_1052 unpow3_binary64_1167
2×div-inv_binary64_1098
1×frac-2neg_binary64_1112 distribute-lft-in_binary64_1050 clear-num_binary64_1100 distribute-rgt-in_binary64_1051 associate-/r*_binary64_1045
Counts
4 → 160
Calls

4 calls:

46.0ms
(*.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))
26.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
16.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
16.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))

series833.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

528.0ms
(*.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))
204.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
68.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
31.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify101.0ms (0%)

Algorithm
1×egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
052543739

prune1.3s (0.2%)

Pruning

56 alts after pruning (56 fresh and 0 done)

PrunedKeptTotal
New11656172
Fresh101
Picked101
Done000
Total11856174

Merged error: 13.4b

Counts
174 → 56
Compiler

Compiled 6994 to 4311 computations (38.4% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
2.8b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
9.0b
(/.f64 (*.f64 t t) l)
13.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite126.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
113×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
65×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
44×associate-*l/_binary64_1044
34×frac-times_binary64_1111
29×pow1_binary64_1162
20×div-exp_binary64_1152 cbrt-undiv_binary64_1135
17×pow-prod-down_binary64_1172
16×*-un-lft-identity_binary64_1101 tan-quot_binary64_1260
15×add-sqr-sqrt_binary64_1123
14×associate-*r/_binary64_1043
11×add-cube-cbrt_binary64_1136 associate-*r*_binary64_1041
9×associate-*l*_binary64_1042
8×flip3-+_binary64_1104 flip-+_binary64_1075
7×times-frac_binary64_1107
4×add-log-exp_binary64_1140
3×*-commutative_binary64_1032 distribute-lft-out_binary64_1052 associate-/r*_binary64_1045
2×div-inv_binary64_1098 unswap-sqr_binary64_1069
1×frac-2neg_binary64_1112 distribute-lft-in_binary64_1050 clear-num_binary64_1100 associate-/l*_binary64_1046 distribute-rgt-in_binary64_1051
Counts
4 → 152
Calls

4 calls:

38.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
38.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
11.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
6.0ms
(/.f64 (*.f64 t t) l)

series922.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

576.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
247.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
77.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
21.0ms
(/.f64 (*.f64 t t) l)

simplify145.0ms (0%)

Algorithm
1×egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
051714110

prune1.8s (0.3%)

Pruning

90 alts after pruning (90 fresh and 0 done)

PrunedKeptTotal
New11549164
Fresh144155
Picked101
Done000
Total13090220

Merged error: 7.2b

Counts
220 → 90
Compiler

Compiled 8051 to 4809 computations (40.3% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
2.3b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
13.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite281.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64_1139
304×add-cbrt-cube_binary64_1137
259×prod-exp_binary64_1150
181×cbrt-unprod_binary64_1134
179×frac-times_binary64_1111
178×associate-*l/_binary64_1044
108×div-exp_binary64_1152
81×associate-*r/_binary64_1043
69×cbrt-undiv_binary64_1135
56×tan-quot_binary64_1260
47×associate-/r/_binary64_1047
40×pow1_binary64_1162
32×flip3-+_binary64_1104 flip-+_binary64_1075
26×pow-prod-down_binary64_1172
21×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
18×1-exp_binary64_1145
16×add-cube-cbrt_binary64_1136
15×associate-*l*_binary64_1042
13×times-frac_binary64_1107
11×associate-*r*_binary64_1041
4×add-log-exp_binary64_1140
3×*-commutative_binary64_1032 distribute-lft-out_binary64_1052 associate-/l*_binary64_1046
2×div-inv_binary64_1098 unswap-sqr_binary64_1069
1×frac-2neg_binary64_1112 distribute-lft-in_binary64_1050 clear-num_binary64_1100 distribute-rgt-in_binary64_1051 associate-/r*_binary64_1045
Counts
4 → 309
Calls

4 calls:

77.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
71.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
28.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
17.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.1s (0.2%)

Counts
4 → 12
Calls

4 calls:

511.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
328.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
226.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
56.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify153.0ms (0%)

Algorithm
1×egg-herbie
Counts
321 → 321
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0513810280

prune4.1s (0.7%)

Pruning

162 alts after pruning (161 fresh and 1 done)

PrunedKeptTotal
New22893321
Fresh216889
Picked011
Done000
Total249162411

Merged error: 6.0b

Counts
411 → 162
Compiler

Compiled 16153 to 9878 computations (38.8% saved)

localize35.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
3.2b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
13.7b
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))

rewrite186.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
193×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
87×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
76×times-frac_binary64_1107
64×div-exp_binary64_1152 cbrt-undiv_binary64_1135
53×add-sqr-sqrt_binary64_1123
49×*-un-lft-identity_binary64_1101
43×add-cube-cbrt_binary64_1136
34×associate-*l*_binary64_1042
24×associate-*r*_binary64_1041
17×pow1_binary64_1162
13×associate-/l*_binary64_1046
11×associate-*l/_binary64_1044
10×associate-*r/_binary64_1043
8×associate-/r/_binary64_1047 pow-prod-down_binary64_1172
7×div-inv_binary64_1098
6×tan-quot_binary64_1260
4×frac-times_binary64_1111 add-log-exp_binary64_1140 unswap-sqr_binary64_1069
3×*-commutative_binary64_1032 distribute-lft-out_binary64_1052
1×frac-2neg_binary64_1112 clear-num_binary64_1100 flip3-+_binary64_1104 associate-/l/_binary64_1048 flip-+_binary64_1075 associate-/r*_binary64_1045
Counts
4 → 215
Calls

4 calls:

73.0ms
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))
24.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
20.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
17.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.0s (0.2%)

Counts
4 → 12
Calls

4 calls:

387.0ms
(*.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))
313.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
245.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
93.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify135.0ms (0%)

Algorithm
1×egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
051046374

prune3.6s (0.6%)

Pruning

210 alts after pruning (210 fresh and 0 done)

PrunedKeptTotal
New14978227
Fresh28132160
Picked101
Done101
Total179210389

Merged error: 6.0b

Counts
389 → 210
Compiler

Compiled 6896 to 2463 computations (64.3% saved)

regimes15.7s (2.6%)

Compiler

Compiled 95311 to 70590 computations (25.9% saved)

bsearch9.4min (94.2%)

Steps
ItersRangePoint
7
4.5728421752699615e-197
1.2572577928381923e-195
1.0062019770114916e-196
9
-2.3689885865584153e-140
-3.183498210043425e-145
-5.484676672401404e-144
Compiler

Compiled 1 to 3 computations (-200% saved)

Profiling

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