Details

Time bar (total: 9.2s)

analyze402.0ms (4.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14
Compiler

Compiled 17 to 16 computations (5.9% saved)

sample83.0ms (0.9%)

Algorithm
1×intervals
Results
24.0ms54×body1024nan
20.0ms256×body128valid
12.0ms90×body128overflowed
7.0ms23×body512nan
3.0ms14×body256nan
2.0ms35×body128nan
1.0ms10×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify145.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0493322
1493322

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.2b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b
(*.f64 (*.f64 2 PI.f64) n)

rewrite33.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64_1107
42×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
33×add-cube-cbrt_binary64_1136
26×add-exp-log_binary64_1139
22×pow-unpow_binary64_1178
18×sqrt-prod_binary64_1117
14×pow1_binary64_1162
10×add-cbrt-cube_binary64_1137
9×prod-exp_binary64_1150
8×unpow-prod-down_binary64_1180 sqr-pow_binary64_1073
6×pow-exp_binary64_1169 difference-of-squares_binary64_1070 pow-prod-down_binary64_1172 associate-/r*_binary64_1045
5×associate-/l*_binary64_1046 div-exp_binary64_1152
3×cbrt-unprod_binary64_1134 add-log-exp_binary64_1140 pow-pow_binary64_1173 distribute-lft-out--_binary64_1053 associate-*r*_binary64_1041
2×div-inv_binary64_1098 pow-sub_binary64_1177 pow-to-exp_binary64_1170 div-sub_binary64_1106
1×*-commutative_binary64_1032 frac-2neg_binary64_1112 clear-num_binary64_1100 associate-/l/_binary64_1048 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042
Counts
3 → 115
Calls

3 calls:

11.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)

series259.0ms (2.8%)

Counts
3 → 9
Calls

3 calls:

159.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
81.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
19.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify82.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049893537
149893537

prune191.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11212124
Fresh101
Picked101
Done000
Total11412126
Error
0.0b
Counts
126 → 12
Compiler

Compiled 3252 to 2225 computations (31.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.2b
(*.f64 (*.f64 2 PI.f64) n)

rewrite40.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
127×add-exp-log_binary64_1139
67×prod-exp_binary64_1150
36×pow-exp_binary64_1169
30×div-exp_binary64_1152
20×pow1_binary64_1162
19×add-cbrt-cube_binary64_1137
15×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
14×times-frac_binary64_1107
13×pow-unpow_binary64_1178
12×pow-to-exp_binary64_1170
9×pow-prod-down_binary64_1172
7×cbrt-unprod_binary64_1134
6×associate-*r*_binary64_1041
5×associate-/l*_binary64_1046
4×add-log-exp_binary64_1140
3×unpow-prod-down_binary64_1180 pow-pow_binary64_1173 sqr-pow_binary64_1073
2×*-commutative_binary64_1032 div-inv_binary64_1098 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042
1×frac-2neg_binary64_1112 clear-num_binary64_1100 associate-/r*_binary64_1045
Counts
4 → 118
Calls

4 calls:

10.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)

series384.0ms (4.2%)

Counts
4 → 12
Calls

4 calls:

238.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
103.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
23.0ms
(*.f64 (*.f64 2 PI.f64) n)
19.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify62.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
052592652

prune169.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh11011
Picked011
Done000
Total13012142
Error
0b
Counts
142 → 12
Compiler

Compiled 3389 to 2351 computations (30.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.2b
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))

rewrite67.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
284×times-frac_binary64_1107
126×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
111×sqrt-prod_binary64_1117
33×add-exp-log_binary64_1139
28×unpow-prod-down_binary64_1180 sqr-pow_binary64_1073
24×associate-/r*_binary64_1045
20×pow1_binary64_1162
19×add-cbrt-cube_binary64_1137
11×div-exp_binary64_1152
9×prod-exp_binary64_1150 pow-prod-down_binary64_1172
8×div-inv_binary64_1098
6×cbrt-unprod_binary64_1134 associate-/l*_binary64_1046 associate-*r*_binary64_1041
4×add-log-exp_binary64_1140
3×pow-exp_binary64_1169 sqrt-pow1_binary64_1119 cbrt-undiv_binary64_1135
2×*-commutative_binary64_1032 associate-*l*_binary64_1042
1×frac-2neg_binary64_1112 clear-num_binary64_1100 associate-/r/_binary64_1047 pow-to-exp_binary64_1170 pow1/2_binary64_1181
Counts
4 → 241
Calls

4 calls:

16.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series304.0ms (3.3%)

Counts
4 → 12
Calls

4 calls:

245.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
23.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
18.0ms
(*.f64 (*.f64 2 PI.f64) n)
18.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify157.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0497611847
1497611847

prune564.0ms (6.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2521253
Fresh3710
Picked011
Done011
Total25510265
Error
0b
Counts
265 → 10
Compiler

Compiled 9372 to 6221 computations (33.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))
1.0b
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))

rewrite232.0ms (2.5%)

Algorithm
1×rewrite-expression-head
Rules
898×times-frac_binary64_1107
500×add-sqr-sqrt_binary64_1123
437×sqrt-prod_binary64_1117
392×*-un-lft-identity_binary64_1101
381×add-cube-cbrt_binary64_1136
209×associate-*r*_binary64_1041
142×add-exp-log_binary64_1139
90×sqr-pow_binary64_1073
78×unpow-prod-down_binary64_1180
71×div-exp_binary64_1152
43×prod-exp_binary64_1150
38×associate-/r*_binary64_1045
33×unswap-sqr_binary64_1069
32×add-cbrt-cube_binary64_1137
17×div-inv_binary64_1098
16×associate-*l*_binary64_1042
15×pow-exp_binary64_1169
13×pow1_binary64_1162 cbrt-undiv_binary64_1135
9×associate-/l*_binary64_1046
8×1-exp_binary64_1145 rec-exp_binary64_1151
6×cbrt-unprod_binary64_1134
5×pow-to-exp_binary64_1170
4×add-log-exp_binary64_1140 sqrt-pow1_binary64_1119 pow-flip_binary64_1175
3×pow-prod-down_binary64_1172
2×frac-2neg_binary64_1112 clear-num_binary64_1100 associate-/r/_binary64_1047 pow1/2_binary64_1181
1×inv-pow_binary64_1186 *-commutative_binary64_1032 frac-times_binary64_1111 associate-*r/_binary64_1043 associate-*l/_binary64_1044
Counts
4 → 616
Calls

4 calls:

102.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
18.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))
2.0ms
(sqrt.f64 (*.f64 2 PI.f64))

series406.0ms (4.4%)

Counts
4 → 8
Calls

4 calls:

260.0ms
(*.f64 (/.f64 1 (sqrt.f64 (*.f64 2 PI.f64))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))))
145.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.0ms
(/.f64 1 (sqrt.f64 (*.f64 2 PI.f64)))
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))

simplify243.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
624 → 624
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0500825887

prune1.7s (18.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New6240624
Fresh077
Picked011
Done022
Total62410634
Error
0b
Counts
634 → 10
Compiler

Compiled 24277 to 14691 computations (39.5% saved)

regimes345.0ms (3.7%)

Accuracy

Total 0.3b remaining (97.9%)

Threshold costs 0.3b (97.9%)

Compiler

Compiled 4490 to 3730 computations (16.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01531
11531

end0.0ms (0%)

sample3.3s (35.3%)

Algorithm
1×intervals
Results
619.0ms8000×body128valid
609.0ms1313×body1024nan
312.0ms2285×body128overflowed
218.0ms687×body512nan
62.0ms991×body128nan
62.0ms350×body256nan
23.0ms250×body128invalid
Compiler

Compiled 1147 to 954 computations (16.8% saved)

Profiling

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