Details

Time bar (total: 12.6s)

analyze1.8s (14.5%)

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
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14
Compiler

Compiled 25 to 23 computations (8% saved)

sample88.0ms (0.7%)

Algorithm
1×intervals
Results
39.0ms60×body1024valid
20.0ms143×body128valid
14.0ms34×body512valid
5.0ms19×body256valid
Compiler

Compiled 49 to 48 computations (2% saved)

simplify250.0ms (2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0487137
1487137

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 16.2b

Counts
2 → 1
Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))
0.3b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite52.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
32×add-exp-log_binary64_1139
22×add-cbrt-cube_binary64_1137
16×*-un-lft-identity_binary64_1101
15×pow1_binary64_1162
13×add-sqr-sqrt_binary64_1123
12×prod-exp_binary64_1150 add-cube-cbrt_binary64_1136
9×cbrt-unprod_binary64_1134
8×sqrt-prod_binary64_1117
7×unpow-prod-down_binary64_1180 associate-*r*_binary64_1041
6×times-frac_binary64_1107 pow-prod-down_binary64_1172 div-exp_binary64_1152
4×pow-exp_binary64_1169 add-log-exp_binary64_1140 sqrt-div_binary64_1118
3×pow-unpow_binary64_1178 associate-/l*_binary64_1046 cbrt-undiv_binary64_1135
2×distribute-lft-out_binary64_1052 flip3-+_binary64_1104 associate-*r/_binary64_1043 div-inv_binary64_1098 flip-+_binary64_1075
1×*-commutative_binary64_1032 rem-sqrt-square_binary64_1114 pow-pow_binary64_1173 frac-2neg_binary64_1112 sqrt-pow1_binary64_1119 clear-num_binary64_1100 associate-*l*_binary64_1042 sqr-pow_binary64_1073 pow-to-exp_binary64_1170 associate-/r*_binary64_1045 unpow2_binary64_1166 pow1/2_binary64_1181
Counts
4 → 91
Calls

4 calls:

17.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.0ms
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))

series944.0ms (7.5%)

Counts
4 → 12
Calls

4 calls:

318.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
277.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
204.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
145.0ms
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))

simplify54.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
051472554

prune198.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New976103
Fresh000
Picked011
Done000
Total977104

Merged error: 10.5b

Counts
104 → 7
Compiler

Compiled 3282 to 2613 computations (20.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.2b
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
32×sqrt-prod_binary64_1117
18×*-un-lft-identity_binary64_1101
16×add-sqr-sqrt_binary64_1123
12×sqrt-div_binary64_1118
10×pow1_binary64_1162 sqrt-pow1_binary64_1119 add-cube-cbrt_binary64_1136
6×rem-sqrt-square_binary64_1114 pow1/2_binary64_1181
4×add-log-exp_binary64_1140 distribute-lft-out_binary64_1052 add-exp-log_binary64_1139 flip3-+_binary64_1104 add-cbrt-cube_binary64_1137 flip-+_binary64_1075
Counts
4 → 76
Calls

4 calls:

12.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.5s (12.1%)

Counts
4 → 12
Calls

4 calls:

504.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
497.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
267.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
256.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify66.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051532368

prune251.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh055
Picked011
Done011
Total87895

Merged error: 10.5b

Counts
95 → 8
Compiler

Compiled 4564 to 3734 computations (18.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2))))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2)))
15.8b
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
15.8b
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))

rewrite41.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
15×*-un-lft-identity_binary64_1101
14×pow1_binary64_1162 cbrt-prod_binary64_1132
13×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
12×add-sqr-sqrt_binary64_1123
11×add-cube-cbrt_binary64_1136
8×sqrt-prod_binary64_1117
7×associate-*r*_binary64_1041
6×cbrt-unprod_binary64_1134 prod-exp_binary64_1150 times-frac_binary64_1107 pow-prod-down_binary64_1172
4×add-log-exp_binary64_1140 sqrt-div_binary64_1118
2×pow1/3_binary64_1183 distribute-lft-out_binary64_1052 flip3-+_binary64_1104 associate-*r/_binary64_1043 div-inv_binary64_1098 flip-+_binary64_1075 cbrt-div_binary64_1133
1×*-commutative_binary64_1032 rem-sqrt-square_binary64_1114 sqrt-pow1_binary64_1119 associate-*l*_binary64_1042 pow1/2_binary64_1181
Counts
4 → 75
Calls

4 calls:

13.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2))))
6.0ms
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
5.0ms
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
5.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2)))

series1.3s (10.7%)

Counts
4 → 12
Calls

4 calls:

385.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2))))
370.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) 2) (cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 2)))
297.0ms
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
293.0ms
(cbrt.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))

simplify121.0ms (1%)

Algorithm
1×egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
049002317
149002317

prune201.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New87087
Fresh055
Picked011
Done022
Total87895

Merged error: 10.5b

Counts
95 → 8
Compiler

Compiled 3676 to 2946 computations (19.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite62.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
17×*-un-lft-identity_binary64_1101
16×pow1_binary64_1162 sqrt-prod_binary64_1117
13×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
12×add-sqr-sqrt_binary64_1123
9×add-cube-cbrt_binary64_1136
8×sqrt-div_binary64_1118
7×associate-*l*_binary64_1042
6×cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-prod-down_binary64_1172
4×add-log-exp_binary64_1140 distribute-lft-out_binary64_1052 flip3-+_binary64_1104 flip-+_binary64_1075
3×rem-sqrt-square_binary64_1114 sqrt-pow1_binary64_1119 pow1/2_binary64_1181
2×associate-*l/_binary64_1044
1×*-commutative_binary64_1032 associate-*r*_binary64_1041
Counts
4 → 75
Calls

4 calls:

17.0ms
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
10.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.1s (9%)

Counts
4 → 12
Calls

4 calls:

365.0ms
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
264.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
250.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
248.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify49.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
050152542

prune420.0ms (3.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New87087
Fresh044
Picked011
Done033
Total87895

Merged error: 10.5b

Counts
95 → 8
Compiler

Compiled 7313 to 5910 computations (19.2% saved)

regimes367.0ms (2.9%)

Compiler

Compiled 4526 to 4002 computations (11.6% saved)

bsearch3.0ms (0%)

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046152
146152

end0.0ms (0%)

sample3.4s (27.3%)

Algorithm
1×intervals
Results
1.3s2027×body1024valid
541.0ms4531×body128valid
406.0ms952×body512valid
134.0ms488×body256valid
2.0ms2×body2048valid
1.0ms1×body1024invalid
0.0ms1×body128invalid
Compiler

Compiled 866 to 760 computations (12.2% saved)

Profiling

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