Details

Time bar (total: 50.8s)

analyze3.5s (6.8%)

Algorithm
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)

sample175.0ms (0.3%)

Algorithm
intervals
Results
90.0ms75×body1024valid
28.0ms135×body128valid
24.0ms31×body512valid
7.0ms15×body256valid
Compiler

Compiled 49 to 48 computations (2% saved)

simplify337.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (170.0ms)

IterNodesCost
0487137
1487137

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
18.9b
Counts
2 → 1
Compiler

Compiled 48 to 44 computations (8.3% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))
0.2b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.2b
(*.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))))
11.5b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite467.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
18.9b
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×add-cube-cbrt_binary64_1136 prod-exp_binary64_1150
cbrt-unprod_binary64_1134
sqrt-prod_binary64_1117
associate-*r*_binary64_1041 unpow-prod-down_binary64_1180
pow-prod-down_binary64_1172 times-frac_binary64_1107 div-exp_binary64_1152
add-log-exp_binary64_1140 sqrt-div_binary64_1118 pow-exp_binary64_1169
pow-unpow_binary64_1178 cbrt-undiv_binary64_1135 associate-/l*_binary64_1046
flip3-+_binary64_1104 flip-+_binary64_1075 distribute-lft-out_binary64_1052 associate-*r/_binary64_1043 div-inv_binary64_1098
pow1/2_binary64_1181 sqrt-pow1_binary64_1119 rem-sqrt-square_binary64_1114 associate-*l*_binary64_1042 *-commutative_binary64_1032 pow-pow_binary64_1173 pow-to-exp_binary64_1170 unpow2_binary64_1166 sqr-pow_binary64_1073 frac-2neg_binary64_1112 clear-num_binary64_1100 associate-/r*_binary64_1045
Counts
4 → 91
Calls

4 calls:

34.0ms
(*.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))))
25.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
16.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
12.0ms
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))
Compiler

Compiled 3313 to 2634 computations (20.5% saved)

series4.0s (7.9%)

Error
0.1b
Counts
4 → 61
Calls

4 calls:

1.7s
(*.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))))
1.1s
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
570.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
514.0ms
(/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))
Compiler

Compiled 4549 to 3906 computations (14.1% saved)

simplify171.0ms (0.3%)

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (98.0ms)

IterNodesCost
049724007
149724007

prune576.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1457152
Fresh000
Picked011
Done000
Total1458153
Error
0.0b
Counts
153 → 8
Compiler

Compiled 4592 to 3542 computations (22.9% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b
(*.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)))
11.5b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.5b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.5b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite1.1s (2.1%)

Algorithm
rewrite-expression-head
Error
0.0b
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
add-cube-cbrt_binary64_1136
sqrt-div_binary64_1118
associate-*l*_binary64_1042
pow-prod-down_binary64_1172 prod-exp_binary64_1150 cbrt-unprod_binary64_1134
add-log-exp_binary64_1140 flip3-+_binary64_1104 flip-+_binary64_1075 distribute-lft-out_binary64_1052
pow1/2_binary64_1181 sqrt-pow1_binary64_1119 rem-sqrt-square_binary64_1114
associate-*l/_binary64_1044
associate-*r*_binary64_1041 *-commutative_binary64_1032
Counts
4 → 75
Calls

4 calls:

32.0ms
(*.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)))
17.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
Compiler

Compiled 6993 to 5666 computations (19% saved)

series5.9s (11.6%)

Error
0.0b
Counts
4 → 85
Calls

4 calls:

1.7s
(*.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)))
1.2s
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.1s
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.1s
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
Compiler

Compiled 17377 to 14304 computations (17.7% saved)

simplify119.0ms (0.2%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050294934

prune1.7s (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1600160
Fresh066
Picked011
Done011
Total1608168
Error
0.0b
Counts
168 → 8
Compiler

Compiled 13437 to 10665 computations (20.6% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
6.1b
(sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
15.0b
(-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
22.7b
(/.f64 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

rewrite1.2s (2.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
18×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
16×sqrt-prod_binary64_1117
15×*-un-lft-identity_binary64_1101
12×add-sqr-sqrt_binary64_1123
10×add-cube-cbrt_binary64_1136
sqrt-div_binary64_1118
times-frac_binary64_1107 associate-/r*_binary64_1045
pow1_binary64_1162 prod-exp_binary64_1150 add-log-exp_binary64_1140 cbrt-unprod_binary64_1134
div-exp_binary64_1152 cbrt-undiv_binary64_1135 distribute-lft-out_binary64_1052 flip3-+_binary64_1104 flip-+_binary64_1075
associate-*l/_binary64_1044 associate-/l/_binary64_1048 associate-/r/_binary64_1047 pow1/2_binary64_1181 sqrt-pow1_binary64_1119 rem-sqrt-square_binary64_1114
frac-2neg_binary64_1112 clear-num_binary64_1100 div-inv_binary64_1098 associate-/l*_binary64_1046 diff-log_binary64_1193 flip3--_binary64_1105 sub-neg_binary64_1094 flip--_binary64_1076 cancel-sign-sub-inv_binary64_1067 distribute-rgt-out--_binary64_1055
Counts
4 → 82
Calls

4 calls:

61.0ms
(/.f64 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
30.0ms
(sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
24.0ms
(-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
Compiler

Compiled 8883 to 7145 computations (19.6% saved)

series15.0s (29.4%)

Error
0.0b
Counts
4 → 74
Calls

4 calls:

8.2s
(/.f64 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) (sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
2.5s
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
2.2s
(-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.6s
(sqrt.f64 (+.f64 (*.f64 1 1) (-.f64 (*.f64 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (*.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
Compiler

Compiled 11939 to 10058 computations (15.8% saved)

simplify244.0ms (0.5%)

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (108.0ms)

IterNodesCost
049678216
149678216

prune1.4s (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1560156
Fresh055
Picked011
Done022
Total1568164
Error
0.0b
Counts
164 → 8
Compiler

Compiled 10369 to 8179 computations (21.1% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (/.f64 1/2 J) 2)
6.2b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2)))))
11.5b
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))))
16.6b
(*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))

rewrite907.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
72×add-sqr-sqrt_binary64_1123
59×unpow-prod-down_binary64_1180
48×add-exp-log_binary64_1139
37×times-frac_binary64_1107
31×add-cube-cbrt_binary64_1136 *-un-lft-identity_binary64_1101
25×unswap-sqr_binary64_1069
24×associate-*r*_binary64_1041
22×prod-exp_binary64_1150
19×associate-*l*_binary64_1042
18×pow-exp_binary64_1169
15×pow1_binary64_1162 add-cbrt-cube_binary64_1137
13×unpow2_binary64_1166 sqr-pow_binary64_1073
pow-to-exp_binary64_1170 div-exp_binary64_1152
pow-prod-down_binary64_1172 cbrt-unprod_binary64_1134
sqrt-prod_binary64_1117
add-log-exp_binary64_1140 sqrt-div_binary64_1118
div-inv_binary64_1098 pow-unpow_binary64_1178
*-commutative_binary64_1032 flip3-+_binary64_1104 flip-+_binary64_1075 associate-*r/_binary64_1043
pow1/2_binary64_1181 sqrt-pow1_binary64_1119 rem-sqrt-square_binary64_1114 pow-pow_binary64_1173
Counts
4 → 157
Calls

4 calls:

34.0ms
(*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))
26.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2)))))
9.0ms
(pow.f64 (/.f64 1/2 J) 2)
7.0ms
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))))
Compiler

Compiled 6095 to 4944 computations (18.9% saved)

series3.8s (7.4%)

Error
0.0b
Counts
4 → 55
Calls

4 calls:

1.7s
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2)))))
1.0s
(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))))
858.0ms
(*.f64 (pow.f64 (/.f64 1/2 J) 2) (pow.f64 (/.f64 U (cos.f64 (/.f64 K 2))) 2))
61.0ms
(pow.f64 (/.f64 1/2 J) 2)
Compiler

Compiled 4140 to 3551 computations (14.2% saved)

simplify205.0ms (0.4%)

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (104.0ms)

IterNodesCost
049875656
149875656

prune887.0ms (1.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New2120212
Fresh044
Picked011
Done033
Total2128220
Error
0.0b
Counts
220 → 8
Compiler

Compiled 6701 to 5219 computations (22.1% saved)

regimes1.6s (3.1%)

Accuracy

Total 9.9b remaining (99.6%)

Threshold costs 0b (0%)

Compiler

Compiled 8347 to 7372 computations (11.7% saved)

bsearch6.0ms (0%)

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
039125
139125

end0.0ms (0%)

sample7.5s (14.7%)

Algorithm
intervals
Results
2.3s2043×body1024valid
962.0ms4461×body128valid
781.0ms994×body512valid
249.0ms499×body256valid
5.0msbody2048valid
1.0msbody1024invalid
0.0msbody128invalid
Compiler

Compiled 1440 to 1268 computations (11.9% saved)

Profiling

Loading profile data...