Details

Time bar (total: 41.1s)

analyze2.0s (4.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%81.1%18.9%7
0%68.6%31.4%8
0%59.2%40.8%9
0%59.2%40.8%10
0%59.2%40.8%11
0.4%49.5%50.1%12
0.8%44.4%54.8%13
1.4%39.9%58.7%14
Compiler

Compiled 36 to 32 computations (11.1% saved)

sample146.0ms (0.4%)

Algorithm
intervals
Results
44.0ms256×body128valid
41.0ms272×body128nan
24.0ms138×body128invalid
Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify165.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0520541

prune12.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
28.7b
Counts
2 → 1
Compiler

Compiled 54 to 46 computations (14.8% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

7.2b
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
3.5b
(/.f64 (*.f64 M D) (*.f64 d 2))
0.3b
(*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l)))
0.2b
(pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)
7.2b
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.4b
(sqrt.f64 (/.f64 d h))
12.5b
(sqrt.f64 (/.f64 d l))
14.0b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))

rewrite71.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
77×add-exp-log_binary64_1139
41×prod-exp_binary64_1150
32×add-sqr-sqrt_binary64_1123
29×times-frac_binary64_1107
26×*-un-lft-identity_binary64_1101 sqrt-prod_binary64_1117 add-cube-cbrt_binary64_1136
21×add-cbrt-cube_binary64_1137
16×associate-*r*_binary64_1041 div-exp_binary64_1152
14×sqrt-div_binary64_1118
13×pow1_binary64_1162
10×pow-exp_binary64_1169
cbrt-unprod_binary64_1134 frac-times_binary64_1111
associate-*r/_binary64_1043 associate-*l/_binary64_1044
rem-sqrt-square_binary64_1114 add-log-exp_binary64_1140 flip--_binary64_1076 flip3--_binary64_1105 pow-prod-down_binary64_1172
div-inv_binary64_1098
*-commutative_binary64_1032 sub-neg_binary64_1094 sqrt-pow1_binary64_1119 distribute-lft-in_binary64_1050 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042 cancel-sign-sub-inv_binary64_1067 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051 pow1/2_binary64_1181
Counts
4 → 127
Calls

8 calls:

21.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
18.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
6.0ms
(sqrt.f64 (/.f64 d l))
3.0ms
(sqrt.f64 (/.f64 d h))
0.0ms
(pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)

series1.9s (4.5%)

Counts
4 → 50
Calls

4 calls:

1.1s
(*.f64 (*.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
664.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
53.0ms
(sqrt.f64 (/.f64 d h))
44.0ms
(sqrt.f64 (/.f64 d l))
Compiler

Compiled 2576 to 2255 computations (12.5% saved)

simplify116.0ms (0.3%)

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049794371
149794371

prune502.0ms (1.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New16017177
Fresh000
Picked101
Done000
Total16117178
Error
13.0b
Counts
178 → 17
Compiler

Compiled 6026 to 2802 computations (53.5% saved)

localize34.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l)))
0.3b
(/.f64 d (cbrt.f64 h))
0.2b
(/.f64 1 (cbrt.f64 h))
0.2b
(pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)
3.5b
(/.f64 (*.f64 M D) (*.f64 d 2))
7.2b
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.5b
(sqrt.f64 (/.f64 d l))
14.0b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))

rewrite70.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
93×add-exp-log_binary64_1139
48×prod-exp_binary64_1150
37×add-cbrt-cube_binary64_1137
22×add-sqr-sqrt_binary64_1123
20×times-frac_binary64_1107 div-exp_binary64_1152
19×*-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
16×cbrt-unprod_binary64_1134 pow1_binary64_1162 associate-*r*_binary64_1041
13×sqrt-prod_binary64_1117 sqrt-div_binary64_1118
12×associate-*r/_binary64_1043
10×pow-exp_binary64_1169
frac-times_binary64_1111
pow-prod-down_binary64_1172
cbrt-undiv_binary64_1135 associate-*l/_binary64_1044
add-log-exp_binary64_1140 flip--_binary64_1076 flip3--_binary64_1105
div-inv_binary64_1098
*-commutative_binary64_1032 rem-sqrt-square_binary64_1114 sub-neg_binary64_1094 distribute-lft-in_binary64_1050 associate-*l*_binary64_1042 cancel-sign-sub-inv_binary64_1067 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051
frac-2neg_binary64_1112 sqrt-pow1_binary64_1119 clear-num_binary64_1100 associate-/l*_binary64_1046 associate-/r*_binary64_1045 pow1/2_binary64_1181
Counts
4 → 126
Calls

8 calls:

18.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
18.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
6.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
3.0ms
(sqrt.f64 (/.f64 d l))
0.0ms
(pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)

series3.2s (7.8%)

Counts
4 → 56
Calls

4 calls:

2.4s
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
628.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
182.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
48.0ms
(sqrt.f64 (/.f64 d l))
Compiler

Compiled 4007 to 3484 computations (13.1% saved)

simplify128.0ms (0.3%)

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
051135785

prune435.0ms (1.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New17111182
Fresh41216
Picked101
Done000
Total17623199
Error
11.3b
Counts
199 → 23
Compiler

Compiled 7945 to 4215 computations (46.9% saved)

localize45.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)
0.2b
(/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
0.2b
(/.f64 d (cbrt.f64 l))
0.1b
(sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
3.5b
(/.f64 (*.f64 M D) (*.f64 d 2))
3.9b
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
7.2b
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
14.0b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))

rewrite101.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
102×add-exp-log_binary64_1139
55×prod-exp_binary64_1150
46×add-cbrt-cube_binary64_1137
37×sqrt-div_binary64_1118
30×add-sqr-sqrt_binary64_1123 associate-*r/_binary64_1043 times-frac_binary64_1107
29×frac-times_binary64_1111
25×*-un-lft-identity_binary64_1101 pow1_binary64_1162 add-cube-cbrt_binary64_1136
23×cbrt-unprod_binary64_1134
22×sqrt-prod_binary64_1117
20×div-exp_binary64_1152
16×associate-*r*_binary64_1041 associate-*l/_binary64_1044
14×pow-prod-down_binary64_1172
10×pow-exp_binary64_1169 cbrt-prod_binary64_1132
flip--_binary64_1076 flip3--_binary64_1105
cbrt-undiv_binary64_1135
add-log-exp_binary64_1140
rem-sqrt-square_binary64_1114 div-inv_binary64_1098
*-commutative_binary64_1032 sub-neg_binary64_1094 distribute-lft-in_binary64_1050 associate-*l*_binary64_1042 cancel-sign-sub-inv_binary64_1067 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051
frac-2neg_binary64_1112 sqrt-pow1_binary64_1119 clear-num_binary64_1100 associate-/l*_binary64_1046 associate-/r*_binary64_1045 pow1/2_binary64_1181
Counts
4 → 154
Calls

8 calls:

41.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
7.0ms
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
6.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
0.0ms
(sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series3.4s (8.3%)

Counts
4 → 56
Calls

4 calls:

2.4s
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
681.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))
168.0ms
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
140.0ms
(/.f64 (*.f64 M D) (*.f64 d 2))
Compiler

Compiled 4631 to 3887 computations (16.1% saved)

simplify152.0ms (0.4%)

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050168277

prune681.0ms (1.7%)

Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New2037210
Fresh02222
Picked101
Done000
Total20429233
Error
10.2b
Counts
233 → 29
Compiler

Compiled 11496 to 5867 computations (49% saved)

localize46.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))
0.2b
(/.f64 (cbrt.f64 h) l)
0.2b
(/.f64 d (cbrt.f64 l))
0.1b
(sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
3.9b
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.8b
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
7.2b
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
7.4b
(*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite132.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
279×add-exp-log_binary64_1139
185×prod-exp_binary64_1150
58×add-cbrt-cube_binary64_1137
47×cbrt-unprod_binary64_1134
41×div-exp_binary64_1152
38×times-frac_binary64_1107
37×pow1_binary64_1162 sqrt-div_binary64_1118
36×add-sqr-sqrt_binary64_1123
31×*-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
30×pow-exp_binary64_1169 associate-*r/_binary64_1043
29×frac-times_binary64_1111
26×associate-*r*_binary64_1041
22×sqrt-prod_binary64_1117 pow-prod-down_binary64_1172
19×cbrt-prod_binary64_1132
16×associate-*l/_binary64_1044
flip--_binary64_1076 flip3--_binary64_1105
pow-to-exp_binary64_1170
cbrt-undiv_binary64_1135
add-log-exp_binary64_1140
*-commutative_binary64_1032 rem-sqrt-square_binary64_1114 associate-*l*_binary64_1042
sub-neg_binary64_1094 distribute-lft-in_binary64_1050 div-inv_binary64_1098 cancel-sign-sub-inv_binary64_1067 distribute-rgt-in_binary64_1051
sqrt-pow1_binary64_1119 pow1/2_binary64_1181
Counts
4 → 200
Calls

8 calls:

34.0ms
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
20.0ms
(*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
20.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.0ms
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
0.0ms
(sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series4.3s (10.5%)

Counts
4 → 59
Calls

4 calls:

2.5s
(*.f64 (*.f64 (*.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
904.0ms
(*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
736.0ms
(*.f64 (*.f64 (*.f64 1/2 (pow.f64 (/.f64 (*.f64 M D) (*.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
192.0ms
(sqrt.f64 (/.f64 d (cbrt.f64 l)))
Compiler

Compiled 5215 to 4303 computations (17.5% saved)

simplify169.0ms (0.4%)

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0497110132
1497110132

prune916.0ms (2.2%)

Pruning

34 alts after pruning (34 fresh and 0 done)

PrunedKeptTotal
New2518259
Fresh22628
Picked101
Done000
Total25434288
Error
9.0b
Counts
288 → 34
Compiler

Compiled 13504 to 6247 computations (53.7% saved)

simplify151.0ms (0.4%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
014707377
114707377

regimes2.2s (5.3%)

Accuracy

Total 7.2b remaining (47.4%)

Threshold costs 0b (0%)

Compiler

Compiled 28228 to 21116 computations (25.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0117101
1117101

end0.0ms (0%)

sample20.1s (48.8%)

Algorithm
intervals
Results
1.5s8000×body128valid
1.4s8334×body128nan
898.0ms4819×body128invalid
Compiler

Compiled 14142 to 10564 computations (25.3% saved)

Pareto

0.35228736622268414

Profiling

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