Details

Time bar (total: 3.2s)

analyze14.0ms (0.4%)

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
49.9%49.9%0.1%5
74.9%25%0.1%6
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14

sample20.0ms (0.6%)

Algorithm
1×intervals
Results
11.0ms256×body80valid

simplify5.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02114
12114

prune6.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.8b

Counts
2 → 1

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
0.1b
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
38.8b
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

rewrite28.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
19×times-frac_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
13×sqrt-prod_binary64
8×add-log-exp_binary64
5×add-exp-log_binary64 add-cbrt-cube_binary64
4×pow1_binary64
3×associate-/r*_binary64 associate-/l*_binary64 sum-log_binary64
2×flip3-+_binary64 associate-/l/_binary64 rem-sqrt-square_binary64 div-inv_binary64 flip-+_binary64
1×pow1/2_binary64 cbrt-undiv_binary64 associate-+l+_binary64 sqrt-pow1_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 +-commutative_binary64 sqrt-div_binary64
Counts
3 → 67
Calls

3 calls:

10.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
10.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
6.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

series65.0ms (2%)

Counts
3 → 9
Calls

3 calls:

35.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))
17.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
13.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))

simplify70.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
050051330

prune117.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New70676
Fresh000
Picked011
Done000
Total70777

Merged error: 21.5b

Counts
77 → 7

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
0.1b
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))
0.5b
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))))
38.8b
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))

rewrite55.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
90×add-sqr-sqrt_binary64
75×times-frac_binary64 sqrt-prod_binary64
53×*-un-lft-identity_binary64
49×add-cube-cbrt_binary64
35×cbrt-prod_binary64
25×associate-*r*_binary64
16×unswap-sqr_binary64
10×associate-*l*_binary64
9×add-log-exp_binary64 pow1_binary64
8×add-exp-log_binary64
7×add-cbrt-cube_binary64
6×associate-/r*_binary64
5×sqrt-div_binary64
4×div-inv_binary64
3×pow-prod-down_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 associate-/l*_binary64 sum-log_binary64
2×flip3-+_binary64 associate-/l/_binary64 flip-+_binary64
1×cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 associate-+l+_binary64 sqrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-exp_binary64 +-commutative_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 157
Calls

4 calls:

24.0ms
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))))
10.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))
8.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))
7.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))

series164.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

63.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))
62.0ms
(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))))
26.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))
13.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))

simplify72.0ms (2.2%)

Algorithm
1×egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049574093
149574093

prune284.0ms (8.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1663169
Fresh055
Picked011
Done011
Total16610176

Merged error: 21.4b

Counts
176 → 10

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
0.4b
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (sqrt.f64 3.0))
38.8b
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

rewrite27.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
45×sqrt-prod_binary64
36×times-frac_binary64
33×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64 add-cube-cbrt_binary64
8×add-log-exp_binary64
6×associate-/r*_binary64 associate-/l*_binary64
5×add-exp-log_binary64 add-cbrt-cube_binary64
4×pow1_binary64 sqrt-div_binary64
3×flip3-+_binary64 flip-+_binary64 sum-log_binary64
2×associate-/l/_binary64
1×pow1/2_binary64 cbrt-undiv_binary64 associate-+l+_binary64 sqrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64
Counts
3 → 91
Calls

3 calls:

10.0ms
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (sqrt.f64 3.0))
8.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
6.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

series83.0ms (2.6%)

Counts
3 → 9
Calls

3 calls:

42.0ms
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (sqrt.f64 3.0))
28.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
13.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))

simplify49.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
054352042

prune121.0ms (3.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New973100
Fresh167
Picked011
Done022
Total9812110

Merged error: 21.3b

Counts
110 → 12

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
0.1b
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
6.0b
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))))
38.8b
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

rewrite35.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
31×add-sqr-sqrt_binary64
28×*-un-lft-identity_binary64 add-cube-cbrt_binary64 times-frac_binary64
26×sqrt-prod_binary64
16×log-prod_binary64 exp-sum_binary64
9×add-log-exp_binary64
7×pow1_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64 exp-prod_binary64
3×associate-/r*_binary64 log-pow_binary64 associate-/l*_binary64 div-inv_binary64 sum-log_binary64
2×flip3-+_binary64 associate-/l/_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64 sqrt-div_binary64
1×cbrt-undiv_binary64 associate-+l+_binary64 rem-exp-log_binary64 exp-diff_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 log-div_binary64 +-commutative_binary64
Counts
4 → 98
Calls

4 calls:

10.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
8.0ms
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))))
7.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
6.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

series103.0ms (3.2%)

Counts
4 → 12
Calls

4 calls:

38.0ms
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))))
36.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))
16.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
13.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))

simplify52.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049401934
149401934

prune110.0ms (3.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New1064110
Fresh088
Picked101
Done033
Total10715122

Merged error: 21.3b

Counts
122 → 15

regimes1.2s (35.5%)

Accuracy

Total 7.9b remaining (29.5%)

Threshold costs 0b (0%)

bsearch23.0ms (0.7%)

Steps
ItersRangePoint
8
1.0509886356214434e+122
2.4543460956080738e+126
1.8007026348918264e+126
4
-4.306891717604255e+48
-2.5516855895429332e+48
-4.2404378484423746e+48

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07443
17443

end0.0ms (0%)

sample538.0ms (16.6%)

Algorithm
1×intervals
Results
374.0ms8000×body80valid

Profiling

Loading profile data...