Details

Time bar (total: 3.4s)

analyze14.0ms

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
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

sample19.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02114
12114

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.4b

Counts
2 → 1

localize9.0ms

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)
35.7b
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

rewrite28.0ms

Algorithm
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:
7.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
13.0ms
(/.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))

series88.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
26.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0)
42.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) 3.0))

simplify73.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050051330

prune133.0ms

Filtered
60 candidates to 76 candidates (-26.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New70676
Fresh000
Picked011
Done000
Total70777

Merged error: 19.8b

Counts
77 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
0.2b
(/.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))))
35.7b
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))

rewrite57.0ms

Algorithm
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:
7.0ms
(+.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)) (cbrt.f64 3.0))
25.0ms
(*.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))))
8.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))
37.0ms
(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0))
93.0ms
(*.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))))
88.0ms
(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049574093
149574093

prune218.0ms

Filtered
131 candidates to 169 candidates (-29.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1663169
Fresh055
Picked011
Done011
Total16610176

Merged error: 19.7b

Counts
176 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0)))
35.7b
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
35.7b
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod_binary64
73×add-sqr-sqrt_binary64
44×times-frac_binary64
36×*-un-lft-identity_binary64 add-cube-cbrt_binary64
25×associate-*r*_binary64
16×sqrt-div_binary64
12×unswap-sqr_binary64
11×pow1_binary64
9×associate-*l*_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
4×flip3-+_binary64 add-log-exp_binary64 flip-+_binary64
3×pow-prod-down_binary64
2×div-inv_binary64 frac-times_binary64 associate-*l/_binary64
1×cbrt-unprod_binary64 associate-*r/_binary64 sqrt-unprod_binary64 prod-exp_binary64 *-commutative_binary64
Counts
4 → 130
Calls
4 calls:
8.0ms
(sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0))
24.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0)))
6.0ms
(sqrt.f64 (+.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)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0))
34.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) 3.0)))
23.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
23.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

simplify52.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
052583564

prune125.0ms

Filtered
96 candidates to 142 candidates (-47.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh077
Picked011
Done022
Total14210152

Merged error: 19.7b

Counts
152 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))))
0.4b
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))
35.7b
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
35.7b
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod_binary64
130×add-sqr-sqrt_binary64
106×times-frac_binary64
64×*-un-lft-identity_binary64 add-cube-cbrt_binary64
47×cbrt-prod_binary64
43×associate-*r*_binary64
24×unswap-sqr_binary64
13×associate-*l*_binary64
10×pow1_binary64 sqrt-div_binary64
8×add-exp-log_binary64
7×add-cbrt-cube_binary64
6×associate-/r*_binary64 associate-/l*_binary64
4×add-log-exp_binary64 pow1/2_binary64 sqrt-pow1_binary64
3×pow-prod-down_binary64 flip3-+_binary64 div-inv_binary64 flip-+_binary64
2×associate-/l/_binary64 rem-sqrt-square_binary64
1×cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 sqrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-exp_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 189
Calls
4 calls:
33.0ms
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))))
11.0ms
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))
7.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
10.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

series148.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (*.f64 (cbrt.f64 3.0) (cbrt.f64 3.0)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))))
40.0ms
(/.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z))) (cbrt.f64 3.0))
27.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))
23.0ms
(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)))

simplify70.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
051236176

prune186.0ms

Filtered
134 candidates to 201 candidates (-50.0%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New2010201
Fresh066
Picked011
Done033
Total20110211

Merged error: 19.7b

Counts
211 → 10

regimes1.0s

Accuracy

62.6% (7.3b remaining)

Error of 25.8b against oracle of 18.5b and baseline of 38.0b

bsearch20.0ms

Steps
ItersRangePoint
7
1.985329277842828e+85
3.2861745400188417e+87
3.114260434348677e+87
4
-3.534183814324744e+116
-1.7790815087299613e+116
-3.0987829915356215e+116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07055
17055

end0.0ms

sample534.0ms

Algorithm
intervals
Results
367.0ms8000×body80valid

Profiling

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