Details

Time bar (total: 3.9s)

analyze18.0ms (0.5%)

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

sample20.0ms (0.5%)

Algorithm
intervals
Results
11.0ms256×body80valid

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 38.4b

Counts
2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite23.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
add-log-exp
add-exp-log add-cbrt-cube
pow1
associate-/r* sum-log associate-/l*
rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls

3 calls:

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

series53.0ms (1.4%)

Counts
3 → 9
Calls

3 calls:

30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
13.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
10.0ms
(+ (+ (* x x) (* y y)) (* z z))

simplify46.0ms (1.2%)

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050051330

prune145.0ms (3.8%)

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 (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite51.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
pow1 add-log-exp
add-exp-log
add-cbrt-cube
associate-/r*
sqrt-div
div-inv
rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
flip3-+ flip-+ associate-/l/
cbrt-undiv +-commutative frac-times associate-+l+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls

4 calls:

22.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
10.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
7.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))

series121.0ms (3.1%)

Counts
4 → 12
Calls

4 calls:

46.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
44.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
21.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
10.0ms
(+ (+ (* x x) (* y y)) (* z z))

simplify66.0ms (1.7%)

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049574093
149574093

prune506.0ms (13.1%)

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 (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
73×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
25×associate-*r*
16×sqrt-div
12×unswap-sqr
11×pow1
associate-*l*
add-exp-log add-cbrt-cube
rem-sqrt-square sqrt-pow1 pow1/2
flip3-+ flip-+ add-log-exp
pow-prod-down
frac-times associate-*l/ div-inv
sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod
Counts
4 → 130
Calls

4 calls:

24.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
7.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series108.0ms (2.8%)

Counts
4 → 12
Calls

4 calls:

40.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
31.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify45.0ms (1.2%)

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050383569

prune239.0ms (6.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh077
Picked011
Done022
Total14210152

Merged error: 19.7b

Counts
152 → 10

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (1.6%)

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod
130×add-sqr-sqrt
106×times-frac
64×add-cube-cbrt *-un-lft-identity
47×cbrt-prod
43×associate-*r*
24×unswap-sqr
13×associate-*l*
10×pow1 sqrt-div
add-exp-log
add-cbrt-cube
associate-/r* associate-/l*
sqrt-pow1 pow1/2 add-log-exp
flip3-+ pow-prod-down flip-+ div-inv
rem-sqrt-square associate-/l/
cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 189
Calls

4 calls:

31.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
10.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
6.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series121.0ms (3.1%)

Counts
4 → 12
Calls

4 calls:

46.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
32.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
24.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms (1.7%)

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
051236176

prune543.0ms (14.1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New2010201
Fresh066
Picked011
Done033
Total20110211

Merged error: 19.7b

Counts
211 → 10

regimes967.0ms (25.1%)

Accuracy

Total 7.3b remaining (28.4%)

Threshold costs 0b (0%)

bsearch21.0ms (0.6%)

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

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07055
17055

end0.0ms (0%)

sample519.0ms (13.5%)

Algorithm
intervals
Results
363.0ms8000×body80valid

Profiling

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