Details

Time bar (total: 2.7s)

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

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02114
12114

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 39.0b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
5.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
11.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series56.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (+ (* x x) (* y y)) (* z z))
5.0ms
(+ (* x x) (* y y))
13.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
27.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
052981461

prune152.0ms

Filtered
72 candidates to 90 candidates (-25.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New84690
Fresh000
Picked101
Done000
Total85691

Merged error: 18.8b

Counts
91 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.1b
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
36.2b
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-log-exp
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×associate-*l/
3×flip3-+ associate-*r* associate-*l* sum-log flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative associate-+r+ pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 46
Calls
3 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
7.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
6.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series52.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
13.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
29.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify61.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04973797
14973797

prune72.0ms

Filtered
37 candidates to 55 candidates (-48.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New55055
Fresh055
Picked011
Done000
Total55661

Merged error: 18.8b

Counts
61 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.3b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
36.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1 sqrt-div
3×flip3-+ sum-log flip-+
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square associate-+r+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
3 → 91
Calls
3 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
9.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
5.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series62.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
31.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
21.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify36.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
051472042

prune119.0ms

Filtered
61 candidates to 100 candidates (-63.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New973100
Fresh044
Picked011
Done011
Total979106

Merged error: 18.7b

Counts
106 → 9

localize16.0ms

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))))
36.2b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

rewrite54.0ms

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*
9×pow1 add-log-exp
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times associate-+r+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
9.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
24.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
8.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
19.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
46.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
41.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049924093
149924093

prune379.0ms

Filtered
132 candidates to 169 candidates (-28.0%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1663169
Fresh066
Picked011
Done022
Total16612178

Merged error: 18.7b

Counts
178 → 12

regimes627.0ms

Accuracy

65.4% (6.8b remaining)

Error of 24.7b against oracle of 17.9b and baseline of 37.7b

bsearch71.0ms

Steps
ItersRangePoint
8
1.7435330640734021e+115
2.4606451512488522e+118
3.075265064076723e+117
9
-9.469490898430142e+133
-1.927765296251176e+128
-1.4682484161638135e+132

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04343
14343

end0.0ms

analyze19.0ms

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

sample518.0ms

Algorithm
intervals
Results
366.0ms8000×body80valid

Profiling

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