Details

Time bar (total: 2.7s)

analyze15.0ms

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

sample20.0ms

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: 38.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls
3 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
12.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series49.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(+ (+ (* x x) (* y y)) (* z z))
13.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050051330

prune132.0ms

Filtered
62 candidates to 76 candidates (-22.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New70676
Fresh000
Picked101
Done000
Total71677

Merged error: 17.6b

Counts
77 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.4b
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
35.2b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
9×sqrt-div
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square sqrt-unprod associate-*r/ prod-exp sum-log *-commutative cbrt-unprod div-inv
Counts
3 → 75
Calls
3 calls:
4.0ms
(+ (* y y) (* z z))
14.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series52.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* y y) (* z z))
29.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify72.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049461444
149461444

prune113.0ms

Filtered
57 candidates to 84 candidates (-47.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh055
Picked011
Done000
Total84690

Merged error: 17.6b

Counts
90 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.4b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
35.2b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 sqrt-div
3×flip3-+ flip-+
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 89
Calls
3 calls:
4.0ms
(+ (* y y) (* z z))
9.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series56.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* y y) (* z z))
32.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
19.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify47.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052401945

prune119.0ms

Filtered
60 candidates to 98 candidates (-63.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New95398
Fresh044
Picked011
Done011
Total959104

Merged error: 17.5b

Counts
104 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 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))))
35.3b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

rewrite51.0ms

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
8×add-exp-log
7×add-cbrt-cube
6×associate-/r* add-log-exp
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num sum-log *-commutative cbrt-unprod
Counts
4 → 155
Calls
4 calls:
4.0ms
(+ (* y y) (* z z))
9.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
23.0ms
(* (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)))

series109.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* y y) (* z z))
19.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
45.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
40.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
055553996

prune410.0ms

Filtered
131 candidates to 167 candidates (-27.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1643167
Fresh066
Picked101
Done022
Total16511176

Merged error: 17.5b

Counts
176 → 11

regimes643.0ms

Accuracy

63.2% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 38.0b

bsearch31.0ms

Steps
ItersRangePoint
6
3.406355682947415e+86
3.906556701427779e+87
3.850702396802878e+87
10
-8.047137634315902e+157
-1.7839014289033485e+141
-4.008206825972018e+143

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05134
15134

end0.0ms

sample525.0ms

Algorithm
intervals
Results
361.0ms8000×body80valid

Profiling

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