Details

Time bar (total: 2.3s)

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

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: 39.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

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))
11.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series61.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ (+ (* x x) (* y y)) (* z z))
18.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify65.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050051330

prune148.0ms

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: 21.1b

Counts
77 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.1b
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
36.4b
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
5×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
4×associate-*l/
3×flip3-+ associate-*r* associate-*l* flip-+
2×sqrt-pow1 sqrt-div pow-prod-down
1×+-commutative pow1/2 prod-exp sum-log sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
3 → 44
Calls
3 calls:
4.0ms
(+ (* y y) (* z z))
8.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
7.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series63.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* y y) (* z z))
18.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
39.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify46.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05370700

prune74.0ms

Filtered
36 candidates to 53 candidates (-47.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New53053
Fresh055
Picked011
Done000
Total53659

Merged error: 21.1b

Counts
59 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(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)))
36.4b
(sqrt (+ (* x x) (+ (* y y) (* z z))))
36.4b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite46.0ms

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
9×associate-*l*
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×flip3-+ flip-+ add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ div-inv
1×sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
8.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
22.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (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))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
26.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
20.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify50.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
054773569

prune170.0ms

Filtered
95 candidates to 142 candidates (-49.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1420142
Fresh044
Picked011
Done011
Total1426148

Merged error: 21.1b

Counts
148 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.3b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
36.4b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite22.0ms

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))))

series53.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* y y) (* z z))
30.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
052401945

prune103.0ms

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

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New95398
Fresh033
Picked011
Done022
Total959104

Merged error: 20.9b

Counts
104 → 9

regimes574.0ms

Accuracy

62.9% (7.1b remaining)

Error of 25.8b against oracle of 18.8b and baseline of 37.8b

bsearch33.0ms

Steps
ItersRangePoint
10
2.331679655756919e+136
4.572138169031349e+151
4.949626136573165e+140
7
-2.3737292770883117e+97
-1.6265798493377916e+95
-1.634413777114509e+97

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03831
13831

end0.0ms

sample540.0ms

Algorithm
intervals
Results
373.0ms8000×body80valid

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