Details

Time bar (total: 3.6s)

sample27.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.1b

Counts
2 → 1

localize16.0ms

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)
34.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
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 → 90
Calls
4 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series310.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(+ (* x x) (* y y))
48.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
195.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0345852
11445759
25001739

prune265.0ms

Filtered
102 candidates to 84 candidates (82.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New966102
Fresh000
Picked101
Done000
Total976103

Merged error: 18.3b

Counts
103 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (fma y y (* z z)))
0.1b
(/ (fma x x (fma y y (* z z))) 3.0)
34.5b
(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×rem-sqrt-square div-inv
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num fma-udef
Counts
3 → 66
Calls
3 calls:
1.0ms
(fma x x (fma y y (* z z)))
3.0ms
(/ (fma x x (fma y y (* z z))) 3.0)
3.0ms
(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

series285.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(fma x x (fma y y (* z z)))
56.0ms
(/ (fma x x (fma y y (* z z))) 3.0)
179.0ms
(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0171537
1518489
22240487
35001485

prune295.0ms

Filtered
75 candidates to 58 candidates (77.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New74175
Fresh145
Picked011
Done000
Total75681

Merged error: 18.3b

Counts
81 → 6

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (fma y y (* z z)))
0.4b
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
34.4b
(sqrt (fma x x (fma y y (* z z))))

rewrite15.0ms

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
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
1.0ms
(fma x x (fma y y (* z z)))
8.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
3.0ms
(sqrt (fma x x (fma y y (* z z))))

series407.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(fma x x (fma y y (* z z)))
245.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
112.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify67.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0179904
1538853
22824830
35001830

prune193.0ms

Filtered
97 candidates to 60 candidates (61.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New94397
Fresh044
Picked011
Done011
Total949103

Merged error: 18.2b

Counts
103 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×sqrt-prod
18×*-un-lft-identity
16×add-cube-cbrt associate-*r*
13×times-frac
11×add-log-exp
9×pow1 sqrt-div
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
3×sqrt-pow1 pow1/2 pow-prod-down
2×+-commutative frac-times associate-*l/
1×rem-sqrt-square associate-+l+ sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod hypot-def div-inv
Counts
4 → 101
Calls
4 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
14.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
32.0ms
(+ (* x x) (* y y))
172.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03721017
11570959
25001931

prune251.0ms

Filtered
113 candidates to 83 candidates (73.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1121113
Fresh066
Picked101
Done112
Total1148122

Merged error: 12.3b

Counts
122 → 8

regimes268.0ms

Accuracy

83.1% (2.5b remaining)

Error of 16.4b against oracle of 13.8b and baseline of 28.8b

bsearch79.0ms

Steps
ItersRangePoint
8
5.011094592848002e+153
6.21497298949409e+156
1.3489153991230233e+154
9
-4.852512101555595e+148
-2.991013381602053e+139
-2.4117855228442057e+146

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03113
13713
23713

end0.0ms

sample541.0ms

Algorithm
intervals
Results
359.0ms8000×body80valid