Details

Time bar (total: 2.9s)

sample17.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

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: 38.4b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms

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:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series287.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x x) (* y y))
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
174.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0345852
11445759
25001739

prune265.0ms

Filtered
102 candidates to 84 candidates (82.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New957102
Fresh000
Picked101
Done000
Total967103

Merged error: 18.6b

Counts
103 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (fma x x (fma y y (* z z))) 3.0)
35.4b
(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
2 → 56
Calls
2 calls:
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))

series232.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(/ (fma x x (fma y y (* z z))) 3.0)
174.0ms
(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0163479
1439438
21747436
35002434

prune144.0ms

Filtered
62 candidates to 48 candidates (77.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New60262
Fresh336
Picked101
Done000
Total64569

Merged error: 18.6b

Counts
69 → 5

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
35.6b
(sqrt (fma x x (fma y y (* z z))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 pow1/2 pow-prod-down
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 62
Calls
2 calls:
9.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma x x (fma y y (* z z))))

series297.0ms

Counts
2 → 6
Calls
2 calls:
187.0ms
(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
110.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify90.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0172554
1517531
21434512
34041501
45001501

prune143.0ms

Filtered
68 candidates to 45 candidates (66.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh044
Picked011
Done000
Total68573

Merged error: 18.6b

Counts
73 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
35.6b
(sqrt (fma x x (fma y y (* z z))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
3×pow1
2×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 div-inv
Counts
2 → 78
Calls
2 calls:
5.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
2.0ms
(sqrt (fma x x (fma y y (* z z))))

series345.0ms

Counts
2 → 6
Calls
2 calls:
237.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
108.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify66.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0156846
1399802
21365779
32676779
45001779

prune153.0ms

Filtered
84 candidates to 51 candidates (60.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New81384
Fresh033
Picked011
Done011
Total81889

Merged error: 18.5b

Counts
89 → 8

regimes173.0ms

Accuracy

62.6% (7.5b remaining)

Error of 25.1b against oracle of 17.7b and baseline of 37.6b

bsearch61.0ms

Steps
ItersRangePoint
10
1.7826190976464906e+97
7.552700620960131e+107
1.3566371815103393e+105
5
-1.7575017886047935e+118
-4.9561533689906815e+117
-1.6174687293654252e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03112
13312
23312

end0.0ms

sample422.0ms

Algorithm
intervals
Results
261.0ms8000×body80valid