Details

Time bar (total: 3.2s)

sample63.0ms

Algorithm
intervals
Results
15.0ms24×body2560valid
13.0ms202×body80valid
6.0ms256×pre80true
6.0ms18×body1280valid
2.0ms6×body640valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

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: 11.4b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
4×fma-def flip3-+ sqrt-div flip-+
2×+-commutative associate-*l* associate-/r/ *-commutative
1×frac-2neg pow1/2 clear-num div-inv
Counts
4 → 18
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
3.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
78.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0142166
1462163
21517160
35001156

prune94.0ms

Filtered
30 candidates to 25 candidates (83.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New23730
Fresh000
Picked101
Done000
Total24731

Merged error: 11.3b

Counts
31 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
4×flip3-+ flip-+
3×pow1/2
2×fma-def
1×+-commutative unpow3 sum-cubes sqr-pow
Counts
4 → 15
Calls
4 calls:
7.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0150206
1478201
21820197
35002197

prune158.0ms

Filtered
27 candidates to 27 candidates (100.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New24327
Fresh246
Picked101
Done000
Total27734

Merged error: 11.3b

Counts
34 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
8×sqrt-div
4×flip3-+ pow1/2 flip-+
Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify129.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
075168
1243164
2724160
31826160
44099160
55001160

prune204.0ms

Filtered
24 candidates to 24 candidates (100.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New23124
Fresh156
Picked011
Done000
Total24731

Merged error: 11.3b

Counts
31 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.6b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
4×flip3-+ associate-/r/ flip-+
3×associate-*r/ associate-*r* clear-num
2×frac-2neg pow1/2 un-div-inv div-inv
1×+-commutative pow-flip *-commutative inv-pow
Counts
4 → 22
Calls
4 calls:
7.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
8.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
57.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
70.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify128.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0147153
1555149
21748145
34893142
45001142

prune86.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New31334
Fresh145
Picked011
Done011
Total32941

Merged error: 11.2b

Counts
41 → 9

regimes208.0ms

Accuracy

0% (0.2b remaining)

Error of 12.5b against oracle of 12.2b and baseline of 12.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03348
13348

end0.0ms

sample825.0ms

Algorithm
intervals
Results
219.0ms6124×body80valid
168.0ms760×body2560valid
108.0ms592×body1280valid
107.0ms8000×pre80true
40.0ms291×body640valid
16.0ms158×body320valid
5.0ms75×body160valid