Details

Time bar (total: 3.4s)

sample33.0ms

Algorithm
intervals
Results
7.0ms202×body80valid
5.0ms24×body2560valid
4.0ms256×pre80true
3.0ms18×body1280valid
1.0ms6×body640valid
0.0ms4×body320valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune2.0ms

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

localize11.0ms

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)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
4×flip3-+ sqrt-div flip-+
2×+-commutative associate-/r/
1×frac-2neg pow1/2 clear-num div-inv
Counts
4 → 14
Calls
4 calls:
11.0ms
(+ (* (* 4.0 p) p) (* x x))
17.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
7.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
56.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify198.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0133170
1413170
21337167
34748166
45002166

prune95.0ms

Filtered
26 candidates to 22 candidates (84.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New19726
Fresh000
Picked101
Done000
Total20727

Merged error: 11.3b

Counts
27 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) x)
2.0b
(/ x (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
5×associate-/r/
4×flip3-+ sqrt-div flip-+ associate-/l/
3×frac-2neg clear-num div-inv
2×pow1/2
1×associate-/r*
Counts
4 → 20
Calls
4 calls:
6.0ms
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) x)
6.0ms
(/ x (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) x)
47.0ms
(/ x (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify83.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0159178
1568177
22232172
35001171

prune210.0ms

Filtered
32 candidates to 27 candidates (84.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New28432
Fresh246
Picked101
Done000
Total31839

Merged error: 11.3b

Counts
39 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x) x)
2.0b
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) 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
9×associate-/l/
4×flip3-+ sqrt-div flip-+
3×frac-2neg clear-num div-inv
2×pow1/2
1×associate-/l*
Counts
4 → 20
Calls
4 calls:
8.0ms
(/ (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x) x)
7.0ms
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) x)
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (/ (+ (* 4.0 (pow p 2)) (pow x 2)) x) x)
59.0ms
(/ (+ (* 4.0 (pow p 2)) (pow x 2)) x)
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0157186
1562185
22420181
35001181

prune201.0ms

Filtered
32 candidates to 26 candidates (81.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New29332
Fresh347
Picked011
Done000
Total32840

Merged error: 11.3b

Counts
40 → 8

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)))

rewrite28.0ms

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))))
11.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
83.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify128.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0139153
1511152
21505152
34040147
45001147

prune76.0ms

Filtered
34 candidates to 25 candidates (73.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New34034
Fresh066
Picked011
Done011
Total34842

Merged error: 11.3b

Counts
42 → 8

regimes226.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
14128

end0.0ms

sample857.0ms

Algorithm
intervals
Results
232.0ms6124×body80valid
175.0ms760×body2560valid
111.0ms592×body1280valid
110.0ms8000×pre80true
45.0ms291×body640valid
17.0ms158×body320valid
5.0ms75×body160valid