Details

Time bar (total: 3.4s)

sample37.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
7.0ms256×pre80true
6.0ms185×body80valid
3.0ms15×body1280valid
1.0ms9×body640valid
1.0ms9×body320valid
0.0ms5×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

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: 14.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
4×flip3-+ flip-+
2×pow1/2 associate-*r/ sqrt-prod associate-/r/
1×+-commutative frac-2neg clear-num *-commutative div-inv
Counts
4 → 16
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify81.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
0146211
1369211
2956211
32264210
45001210

prune87.0ms

Filtered
28 candidates to 26 candidates (92.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New23528
Fresh000
Picked101
Done000
Total24529

Merged error: 14.5b

Counts
29 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×sqrt-div
4×flip3-+ pow1/2 flip-+
Counts
4 → 12
Calls
4 calls:
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify125.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
071168
1214168
2608168
31435168
42892168
55002168

prune156.0ms

Filtered
24 candidates to 24 candidates (100.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New22224
Fresh134
Picked011
Done000
Total23629

Merged error: 14.5b

Counts
29 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)
0.5b
(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
1.5b
(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
5×associate-/r/
4×flip3-+ clear-num flip-+ associate-/l/
3×frac-2neg div-inv
1×+-commutative pow1/2 associate-/r* remove-double-div inv-pow
Counts
4 → 22
Calls
4 calls:
10.0ms
(/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)
8.0ms
(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
8.0ms
(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)
81.0ms
(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
81.0ms
(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0154207
1453205
21765203
35001202

prune115.0ms

Filtered
34 candidates to 30 candidates (88.2%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New32234
Fresh134
Picked011
Done011
Total33740

Merged error: 14.5b

Counts
40 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x)
4.9b
(+ 1.0 (* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div
4×flip3-+ associate-/r/ flip-+
3×associate-*l* associate-*l/
2×frac-2neg pow1/2 clear-num div-inv
1×+-commutative pow-flip *-commutative inv-pow
Counts
4 → 20
Calls
4 calls:
7.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
8.0ms
(* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x)
4.0ms
(+ 1.0 (* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms
(* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x)
81.0ms
(+ 1.0 (* (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))) x))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify121.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0137162
1496161
21509161
34013156
45001156

prune80.0ms

Filtered
32 candidates to 27 candidates (84.4%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New30232
Fresh134
Picked011
Done022
Total31839

Merged error: 14.5b

Counts
39 → 8

regimes169.0ms

Accuracy

0% (0.2b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03136
13136

end0.0ms

sample895.0ms

Algorithm
intervals
Results
234.0ms5980×body80valid
197.0ms832×body2560valid
113.0ms611×body1280valid
111.0ms8000×pre80true
47.0ms332×body640valid
18.0ms167×body320valid
6.0ms78×body160valid