Details

Time bar (total: 3.2s)

sample34.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
6.0ms185×body80valid
4.0ms256×pre80true
3.0ms15×body1280valid
1.0ms9×body640valid
1.0ms9×body320valid
0.0ms5×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

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

localize15.0ms

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)))

rewrite22.0ms

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:
5.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
4.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify83.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 4 (79.0ms)

IterNodesCost
0154211
1410210
21113209
32793208
45002199

prune91.0ms

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

localize22.0ms

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)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×sqrt-div
4×flip3-+ pow1/2 flip-+
Counts
4 → 12
Calls
4 calls:
9.0ms
(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)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify132.0ms

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
075168
1243164
2724160
31826160
44099160
55001160

prune152.0ms

Filtered
24 candidates to 24 candidates (100.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New23124
Fresh134
Picked011
Done000
Total24529

Merged error: 14.5b

Counts
29 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

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

series246.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify133.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0147153
1555149
21748145
34893142
45001142

prune103.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New31334
Fresh123
Picked101
Done011
Total33639

Merged error: 14.4b

Counts
39 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.3b
(/ x (fma (* 4.0 p) p (* x x)))
14.3b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
30.7b
(fma (/ x (fma (* 4.0 p) p (* x x))) (- x) (* 1.0 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
2×sqrt-div
1×sub-neg flip3-- frac-2neg flip3-+ pow1/2 clear-num flip-- flip-+ fma-udef div-inv
Counts
4 → 11
Calls
4 calls:
2.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(/ x (fma (* 4.0 p) p (* x x)))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
1.0ms
(fma (/ x (fma (* 4.0 p) p (* x x))) (- x) (* 1.0 1.0))

series239.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
50.0ms
(/ x (fma (* 4.0 p) p (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(fma (/ x (fma (* 4.0 p) p (* x x))) (- x) (* 1.0 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 4 (75.0ms)

IterNodesCost
0135122
1367120
2972119
32345112
45001109

prune83.0ms

Filtered
23 candidates to 19 candidates (82.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New19423
Fresh314
Picked101
Done011
Total23629

Merged error: 14.2b

Counts
29 → 6

regimes133.0ms

Accuracy

0% (0.5b remaining)

Error of 13.7b against oracle of 13.2b and baseline of 13.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03136
13136

end0.0ms

sample888.0ms

Algorithm
intervals
Results
221.0ms5980×body80valid
198.0ms832×body2560valid
116.0ms611×body1280valid
115.0ms8000×pre80true
48.0ms332×body640valid
21.0ms167×body320valid
6.0ms78×body160valid