Details

Time bar (total: 3.9s)

analyze839.0ms (21.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14

sample43.0ms (1.1%)

Algorithm
intervals
Results
10.0ms193×body80valid
9.0ms27×body2560valid
6.0ms22×body1280valid
5.0ms256×pre80true
2.0msbody640valid
1.0msbody320valid
0.0msbody160valid

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03817
13817

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 13.5b

Counts
2 → 1

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
add-log-exp
add-exp-log associate-/r* add-cbrt-cube
pow1
flip3-+ sqrt-div flip-+
associate-/l*
+-commutative sum-log associate-/r/
cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls

4 calls:

13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series35.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(+ (* (* 4.0 p) p) (* x x))

simplify39.0ms (1%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
049941385
149941385

prune254.0ms (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New801191
Fresh000
Picked101
Done000
Total811192

Merged error: 13.3b

Counts
92 → 11

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
0.7b
(log (exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
12.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite55.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
add-sqr-sqrt add-log-exp
add-cube-cbrt exp-prod
pow1
log-pow
add-exp-log log-prod add-cbrt-cube
sqrt-prod distribute-lft-out
flip3-+ sqrt-div exp-sum sum-log flip-+ rem-exp-log
+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 58
Calls

4 calls:

18.0ms
(exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
15.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
14.0ms
(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

series53.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

21.0ms
(exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
12.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify66.0ms (1.7%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
05009927

prune208.0ms (5.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New69170
Fresh01010
Picked101
Done000
Total701181

Merged error: 13.3b

Counts
81 → 11

localize14.0ms (0.4%)

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)))))
4.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
12.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite38.0ms (1%)

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
pow1
sqrt-div associate-/r* add-log-exp
unswap-sqr
flip3-+ div-exp prod-exp associate-/r/ flip-+
pow-flip associate-*l* associate-/l*
cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls

4 calls:

15.0ms
(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
9.0ms
(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))

series40.0ms (1%)

Counts
4 → 12
Calls

4 calls:

12.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
12.0ms
(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
9.0ms
(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify72.0ms (1.8%)

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049321899
149321899

prune350.0ms (9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1322134
Fresh2810
Picked101
Done000
Total13510145

Merged error: 13.3b

Counts
145 → 10

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

4.3b
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
12.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
12.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
12.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite24.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
sqrt-prod
pow1 add-cube-cbrt *-un-lft-identity
sqrt-div add-log-exp
add-exp-log flip3-+ add-cbrt-cube flip-+
rem-sqrt-square sqrt-pow1 pow1/2
+-commutative sum-log
Counts
4 → 56
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)))
4.0ms
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))

series41.0ms (1%)

Counts
4 → 12
Calls

4 calls:

17.0ms
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify35.0ms (0.9%)

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
05159810

prune226.0ms (5.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh099
Picked011
Done000
Total681078

Merged error: 13.3b

Counts
78 → 10

regimes156.0ms (4%)

Accuracy

Total 0.6b remaining (4.5%)

Threshold costs 0.6b (4.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02649
12649

end0.0ms (0%)

sample1.2s (31.1%)

Algorithm
intervals
Results
332.0ms6003×body80valid
281.0ms809×body2560valid
171.0ms628×body1280valid
151.0ms8000×pre80true
68.0ms320×body640valid
27.0ms171×body320valid
7.0ms69×body160valid

Profiling

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