Details

Time bar (total: 4.7s)

sample38.0ms

Algorithm
intervals
Results
11.0ms201×body80valid
5.0ms25×body1280valid
4.0ms18×body2560valid
4.0ms256×pre80true
1.0ms8×body640valid
0.0ms4×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
293.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune290.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

localize21.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
8.0ms
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0238907
1664877
22370866
35001863

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 57
Calls
4 calls:
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify121.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0167517
1465490
21264489
33249489
45001489

prune353.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize31.0ms

Local error

Found 4 expressions with local error:

16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify97.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
098500
1283484
2827484
32050484
45001484

prune413.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

regimes260.0ms

Accuracy

0% (0.7b remaining)

Error of 13.8b against oracle of 13.1b and baseline of 13.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03151
13151

end0.0ms

sample878.0ms

Algorithm
intervals
Results
220.0ms6010×body80valid
195.0ms842×body2560valid
122.0ms627×body1280valid
111.0ms8000×pre80true
46.0ms298×body640valid
18.0ms162×body320valid
4.0ms61×body160valid