Details

Time bar (total: 4.5s)

sample86.0ms

Algorithm
intervals
Results
17.0ms542×body80nan
16.0ms91×body2560nan
12.0ms78×body1280nan
10.0ms256×body80valid
7.0ms62×body640nan
2.0ms19×body320nan
0.0msbody160nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
32.5b
(sqrt (- (* x x) 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
sqrt-prod add-log-exp
pow1 add-cube-cbrt
add-exp-log sqrt-div add-cbrt-cube
+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 28
Calls
2 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series151.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(+ x (sqrt (- (* x x) 1.0)))
68.0ms
(sqrt (- (* x x) 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0217221
1657211
22555205
35001204

prune126.0ms

Filtered
34 candidates to 29 candidates (14.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New33134
Fresh000
Picked101
Done000
Total34135

Merged error: 0b

Counts
35 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
0.0b
(sqrt (- x (sqrt 1.0)))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×sqrt-prod
18×*-un-lft-identity
16×sqrt-div
10×pow1 add-cube-cbrt
associate-*r*
associate-*l*
add-exp-log add-cbrt-cube add-log-exp
flip3-+ flip-+
frac-times flip3-- sqrt-pow1 pow1/2 flip-- difference-of-squares unswap-sqr
pow-prod-down
rem-sqrt-square associate-*r/ associate-*l/ distribute-lft-out distribute-lft-out--
+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
3.0ms
(sqrt (+ x (sqrt 1.0)))
4.0ms
(sqrt (- x (sqrt 1.0)))
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (+ x (sqrt 1.0)))
100.0ms
(sqrt (- x (sqrt 1.0)))
179.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
261.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0470936
11775896
25002880

prune842.0ms

Filtered
99 candidates to 75 candidates (24.2%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New99099
Fresh000
Picked011
Done000
Total991100

Merged error: 0b

Counts
100 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.5s

Algorithm
intervals
Results
548.0ms3003×body2560nan
532.0ms16706×body80nan
392.0ms2572×body1280nan
303.0ms8000×body80valid
157.0ms1289×body640nan
59.0ms654×body320nan
20.0ms308×body160nan

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