Details

Time bar (total: 2.7s)

sample74.0ms

Algorithm
intervals
Results
16.0ms84×body2560nan
14.0ms256×body80valid
11.0ms75×body1280nan
10.0ms268×body80nan
5.0ms38×body640nan
2.0ms19×body320nan
1.0ms17×body160nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
26.1b
(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:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series8.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

simplify75.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0217221
1657211
22555205
35001204

prune56.0ms

Filtered
29 candidates to 34 candidates (-17.2%)
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 3 expressions with local error:

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))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×sqrt-prod
14×*-un-lft-identity sqrt-div
associate-*r*
pow1 add-cube-cbrt
associate-*l*
add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
frac-times unswap-sqr
flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 69
Calls
3 calls:
3.0ms
(sqrt (+ x (sqrt 1.0)))
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
11.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series26.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
8.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0416781
11587743
25002731

prune168.0ms

Filtered
59 candidates to 78 candidates (-32.2%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh000
Picked011
Done000
Total78179

Merged error: 0b

Counts
79 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.2s

Algorithm
intervals
Results
568.0ms2936×body2560nan
393.0ms2457×body1280nan
326.0ms8000×body80valid
292.0ms8298×body80nan
164.0ms1283×body640nan
61.0ms615×body320nan
19.0ms289×body160nan

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