Details

Time bar (total: 2.2s)

sample44.0ms

Algorithm
intervals
Results
12.0ms559×body80nan
11.0ms250×body160nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

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: 32.4b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
30.1b
(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
*-un-lft-identity
add-log-exp
add-cube-cbrt
pow1 sqrt-prod
add-exp-log expm1-log1p-u fma-def prod-diff add-cbrt-cube log1p-expm1-u
flip3-- sqrt-div flip-- difference-of-squares
+-commutative sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log sum-log flip-+ distribute-lft-out
Counts
3 → 54
Calls
3 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
5.0ms
(sqrt (- (* x x) 1.0))

series155.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(+ x (sqrt (- (* x x) 1.0)))
37.0ms
(- (* x x) 1.0)
52.0ms
(sqrt (- (* x x) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0280334
1959293
25002289

prune120.0ms

Filtered
63 candidates to 51 candidates (81.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New62163
Fresh000
Picked101
Done000
Total63164

Merged error: 0b

Counts
64 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
associate-*r*
add-cube-cbrt associate-*l*
pow1
add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
flip3-- fma-def pow-prod-down flip--
expm1-log1p-u sqrt-pow1 pow1/2 associate-*r/ associate-*l/ log1p-expm1-u difference-of-squares
+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 60
Calls
2 calls:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series350.0ms

Counts
2 → 6
Calls
2 calls:
142.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
208.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0382708
11369643
25002629

prune143.0ms

Filtered
66 candidates to 51 candidates (77.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New66066
Fresh000
Picked011
Done000
Total66167

Merged error: 0b

Counts
67 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.3s

Algorithm
intervals
Results
356.0ms16316×body80nan
347.0ms7798×body160nan
221.0ms8000×body80valid

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