Details

Time bar (total: 3.9s)

sample92.0ms

Algorithm
intervals
Results
22.0ms114×body2560nan
19.0ms556×body80nan
16.0ms82×body1280nan
11.0ms256×body80valid
5.0ms36×body640nan
2.0ms18×body320nan
0.0msbody160nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

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: 30.9b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(+ x (sqrt (- (* x x) 1.0)))
28.8b
(sqrt (- (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity
add-sqr-sqrt
pow1 add-cube-cbrt add-log-exp
add-exp-log log-prod sqrt-prod
add-cbrt-cube
log-div flip3-+ sqrt-div flip-+ distribute-lft-out
+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series296.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
64.0ms
(+ x (sqrt (- (* x x) 1.0)))
52.0ms
(sqrt (- (* x x) 1.0))

simplify131.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
0316408
11042379
24663366
35001365

prune101.0ms

Filtered
52 candidates to 43 candidates (82.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New51152
Fresh000
Picked101
Done000
Total52153

Merged error: 0.0b

Counts
53 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b
(log (+ 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
20×add-sqr-sqrt
15×sqrt-prod
12×*-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
log-prod flip3-- pow-prod-down flip--
log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 67
Calls
3 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series640.0ms

Counts
3 → 9
Calls
3 calls:
146.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
279.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
214.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0424932
11608865
25002852

prune171.0ms

Filtered
76 candidates to 58 candidates (76.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh000
Picked011
Done000
Total76177

Merged error: 0.0b

Counts
77 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.4s

Algorithm
intervals
Results
552.0ms3002×body2560nan
530.0ms16259×body80nan
387.0ms2546×body1280nan
316.0ms8000×body80valid
146.0ms1222×body640nan
58.0ms623×body320nan
20.0ms315×body160nan

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