Details

Time bar (total: 3.1s)

sample90.0ms

Algorithm
intervals
Results
19.0ms102×body2560nan
17.0ms525×body80nan
16.0ms97×body1280nan
13.0ms256×body80valid
4.0ms29×body640nan
2.0ms25×body320nan
1.0msbody160nan

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
052579

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.6b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
33.2b
(sqrt (- (* x x) 1.0))

rewrite13.0ms

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:
8.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series18.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(+ x (sqrt (- (* x x) 1.0)))
7.0ms
(sqrt (- (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
04917352
14917352

prune55.0ms

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 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
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
10×*-un-lft-identity
associate-*r*
associate-*l*
pow1 add-cube-cbrt
add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
flip3-- pow-prod-down flip--
sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 53
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))))

series30.0ms

Counts
2 → 6
Calls
2 calls:
15.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
15.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05519906

prune113.0ms

Filtered
44 candidates to 59 candidates (-34.1%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New59059
Fresh000
Picked011
Done000
Total59160

Merged error: 0b

Counts
60 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02314
12314

end0.0ms

sample2.6s

Algorithm
intervals
Results
601.0ms3054×body2560nan
535.0ms15957×body80nan
385.0ms2425×body1280nan
316.0ms8000×body80valid
157.0ms1248×body640nan
59.0ms599×body320nan
21.0ms316×body160nan

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