Details

Time bar (total: 2.4s)

sample48.0ms

Algorithm
intervals
Results
10.0ms237×body160nan
10.0ms524×body80nan
10.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
29.4b
(sqrt (- (* x x) 1.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity
add-cube-cbrt sqrt-prod add-log-exp
pow1 fma-def
add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
17.0ms
(+ x (sqrt (- (* x x) 1.0)))
12.0ms
(sqrt (- (* x x) 1.0))

series109.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(+ x (sqrt (- (* x x) 1.0)))
47.0ms
(sqrt (- (* x x) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0235239
1739223
22858218
35001216

prune99.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

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))))

rewrite57.0ms

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:
5.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
49.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series302.0ms

Counts
2 → 6
Calls
2 calls:
126.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
176.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0382708
11369643
25002629

prune172.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.4s

Algorithm
intervals
Results
352.0ms7577×body160nan
334.0ms16440×body80nan
237.0ms8000×body80valid