Details

Time bar (total: 6.1s)

sample76.0ms

Algorithm
intervals
Results
18.0ms229×body160nan
18.0ms493×body80nan
12.0ms256×body80valid

simplify20.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
28.2b
(sqrt (- (* x x) 1.0))

rewrite51.0ms

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:
38.0ms
(+ x (sqrt (- (* x x) 1.0)))
12.0ms
(sqrt (- (* x x) 1.0))

series146.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(+ x (sqrt (- (* x x) 1.0)))
59.0ms
(sqrt (- (* x x) 1.0))

simplify911.0ms

Counts
34 → 34

prune134.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

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))))

rewrite115.0ms

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:
10.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
101.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series453.0ms

Counts
2 → 6
Calls
2 calls:
199.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
253.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify611.0ms

Counts
59 → 59

prune206.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify18.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.2s16392×body80nan
770.0ms7647×body160nan
526.0ms8000×body80valid