Details

Time bar (total: 2.3s)

sample50.0ms

Algorithm
intervals
Results
13.0ms487×body80nan
11.0ms244×body160nan
7.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115
done115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
28.5b
(sqrt (- (* x x) 1.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity
4×sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×add-exp-log sqrt-div add-cbrt-cube
1×+-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:
17.0ms
(+ x (sqrt (- (* x x) 1.0)))
10.0ms
(sqrt (- (* x x) 1.0))

series123.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ x (sqrt (- (* x x) 1.0)))
54.0ms
(sqrt (- (* x x) 1.0))

simplify78.0ms

Counts
34 → 34
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0217221
1657211
22555205
35001204
done5001204

prune80.0ms

Pruning

1 alts after pruning (1 fresh and 0 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))))

rewrite56.0ms

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

series330.0ms

Counts
2 → 6
Calls
2 calls:
135.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
194.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify37.0ms

Counts
59 → 59
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0360656
11271612
25002600
done5002600

prune155.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139
done139

end0.0ms

sample1.3s

Algorithm
intervals
Results
328.0ms7451×body160nan
319.0ms15865×body80nan
223.0ms8000×body80valid