Details

Time bar (total: 10.0s)

sample98.0ms

Algorithm
intervals
Results
38.0ms544×body80nan
19.0ms223×body160nan
12.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
31.5b
(sqrt (- (* x x) 1.0))

rewrite45.0ms

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-cbrt-cube sqrt-div add-exp-log
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 flip-+ flip-- distribute-lft-out difference-of-squares
Counts
2 → 28
Calls
2 calls:
26.0ms
(+ x (sqrt (- (* x x) 1.0)))
18.0ms
(sqrt (- (* x x) 1.0))

series173.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(+ x (sqrt (- (* x x) 1.0)))
84.0ms
(sqrt (- (* x x) 1.0))

simplify510.0ms

Counts
34 → 34
Iterations

Useful iterations: done (508.0ms)

IterNodesCost
090451
1223402
2892366
done5001358

prune246.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.4b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite58.0ms

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×frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp unswap-sqr
3×flip3-- pow-prod-down flip--
2×sqrt-pow1 pow1/2 associate-*l/ associate-*r/ difference-of-squares
1×+-commutative sum-log sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 53
Calls
2 calls:
8.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
46.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series495.0ms

Counts
2 → 6
Calls
2 calls:
213.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
282.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify617.0ms

Counts
59 → 59
Iterations

Useful iterations: 2 (196.0ms)

IterNodesCost
01521150
1370981
21483924
done5002924

prune291.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (sqrt 1.0))))
0.1b
(sqrt (sqrt (+ x (sqrt 1.0))))
0.2b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.3b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-div
62×sqrt-prod
36×add-sqr-sqrt
32×frac-times
26×*-un-lft-identity
23×flip3-+ flip-+
20×pow1 associate-*l*
16×associate-*r/ add-cube-cbrt
13×sqrt-pow1
12×flip3-- flip--
11×add-cbrt-cube add-exp-log
10×associate-*r* pow-prod-down associate-*l/
9×pow1/2
6×unswap-sqr
4×rem-sqrt-square prod-exp cbrt-unprod distribute-lft-out add-log-exp
3×sqrt-unprod
2×*-commutative difference-of-squares
1×distribute-lft-out--
Counts
4 → 145
Calls
4 calls:
18.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
17.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
141.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
73.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
198.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
271.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
491.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify1.5s

Counts
157 → 157
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03053775
18073273
232612892
done50002816

prune880.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11622
done1622

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.3s16578×body80nan
906.0ms7736×body160nan
616.0ms8000×body80valid