Details

Time bar (total: 9.9s)

sample92.0ms

Algorithm
intervals
Results
24.0ms544×body80nan
22.0ms223×body160nan
14.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done11
211
110
07

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

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:
17.0ms
(+ x (sqrt (- (* x x) 1.0)))
34.0ms
(sqrt (- (* x x) 1.0))

series141.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(+ x (sqrt (- (* x x) 1.0)))
63.0ms
(sqrt (- (* x x) 1.0))

simplify555.0ms

Counts
34 → 34
Iterations
IterNodes
done5001
2892
1223
090

prune204.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite69.0ms

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:
4.0ms
(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
63.0ms
(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

series469.0ms

Counts
2 → 6
Calls
2 calls:
203.0ms
(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
266.0ms
(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

simplify728.0ms

Counts
59 → 59
Iterations
IterNodes
done5002
21488
1381
0159

prune329.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

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:
19.0ms
(sqrt (sqrt (+ (sqrt 1.0) x)))
10.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
98.0ms
(* (sqrt (sqrt (+ (sqrt 1.0) x))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
63.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
180.0ms
(sqrt (sqrt (+ (sqrt 1.0) x)))
185.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
262.0ms
(* (sqrt (sqrt (+ (sqrt 1.0) x))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
443.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify1.4s

Counts
157 → 157
Iterations
IterNodes
done5001
23468
1861
0344

prune979.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify6.0ms

Iterations
IterNodes
done19
219
118
015

end0.0ms

sample3.5s

Algorithm
intervals
Results
984.0ms8000×body80valid
902.0ms16578×body80nan
855.0ms7736×body160nan