Details

Time bar (total: 5.6s)

sample276.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms234×body80nan

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 associate-/r/ associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
2 → 53
Calls
2 calls:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
13.0ms
(/ (- 1.0 x) (+ 1.0 x))

series56.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts
59 → 59
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0102765
1230738
2571684
32276682
done5001681

prune147.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
0.0b
(sqrt (+ 1.0 x))
0.0b
(sqrt (+ 1.0 x))
0.0b
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×add-sqr-sqrt
35×times-frac
32×sqrt-prod
26×add-cube-cbrt
8×distribute-lft-out distribute-lft-out-- difference-of-squares
7×associate-/r*
6×pow1 add-exp-log sqrt-div add-cbrt-cube
5×associate-/l*
4×add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 103
Calls
4 calls:
0.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
6.0ms
(sqrt (+ 1.0 x))
4.0ms
(sqrt (+ 1.0 x))
12.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series154.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
30.0ms
(sqrt (+ 1.0 x))
30.0ms
(sqrt (+ 1.0 x))
92.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify1.4s

Counts
115 → 115
Iterations

Useful iterations: 3 (434.0ms)

IterNodesCost
01521615
13391420
28281346
334751338
done50001338

prune260.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
109×sqrt-prod
108×*-un-lft-identity
96×add-sqr-sqrt
91×times-frac
60×add-cube-cbrt
26×difference-of-squares
17×distribute-lft-out--
15×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1
4×flip3-- associate-/r/ flip-- associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ div-inv
1×sqrt-undiv div-sub
Counts
4 → 185
Calls
4 calls:
4.0ms
(sqrt (- 1.0 x))
4.0ms
(sqrt (+ 1.0 x))
15.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (sqrt (- 1.0 x)))
12.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (- 1.0 x))
29.0ms
(sqrt (+ 1.0 x))
62.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (sqrt (- 1.0 x)))
90.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify579.0ms

Counts
197 → 197
Iterations

Useful iterations: done (567.0ms)

IterNodesCost
02583633
15173239
214793141
done50013125

prune522.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01726
11926
done1926

end0.0ms

sample746.0ms

Algorithm
intervals
Results
324.0ms8000×body80valid
212.0ms8035×body80nan