Details

Time bar (total: 9.6s)

sample44.0ms

Algorithm
intervals
Results
20.0ms680×body80nan
9.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 119
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
29.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series635.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (- 1.0 (* x x)))
321.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
144.0ms
(/ (sqrt (- 1.0 (* x x))) x)
110.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify671.0ms

Counts
131 → 131
Iterations

Useful iterations: 2 (174.0ms)

IterNodesCost
02342010
15381869
218431735
done50001735

prune383.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
60×*-un-lft-identity
56×times-frac
28×add-cube-cbrt
26×fma-def
20×sqrt-prod
16×distribute-lft-out
12×hypot-def
10×div-inv
8×add-log-exp
6×pow1 sqrt-div
4×add-exp-log expm1-log1p-u distribute-rgt-out flip3-+ frac-add add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 122
Calls
4 calls:
37.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
32.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
63.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
66.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
137.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
212.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
226.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify541.0ms

Counts
134 → 134
Iterations

Useful iterations: done (536.0ms)

IterNodesCost
01682034
14181880
214221756
done50001746

prune621.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.3b
(/ (sqrt 1.0) (sqrt x))
0.3b
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.3b
(hypot (/ (sqrt 1.0) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
162×sqrt-prod
109×times-frac
105×add-sqr-sqrt
86×*-un-lft-identity
78×add-cube-cbrt
16×associate-/l*
12×associate-/r*
8×add-exp-log add-cbrt-cube
7×sqrt-div difference-of-squares
6×hypot-def
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv distribute-lft-out add-log-exp
2×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num associate-/l/
1×rem-sqrt-square hypot-udef distribute-rgt-out flip3-- sqrt-pow1 flip3-+ pow1/2 frac-add flip-- flip-+
Counts
4 → 195
Calls
4 calls:
58.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
4.0ms
(/ (sqrt 1.0) (sqrt x))
9.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.0ms
(hypot (/ (sqrt 1.0) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series1.9s

Counts
4 → 12
Calls
4 calls:
229.0ms
(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
72.0ms
(/ (sqrt 1.0) (sqrt x))
183.0ms
(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
1.4s
(hypot (/ (sqrt 1.0) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify1.5s

Counts
207 → 207
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
05194543
112324040
249023812
done50003812

prune856.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01832
12032
done2032

end0.0ms

sample1.4s

Algorithm
intervals
Results
705.0ms24232×body80nan
288.0ms8000×body80valid