Details

Time bar (total: 10.8s)

sample115.0ms

Algorithm
intervals
Results
71.0ms789×body80nan
24.0ms256×body80valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
done20
320
218
114
09

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0b
(/ (sqrt (- 1 (* x x))) x)
0.0b
(sqrt (- 1 (* x x)))
0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
59×times-frac
50×add-sqr-sqrt
38×add-cube-cbrt
31×sqrt-prod
16×distribute-lft-out
15×log-prod
14×div-inv
13×fma-def
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×log-div associate-/r*
2×flip3-+ flip3-- frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp log-pow
Counts
4 → 142
Calls
4 calls:
25.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
16.0ms
(/ (sqrt (- 1 (* x x))) x)
9.0ms
(sqrt (- 1 (* x x)))
28.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series465.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
112.0ms
(/ (sqrt (- 1 (* x x))) x)
60.0ms
(sqrt (- 1 (* x x)))
87.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify1.3s

Counts
154 → 154
Iterations
IterNodes
done2000
32000
21562
1555
0247

prune745.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.2b
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.2b
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
102×*-un-lft-identity
94×times-frac
48×sqrt-prod
36×add-cube-cbrt
32×distribute-lft-out
26×fma-def div-inv
18×hypot-def
12×distribute-rgt-out
8×add-log-exp
6×pow1 sqrt-div
4×expm1-log1p-u flip3-+ add-cbrt-cube frac-add distribute-rgt1-in add-exp-log flip-+ insert-posit16 log1p-expm1-u
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 160
Calls
4 calls:
34.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
33.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
42.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
35.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
97.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
168.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
192.0ms
(sqrt (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

simplify977.0ms

Counts
172 → 172
Iterations
IterNodes
done2002
32002
2966
1332
0148

prune950.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done14
114
011

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.8s23583×body80nan
1.1s8000×body80valid