Details

Time bar (total: 10.5s)

sample104.0ms

Algorithm
intervals
Results
60.0ms749×body80nan
20.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done18
218
114
09

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
37×times-frac
34×add-sqr-sqrt
28×sqrt-prod
25×add-cube-cbrt
10×difference-of-squares
8×distribute-lft-out associate-/l*
7×div-inv
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 sqrt-div
3×associate-/r* distribute-rgt-out insert-posit16
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add distribute-rgt1-in flip-+
Counts
3 → 93
Calls
3 calls:
19.0ms
(/ (sqrt (- 1 (* x x))) x)
5.0ms
(sqrt (- 1 (* x x)))
59.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series239.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(/ (sqrt (- 1 (* x x))) x)
50.0ms
(sqrt (- 1 (* x x)))
88.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify2.3s

Counts
102 → 102
Iterations
IterNodes
done5068
33610
21126
1411
0183

prune478.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×*-un-lft-identity
13×associate-*l*
12×add-exp-log add-cube-cbrt
11×times-frac
8×add-cbrt-cube
7×sqrt-prod
6×pow1
5×associate-*r* add-log-exp
4×prod-exp distribute-lft-out
3×flip3-+ flip-+ insert-posit16 unswap-sqr
2×frac-times sqrt-div div-exp associate-*r/ cbrt-unprod difference-of-squares
1×distribute-rgt-in cbrt-undiv +-commutative rem-sqrt-square rec-exp sum-log distribute-lft-in sqrt-pow1 flip3-- pow1/2 1-exp pow-prod-down associate-*l/ *-commutative div-inv flip--
Counts
3 → 76
Calls
3 calls:
7.0ms
(sqrt (- 1 (* x x)))
24.0ms
(+ 1 (sqrt (- 1 (* x x))))
118.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))

series224.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(sqrt (- 1 (* x x)))
61.0ms
(+ 1 (sqrt (- 1 (* x x))))
90.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))

simplify2.6s

Counts
85 → 85
Iterations
IterNodes
done5007
33512
21363
1514
0168

prune394.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.3s24333×body80nan
1.1s8000×body80valid