Details

Time bar (total: 11.5s)

sample65.0ms

Algorithm
intervals
Results
34.0ms749×body80nan
14.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done20
320
218
114
09

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
46×times-frac
41×add-sqr-sqrt
32×add-cube-cbrt
28×sqrt-prod
13×fma-def
10×difference-of-squares
8×div-inv distribute-lft-out associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 sqrt-div
3×expm1-log1p-u associate-/r* distribute-rgt-out insert-posit16 log1p-expm1-u
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 → 112
Calls
3 calls:
20.0ms
(/ (sqrt (- 1 (* x x))) x)
20.0ms
(sqrt (- 1 (* x x)))
41.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series294.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (sqrt (- 1 (* x x))) x)
76.0ms
(sqrt (- 1 (* x x)))
95.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify2.8s

Counts
121 → 121
Iterations
IterNodes
done5000
34124
21215
1434
0189

prune529.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

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)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×*-un-lft-identity
13×associate-*l* add-cube-cbrt
12×add-exp-log
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×expm1-log1p-u fma-def flip3-+ flip-+ insert-posit16 log1p-expm1-u 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 → 85
Calls
3 calls:
14.0ms
(sqrt (- 1 (* x x)))
15.0ms
(+ 1 (sqrt (- 1 (* x x))))
83.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))

series181.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(sqrt (- 1 (* x x)))
47.0ms
(+ 1 (sqrt (- 1 (* x x))))
69.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))

simplify3.2s

Counts
94 → 94
Iterations
IterNodes
done5000
33894
21404
1537
0174

prune447.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations
IterNodes
done13
113
09

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.0s24333×body80nan
1.2s8000×body80valid