Details

Time bar (total: 13.6s)

sample117.0ms

Algorithm
intervals
Results
50.0ms749×body80nan
29.0ms256×body80valid

simplify43.0ms

Counts
1 → 1
Iterations
IterNodes
done18
318
216
112
09

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 3 expressions with local error:

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

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
36×times-frac
35×add-sqr-sqrt
29×add-cube-cbrt
20×sqrt-prod
13×fma-def
7×associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp difference-of-squares
4×pow1 sqrt-div div-inv distribute-lft-out
3×expm1-log1p-u associate-/r* 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-+ distribute-rgt-out pow1/2 div-exp frac-add flip-+
Counts
3 → 100
Calls
3 calls:
12.0ms
(sqrt (- 1.0 (* x x)))
31.0ms
(/ (sqrt (- 1.0 (* x x))) x)
63.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series426.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(sqrt (- 1.0 (* x x)))
179.0ms
(/ (sqrt (- 1.0 (* x x))) x)
164.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify2.7s

Counts
109 → 109
Iterations
IterNodes
done5000
21272
1418
0184

prune1.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(+ 1.0 (sqrt (- 1.0 (* x x))))
0.0b
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*l* add-cube-cbrt
12×add-exp-log
11×times-frac
8×add-cbrt-cube
6×pow1
5×add-log-exp
4×associate-*r* prod-exp sqrt-prod
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 distribute-lft-out
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-- difference-of-squares
Counts
3 → 82
Calls
3 calls:
14.0ms
(sqrt (- 1.0 (* x x)))
34.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
124.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

series378.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(sqrt (- 1.0 (* x x)))
89.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
178.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

simplify3.7s

Counts
91 → 91
Iterations
IterNodes
done5002
21832
1545
0181

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations
IterNodes
done14
114
010

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.2s24333×body80nan
612.0ms8000×body80valid