Details

Time bar (total: 5.1s)

sample47.0ms

Algorithm
intervals
Results
22.0ms739×body80nan
10.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
done1613

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
28×add-sqr-sqrt
27×times-frac
22×add-cube-cbrt
20×sqrt-prod
7×associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
4×pow1 sqrt-div distribute-lft-out
3×associate-/r* div-inv
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num sum-log flip-+
Counts
3 → 78
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
28.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series285.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(sqrt (- 1.0 (* x x)))
129.0ms
(/ (sqrt (- 1.0 (* x x))) x)
101.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify1.8s

Counts
87 → 87
Iterations

Useful iterations: 3 (870.0ms)

IterNodesCost
01751379
13921272
210901200
340741185
done50011185

prune215.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
21×add-exp-log add-cbrt-cube
18×pow-plus
13×pow2
12×sqrt-prod
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt prod-exp cbrt-unprod
7×times-frac associate-/l*
6×sqrt-div add-log-exp
3×difference-of-squares
2×cbrt-undiv flip3-- flip3-+ associate-*r/ div-exp associate-/r/ flip-- flip-+ associate-/l/
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 swap-sqr associate-*r* associate-*l* frac-add clear-num associate-/r* sum-log *-commutative div-inv distribute-lft-out unswap-sqr
Counts
4 → 125
Calls
4 calls:
10.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x)))))
4.0ms
(sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))
22.0ms
(+ (/ 1.0 x) (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x))))))
12.0ms
(* (* x x) (* x x))

series460.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x)))))
103.0ms
(sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))
142.0ms
(+ (/ 1.0 x) (/ (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (* x (sqrt (+ 1.0 (* x x))))))
35.0ms
(* (* x x) (* x x))

simplify571.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (184.0ms)

IterNodesCost
02002466
15061680
216751538
done50001538

prune278.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11726
done1726

end0.0ms

sample1.4s

Algorithm
intervals
Results
720.0ms24242×body80nan
298.0ms8000×body80valid